{"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/efficient-uninformative-sampling-of-limb-1","title":"Efficient, uninformative sampling of limb-darkening coefficients for a three-parameter law","arxiv_id":"1509.03483","date":"2015-09-11","proceeding":null,"authors":["David M. Kipping"],"abstract":"Stellar limb-darkening impacts a wide range of astronomical measurements. The accuracy to which it is modelled limits the accuracy in any covariant parameters of interest, such as the radius of a transiting planet. With the ever growing availability of precise observations and the importance of robust estimates of astrophysical parameters, an emerging trend has been to freely fit the limb-darkening coefficients (LDCs) describing a limb-darkening law of choice, in order to propagate our ignorance of the true intensity profile. In practice, this approach has been limited to two-parameter limb-darkening laws, such as the quadratic law, due to the relative ease of sampling the physically allowed range of LDCs. Here, we provide a highly efficient method for sampling LDCs describing a more accurate three-parameter non-linear law. We first derive analytic criteria which can quickly test if a set of LDCs are physical, although naive sampling with these criteria leads to an acceptance rate less than 1%. We then show that the loci of allowed LDCs can be transformed into a cone-like volume, from which we are able to draw uniform samples. We show that samples drawn uniformly from the conal region are physically valid in 97.3% of realizations and encompass 94.4% of the volume of allowed parameter space. We provide Python and Fortran code (LDC3) to sample from this region (and perform the reverse calculation) at https://github.com/davidkipping/LDC3, which also includes a subroutine to efficiently test whether a sample is physically valid or not.","url_abs":"http://arxiv.org/abs/1509.03483v2","url_pdf":"http://arxiv.org/pdf/1509.03483v2.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":"efficient-uninformative-sampling-of-limb-1","repo_url":"https://github.com/davidkipping/LDC3","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}