{"paper":{"title":"Analytical and fitting formulae for solutions to Lyman-alpha radiative transfer equations: the effects of geometry, recoil, and velocity gradients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Pengfei Li, Zheng Zheng","submitted_at":"2026-06-25T18:00:01Z","abstract_excerpt":"Lyman-alpha (Ly$\\alpha$) radiative transfer (RT) is important in many astrophysical environments and governed by multiple physical processes. In this paper, we provide analytical formulae/procedures for the solutions to Ly$\\alpha$ RT equations under three simple geometrical symmetries and investigate the effects of atomic recoil and gas bulk motion. We first study Ly$\\alpha$ spectra by solving Ly$\\alpha$ RT equations for a static, uniform gas cloud under cylindrical geometry. The solution is verified through Ly$\\alpha$ Monte Carlo RT simulations, and compared to those under slab and spherical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27423","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27423/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}