{"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/discovering-black-hole-mass-scaling-relations","title":"Discovering Black Hole Mass Scaling Relations with Symbolic Regression","arxiv_id":"2310.19406","date":"2023-10-30","proceeding":null,"authors":["Zehao Jin","Benjamin L. Davis"],"abstract":"Our knowledge of supermassive black holes (SMBHs) and their relation to their host galaxies is still limited, and there are only around 150 SMBHs that have their masses directly measured and confirmed. Better black hole mass scaling relations will help us reveal the physics of black holes, as well as predict black hole masses that are not yet measured. Here, we apply symbolic regression, combined with random forest to those directly-measured black hole masses and host galaxy properties, and find a collection of higher-dimensional (N-D) black hole mass scaling relations. These N-D black hole mass scaling relations have scatter smaller than any of the existing black hole mass scaling relations. One of the best among them involves the parameters of central stellar velocity dispersion, bulge-to-total ratio, and density at the black hole's sphere-of-influence with an intrinsic scatter of $\\epsilon=0.083\\,\\ \\text{dex}$, significantly lower than $\\epsilon \\sim 0.3\\,\\ \\text{dex}$ for the M-$\\sigma$ relation. These relations will inspire black hole physics, test black hole models implemented in simulations, and estimate unknown black hole masses on an unprecedented precision.","url_abs":"https://arxiv.org/abs/2310.19406v2","url_pdf":"https://arxiv.org/pdf/2310.19406v2.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":"discovering-black-hole-mass-scaling-relations","repo_url":"https://github.com/zehaojin/ultimate_black_hole_mass_scaling_relations_symbolic_regression","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2310.19406","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2310.19406"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/zehaojin/ultimate_black_hole_mass_scaling_relations_symbolic_regression","reach":null}],"summary":{"ran_draft_wrong":2},"by_repo_kind":{"official":{"samples":2,"ran":2,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":2,"samples":[{"code_sha256_prefix":"7035c61ce94ddce9","entry":"simplify_equation","repo":"zehaojin/ultimate_black_hole_mass_scaling_relations_symbolic_regression","repo_kind":"official","path":"Blackhole_properties/Ultimate_paper/general_fit_function.py","file_url":"https://github.com/zehaojin/ultimate_black_hole_mass_scaling_relations_symbolic_regression/blob/HEAD/Blackhole_properties/Ultimate_paper/general_fit_function.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"7035c61ce94ddce9"}},{"code_sha256_prefix":"03b25c0ce119ef66","entry":"str2equ","repo":"zehaojin/ultimate_black_hole_mass_scaling_relations_symbolic_regression","repo_kind":"official","path":"Blackhole_properties/Ultimate_paper/general_fit_function.py","file_url":"https://github.com/zehaojin/ultimate_black_hole_mass_scaling_relations_symbolic_regression/blob/HEAD/Blackhole_properties/Ultimate_paper/general_fit_function.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"03b25c0ce119ef66"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}