Accurate M Dwarf Metallicities from Spectral Synthesis: A Critical Test of Model Atmospheres

We describe a method for accurately determining M dwarf metallicities with spectral synthesis based on abundance analyses of visual binary stars. We obtained high resolution, high signal-to-noise spectra of each component of five visual binary pairs at McDonald Observatory. The spectral types of the components range from F7 to K3 V for the primaries and M0.5 to M3.5 V for the secondaries. We have determined the metallicities of the primaries differentially with respect to the Sun by fitting synthetic spectra to Fe \textsc{i} line profiles in the observed spectra. In the course of our analysis of the M dwarf secondaries we have made significant improvements to the PHOENIX cool-star model atmospheres and the spectrum analysis code MOOG. Our analysis yields a RMS deviation of 0.11 dex in metallicity values between the binary pairs. We estimate the uncertainties in the derived stellar parameters for the M dwarfs to be 48 K, 0.10 dex, 0.12 dex, 0.15 km s$^{-1}$, and 0.20 km s$^{-1}$ for {T}$_{eff}$, log \textsl{g}, [M/H], $\xi$, and $\eta$ respectively. Accurate stellar evolutionary models are needed to progress further in the analysis of cool-star spectra; the new model atmospheres warrant recalculation of the evolutionary models.