{"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/a-novel-analytic-atmospheric-t-t-relation-for","title":"A novel analytic atmospheric $T(τ)$ relation for stellar models","arxiv_id":"2101.04693","date":"2021-01-12","proceeding":null,"authors":["Warrick H. Ball"],"abstract":"Stellar models often use relations between the temperature $T$ and optical depth $\\tau$ to evaluate the structure of their optically-thin outer layers. We fit a novel analytic function to the Hopf function $q(\\tau)$ of a radiation-coupled hydrodynamics simulation of near-surface convection with solar parameters by Trampedach et al. (2014). The fit is accurate to within 0.82 per cent for the solar simulation and to within 13 per cent for all the simulations that are not on either the low-temperature or low-gravity edges of the grid of simulations.","url_abs":"https://arxiv.org/abs/2101.04693v1","url_pdf":"https://arxiv.org/pdf/2101.04693v1.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":"a-novel-analytic-atmospheric-t-t-relation-for","repo_url":"https://github.com/warrickball/atm_rnaas2021","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","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}