{"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/inferring-the-rotation-period-distribution-of","title":"Inferring the Rotation Period Distribution of Stars from their Projected Rotation Velocities and Radii: Application to late-F/early-G Kepler Stars","arxiv_id":"2112.07162","date":"2021-12-14","proceeding":null,"authors":["Kento Masuda","Erik A. Petigura","Oliver J. Hall"],"abstract":"While stellar rotation periods $P_\\mathrm{rot}$ may be measured from broadband photometry, the photometric modulation becomes harder to detect for slower rotators, which could bias measurements of the long-period tail of the $P_\\mathrm{rot}$ distribution. Alternatively, the $P_\\mathrm{rot}$ distribution of stars can be inferred from their projected rotation velocities $v\\sin i$ and radii $R$, without being biased against photometrically quiet stars. We solve this inference problem using a hierarchical Bayesian framework, which (i) is applicable to heteroscedastic measurements of $v\\sin i$ and $R$ with non-Gaussian uncertainties and (ii) does not require a simple parametric form for the true $P_\\mathrm{rot}$ distribution. We test the method on simulated data sets and show that the true $P_\\mathrm{rot}$ distribution can be recovered from $\\gtrsim 100$ sets of $v\\sin i$ and $R$ measured with precisions of $1\\,\\mathrm{km/s}$ and $4\\%$, respectively, unless the true distribution includes sharp discontinuities. We apply the method to a sample of 144 late-F/early-G dwarfs in the Kepler field with $v\\sin i$ measured from Keck/HIRES spectra, and find that the typical rotation periods of these stars are similar to the photometric periods measured from Kepler light curves: we do not find a large population of slow rotators that are missed in the photometric sample, although we find evidence that the photometric sample is biased for young, rapidly-rotating stars. Our results also agree with asteroseismic measurements of $P_\\mathrm{rot}$ for Kepler stars with similar ages and effective temperatures, and show that $\\approx 1.1\\,M_\\odot$ stars beyond the middle of their main-sequence lifetimes rotate faster than predicted by standard magnetic braking laws.","url_abs":"https://arxiv.org/abs/2112.07162v1","url_pdf":"https://arxiv.org/pdf/2112.07162v1.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":"inferring-the-rotation-period-distribution-of","repo_url":"https://github.com/kemasuda/prot_from_vsini","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","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}