How to Constrain Your M Dwarf. II. The Mass–Luminosity–Metallicity Relation from 0.075 to 0.70 Solar Masses

The mass-luminosity relation for late-type stars has long been a critical tool for estimating stellar masses. However, there is growing need for both a higher-precision relation and a better understanding of systematic effects (e.g., metallicity). Here we present an empirical relationship between Mks and mass spanning $0.075M_\odot<M<0.70M_\odot$. The relation is derived from 62 nearby binaries, whose orbits we determine using a combination of Keck/NIRC2 imaging, archival adaptive optics data, and literature astrometry. From their orbital parameters, we determine the total mass of each system, with a precision better than 1% in the best cases. We use these total masses, in combination with resolved Ks magnitudes and system parallaxes, to calibrate the mass-Mks relation. The result can be used to determine masses of single stars with a precision of 2-3%, which we confirm by a comparison to dynamical masses from the literature. The precision is limited by scatter around the best-fit relation beyond mass uncertainties, perhaps driven by intrinsic variation in the mass-Mks relation or underestimated measurement errors. We find the effect of [Fe/H] on the mass-Mks relation is likely negligible for metallicities in the Solar neighborhood (0.0+/-2.2% change in mass per dex change in [Fe/H]). This weak effect is consistent with predictions from the Dartmouth Stellar Evolution Database, but inconsistent with those from MESA Isochrones and Stellar Tracks. A sample of binaries with a wider range of abundances will be required to discern the importance of metallicity in extreme populations (e.g., in the Galactic Halo or thick disk).

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