A Unified Empirical Timescale for Galaxy Dynamics from Kinematic Scale Competition

A Unified Empirical Timescale for Galaxy Dynamics from Kinematic Scale Competition | 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 A Unified Empirical Timescale for Galaxy Dynamics from Kinematic Scale Competition Lachlan McGill This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8546380/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 define a unified, empirically constructed dynamical observable τ, expressed as a signed characteristic timescale (in Myr), derived from two structural scales extracted directly from kinematic data: a dynamical coherence length ξ_GL and a baryonic confinement scale r_core. These scales are obtained consistently from TDGL-inspired fits to galaxy rotation curves and velocity-dispersion profiles, without imposing morphology priors or assuming a specific microphysical mechanism. Using 165 rotation-supported galaxies from SPARC and 50 pressure-supported ellipticals from ATLAS³D with resolved kinematics, we measure τ across a broad range of galaxy types. We find that τ exhibits a strongly bimodal distribution: rotation-supported galaxies overwhelmingly occupy the positive regime (97.0% with τ > 0) while pressure-supported ellipticals predominantly occupy the negative regime (96.0% τ < 0) with No rotation-supported galaxy exhibits τ < 0; instead, a small boundary population lies near τ ≈ 0. Lenticular (S0) galaxies cluster narrowly around this boundary. A Kolmogorov–Smirnov test rejects the hypothesis that rotation-supported and pressure-supported systems are drawn from the same parent τ distribution at p < 10⁻¹⁴. We further show that τ correlates strongly with long-term baryonic evolution, decreasing with stellar population age and increasing with gas fraction, while remaining independent of instantaneous star-formation rate and environmental metrics. These results establish τ as a robust, empirically measurable structural indicator of galaxy dynamical state, directly derived from kinematics. The observed bimodality and the sharp structural boundary near τ ≈ 0 are consistent with an interpretive framework in which galaxy-scale dynamics reflect competition between coherence and confinement. Subsequent papers examine τ's orthogonality to instantaneous star formation and extend the analysis deeper into the pressure-supported regime. Astrophysics and Cosmology Theoretical Astrophysics Galaxy dynamics Astrophysics SPARC ATLAS³D Rotation curves Scaling relations Galaxy evolution Empirical astrophysics Full Text Additional Declarations The authors declare no competing interests. Supplementary Files TableA1DeriveddynamicalparametersfortheSPARCgalaxysample1.csv TableA2DeriveddynamicalparametersfortheATLAS3Dgalaxysample.csv statisticsbystellarmassbin.csv 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8546380","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":571173876,"identity":"e630328a-3f4e-45d8-b7ce-fcd6b5b6f8a8","order_by":0,"name":"Lachlan 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evolution, Empirical astrophysics","lastPublishedDoi":"10.21203/rs.3.rs-8546380/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8546380/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe define a unified, empirically constructed dynamical observable τ, expressed as a signed characteristic timescale (in Myr), derived from two structural scales extracted directly from kinematic data: a dynamical coherence length ξ_GL and a baryonic confinement scale r_core. These scales are obtained consistently from TDGL-inspired fits to galaxy rotation curves and velocity-dispersion profiles, without imposing morphology priors or assuming a specific microphysical mechanism.\u003c/p\u003e\n\u003cp\u003eUsing 165 rotation-supported galaxies from SPARC and 50 pressure-supported ellipticals from ATLAS³D with resolved kinematics, we measure τ across a broad range of galaxy types. We find that τ exhibits a strongly bimodal distribution: rotation-supported galaxies overwhelmingly occupy the positive regime (97.0% with τ \u0026gt; 0) while pressure-supported ellipticals predominantly occupy the negative regime (96.0% τ \u0026lt; 0) with \u0026nbsp;No rotation-supported galaxy exhibits τ \u0026lt; 0; instead, a small boundary population lies near τ ≈ 0. Lenticular (S0) galaxies cluster narrowly around this boundary. A Kolmogorov–Smirnov test rejects the hypothesis that rotation-supported and pressure-supported systems are drawn from the same parent τ distribution at p \u0026lt; 10⁻¹⁴.\u003c/p\u003e\n\u003cp\u003eWe further show that τ correlates strongly with long-term baryonic evolution, decreasing with stellar population age and increasing with gas fraction, while remaining independent of instantaneous star-formation rate and environmental metrics. These results establish τ as a robust, empirically measurable structural indicator of galaxy dynamical state, directly derived from kinematics. The observed bimodality and the sharp structural boundary near τ ≈ 0 are consistent with an interpretive framework in which galaxy-scale dynamics reflect competition between coherence and confinement. 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