{"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/precise-dynamical-masses-and-orbital-fits-for","title":"Precise Dynamical Masses and Orbital Fits for $β$ Pic b and $β$ Pic c","arxiv_id":"2011.06215","date":"2020-11-12","proceeding":null,"authors":["G. Mirek Brandt","Timothy D. Brandt","Trent J. Dupuy","Yiting Li","Daniel Michalik"],"abstract":"We present a comprehensive orbital analysis to the exoplanets $\\beta$ Pictoris b and c that resolves previously reported tensions between the dynamical and evolutionary mass constraints on $\\beta$ Pic b. We use the MCMC orbit code orvara to fit fifteen years of radial velocities and relative astrometry (including recent GRAVITY measurements), absolute astrometry from Hipparcos and Gaia, and a single relative radial velocity measurement between $\\beta$ Pic A and b. We measure model-independent masses of $9.3^{+2.6}_{-2.5}\\, M_{\\rm Jup}$ for $\\beta$ Pic b and $8.3\\pm 1.0\\,M_{\\rm Jup}$ for $\\beta$ Pic c. These masses are robust to modest changes to the input data selection. We find a well-constrained eccentricity of $0.119 \\pm 0.008$ for $\\beta$ Pic b, and an eccentricity of $0.21^{+0.16}_{-0.09}$ for $\\beta$ Pic c, with the two orbital planes aligned to within $\\sim$0.5$^\\circ$. Both planets' masses are within $\\sim$1$\\sigma$ of the predictions of hot-start evolutionary models and exclude cold starts. We validate our approach on $N$-body synthetic data integrated using REBOUND. We show that orvara can account for three-body effects in the $\\beta$ Pic system down to a level $\\sim$5 times smaller than the GRAVITY uncertainties. Systematics in the masses and orbital parameters from orvara's approximate treatment of multiplanet orbits are a factor of $\\sim$5 smaller than the uncertainties we derive here. Future GRAVITY observations will improve the constraints on $\\beta$ Pic c's mass and (especially) eccentricity, but improved constraints on the mass of $\\beta$ Pic b will likely require years of additional RV monitoring and improved precision from future Gaia data releases.","url_abs":"https://arxiv.org/abs/2011.06215v3","url_pdf":"https://arxiv.org/pdf/2011.06215v3.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":"precise-dynamical-masses-and-orbital-fits-for","repo_url":"https://github.com/gmbrandt/HTOF","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"precise-dynamical-masses-and-orbital-fits-for","repo_url":"https://github.com/t-brandt/orvara","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}