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, stellar mass measurements 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 $>3,800$ wide binary systems comprising low-mass stars to establish a Mass-Magnitude relation in the Gaia $G_\mathrm{RP}$ band spanning the absolute magnitude range $14.5>M_{G_\mathrm{RP}}>4.0$, corresponding to a mass range of $0.08$~M$_{\odot}\lesssim M\lesssim1.0$~M$_{\odot}$. This relation is directly applicable to $>30$ million stars in the Gaia catalog. Based on comparison to existing Mass-Magnitude relations calibrated for 2MASS $K_{s}$ magnitudes, we estimate that the internal precision of our mass estimates is $\sim$10$\%$. We use this relation to estimate masses for a volume-limited sample of $\sim$18,200 stars within 50~pc of the Sun and the present-day field mass function for stars with $M\lesssim 1.0$~M$_{\odot}$, which we find peaks at 0.16~M$_{\odot}$. 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 uniformly distributed, rather decreasing towards $q=1.0$.