SIMBAD references

Hydrogen Balmer lines are commonly used as spectroscopic effective temperature diagnostics of late-type stars. However, reliable inferences require accurate model spectra, and the absolute accuracy of classical methods that are based on one-dimensional (1D) hydrostatic model atmospheres and local thermodynamic equilibrium (LTE) is still unclear. To investigate this, we carry out 3D non-LTE calculations for the Balmer lines, performed, for the first time, over an extensive grid of 3D hydrodynamicSTAGGER model atmospheres. For Hα, Hβ, and Hγ we find significant 1D non-LTE versus 3D non-LTE differences (3D effects): the outer wings tend to be stronger in 3D models, particularly for Hγ, while the inner wings can be weaker in 3D models, particularly for Hα. For Hα, we also find significant 3D LTE versus 3D non-LTE differences (non-LTE effects): in warmer stars (T_eff~=6500K) the inner wings tend to be weaker in non-LTE models, while at lower effective temperatures (T_eff~=4500K) the inner wings can be stronger in non-LTE models; the non-LTE effects are more severe at lower metallicities. We test our 3D non-LTE models against observations of well-studied benchmark stars. For the Sun, we infer concordant effective temperatures from Hα, Hβ, and Hγ; however the value is too low by around 50K which could signal residual modelling shortcomings. For other benchmark stars, our 3D non-LTE models generally reproduce the effective temperatures to within 1σ uncertainties. For Hα, the absolute 3D effects and non-LTE effects can separately reach around 100K, in terms of inferred effective temperatures. For metal-poor turn-off stars, 1D LTE models of Hα can underestimate effective temperatures by around 150K. Our 3D non-LTE model spectra are publicly available, and can be used for more reliable spectroscopic effective temperature determinations.