{"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/hyrec-2-a-highly-accurate-sub-millisecond","title":"HYREC-2: a highly accurate sub-millisecond recombination code","arxiv_id":"2007.14114","date":"2020-07-28","proceeding":null,"authors":["Nanoom Lee","Yacine Ali-Haïmoud"],"abstract":"We present the new recombination code HYREC-2, holding the same accuracy as the state-of-the-art codes HYREC and COSMOREC and, at the same time, surpassing the computational speed of the code RECFAST commonly used for CMB-anisotropy data analyses. HYREC-2 is based on an effective 4-level atom model, accounting exactly for the non-equilibrium of highly excited states of hydrogen, and very accurately for radiative transfer effects with a correction to the Lyman-$\\alpha$ escape rate. The latter is computed with the original HYREC, and tabulated, as a function of temperature, along with its derivatives with respect to the relevant cosmological parameters. This enables the code to keep the same accuracy as the original HYREC-2 over the full 99.7% confidence region of cosmological parameters currently allowed by Planck, while running in under one millisecond on a standard laptop. Our code leads to no noticeable bias in any cosmological parameters even in the case of an ideal cosmic-variance limited experiment up to $\\ell$ = 5000. Beyond CMB anisotropy calculations, HYREC-2 will be a useful tool to compute various observables that depend on the recombination and thermal history, such as the recombination spectrum or the 21-cm signal.","url_abs":"https://arxiv.org/abs/2007.14114v2","url_pdf":"https://arxiv.org/pdf/2007.14114v2.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":"hyrec-2-a-highly-accurate-sub-millisecond","repo_url":"https://github.com/nanoomlee/HYREC-2","is_official":1,"mentioned_in_paper":1,"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}