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We determine Mg abundances in 6 Gaia benchmark stars using theoreticalone-dimensional (1D) hydrostatic model atmospheres, as well as temporally- andspatially-averaged 3D model atmospheres (<3D>). The stars cover a range of Tefffrom 4700 to 6500 K, log g from 1.6 to 4.4 dex, and [Fe/H] from -3.0 dex tosolar. Spectrum synthesis calculations are performed in local thermodynamicequilibrium (LTE) and in non-LTE (NLTE) using the oscillator strengths recentlypublished by Pehlivan Rhodin et al. We find that: a) Mg abundances determinedfrom the infrared spectra are as accurate as the optical diagnostics, b) theNLTE effects on Mg I line strengths and abundances in this sample of stars areminor (although for a few Mg I lines the NLTE effects on abundance exceed 0.6dex in <3D> and 0.1 dex in 1D, c) the solar Mg abundance is 7.56 +/- 0.05 dex(total error), in the excellent agreement with the Mg abundance measured in CIchondritic meteorites, d) the 1D NLTE and <3D> NLTE approach can be used withconfidence to analyse optical Mg I lines in spectra of dwarfs and sub-giants,but for red giants the Mg I 5711 A line should be preferred, e) low-excitationMg I lines are sensitive to the atmospheric structure; for these lines, LTEcalculations with <3D> models lead to significant systematic abundance errors.The methods developed in this work will be used to study Mg abundances of alarge sample of stars in the next paper in the series.

astrophysical journal/the astrophysical journal

Non-local thermodynamic equilibrium stellar spectroscopy with 1D and  <3D> models - I. Methods and application to magnesium abundances in standard  stars