{"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/mass-functions-of-dark-matter-halos-from","title":"Halo mass functions from maximum entropy distributions in collisionless dark matter flow","arxiv_id":"2110.09676","date":"2021-10-19","proceeding":null,"authors":["Zhijie Xu"],"abstract":"The halo-mediated inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). A broad spectrum of halos and halo groups are necessary to form from inverse mass cascade for long-range interaction system to maximize its entropy. The limiting velocity ($\\textbf X$), speed ($\\textbf Z$), and energy ($\\textbf E$) distributions of collisionless particles can be obtained analytically from a maximum entropy principle. Halo mass function, the distribution of total mass in halos, is a fundamental quantity for structure formation and evolution. Instead of basing mass functions on simplified spherical/elliptical collapse models, it is possible to reformulate mass function as an intrinsic distribution to maximize system entropy during the everlasting statistically steady state. Starting from halo-based description of non-equilibrium dark matter flow, distributions of particle virial dispersion ($\\textbf H$), square of particle velocity ($\\textbf P$), and number of halos ($\\textbf J$) are proposed. Their statistical properties and connections with velocity distribution ($\\textbf X$) are well studied and established. With $\\textbf H$ being essentially the halo mass function, two limiting cases of $\\textbf H$ distribution are analyzed for large halos ($\\textbf H_\\infty$) and small halos ($\\textbf H_s$), respectively. For large halos, $\\textbf H_\\infty$ is shown to also be a maximum entropy distribution. For small halos, $\\textbf H_s$ approximates the $\\textbf P$ distribution and recovers the Press-Schechter mass function. The full solution of $\\textbf H$ distribution is determined by the velocity distribution ($\\textbf X$) that maximizes system entropy and the exact model of halo velocity dispersion.","url_abs":"https://arxiv.org/abs/2110.09676v2","url_pdf":"https://arxiv.org/pdf/2110.09676v2.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":"mass-functions-of-dark-matter-halos-from","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}