Nested Tests of Non-Keplerian Scaling in Exoplanet Systems: Solar-System Calibration and Population-Level Upper Limits

Nested Tests of Non-Keplerian Scaling in Exoplanet Systems: Solar-System Calibration and Population-Level Upper Limits | 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 Nested Tests of Non-Keplerian Scaling in Exoplanet Systems: Solar-System Calibration and Population-Level Upper Limits kazufumi kimura This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7476716/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 revisit Kepler’s third law in an instrument-aware, catalog-wide setting by casting the Keplerian scaling as a nested null model. The alternative augments log P with a minimal logistic term. Using the Solar System as a calibrated positive control, we recover a modest yet detectable effect localized near a trajectory-dependent encounter scale. Applying the same pipeline to public exoplanet catalogs (PSCompPars and KOI), the logistic extension is disfavored by information criteria (AICc/BIC) with negative likelihood-ratio statistics; the maximum-likelihood amplitude is â = 0. We therefore report a 95% profile-likelihood upper bound α 95 , providing a falsifiable benchmark for future, physically motivated multivariate corrections. Using the Solar System as a calibrated positive control, we find a modest yet detectable improvement: ∆AICc = −1.6, ∆BIC = −0.5, LRT = 3.1 (p = 0.078), and a 4.2% reduction in cross-validated residual scale. By contrast, the exoplanet ensembles are disfavored, with ∆AICc = +2.8 and ∆BIC = +5.3 (> 0), â = 0, and α95 = 0.07. Exoplanet dynamics Kepler’s laws Model comparison Information criteria Model comparison Full Text Additional Declarations No competing interests reported. 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-7476716","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":507584980,"identity":"4333edbf-65ea-4c47-9f32-ad339d2f815b","order_by":0,"name":"kazufumi kimura","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYBACCWYwZZPAwAOi2YjXkoashZmAFgh1mAQtku3cadIVNefz+HvOmEn8KLNhMGfvP4BXizQz7zbJM8duF0uc7TGT7DmXxmDZcxi/LXIgLQ1stxMbzvOY3eBtO8xgcCOZGC3/ziXOB2q5+Rek5f5j/FrADmtsO5C4Aeiw2xBbCHm/mXezZWNfcuLGM8fKf8ucS+MxOJNsgFeLxPmzG282fLNLnHcmebPhmzIbOYPjBx/gtwYd8JCmfBSMglEwCkYBVgAAWepFmDCQrfQAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"kazufumi","middleName":"","lastName":"kimura","suffix":""}],"badges":[],"createdAt":"2025-08-28 06:08:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7476716/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7476716/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92417525,"identity":"b5013561-83af-44d3-b687-47a2ee1e7413","added_by":"auto","created_at":"2025-09-29 13:38:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":607881,"visible":true,"origin":"","legend":"","description":"","filename":"NestedTestsofNonKeplerianScalinginExoplanetSystems.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7476716/v1_covered_d67d23f3-ec12-4778-8819-37ab6c13673d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eNested Tests of Non-Keplerian Scaling in Exoplanet Systems: Solar-System Calibration and Population-Level Upper Limits\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Exoplanet dynamics, Kepler’s laws, Model comparison, Information criteria, Model comparison","lastPublishedDoi":"10.21203/rs.3.rs-7476716/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7476716/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe revisit Kepler’s third law in an instrument-aware, catalog-wide setting by casting the Keplerian scaling as a nested null model. 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