Metallicity and Temperature Indicators in M Dwarf K-band Spectra: Testing New and Updated Calibrations with Observations of 133 Solar Neighborhood M Dwarfs

We present K-band spectra for 133 nearby (d < 33 ps) M dwarfs, including 18 M dwarfs with reliable metallicity estimates (as inferred from an FGK type companion), 11 M dwarf planet hosts, more than 2/3 of the M dwarfs in the northern 8 pc sample, and several M dwarfs from the LSPM catalog. From these spectra, we measure equivalent widths of the Ca and Na lines, and a spectral index quantifying the absorption due to H₂O opacity (the H₂O-K2 index). Using empirical spectral type standards and synthetic models, we calibrate the H₂O-K2 index as an indicator of an M dwarf's spectral type and effective temperature. We also present a revised relationship that estimates the [Fe/H] and [M/H] metallicities of M dwarfs from their Na I, Ca I, and H₂O-K2 measurements. Comparisons to model atmosphere provide a qualitative validation of our approach, but also reveal an overall offset between the atomic line strengths predicted by models as compared to actual observations. Our metallicity estimates also reproduce expected correlations with Galactic space motions and Hα emission line strengths, and return statistically identical metallicities for M dwarfs within a common multiple system. Finally, we find systematic residuals between our H₂O-based spectral types and those derived from optical spectral features with previously known sensitivity to stellar metallicity, such as TiO, and identify the CaH1 index as a promising optical index for diagnosing the metallicities of near-solar M dwarfs.