A Physically-Motivated Photometric Calibration of M Dwarf Metallicity

The location of M dwarfs in the V-K_s--M_Ks color-magnitude diagram (CMD) has been shown to correlate with metallicity. We demonstrate that previous empirical photometric calibrations of M dwarf metallicity exploiting this correlation systematically underestimate or overestimate metallicity at the extremes of their range. We improve upon previous calibrations in three ways. We use both a volume-limited and kinematically-matched sample of F and G dwarfs from the Geneva-Copehnagen Survey (GCS) to infer the mean metallicity of M dwarfs in the Solar Neighborhood, we use theoretical models of M dwarf interiors and atmospheres to determine the effect of metallicity on M dwarfs in the V-K_s--M_Ks CMD, and we base our final calibration purely on high-resolution spectroscopy of FGK primaries with M dwarf companions. As a result, we explain an order of magnitude more of the variance in the calibration sample than previous photometric calibrations. We non-parametrically quantify the significance of the observation that M dwarfs that host exoplanets are preferentially in a region of the V-K_s--M_Ks plane populated by metal-rich M dwarfs. We find that the probability p that planet-hosting M dwarfs are distributed across the V-K_s--M_Ks CMD in the same way as field M dwarfs is p = 0.06 +/- 0.008. Interestingly, the subsample of M dwarfs that host Neptune and sub-Neptune mass planets may also be preferentially located in the region of the V-K_s--M_Ks plane populated by high-metallicity M dwarfs. The probability of this occurrence by chance is p = 0.40 +/- 0.02, and this observation hints that low-mass planets may be more likely to be found around metal-rich M dwarfs. An increased rate of low-mass planet occurrence around metal-rich M dwarfs would be a natural consequence of the core-accretion model of planet formation. (abridged)