{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-mass-magnitude-relation-for-low-mass-stars","title":"A Mass-Magnitude Relation for Low-mass Stars Based on Dynamical Measurements of Thousands of Binary Star Systems","arxiv_id":"2208.12112","date":"2022-08-25","proceeding":null,"authors":["Mark R. Giovinazzi","Cullen H. Blake"],"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, 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 $q=1.0$.","url_abs":"https://arxiv.org/abs/2208.12112v1","url_pdf":"https://arxiv.org/pdf/2208.12112v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-mass-magnitude-relation-for-low-mass-stars","repo_url":"https://github.com/markgiovinazzi/gorp_masses","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}