calculation of the equation of state.

Synthetic spectra were calculated adopting the atmospheric parameters determined in Sect.\[s-teff\_logg\], and including approximately 2500 metal lines. The basic source of atomic line data (wavelengths, excitation energies, transition probabilities $\log$gf, Stark broadening constant $\Gamma_4$) was VALD (Vienna Atomic Line Database), which is described in [@piskunovetal95-1], [@ryabchikovaetal97-1], and [@kupkaetal99-1; @kupkaetal00-1]. The ion [Si]{} has a large number of lines in the ultraviolet, and we noted a significant scatter in the abundances derived from different lines. Replacing the $\log$ gf values from VALD values with those from the NIST (National Institute of Standards) database, which differ for some lines by up to 0.3dex, leads to more consistent results. Nevertheless, the situation for this ion is not satisfactory (Sect.\[s-silicon\]), and we have consulted a number of original sources in the literature [@lanz+artru85-1; @nahar98-1; @bautistaetal09-1] during the compilation of the most reliable atomic data.

The abundances were varied until a satisfactory fit, as judged by visual inspection, was achieved for each element. We then changed the abundances in several steps of 0.1 - 0.2 dex, until the fit was clearly worse. The resulting difference was used as a conservative estimate for the abundance error, or for an upper 