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

Abstract

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 > > 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.