{"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/restoration-of-the-tully-fisher-relation-by","title":"Restoration of the Tully-Fisher Relation by Statistical Rectification","arxiv_id":"2401.13738","date":"2024-01-24","proceeding":null,"authors":["Hai Fu"],"abstract":"I employ the Lucy rectification algorithm to recover the inclination-corrected distribution of local disk galaxies in the plane of absolute magnitude ($M_i$) and HI velocity width ($W_{20}$). By considering the inclination angle as a random variable with a known probability distribution, the novel approach eliminates one major source of uncertainty in studies of the Tully-Fisher relation: inclination angle estimation from axial ratio. Leveraging the statistical strength derived from the entire sample of 28,264 HI-selected disk galaxies at $z < 0.06$ from the Arecibo Legacy Fast ALFA (ALFALFA) survey, I show that the restored distribution follows a sharp correlation that is approximately a power law between $-16 > M_i > -22$: $M_i = M_0 - 2.5\\beta \\ [\\log(W_{\\rm 20}/250 {\\rm km/s})]$, with $M_0 = -19.77\\pm0.04$ and $\\beta = 4.39\\pm0.06$. At the brighter end ($M_i < -22$), the slope of the correlation decreases to $\\beta \\approx 3.3$, confirming previous results. Because the method accounts for measurement errors, the intrinsic dispersion of the correlation is directly measured: $\\sigma(\\log W_{20}) \\approx 0.06$ dex between $-17 > M_i > -23$, while $\\sigma(M_i)$ decreases from $\\sim$0.8 in slow rotators to $\\sim$0.4 in fast rotators. The statistical rectification method holds significant potential, especially in the studies of intermediate-to-high-redshift samples, where limited spatial resolution hinders precise measurements of inclination angles.","url_abs":"https://arxiv.org/abs/2401.13738v3","url_pdf":"https://arxiv.org/pdf/2401.13738v3.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":"restoration-of-the-tully-fisher-relation-by","repo_url":"https://github.com/fuhaiastro/tfr_lucy","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}