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

<jats:title>Abstract</jats:title> <jats:p>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 <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{{K}_{S}}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaaf3bcieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and <jats:italic>M</jats:italic> <jats:sub>*</jats:sub> spanning 0.075 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> < <jats:italic>M</jats:italic> <jats:sub>*</jats:sub> < 0.70 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>. 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 <jats:italic>K</jats:italic> <jats:sub> <jats:italic>S</jats:italic> </jats:sub> magnitudes and system parallaxes, to calibrate the <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{{K}_{S}}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaaf3bcieqn2.gif" xlink:type="simple" /> </jats:inline-formula>–<jats:italic>M</jats:italic> <jats:sub>*</jats:sub> relation. The resulting posteriors can be used to determine masses of single stars with a precision of 2%–3%, which we confirm by testing the relation on stars with individual dynamical masses from the literature. The precision is limited by scatter around the best-fit relation beyond measured <jats:italic>M</jats:italic> <jats:sub>*</jats:sub> uncertainties, perhaps driven by intrinsic variation in the <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{{K}_{S}}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaaf3bcieqn3.gif" xlink:type="simple" /> </jats:inline-formula>–<jats:italic>M</jats:italic> <jats:sub>*</jats:sub> relation or underestimated uncertainties in the input parallaxes. We find that the effect of [Fe/H] on the <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{{K}_{S}}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaaf3bcieqn4.gif" xlink:type="simple" /> </jats:inline-formula>–<jats:italic>M</jats:italic> <jats:sub>*</jats:sub> 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 (at 5<jats:italic>σ</jats:italic>). 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).</jats:p>