The elemental composition of the Sun I. The intermediate mass elements Na to CaThe elemental composition of the Sun I. The intermediate mass elements Na to Ca

The chemical composition of the Sun is an essential piece of reference data for astronomy, cosmology, astroparticle, space and geo-physics: elemental abundances of essentially all astronomical objects are referenced to the solar composition, and basically every process involving the Sun depends on its composition. This article, dealing with the intermediate-mass elements Na to Ca, is the first in a series describing the comprehensive re-determination of the solar composition. In this series we severely scrutinise all ingredients of the analysis across all elements, to obtain the most accurate, homogeneous and reliable results possible. We employ a highly realistic 3D hydrodynamic model of the solar photosphere, which has successfully passed an arsenal of observational diagnostics. For comparison, and to quantify remaining systematic errors, we repeat the analysis using three different 1D hydrostatic model atmospheres (MARCS, MISS and Holweger & Muller 1974, Sol. Phys., 39, 19) and a horizontally and temporally-averaged version of the 3D model (? 3D ?). We account for departures from local thermodynamic equilibrium (LTE) wherever possible. We have scoured the literature for the best possible input data, carefully assessing transition probabilities, hyperfine splitting, partition functions and other data for inclusion in the analysis. We have put the lines we use through a very stringent quality check in terms of their observed profiles and atomic data, and discarded all that we suspect to be blended. Our final recommended 3D+NLTE abundances are: log epsilon(Na) = 6.21 +/- 0.04, log epsilon(Mg) = 7.59 +/- 0.04, log epsilon(Al) = 6.43 +/- 0.04, log epsilon(Si) = 7.51 +/- 0.03, log epsilon(P) = 5.41 +/- 0.03, log epsilon(S) = 7.13 +/- 0.03, log epsilon(K) = 5.04 +/- 0.05 and log epsilon(Ca) = 6.32 +/- 0.03. The uncertainties include both statistical and systematic errors. Our results are systematically smaller than most previous ones with the 1D semi-empirical Holweger & Muller model, whereas the < 3D > model returns abundances very similar to the full 3D calculations. This analysis provides a complete description and a slight update of the results presented in Asplund et al. (2009, ARA&A, 47, 481) for Na to Ca, and includes full details of all lines and input data used.