{"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/on-the-evolution-of-rotational-modulation","title":"On the Evolution of Rotational Modulation Amplitude in Solar-mass Main-sequence Stars","arxiv_id":"2206.01595","date":"2022-06-03","proceeding":null,"authors":["Kento Masuda"],"abstract":"We investigate the relation between rotation periods $P_\\mathrm{rot}$ and photometric modulation amplitudes $R_\\mathrm{per}$ for $\\approx 4,000$ Sun-like main-sequence stars observed by Kepler, using $P_\\mathrm{rot}$ and $R_\\mathrm{per}$ from McQuillan et al. (2014), effective temperature $T_\\mathrm{eff}$ from LAMOST DR6, and parallax data from Gaia EDR3. As has been suggested in previous works, we find that $P_\\mathrm{rot}$ scaled by the convective turnover time $\\tau_\\mathrm{c}$, or the Rossby number $\\mathrm{Ro}=P_\\mathrm{rot}/\\tau_\\mathrm{c}$, serves as a good predictor of $R_\\mathrm{per}$: $R_\\mathrm{per}$ plateaus around $1\\%$ in relative flux for $0.2 \\lesssim \\mathrm{Ro}/\\mathrm{Ro}_\\odot \\lesssim 0.4$, and decays steeply with increasing $\\mathrm{Ro}$ for $0.4 \\lesssim \\mathrm{Ro}/\\mathrm{Ro}_\\odot \\lesssim 0.8$, where $\\mathrm{Ro}_\\odot$ denotes $\\mathrm{Ro}$ of the Sun. In the latter regime we find $\\mathrm{d}\\ln R_\\mathrm{per}/\\mathrm{d}\\ln\\mathrm{Ro} \\sim -4.5$ to $-2.5$, although the value is sensitive to detection bias against weak modulation and may depend on other parameters including $T_\\mathrm{eff}$ and surface metallicity. The existing X-ray and Ca II H&K flux data also show transitions at $\\mathrm{Ro}/\\mathrm{Ro}_\\odot\\sim 0.4$, suggesting that all these transitions share the same physical origin. We also find that the rapid decrease of $R_\\mathrm{per}$ with increasing $\\mathrm{Ro}$ causes rotational modulation of fainter Kepler stars with $\\mathrm{Ro}/\\mathrm{Ro}_\\odot \\gtrsim 0.6$ to be buried under the photometric noise. This effect sets the longest $P_\\mathrm{rot}$ detected in the McQuillan et al. (2014) sample as a function of $T_\\mathrm{eff}$, and obscures the signature of stalled spin down that has been proposed to set in around $\\mathrm{Ro}/\\mathrm{Ro}_\\odot \\sim 1$.","url_abs":"https://arxiv.org/abs/2206.01595v2","url_pdf":"https://arxiv.org/pdf/2206.01595v2.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":"on-the-evolution-of-rotational-modulation","repo_url":"https://github.com/kemasuda/acheron","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","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}