Density Exponent Analysis -- A new vision towards gravitational collapse of molecular clouds

Density Exponent Analysis -- A new vision towards gravitational collapse of molecular clouds | 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 Article Density Exponent Analysis -- A new vision towards gravitational collapse of molecular clouds Guang-Xing Li, Ji-Xuan Zhou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-669614/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 The evolution of molecular interstellar clouds, during which stars form, is a complex, multi-scale process. The power-law density exponent describes the steepness of density profiles in the log-log space, and it has been used to characterize the density structures of the clouds. Its effectiveness results from the widespread emergence of power-law-like density structures in complex systems that have reached intermediate asymptotic states. However, its usage is usually limited to spherically symmetric systems. Importing the Level-Set Method, we develop a new formalism that generates robust maps of a generalized density exponent k p at every location for complex density distributions. By applying it to a high fidelity, high dynamical range map of the Perseus molecular cloud constructed using data from the Herschel and Planck satellites, we find that the density exponent exhibits a surprisingly wide range of variation (-3.5 < k p < -0.5) Regions at later stages of gravitational collapse are associated with steeper density profiles. Inside a region, gas located in the vicinities of dense structures has very steep density profiles with k p ~ -3, which form because of depletion. This density exponent analysis reveals diverse density structures in a molecular cloud, forming a coherent picture that gravitational collapse and accretion contribute to a continued steepening of the density profile. We expect our method to be effective in studying other power-law-like density structures, including the density structure of granular materials and the Large-Scale Structure of the Universe. Astronomy Astrophysics and Cosmology Planetary Science molecular clouds Density Exponent Analysis gravitational collapse Full Text Additional Declarations There is NO Competing Interest. 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-669614","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":42252515,"identity":"7108ba09-59ec-46fa-b283-682696741391","order_by":0,"name":"Guang-Xing Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtUlEQVRIiWNgGAWjYFAC5oYDHyAsA2K1MDYcnEGyFmYekrTIRyQ2HrZtu5PYwN68TYKh5g5hLYZnDjYczm17ltjAc6xMguHYMyK0tDeCtBxObJDIMZNgbDhMhJZmoDJLkBb5N0RqkWcH2sIItoWHSC0GPAcbDvacO2zcxpNWbJFwjBhbZiQf/vCj7LBsP/vhjTc+1BBjywEgwcjGwMAG4iUQ1gC0pQFE/iFG6SgYBaNgFIxYAADZ8D5rjxWaDAAAAABJRU5ErkJggg==","orcid":"","institution":"South-Western Institute for Astronomy Research, Yunnan University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Guang-Xing","middleName":"","lastName":"Li","suffix":""},{"id":42252516,"identity":"c05bca9d-1da5-4cd2-8630-d8783fafbd2a","order_by":1,"name":"Ji-Xuan Zhou","email":"","orcid":"","institution":"South-Western Institute for Astronomy Research, Yunnan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ji-Xuan","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2021-06-30 07:37:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-669614/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-669614/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":13663548,"identity":"af6feab3-30e0-487e-9024-58eb87a87361","added_by":"auto","created_at":"2021-09-17 10:37:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1217309,"visible":true,"origin":"","legend":"","description":"","filename":"densityexponentli.pdf","url":"https://assets-eu.researchsquare.com/files/rs-669614/v1_covered.pdf"},{"id":11920208,"identity":"795545ae-b241-4312-ba36-70f405b095f0","added_by":"auto","created_at":"2021-07-29 14:26:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1213732,"visible":true,"origin":"","legend":"","description":"","filename":"densityexponentli.pdf","url":"https://assets-eu.researchsquare.com/files/rs-669614/v1_covered.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Density Exponent Analysis -- A new vision towards gravitational collapse of molecular clouds","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-669614/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"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":"molecular clouds, Density Exponent Analysis, gravitational collapse","lastPublishedDoi":"10.21203/rs.3.rs-669614/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-669614/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe evolution of molecular interstellar clouds, during which stars form, is a complex, multi-scale process. The power-law density exponent describes the steepness of density profiles in the log-log space, and it has been used to characterize the density structures of the clouds. Its effectiveness results from the widespread emergence of power-law-like density structures in complex systems that have reached intermediate asymptotic states. However, its usage is usually limited to spherically symmetric systems. Importing the Level-Set Method, we develop a new formalism that generates robust maps of a generalized density exponent \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e at every location for complex density distributions. By applying it to a high fidelity, high dynamical range map of the Perseus molecular cloud constructed using data from the Herschel and Planck satellites, we find that the density exponent exhibits a surprisingly wide range of variation (-3.5 \u0026lt; \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e \u0026lt; -0.5) Regions at later stages of gravitational collapse are associated with steeper density profiles. Inside a region, gas located in the vicinities of dense structures has very steep density profiles with \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e \u003c/sub\u003e~ -3, which form because of depletion. This density exponent analysis reveals diverse density structures in a molecular cloud, forming a coherent picture that gravitational collapse and accretion contribute to a continued steepening of the density profile. We expect our method to be effective in studying other power-law-like density structures, including the density structure of granular materials and the Large-Scale Structure of the Universe.\u003c/p\u003e","manuscriptTitle":"Density Exponent Analysis -- A new vision towards gravitational collapse of molecular clouds","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-07-29 14:26:47","doi":"10.21203/rs.3.rs-669614/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"2e9a81e4-c0b3-446e-a5f7-0d257aa01997","owner":[],"postedDate":"July 29th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":6079712,"name":"Astronomy"},{"id":6079713,"name":"Astrophysics and Cosmology"},{"id":6079714,"name":"Planetary Science"}],"tags":[],"updatedAt":"2021-10-05T16:15:58+00:00","versionOfRecord":[],"versionCreatedAt":"2021-07-29 14:26:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-669614","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-669614","identity":"rs-669614","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}