Galaxy Rotation Curves and Baryonic Scaling Relations in Time-Field General Relativity: A Systematic Analysis of the SPARC Sample

Galaxy Rotation Curves and Baryonic Scaling Relations in Time-Field General Relativity: A Systematic Analysis of the SPARC Sample | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Galaxy Rotation Curves and Baryonic Scaling Relations in Time-Field General Relativity: A Systematic Analysis of the SPARC Sample Takahiro Mitsui This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9064232/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We present a systematic phenomenological analysis of galaxy rotation curves in the framework of Time-Field General Relativity (TFGR), using the SPARC database of late-type galaxies [Lelli et al., 2016]. The working hypothesis is that galactic dynamics may encode a finite response scale in gravitational behavior, represented here by a TFGR-inspired velocity profile with saturation velocity V0, transition radius rc, and transition sharpness n. We compare this profile with baryonic-only rotation curves built from the observed gas, stellar disk, and bulge contributions. Across 165 successful fits, the TFGR profile improves upon the baryonic-only description in 157 galaxies, with a median improvement of ΔAIC ≃ 331. The median reduced chi-square decreases from χ2ν ≃ 18.5 for baryonic-only models to χ2ν ≃ 0.41 for TFGR fits. In a robust subsample of 34 galaxies, the TFGR saturation velocity closely tracks the observed outer rotation velocity, with a tight correlation between V0 and Vflat. We further examine baryonic Tully–Fisher-like relations and structural scaling relations involving rc. The transition radius exhibits a weak positive trend with global galaxy size and disk scale length, while the ratio rc/Rdisk has a median value of about 1.8. These results indicate that the TFGR phenomenological profile captures systematic regularities in the SPARC sample and motivates further investigation of whether galaxy rotation curves may encode a characteristic dynamical response scale. Astronomy Galaxy rotation curves SPARC database Baryonic Tully–Fisher relation Galactic dynamics Scaling relations Modified gravity phenomenology Time-Field General Relativity Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9064232","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":602591259,"identity":"4bccbb98-380b-42a2-a194-ec1c602469d0","order_by":0,"name":"Takahiro Mitsui","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYHACNiCqSTBgb2A8kFAB5DMzN+BVzwPRcizBgOcAw4EPZ0BaGInSwpxgIJHAcHBmG0iMgBZ7sQNsjwvK2PLMGdIfHOadVxvN3w7U8qNiG25bpBPYjWeckym2bDhjcJh32/HcGYcZGxh7ztzGp4VNmreNLXHDwR4GoJZjuQ1ALcyMbQS1MCduOMwOdNicY7nziddyjMHg4MyGmtwNBLXcTmyT5jl3rNiyh8fgwIdjB3I3ArUcxOcX9tnJx6R5ymryzOWfP3yQUFOXO+/84YMPflTg1oIeC4fB5AE86jFAHSmKR8EoGAWjYIQAABoUXQvcwduMAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0006-6576-0352","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Takahiro","middleName":"","lastName":"Mitsui","suffix":""}],"badges":[],"createdAt":"2026-03-08 12:43:55","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9064232/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9064232/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104780398,"identity":"bb8c70ae-9550-4525-9406-477717f84684","added_by":"auto","created_at":"2026-03-17 07:52:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":913759,"visible":true,"origin":"","legend":"","description":"","filename":"tfgrcqgsubmissionarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9064232/v1_covered_eafd4e07-b2fc-4296-a53f-5e5251c56af6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eGalaxy Rotation Curves and Baryonic Scaling Relations in Time-Field General Relativity: A Systematic Analysis of the SPARC Sample\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Galaxy rotation curves, SPARC database, Baryonic Tully–Fisher relation, Galactic dynamics, Scaling relations, Modified gravity phenomenology, Time-Field General Relativity","lastPublishedDoi":"10.21203/rs.3.rs-9064232/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9064232/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe present a systematic phenomenological analysis of galaxy rotation curves in the framework of Time-Field General Relativity (TFGR), using the SPARC database of late-type galaxies [Lelli et al., 2016]. 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