SIMBAD references

We determine Mg abundances in six Gaia benchmark stars using theoretical one-dimensional (1D) hydrostatic model atmospheres, as well as temporally and spatially averaged three-dimensional (<3D>) model atmospheres. The stars cover a range of T_eff from 4700 to 6500 K, logg from 1.6 to 4.4 dex, and [Fe/H] from -3.0 dex to solar. Spectrum synthesis calculations are performed in local thermodynamic equilibrium (LTE) and in non-LTE (NLTE) using the oscillator strengths recently published by Pehlivan Rhodin et al. We find that: (a) Mg abundances determined from the infrared spectra are as accurate as the optical diagnostics, (b) the NLTE effects on Mg I line strengths and abundances in this sample of stars are minor (although for a few Mg I lines the NLTE effects on abundance exceed 0.6 dex in <3D>and 0.1 dex in 1D, (c) the solar Mg abundance is 7.56±0.05 dex (total error), in excellent agreement with the Mg abundance measured in CI chondritic meteorites, (d) the 1D NLTE and <3D>NLTE approaches can be used with confidence to analyze optical Mg I lines in spectra of dwarfs and sub-giants, but for red giants the Mg I 5711 Å line should be preferred, (e) low-excitation Mg I lines are sensitive to the atmospheric structure; for these lines, LTE calculations with <3D>models lead to significant systematic abundance errors. The methods developed in this work will be used to study Mg abundances of a large sample of stars in the next paper in the series.