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A Mass-Magnitude Relation for Low-mass Stars Based on Dynamical Measurements of Thousands of Binary Star Systems
Mark R. Giovinazzi, Cullen H. Blake
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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_(RP) band spanning the absolute magnitude range 14.5>M_(G_(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 2MASS Kₛ magnitudes, 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 uniformly distributed, rather decreasing towards q=1.0.
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