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. First, 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. Second, 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. Third, though we use the GCS to infer the mean metallicity of M dwarfs in the Solar Neighborhood, our final calibration is based purely on high-resolution spectroscopy of FGK primaries with M dwarf companions as well as the trigonometric parallaxes and apparent V- and K_s-band magnitudes of those M dwarf companions. As a result, our photometric calibration explains an order of magnitude more of the variance in the calibration sample than previous photometric calibrations. We use our calibration to 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. The confirmation of this hint would be in contrast to the result obtained for FGK stars, where it appears that metal-rich and metal-poor stars hosts Neptune-mass planets with approximately equal probability. 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.