Effects of magma-generation and migration on the expansion and contraction history of the Moon.

Effects of magma-generation and migration on the expansion and contraction history of the Moon. | 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 Effects of magma-generation and migration on the expansion and contraction history of the Moon. Kenyo U, Hiroki Hasumi, Masaki Ogawa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1278795/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Geological and geodetic observations of the Moon from spacecraft revealed that it expanded by a few km for the first several hundred million years and then contracted later. The period when the planet expanded most coincides with that when the mare volcanism of the Moon was active. Given the high initial temperature of the deep mantle inferred from the giant impact and mantle overturn hypotheses of the Moon, the observed early expansion is difficult to account for by thermal expansion only. To understand the observed radial change of the Moon, we numerically calculated the thermal evolution of a one-dimensional spherically symmetric mantle caused by transport of heat, mass, and incompatible heat-producing elements (HPEs) by migration of magma that is generated by internal heating. The mantle is assumed to be enriched in HPEs at its base in the initial condition. The calculated mantle expands for the first several hundred million years by melting of the deep mantle and upward migration of the generated magma to the uppermost mantle; the top of the partially molten region rises up to the depth level of around 300 km, shallow enough to generate mare basalts of the Moon. The migrating magma, however, extracts HPEs from the deep interior, and the planet then contracts gradually by cooling and solidification of the partially molten mantle. We obtained a thermal history that is consistent with the observed history of radial change of the Moon when the initial mid-mantle temperature \({T}_{M}\approx 1600 K\) and the initial ratio of the concentration of HPEs in the crust to that of the mantle \({F}_{crst}\le 12\) . This initial state of the mantle inferred from its thermal history constrains the earliest evolution of the Moon dominated by the magma ocean and mantle overturn. Moon Magma-migration Magma-generation Expansion/Contraction history. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Full Text Tables Tables are available in the Supplemental Files section. Supplementary Files EPSwordTablesU.docx graphicalabstractU.png Cite Share Download PDF Status: Under Review Version 1 posted Reviewer # 2 agreed at journal 24 Jan, 2022 Reviews received at journal 24 Jan, 2022 Reviewer # 1 agreed at journal 23 Jan, 2022 Reviewers invited by journal 21 Jan, 2022 Editor assigned by journal 20 Jan, 2022 First submitted to journal 19 Jan, 2022 Submission checks completed at journal 19 Jan, 2022 Editor invited by journal 19 Jan, 2022 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. 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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-1278795","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":78194584,"identity":"f5287739-75de-4260-8673-ce8e5b98f0a2","order_by":0,"name":"Kenyo U","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-1700-138X","institution":"The University of Tokyo Graduate School of Arts and Sciences: Tokyo Daigaku Daigakuin Sogo Bunka Kenkyuka Kyoyo Gakubu","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Kenyo","middleName":"","lastName":"U","suffix":""},{"id":78194585,"identity":"df15aeab-5512-4612-96f9-34ea6a78d05a","order_by":1,"name":"Hiroki Hasumi","email":"","orcid":"","institution":"Ministry of Internal Affairs","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hiroki","middleName":"","lastName":"Hasumi","suffix":""},{"id":78194586,"identity":"cc75ba74-6dfc-4449-b0a4-0025640ebb1a","order_by":2,"name":"Masaki Ogawa","email":"","orcid":"","institution":"The University of Tokyo Graduate School of Arts and Sciences: Tokyo Daigaku Daigakuin Sogo Bunka Kenkyuka Kyoyo Gakubu","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Masaki","middleName":"","lastName":"Ogawa","suffix":""}],"badges":[],"createdAt":"2022-01-20 07:51:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1278795/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1278795/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":17698783,"identity":"f43aacf8-e600-4657-87b0-c9dabee84dde","added_by":"auto","created_at":"2022-01-27 14:08:28","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":79421,"visible":true,"origin":"","legend":"\u003cp\u003eInitial condition.\u003c/p\u003e\u003cp\u003eIllustration of the initial distribution of (a) internal heating rate, (b) bulk composition, and (c) temperature. The assumed parameter values in the figure are: the temperature of the mid-mantle \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e=1650\u003cem\u003eK\u003c/em\u003e; the ratio of the concentration of HPEs in the crust to the mantle \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrst\u003c/em\u003e\u003c/sub\u003e=8; the thickness of the high-density layer after mantle overturn L=1/5.5.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/f77da160c09ea3ba6c9aed8b.png"},{"id":17698833,"identity":"96cad6f6-0e39-4394-b1e0-3cdce035b515","added_by":"auto","created_at":"2022-01-27 14:11:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":614288,"visible":true,"origin":"","legend":"\u003cp\u003eReference model.\u0026nbsp;\u003c/p\u003e\u003cp\u003e(a) a plot of radius changes against time, (b) temperature profile as a function of time, and the evolution of the distribution of (c) temperature, (d) internal heating rate, (e)melt-content, and (f) bulk composition \u003cem\u003eξ\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e. The assumed parameter values are \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e=1550\u003cem\u003eK\u003c/em\u003e,M=28,\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrst\u003c/em\u003e\u003c/sub\u003e=8,L=1/5.5. In (a), the green and light blue lines indicate the contribution of thermal expansion and melting, respectively, to the total radius change (the purple line). In (c), the contour lines show the distribution of melt-content with the contour interval of 0.05 starting from 0 (indicated by the dashed line); in (e), the contour lines show the distribution of temperature.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/8523f657b6efbece95ec2b20.png"},{"id":17698781,"identity":"5056fef9-a1b1-486b-bee2-bf9b402333a3","added_by":"auto","created_at":"2022-01-27 14:08:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":262721,"visible":true,"origin":"","legend":"\u003cp\u003eModel 1.\u003c/p\u003e\u003cp\u003e(a) and (b) the same as Figures 2a and 2c, respectively, but for Model 1 where only the effects of thermal diffusion, internal heating and melting are considered; magma does not migrate. The assumed parameter values are \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e=1550\u003cem\u003eK\u003c/em\u003e,M=28,\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrst\u003c/em\u003e\u003c/sub\u003e=8,L=1/5.5. In (b), the contour lines show the distribution of melt with the contour interval of 0.2 starting from 0 (indicated by the dashed line).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/116f78bd032d1a64a8a6f385.png"},{"id":17698784,"identity":"7c66f569-b04e-4c67-a1c6-aeb48b8e9df3","added_by":"auto","created_at":"2022-01-27 14:08:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":185592,"visible":true,"origin":"","legend":"\u003cp\u003eModel 2.\u003c/p\u003e\u003cp\u003eThe same as Figure 3 but for Model 2 where magma migration is added to Model 1 shown in Figure 3. In (b), the contour lines show the distribution of melt with the contour drawn at 0.01 intervals from 0.05. The dashed line indicates the molten region (ϕ=0).\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/99717471712385dbade39006.png"},{"id":17698785,"identity":"b4baafc7-8e9d-4dc1-9d4e-04700e071ede","added_by":"auto","created_at":"2022-01-27 14:08:28","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":305355,"visible":true,"origin":"","legend":"\u003cp\u003eModel 3.\u003c/p\u003e\u003cp\u003e(a), (b) the same as Figures 4a, b but for Model 3 where HPE-transport by migrating magma is added to Model 2 shown in Figure 4; transport of the end-members \u003cem\u003eA\u003c/em\u003e and \u003cem\u003eB\u003c/em\u003e by migrating magma is not considered. (c) The evolution of HPE-distribution for Model 3. In (b), the contour lines show the distribution of melt with the contour interval of 0.01 starting from 0 (indicated by the dashed line).\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/0b84ebacc725784038e59ab6.png"},{"id":17698788,"identity":"c8dfd8fb-5e61-4e28-93ed-69f96c8eac3b","added_by":"auto","created_at":"2022-01-27 14:08:28","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":380981,"visible":true,"origin":"","legend":"\u003cp\u003eRadial change at various free parameters.\u003c/p\u003e\u003cp\u003ePlots of radial change against time calculated at various values of (a) \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e, (b) \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrst\u003c/em\u003e\u003c/sub\u003e, (c) L, (d) M. The dotted lines show the reference model indicated by the purple line in Figure 2a.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/f69e9902b4ef6da51ed37f3f.png"},{"id":17698787,"identity":"b3f5f428-3f9c-4502-831d-7cb62bf310d0","added_by":"auto","created_at":"2022-01-27 14:08:28","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":169969,"visible":true,"origin":"","legend":"\u003cp\u003eIllustration of thermal and structural history of the Moon.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/686c1a26f4155433addbe6ad.png"},{"id":17698836,"identity":"f106cfcf-65e7-4ae4-8beb-705d6f327f94","added_by":"auto","created_at":"2022-01-27 14:11:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":589261,"visible":true,"origin":"","legend":"","description":"","filename":"EPSwordManuscriptU.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1_covered.pdf"},{"id":17698782,"identity":"58f109d5-4a84-4c66-ae61-4440e1e59a2c","added_by":"auto","created_at":"2022-01-27 14:08:28","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":18866,"visible":true,"origin":"","legend":"","description":"","filename":"EPSwordTablesU.docx","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/3fde1fe2d1d0f61cc3e673d4.docx"},{"id":17698834,"identity":"12f5b7d7-13b9-4eb0-a86c-d1b88c757607","added_by":"auto","created_at":"2022-01-27 14:11:28","extension":"png","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1159844,"visible":true,"origin":"","legend":"","description":"","filename":"graphicalabstractU.png","url":"https://assets-eu.researchsquare.com/files/rs-1278795/v1/42785100abc960ff408d9f0b.png"}],"financialInterests":"","formattedTitle":"Effects of magma-generation and migration on the expansion and contraction history of the Moon.","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1278795/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."},{"header":"Tables","content":"\u003cp\u003eTables are available in the Supplemental Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Moon, Magma-migration, Magma-generation, Expansion/Contraction history. ","lastPublishedDoi":"10.21203/rs.3.rs-1278795/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1278795/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGeological and geodetic observations of the Moon from spacecraft revealed that it expanded by a few km for the first several hundred million years and then contracted later. The period when the planet expanded most coincides with that when the mare volcanism of the Moon was active. Given the high initial temperature of the deep mantle inferred from the giant impact and mantle overturn hypotheses of the Moon, the observed early expansion is difficult to account for by thermal expansion only. To understand the observed radial change of the Moon, we numerically calculated the thermal evolution of a one-dimensional spherically symmetric mantle caused by transport of heat, mass, and incompatible heat-producing elements (HPEs) by migration of magma that is generated by internal heating. The mantle is assumed to be enriched in HPEs at its base in the initial condition. The calculated mantle expands for the first several hundred million years by melting of the deep mantle and upward migration of the generated magma to the uppermost mantle; the top of the partially molten region rises up to the depth level of around 300 km, shallow enough to generate mare basalts of the Moon. The migrating magma, however, extracts HPEs from the deep interior, and the planet then contracts gradually by cooling and solidification of the partially molten mantle. We obtained a thermal history that is consistent with the observed history of radial change of the Moon when the initial mid-mantle temperature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{M}\\approx 1600 K\\)\u003c/span\u003e\u003c/span\u003e and the initial ratio of the concentration of HPEs in the crust to that of the mantle \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{crst}\\le 12\\)\u003c/span\u003e\u003c/span\u003e. This initial state of the mantle inferred from its thermal history constrains the earliest evolution of the Moon dominated by the magma ocean and mantle overturn.\u003c/p\u003e","manuscriptTitle":"Effects of magma-generation and migration on the expansion and contraction history of the Moon.","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-01-27 14:08:26","doi":"10.21203/rs.3.rs-1278795/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2022-01-25T00:00:00+00:00","index":2,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-01-24T14:39:42+00:00","index":0,"fulltext":""},{"type":"reviewerAgreed","content":"","date":"2022-01-24T00:00:00+00:00","index":1,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-01-21T09:02:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-01-20T14:23:05+00:00","index":"","fulltext":""},{"type":"submitted","content":"Earth, Planets and Space","date":"2022-01-20T02:50:57+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2022-01-19T23:00:00+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2022-01-19T23:00:00+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"46df2602-fbc8-4b1d-8ccf-54c9308e9791","owner":[],"postedDate":"January 27th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2022-04-13T09:57:36+00:00","versionOfRecord":[],"versionCreatedAt":"2022-01-27 14:08:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1278795","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1278795","identity":"rs-1278795","version":["v1"]},"buildId":"-HB7Z8yhvgn0wM9Nzuekk","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}