A Mass-Magnitude Relation for Low-mass Stars Based on Dynamical Measurements of Thousands of Binary Star Systems

Stellar mass is a fundamental parameter that is key to our understanding of stellar formation and evolution, as well as the characterization of nearby exoplanet companions. Historically, stellar masses have been derived from long-term observations of visual or spectroscopic binary star systems. While advances in high-resolution imaging have enabled observations of systems with shorter orbital periods, measurements of stellar masses remain challenging, and relatively few have been precisely measured. We present a new statistical approach to measuring masses for populations of stars. Using Gaia astrometry, we analyze the relative orbital motion of >3800 wide binary systems comprising low-mass stars to establish a mass-magnitude relation in the Gaia G _RP band spanning the absolute magnitude range 14.5 > ${M}_{{G}_{\mathrm{RP}}}$ > 4.0, corresponding to a mass range of 0.08 M _⊙ ≲ M ≲ 1.0 M _⊙. This relation is directly applicable to >30 million stars in the Gaia catalog. Based on comparison to existing mass-magnitude relations calibrated for K _s magnitudes from the Two Micron All Sky Survey, we estimate that the internal precision of our mass estimates is ~10%. We use this relation to estimate masses for a volume-limited sample of ~18,200 stars within 50 pc of the Sun and the present-day field mass function for stars with M ≲ 1.0 M _⊙, which we find peaks at 0.16 M _⊙. We investigate a volume-limited sample of wide binary systems with early-K dwarf primaries, complete for binary mass ratios q > 0.2, and measure the distribution of q at separations >100 au. We find that our distribution of q is not uniform, rather decreasing toward q = 1.0.