{"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/the-baryonic-to-halo-mass-relation-from-mass","title":"The baryonic-to-halo mass relation from mass and energy cascade in self-gravitating collisionless dark matter flow","arxiv_id":"2203.06899","date":"2022-03-14","proceeding":null,"authors":["Zhijie Xu"],"abstract":"The relation between properties of galaxies and dark matter halos they reside in can be valuable for structure formation and evolution. This paper focus on the baryonic-to-halo mass ratio (BHMR) and its evolution. We first review unique properties of self-gravitating collisionless dark matter flow (SG-CFD), followed by their application to derive BHMR. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate inverse mass and energy cascade from small to large scales with a constant rate of energy cascade $\\varepsilon_u$. In addition, dark matter flow exhibits scale-dependent flow behaviors that is incompressible on small scale and irrotational on large scale. With these properties and considering a given halo with a total baryonic mass $m_b$, halo mass $m_h$, halo virial size $r_h$, and flat rotation speed $v_f$, BHMR can be analytically derived by combining the baryonic Tully-Fisher relation and constant $\\varepsilon_u$ in small and large halos. A maximum BHMR ratio ~0.076 is found for halos with a critical mass $m_{hc}\\sim 10^{12}M_{\\odot}$ at z=0. That ratio is much lower for both smaller and larger halos such that two regimes can be identified: i) for incompressible small halos with mass $m_h<m_{hc}$, we have $\\varepsilon_u\\propto v_f/r_h$, $v_f\\propto r_h$, and $m_b\\propto m_h^{4/3}$; ii) for large halos with mass $m_h>m_{hc}$, we have $\\varepsilon_u\\propto v_f^3/r_h$, $v_f\\propto r_h^{1/3}$, and $m_b\\propto m_h^{4/9}$. Combined with double-$\\lambda$ halo mass function, the average BHMR ratio in all halos (~0.024 at z=0) can be analytically derived, along with its redshift evolution. The fraction of total baryons in all galaxies is ~7.6% at z=0 and increases with time $\\propto t^{1/3}$. The SPARC (Spitzer Photometry \\& Accurate Rotation Curves) data with 175 late-type galaxies were used for derivation and comparison.","url_abs":"https://arxiv.org/abs/2203.06899v2","url_pdf":"https://arxiv.org/pdf/2203.06899v2.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":"the-baryonic-to-halo-mass-relation-from-mass","repo_url":"https://github.com/ZhijieXu2022/dark_matter_flow_dataset","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}