A. Morbidelli
a,∗, G. Libourel
a, H. Palme
b, S.A. Jacobson
c, D.C. Rubie
daLaboratoireLagrange,UMR7293,UniversitédeNiceSophia-Antipolis,CNRS,ObservatoiredelaCôted’Azur,Boulevarddel’Observatoire,06304NiceCedex4, France
bSenckenberg,worldofbiodiversity,SektionMeteoritenforschung,Senckenberganlage25,60325FrankfurtamMain,Germany cNorthwesternUniversity,Dept.ofEarthandPlanetarySciences,Evanston,60208IL,UnitedStatesofAmerica
dBayerischesGeoinstitut,UniversityofBayreuth,95440,Bayreuth,Germany
a r t i c l e i n f o a b s t ra c t
Articlehistory:
Received2July2019
Receivedinrevisedform4March2020 Accepted10March2020
Availableonline23March2020 Editor:F.Moynier
Keywords:
meteorites
condensationsequence refractoryelements volatileelements
TheAl/SiandMg/Siratiosinnon-carbonaceouschondritesarelowerthanthesolar(i.e., CI-chondritic) values,insharpcontrast tothenon-CI carbonaceousmeteoritesand theEarth, whichare enrichedin refractory elements and have Mg/Siratios thatare solarorlarger. We show that the formation ofa firstgenerationofplanetesimalsduringthecondensationofrefractoryelementsimpliesthesubsequent formationofresidualcondensateswithstronglysub-solarAl/SiandMg/Siratios.Themixingofresidual condensates with different amounts of material with solar refractory/Si element ratios explains the Al/SiandMg/Sivaluesofnon-carbonaceouschondrites.Tomatchquantitativelytheobservedratios,we findthatthefirst-planetesimalsshouldhave accretedwhenthe disktemperaturewas∼1,330–1,400 K dependingonpressureandassumingasolarC/Oratioofthedisk.Wediscusshowthismodelrelatesto ourcurrentunderstandingofdiskevolution,graindynamics,andplanetesimalformation.Wealsoextend the discussionto moderately volatileelements (e.g., Na),explaininghow itmay be possible that the depletionoftheseelementsinnon-carbonaceouschondritesiscorrelatedwiththedepletionofrefractory elements(e.g.,Al).ExtendingtheanalysistoCr,wefindevidenceforahigherthansolarC/Oratiointhe protosolardisk’sgaswhen/wherecondensationfromafractionatedgasoccurred.Finally,wediscussthe possibilitythatthesupra-solarAl/SiandMg/SiratiosoftheEarthareduetotheaccretionof∼40%of themassofourplanetfromthefirst-generationofrefractory-richplanetesimals.
©2020ElsevierB.V.Allrightsreserved.
1. Introduction
Carbonaceouschondrites(CCs),fromCItoCM,COandCV,show aprogressive increase in Al/SiandMg/Siratios together with an increasing depletion in moderately volatile elements (e.g., Na) – see Fig. 1, table S1 and references therein. CI meteorites reflect the solar composition and the observed trend is interpreted as the consequenceof an increasing abundance of minerals formed inhigh-temperatureregions oftheprotoplanetarydisk(e.g.,CAIs:
Hezelet al., 2008). The trendcontinues for theEarth, ifthe up- per mantle Mg/Si andAl/Si ratios are validfor the bulk mantle, whichisoftenassumed(e.g.,PalmeandO’Neill,2014;Hyungetal., 2016), butthere arealsoargumentsagainst achemicallyuniform mantle(e.g.,Ballmeretal.,2017).Thereisalsosomediscussionon
*
Correspondingauthor.E-mailaddress:[email protected](A. Morbidelli).
theamountofSiinthecore(Rubieetal.,2015).Thus,inFig.1we reporttwovaluesforthebulkAl/SiandMg/Siratios,computedas- sumingthat themantleishomogeneous (Hyungetal., 2016) but thecorecontains 0%or7% Siby mass.Thisisintended togive a senseofthesystematicuncertaintyonthebulkcompositionratios oftheEarth.Itremainsclear,however,thattheEarthisenrichedin refractory elements anddepletedin moderatelyvolatileelements atleastatthelevelofCO-CVmeteorites.
Enstatite chondrites, rumuruti and ordinary chondrites (ECs, RCsandOCshereafter,genericallydenotedNCCsfornon-carbona- ceouschondrites)surprisinglydonotfollowthistrend,despitethe factthattheyshouldhaveformedintherelativelyhot,innersolar system.TheirAl/SiandMg/Siratiosaresub-solarwhiletheyhave only a small Na depletion compared to COs, CVs and the Earth (Fig.1).
The strong difference in Al/Si and Mg/Si ratios between the EarthandECsposesa conundrum.Mostelementshavethe same https://doi.org/10.1016/j.epsl.2020.116220
0012-821X/©2020ElsevierB.V.Allrightsreserved.
Fig. 1.AbundancesofAl,Mg,Fe,Cr,Na,S,relativetoSiandnormalizedtotheCIratiosfordifferentchondritesandtheEarth(dataandreferencesreportedintable S1).For thebulkEarth(BE)twocasesaregivenassuming0and7 wt%ofSiinthecorerespectively.Thereisacleardifferenceinchemistrybetweenthecarbonaceouschondrites (CC)andthenon-carbonaceouschondrites.
ratiosofstableisotopes(e.g.,O-isotopes)inECsandEarth,whereas other chondritic meteorites show significant differences. Only small nucleosynthetic anomalies for ECs relative to Earth have beenreportedforMo,RuandNd.Forthisreasonitissometimes suggestedthattheEarthaccretedmostlyfromenstatitechondrites (seeforinstanceJavoy, 1995;Lodders,2000; Dauphas,2017).But thelarge differencesin Al/SiandMg/Siratios betweenthe Earth andECsseemtoprecludethispossibility,althoughsomesolutions have been proposed (e.g., incongruent vaporization of enstatite:
seeMysenandKushiro,1988).Dauphas(2017) postulatedthatthe precursorsoftheEarthhadthesameisotopiccompositionasECs butadifferentelementcomposition.
Ithasbeenproposedthatthesub-solarAl/SiandMg/Siratiosin theNCCsare duetothelossofarefractory-richcomponentfrom adiskwithan original solarcomposition (see Larimer,1979;see alsoAlexander,2019andreferencestherein).Ithasalsobeensug- gestedthat thisrefractory componentwas accreted by theEarth, thusexplainingitsenrichmentinrefractoryelements.Forinstance, toexplain theMg-enrichmentoftheEarth,Dauphasetal.(2015) suggested that the ECs were depleted in a forsterite condensate andarecomplementary totheforsteriteenrichedEarth. Thispos- sibilityhas beenexplicitly excluded by Alexander(2019), forthe reasonsdiscussedinSect.5.Analternativeexplanationfortherel- ativedeficiencyofSiandMgintheEarthistheevaporationfrom themolten surface ofthe protoplanetaryembryosthat madeour planet(Pringleetal.,2014;MysenandKushiro,1988;Youngetal., 2019). However, the sub-solarAl/SiandMg/Si ratiosofthe NCCs cannot beexplained byevaporationmodels becauseSishould be lostpreferentiallyrelativetoMgandAl.
Inthispaper,we revisit theidea ofthe sequestrationof are- fractory componentfrom theprotoplanetary disk inorder to ex- plainthedepletionofrefractoryelementsintheNCCs.Insection2, wediscusshowarefractory-richcomponentcouldbesequestered, inthe framework of modern models of diskevolution andplan- etesimal formation. In section 3, we determine the temperature at which this refractory-rich component should have been iso- latedfromthecondensationsequenceinordertoexplaintheAl/Si and Mg/Si of the NCCs. In section 4, we extend our considera- tions to other elements:Fe, Na,Cr andS. Insection 5,we show that the enrichment in refractory elements of the Earth can be explained, within uncertainties, by the addition of the refractory component removed fromthe NCCs. We discuss how the issues thatledAlexander(2019) toexcludethispossibilitycanbesolved, sothatthispossibilityremainsthemostviableone.Section6sum- marizestheresultsandhighlightsthepredictionsoftheproperties
oftheprotoplanetarydiskthatourresultsimply,thatwillneedto bevalidatedbyfuturemodelsofdisk’sformationandevolution.
2. Anastrophysicalscenarioforthesequestrationofrefractory material
Asoftenassumed,weconsiderthattheinnerdiskwasinitially veryhot,soallmaterialwasinagaseousform,includingrefractory elements. Asthe diskwasrapidlycooling, variousspeciesstarted to condense in sequence, from the most refractory to the more volatile. This is typical of equilibrium condensation where, with declining temperature, some earlier condensed species are de- stroyedtoformnewones,inadditiontocondensingnewspecies.
However,itisunlikelythatthisprocesscontinuedundisturbed to low temperatures. When enough solid grains condensed, but well beforethe completionofthe wholesequence,theionization levelofthegaswasstronglyreducedbythenowpresentdustand the magneto-rotational instability (MRI) generating turbulence in themidplaneofthediskwasquenched(Desch andTurner,2015).
Because the disk hada radial temperaturegradient, this didnot happen everywhere atthe sametime. The innermostpart ofthe disk,hotenoughtocontainonlysmallamountsofdust,remained MRI-active while the outer part located beyond a threshold dis- tancecorrespondingtosometemperatureTM R I wasMRI-inactive;
theboundarybetweenthetwopartsmovedsunwardsasthedisk cooled with time. The value of TM R I is not known precisely. In thiswork,wewillconsideritasafreeparameterandwediscuss itsbest-fitvalueinsection3.1.
ThetransitionfromaMRI-activetoaMRI-inactiveregionofthe diskshould correspondtoa transitioningasdensity.Thesurface densityofgas hastobe largerinthe MRI-inactiveregion forthe conservation ofmass flux: FM=2
π
rvr, where FM isthe mass flux, r is the distance fromthe star, is the surface densityof gas andvr its radial velocity. Infact, vr= −3/2(ν
/r)whereν
is thegasviscosity,sothereisananti-correlationbetweenandν
, the latterbeingmuch largerintheMRI-active regionofthedisk.Thissteepdensitygradient,creatingapressuremaximum,actsas a barriertothe inwardradial driftofdust dueto gasdrag. Thus, attheboundarybetweentheMRI-activeandMRI-inactivepartsof the disk we expect to findnot just the locally-condensed grains correspondingtothattemperature,butalsograinsthatcondensed earlierandfartherawayandwhoseradial migrationwas stopped at thisboundary (Flocket al., 2017).Incidentally, these migrated grains trappedat TM R I would evolve toacquire thesame chem- istryasthosecondensedlocallyatTM R I.Hence,thedust/gasratio
Fig. 2.Aflow-chartofthescenarioexploredinthispaper.Theverticalaxisrepresentstheevolutionoftime,fromtoptobottom,duringwhichthetemperaturedecreases.
Theblueellipsesshowthematerialavailable(lightblueforgasthen-withincreasingintensityofthecolor- grains,planetesimalsandtheEarth)andtheredrectanglesshow thetransformationprocesses.Forsimplicity,wedonottrackvolatilescondensingbelow1,250 K,norHandHe.SeealsoSupplementaryFig.3foramorecomprehensive(but complicated!)sketchoftheevolutionofgasandsolidsinthediskasafunctionofdistance,timeanddecliningtemperature.(Forinterpretationofthecolorsinthefigure(s), thereaderisreferredtothewebversionofthisarticle.)
at TM R I can become much larger with time than the value due solelytothelocally-condensedgrains.
Thisaccumulationofdust(Flocketal.,2017)shouldhavetrig- gered rapid planetesimal formation via the streaming instability (YoudinandGoodman,2005;JohansenandYoudin,2007).Itisin- deed known that this instability is triggered when the solid/gas mass ratioexceeds by 3-4 times the value corresponding to the condensation of dust from a gas of solar composition (the ex- actvalue depending onparticlesize; Yangetal., 2017).Withthe formationofplanetesimals, thealready condensed materialstops participatinginthegas-solidequilibriumchemistrybecauseitbe- comeslocked-upinlargeobjectsinsteadofsmallgrains.
Consequently,atthetemperatureTM R I thereshouldhavebeen a bifurcation in the chemistry of the disk due to the fraction- ation of solids from gas. Below TM R I, condensation could form new solid species only from the residual gas. Consequently, the firstgenerationofplanetesimalsshouldhavebeenrefractory-rich, withstronglysupra-solarAl/SiandMg/Siratios,whereas thesec- ondgenerationofsolidscondensedfromtheresidualgas(denoted
“residualcondensates”hereafterforbrevity)shouldhavebeenex- tremely refractory-poor, with strongly sub-solar Al/Si and Mg/Si ratios.
Thissequenceofeventsandtherolesofresidualcondensates, first planetesimalsand solar-composition material in making the NCCs and the Earth are depicted in Fig. 2 and are described in moredetailsinthesubsequentsections.
3. Determiningthetemperatureofsequestrationofrefractory material
To determine TM R I, the temperature of sequestration of the firstcondensatesinplanetesimals,wefollowthecondensationse-
quence fromagas ofsolarcomposition totrackthe speciescon- densed and the chemical composition of the residual gas as a functionoftemperature(sect.3.1).Then,weusethesedatatode- terminethetemperaturethatfitsbesttheobservedAl/SiandMg/Si ratiosoftheNCCs(sect.3.2).
3.1. Condensationsequence
We havecomputedacondensationsequence, duringthe cool- ingofthediskatthemid-planeoftheSolarNebula,startingfrom 2,000 Kandassumingatotalpressureof10−3 barandasolarC/O ratio.Some resultsfordifferentpressures andC/Oratios are also reportedbelow.Thesecalculationsdescribetheequilibriumdistri- bution of theelements andtheir compounds between coexisting phases(solids,liquid,vapor)inaclosedchemicalsystemwithva- poralways present uponcooling. We haveused forthisproof of concept a simplified solar gas composition taken from Ebel and Grossman(2000) composedofthemostabundantelementsofthe solarphotosphere:H,C,O,Mg,Si,Fe,Ni,Al,Ca,Ti,Cr,SandNa.
Theequilibriumcondensationsequenceofthissimplified solar gashasbeencalculatedusingtheFactSagesoftwarepackage(Bale etal.,2016)bymeansofageneralGibbsfreeenergyminimization method (Eriksson and Hack, 1990). The thermodynamic data for eachcompoundaretakenfromthedatabaseprovidedbytheFact- Sagepackage.Thepotentialnumberofspeciesthatcanbeformed fromthe combinationofthe 13elements considered inthis sys- temisover450,comprising150gases and320pure solidphases (see tables S2, S3).Forthisproof ofconcept,condensationcalcu- lationshavebeenperformedinsteps of10 K,allowing onlypure solidphasestocondense,nosolidsolutions(seebelow).
Fig.3 showsthe fractionsof thecondensablemass andofAl, Mg, andSithat havecondensedasafunctionoftemperature, re-
Fig. 3. a) Fractionofthe totalcondensablemass from acooling vaporofsolar composition(i.e.,CIcomposition,includingvolatiles)atPtot=10−3bar.Arrowsin- dicatetheonsetofpuresolidphasecondensationtogetherwiththeirtemperature.
Abbreviations,cor:corundum(Al2O3);hib:hibonite(CaAl12O19);per:perovskite (CaTiO3);grs:grossite(CaAl4O7);mel:mellitite(Ca2Al2SiO7);fas:Aluminous-rich clinopyroxene(CaAl2SiO6 –mimickingfassaite-likeFepoor,Ca,Al,Tipyroxene);
sp: spinel (MgAl2O4); met:Fe-Nimetal; fo: forsterite (Mg2SiO4); an: anorthite (CaAl2Si2O8);en:enstatite(MgSiO3);alb:albite(NaAlSi3O8).b)Fractionsofavail- ableAl, MgandSicondensedasafunctionoftemperature.NotethatAl/Siand Mg/Siratiosofcondensatesbecomesolaratatemperatureof∼1,250 K.Notealso thattheAl/MgratiobecomessolaratlargertemperaturethantheAl/Siratio.
spectively.Thecomparisonwithpublishedresultsontheconden- sationofagasofsolarcomposition(YonedaandGrossman,1995;
EbelandGrossman,2000;Ebel,2006)showsagoodagreementin terms of both the computed condensation temperatures andthe sequenceofappearanceofsolidphasesuponcooling(Fig.3a),de- spitetheuseofonlypuresolidphases.
Asiswell known,corundumstartsto condensefirstata tem- peratureof∼1,775 Katthepressureconsideredhere(10−3bar).
Itisfollowedbycalciumaluminates(hibonite,perovskite,grossite andmelilite),whichsettheAlcontentsofthefirstcondensatesto beveryhigh.MagnesiumandSistarttocondenselater,almostsi- multaneouslyatT∼1,600 Kwiththeonsetofthecondensationof melilite.Both MgandSicontents increaseascooling proceedsin response tocondensation offassaiteand spinelatlower temper- ature.Initially, Si exceedsMg intermsof fractioncondensed but then,at1,250 K<T <1,450 K,Mgexceeds Sibecauseofthecon- densationofforsterite(Mg2SiO4),thefirstphasetoremovemajor fractionsof Siand Mgfromthe gas.Further cooling ofthe solar gaspromotesthecondensationofenstatite(∼1,370 K)andleads tothesubsequentincreaseinSiofthesolid.Bythetimethetem- perature has decreased to ∼1,250 K, all available Al, Mg andSi atomshave condensed,which impliesthat thesolar composition intermsofAl/SiandMg/Siisachievedatthistemperature.
The top panel of Fig. 4 shows the resulting Al/Si (red) and Mg/Si ratios (blue) as a function of temperature, normalized to
Fig. 4.Toppanel:thesolidcurvesshowtheAl/Si(red)andMg/Si(blue)ratios(nor- malizedtoCIvalues)ofthecondensedmaterialasafunctionofgastemperature.
ThearrowindicatesthattheAl/Siratioincreasesabovetheupperlimitoftheplot forT>1,430 K.Bottompanel:thesamebutfortheresidualcondensates,assum- ingthatalltheearlycondensedmaterialhasbeensequesteredinplanetesimalsat thetemperatureTM R I.ThehorizontallinesshowthemeanAl/SiandMg/Siratios forECs.
the respective ratios in CI meteorites (i.e., the solar composition ratios). The Al/Siratio drops monotonicallywith decreasingtem- peratureandreachesthesolarratio(i.e.,1.0 whennormalized)at T∼1,250 K.TheMg/Siratioinsteadstartssub-solarbutthenbe- comes supra-solarfor1,250 K<T <1,450 K, withthe bumpdue tothecondensationofforsterite.
IfcondensatesareisolatedfromthegasatatemperatureTM R I, they maintain the composition of the solids condensed at that temperature;thus,theirAl/SiandMg/Siratiosarethoseshownin Fig.4a atT =TM R I.Strictlyspeaking,isolation occurswhencon- densates growbigenoughtoprevent furthergas-solidexchanges.
Forexample,givena diffusioncoefficient ofabout10−16 m2/sat 1,400 KforFe-Mginterdiffusioninolivine(Holzapfeletal.,2003), a mm-size grain wouldequilibrate inapproximately300 y anda cm-size grain in30,000 y.However, accordingto aggregationex- perimentsitislikelythatmostgrainsaresub-mminsize(Güttler et al., 2010). Thus the mosteffective way to isolate solid mate- rial fromexchangereactions withthegasistoincorporateitinto macroscopicplanetesimals,asexplainedintheprevioussection.
Consider now the possibility that at some temperature TM R I thecondensedsolidsaresequesteredinplanetesimals.Then,with furtherdecreasingtemperature,newsolidswillcondensefromthe residualgas.ThebottompanelofFig.4showstheAl/SiandMg/Si ratiosoftheseresidualcondensatesasafunctionofTM R I.Theyare completelydifferentfromthoseofthefirstcondensates.TheAl/Si ratioofthe residualcondensatesisstrongly sub-solar(essentially zerobelow1600K,whenallAl iscondensed)andtheMg/Siratio isalsosub-solarforTM R I<1,450 K.Fig.4bshows,forcomparison,
disk.We stress that these grainsdid not necessarily havethe CI contentofwaterandofotherhighlyvolatilecomponents,conden- sible only at low temperature.1 Likewise, the isotopic properties ofthismaterialare notnecessarilythesameasforCImeteorites.
Thus,hereafterwhenusingtheterm“solar-composition”wesim- plyrefer tomaterial characterized bysolar abundancesof refrac- toryandmoderatelyvolatileelements.WepostulatethattheNCCs formedasasecond generationofplanetesimalsfromamixtureof thesesolar-composition grainsand residual condensates, so that they appear asifa refractory-rich componenthadbeen partially subtracted,asthedatasuggest.
Thus, for each temperature TM R I we compute the relative amountofsolar-composition material MSol that hasto be mixed withthe residual condensates to reproduce the Al/Siand/or the Mg/Siratioof theNCCs (Fig.5). MSol is computedfromthe two equations:
RNC C
=
fres
Al,M gMres
+ ˜
fAlC I,M gMSolfSiresMres
+ ˜
fSiC IMSol1
=
Mres+
MSol (1)where RNC C isthe Al/SiortheMg/Siweight ratiointheconsid- eredNCCs (ECs,RCs orOCs); fresAl,M g and fSires are the concentra- tionsby massof Al,MgandSiin residualcondensates(allthese quantitiesdependon TM R I andareshowninFig.S1),whosetotal massis Mres; ˜fC I
Al,M g and ˜fC I
Si are1.66timestheconcentrationsof Al,MgandSiinCImeteorites(seetable S1forelementfractionin meteorites).Thefactor1.66takesintoaccountthelackofvolatiles (e.g., water) in the solar-composition material that we consider comparedtoCImeteorites,whichreducestheirtotalmassto60%.
Obviously,foreachmeteoriteclass theconcordia situationoc- cursattheintersectionbetweenthetwosolutions,whenboththe Al/Siand Mg/Si ratios are reproduced forthe same combination ofTM R I andMSol.Notethatthesolutionsfor TM R I areverysim- ilar (1,385–1,405 K) for all the NCC classes. This means that the residual condensate material (or, equivalently, the subtracted re- fractory component) is the same for these classes of meteorites and that the different bulk chemical compositions of the ECs andOCs are mostlydueto differentmixingproportionswiththe solar-compositionmaterial.Noticethattherelative massofsolar- compositionmaterialexceedsinallcasesthefractionofmatrixin thesemeteorites.Thismeansthattheformationofchondrulesand matrixoccurredaftermixingsolar-compositionmaterialandresid- ualcondensates.Hence,itdoesnotcontradictourmodelthatthe RCsareintermediatebetweenECsandOCsintermsofproportion
1 Aswewillseebelow,60–90%ofsolar-compositionmaterialisrequiredinthe NCCsandthe Earth.Ifthesolar-compositionmaterialhadbeenrealCImaterial, boththesechondritesandtheEarthwouldberichinwaterandothervolatileele- mentsofcomparablevolatility,whichisnotthecase.
Fig. 5.Thefractionofsolar-compositionmaterialthatneedstobemixedwithresid- ualcondensatestoreproducetheAl/Si(red)andMg/Si(blue)ratiosofECs(solid), OCs(dashed)andRCs(dotted),asafunctionofthetemperatureofformationofthe firstplanetesimals,TM R I.ForECsandOCsweusethemeanoftheratiosofthevari- oussub-classes:Al/Si=0.67andMg/Si=0.78andAl/Si=0.83andMg/Si=0.91re- spectively,relativetoCIratios.TheverticalbandshowstherangeofvaluesofTM R I thatsatisfytheconsideredelementalratiosofalltheNCCstypes:1,385–1,410 K.
ofsolar-compositionmaterialeveniftheyhavethelargestpropor- tionofmatrix.
Theelementalandthemineralogicalcompositionsoftherefrac- torymaterialsequesteredat1,400 Kareshowninthetoppanelsof Fig.6.Wehaverepeatedthecalculationforapressureof10−4bar.
Conceptuallythe resultsare the same,butall condensation tem- peratures shifttolower values; TM R I is foundto beinthe range 1,310–1,330 K.
4. Otherelements
Nowthat TM R I isdetermined,wecanchecktheconsistencyof the modelwithother elements withdifferentcondensation tem- peratures.
We startour analysiswithamoderaterefractory element like Fe.For P=10−3 bar,theresidualcondensateswouldhaveasub- solar Fe/Si ratio (Fig. S1). However, for P =10−4 bar Fe is less refractory andthe Fe/Si ratio at TM R I isbasically unfractionated.
TheamountofFevarieswidelywithintheECsandOCs,fromEHto ELandHtoLL.Thesechangescannot beexplainedbyoursimple modelhere.Theymayrequiredifferentoxidationconditions,inthe disk,duringchondruleformation(Larimer,1979;Alexander,2019).
We notice that because Fe tends to be present in meteorites as distinctmetalblebs,Feenrichmentanddepletionmayalsobedue tosize-sortingeffectsduringthestreaminginstability.
NoticethatinthetoppanelsofFig.6Ni doesnotappear.This isanartifactofourcalculationschemesinceonlypureFeandpure Nimetalphases(andnotthesingleFeNisolidsolution)havebeen takenintoaccount.Thus,theNi/Feratiosinboththefirstandthe residualcondensatesarenotrealistic.
Sodium isa more interesting case, because inthe NCCs, with theexceptionoftheEHmeteorites,itshowsastrikingcorrelation withAl(seeFig.1).Thesameistruefortheotheralkalielements (Alexander, 2019). According to our model, when the refractory material issequestered at1,400 K,Na hasnot yet condensed,so theNa-Alcorrelationisnotexpected.
However, aspointedout byBarshay andLewis(1976), these- questration ofrefractory elements prevents their further reaction withthe gasatlower temperatures, makingNa lessableto con- dense, i.e., morevolatile.Forinstance, inan equilibriumconden- sationsequence, at P=10−3 bar, the condensation ofNa would start by forming NaAlSi3O8 (albite) at 1,150 K. But as Al has been removed from the gas, this mineral cannot form. The first refractory-element-freecondensate thatNa canformisNa2S (Fe-
Fig. 6.Theelemental(leftpie-charts)andmineralogical(rightpie-charts)weightfractionsforthefirstcondensatesat1,400 K(top)andresidualcondensatesdownto830 K (bottom).
gleyand Lewis, 1980), which starts to condense below830 K at P=10−3 bar.Thus,ifgascondensation“ends”beforethistemper- atureis reachedthe residual condensatesdo notcontain Na and the final depletion in Nain theECs andOCs correlates perfectly withthedepletioninAl,becausebothNaandAlareacquiredonly fromthesolar-compositioncomponentofthesemeteorites.
Westressthatitisnaturalthatthecondensationsequenceends when there is still gas left in the system. In fact, condensation requires cooling the gas but, although the disk cools over time at each location, parcels of gas are also radially transported to- wards the star. Thus, there is a competition between heating of gasdueto itsinward radial drift andsecularcooling ofthe disk.
Morbidellietal.(2016) showedthataviscouslyevolvingdisktran- sitions fromcondensing(cooling) gasparcelsto inwardly drifting (heating) parcelsafterhalf a viscous timescale (r2/
ν
),which isa small fraction of the disk’s lifetime. In the disk model of Bitsch etal.(2015) thishappensat1 AU att∼104 y,when thestellar accretion rateis 10−6M⊕/y, before the temperature has reached∼800 K.Assuming thisis thecase, we show in thebottom row ofFig.6theelementalandthemineralogical compositionsofthe residualcondensates.
The case ofCr is more difficult.Still forour nominal case of P=10−3 bar 50% ofCr condenses at1,300 K,too closeto TM R I to invoke the premature end of the condensation sequence, but not high enough to remove most of the Cr with the first con- densates. Thus, we should expect that the residual condensates were enriched in Cr and that the NCCs have Cr/Si higher than theCIvalue.Instead,thedepletionofCrcorrelateswiththatofAl (Alexander, 2019). Accounting forthesolubilityof Crin Fe-metal andolivineallowsfortheremovalof∼50%oftheCrwiththefirst condensates,but∼50%ofSiisalsoremoved,so thattheresidual condensates should be at best un-fractionated in Cr/Si, which is insufficienttoexplaintheobservedAl-Crcorrelation.However,we findthat iftheC/Oratio ofthegasis increasedto0.9, TM R I de- creasesto 1,280 K(because thecondensationtemperatures ofAl, MgandSidecrease),sothatnearly100%ofCrisboundinthefirst condensatesif one accountsfor its solubilityin iron andolivine.
Thus a C/O≥0.9 enablesthe Cr-Al correlation in theNCCs to be explained. The sameis true at lower pressure. A similar C/O ra- tiohasbeeninvokedbyseveralauthors(e.g.,LoddersandFegley, 1993) as the sole way to explain various properties of enstatite
chondrites. It is interesting that from a completely different ap- proach we alsoreach thisconclusion,with thedifference that in our model the high C/O ratio affected the formation of residual condensatesthatare acomponentofalltheNCCs,notjust ofthe ECs (although more prominentin ECs). The equivalent of Fig. 6, exceptforC/O=0.9,isgiveninFig.S4.
Sulfur is more volatile than Na in a gas with solar C/O. But it starts to behave as a refractory element for C/O>0.9, when oldhmite(CaS)beginstocondense.ForC/O=1.2,40%ofSiscon- densedatTM R I (=1,130 KforP=10−3bar).NoScondensesfrom theresidualgasbefore Na.Thus,S andNadepletionsshouldcor- relate in theNCCs, butsuch a correlation isnot observed. Sulfur is mostly found in the matrix and high concentrations of S are onlyobservedinECchondrules.Rememberingthatthemixingbe- tweenresidualcondensatesandsolar-compositionmaterialshould bedoneatthelevelofchondruleprecursorsthisobservationsug- geststhat,forsomereason,SwaslostintheformationofOCsand RCschondrules,butnotNa(Alexanderetal.,2008).
5. TheEarth
Ifthe first-formedplanetesimalshadaccreted witheachother and possibly with additional solar-composition material, they wouldhaveformeda planetenriched inrefractoryelements. Itis therefore importanttocheck whetherthisscenario couldexplain thesupra-solarAl/SiandMg/SiratiosoftheEarth.
For simplicitywe consider our nominalcaseof P=10−3 bar and a solar C/O ratio. We assume that the composition of the first-formed planetesimals is that obtained from the equilibrium condensationatTM R I=1,400 K(Fig.6,top- seealsoFig.S2)and useeq.(1)again. TheAl/SiandMg/SiratiosoftheEarthincrease as the relative mass fraction ofthese planetesimals incorporated in the planet increases (the rest of Earth’s mass having a solar composition)andwefindthatratiosconsistentwiththeobserved valueswithintheirbroaduncertaintiescanbeobtainedforamass fractionofabout35–45%(Fig.7).2
2 WenotethatcombiningfirstplanetesimalswithECswouldleadtoequivalent results.Infact,thecombination offirst-condensedmaterialwithitscomplement ofresidualcondensatesgivesbydefinitionmaterialwithasolarbulkcomposition.
Fig. 7.TheAl/Si(red)andMg/Si(blue)ratiosasafunctionofthemassfractionof first,refractoryrichplanetesimalscontributingtotheEarth,therestbeingaccreted fromsolar-compositionmaterial.Thehorizontalcoloredbandsshowtheestimated bulkterrestrialMg/SiandAl/Siratiosandtheiruncertainties.Thesearereproduced iftheEarthcomprises35–45%bymassoffirstplanetesimals.
Alexander (2019) explicitly excluded the possibility that the refractory material missing from the NCCs (i.e., our first-formed planetesimals) has been accreted by the Earth. His conclusion is motivatedbythreearguments,whichwereviewanddiscusshere.
First,hepointedoutthattheadditiontosolar-compositionma- terialoftherefractorymaterialmissingfromtheNCCsdoesnotfit welltheEarth’scomposition.ThisisvisiblealsoinFig.7because theAl/SiandMg/Siratioscanbe simultaneouslyreproducedonly atthe opposite extremes oftheir error bars. If the uncertainties ontheseratiosare entirelydueto theamountofSiincorporated inthe terrestrialcore, they are not independent. So, inthis case one cannot claim success ifone ratio isreproduced at the high- endofitsuncertaintylimitandtheotheratitslow-end.However, Young et al. (2019) argued that the Earth or its precursors lost by evaporationabout12% ofMg and15% ofSi. Thiswouldhave left the Mg/Si ratio ofthe Earth basically unchanged, butwould haveincreasedtheAl/Siratio by 17%.Forinstance,in Fig.7 ata valueof0.3onthex-axis,theMg/Siratiopredictedbyourmodel fallsinthemiddleoftheobserveduncertainty.TheAl/Siratiopre- dictedbythemodelistoolow (1.2),butwith15%Sievaporation it would have increased to 1.38, i.e.again in the middle of ob- served uncertainty. Thus, our model is consistent with the Al/Si andMg/Siratios ofthebulk Earth,eveniftheir uncertainties are correlated,providedthat theevaporationofSiandMginvokedto explaintheirisotopicfractionationistakenintoaccount.
Second,Alexander(2019) noted acorrelation betweenthede- pletionofAlandthedepletionofalkalielementsintheNCCs.He concluded that alkalis were sequestered in the refractory mate- rial subtracted from these meteorites. Thus, if this material had beenadded tothe Earth, our planetwouldbe alkali-rich instead ofalkali-poor. AlthoughwehavebasedourargumentonlyonNa, inSect.4weshowedthattheremovalofarefractorycomponent makesalkalismuchmorevolatilethanexpectedinanequilibrium condensation.Thus,thecorrelationbetweenthedepletionsofalka- lisandAlcanbeexplainedwithoutthesequestrationofthealkalis intherefractorymaterial.Consequently,theadditionoftherefrac- torymaterialtotheEarthwouldmakeourplanetalkali-poor, not alkali-rich.
Finally,Alexander(2019) noteda correlation betweenthe de- pletionofAlintheNCCsandtheisotopicratiosofsomeelements, suchasTiandCr.Heconcludedthattheremovedrefractorymate- rialcarriedstrongisotopicanomaliesfortheseelements.However,
Thus,thex-axisofFig.7canbesimplyinterpretedastheexcessoffirst-condensed materialintheEarth,whateverthecombinationofmaterialthatisenvisioned.
depletedinCr.
Weendthisdiscussionbycommentingthatitiscertainlypos- sibletoenvisionthattherefractorymaterialsequesteredfromthe NCCs disappeared without contaminating theEarth. Forinstance, refractory elements could belocked-up ingrainslarge enoughto be out ofequilibriumwiththegas,butstill smallenoughto mi- grate by gas-drag intothe Sun.But then, one hasto invokethat theEarthaccretedsomeotherrefractory-richmaterial,thatdidnot contaminatetheNCCs althoughbeingisotopicallyidenticaltothe ECs.Possiblybylackofimagination,wecannotenvisionareason- able scenario forthis to have happened.Thus, we concludethat the addition to the Earth of the refractory material sequestered fromtheNCCsremainsthebestoption.
6. Conclusionsanddiscussions 6.1. Summaryofresults
Inthiswork,wehaveproposedanastrophysicalscenario,con- sistentwithcurrentmodelsofdiskevolutionandplanetesimalfor- mation, that canexplain the sequestration ofrefractory elements fromthesourceregionofthenon-carbonaceous(NCC)chondrites and,therefore,theirsub-solarAl/SiandMg/Siratios.
Inbrief, whilethediskwas cooling,the massivecondensation ofolivinechangedthediskfromalow-dusttoahigh-dustenviron- ment,quenchedthemagneto-rotationalinstabilityofthedisk,trig- geringthesuddenformationofafirstgenerationofplanetesimals andthesequestrationofthealreadycondensedsolidmaterial.That materialwas,therefore,nolongeravailablefortheevolutionofthe gas-solid equilibrium chemistry. Witha furtherdecrease in tem- perature,newsolidscouldformfromresidualgas.Wecalledthese
“residual condensates” and the region where these events hap- penedthe“residualcondensateregion”(RCR).Forgeneticreasons, the first planetesimals andthe residual condensates are comple- mentaryrelativetothesolar(CI)valuesintermsofAl/SiandMg/Si ratios.
We envisioned that the NCCs formed from a combination of these residual condensatesand material that had solarcomposi- tionintermsofrefractory andmoderatelyvolatileelements. This materialconsistedoflocalgrainsthatwerenotincorporatedinthe firstplanetesimals andremainedatequilibriumwiththe gasand -possibly- alsograinsthatformedfartherout inthedisk,andmi- gratedintotheRCRwithoutsufferingelementfractionation.
We have shown that, if the first planetesimals formed at a temperatureof ∼1,400 K,(for a pressureof 10−3 bar andsolar C/O,andalower temperature,neverthelessexceeding1,000 K,for lower pressure and/or increasedC/O) the mixtureof appropriate proportions ofsolar-composition grains andresidual condensates canreproducesimultaneouslytheAl/SiandMg/Siratiosofall the NCCs.Obviously,theamountofsolar-compositionmaterial hasto increasefromtheECstoOCs,asthelatterhavecompositionsthat
anequilibriumcondensationsequence(seeSect.4).Toexplainthe correlation between the deficits of Cr and Al, we hadto invoke thatthefirstcondensatesformedinagaswithC/O≥0.9,inagree- mentwithprevious workontheECs (e.g.,Larimer,1975;Lodders andFegley,1993).
WeshowedthattheAl/SiandMg/SiratiosoftheEarthcanalso be understoodifourplanet formedfroma mixtureof firstplan- etesimalsandsolar-compositionmaterial.Alexander(2019) explic- itlyexcludedthispossibility,butweprovidedinSect.5somepos- siblesolutionstotheobstaclesthathediscussedforthisscenario.
Our full scenario is sketched in Fig. S3, which presents a global viewofthecompositionofthediskastimeevolves.
Our model is appealing in that it solves two long-standing problems.First,itexplainsthesub-solar Al/SiandMg/Siratios of theNCCs within afractionatedcondensationsequence. Second,it clarifiesthegeneticrelationshipbetweentheEarthandtheECs,as discussedbelow.Nevertheless,ourmodelissimpleandshouldbe regardedmostly asa proof ofconcept. Forinstance,we assumed thatallfirstplanetesimalsformedatthesametemperature,sothat all the objectswe considered are composed ofonly two compo- nents:residualcondensatesandsolar-compositionmaterialforthe NCCsorrefractory-richplanetesimalsandsolar-compositionmate- rialfortheEarth.
6.2. Earth–enstatitechondritesrelationship
As discussed inthe introduction,the isotopic compositionsof theEarthandoftheECsintermsofnon-massdependentisotopic variations are extremelysimilar. No other known meteoriteclass approximatestheEarthbetterthantheECsfromtheisotopicpoint of view.But element ratios are so different that it is difficult to envision making the Earth out of the ECs. Here we findthat an importantcomponentoftheEarthisrepresentedbythefirstplan- etesimals,whileanimportantcomponentoftheECsisrepresented by residualcondensates.First planetesimalsandresidual conden- satesarecomplementaryintermsofelementratios,buttheyboth formout ofthe samegasin theRCR,so itis not surprisingthat they are isotopically very similar. In some sense, with the first refractory-richplanetesimalswehaveidentifiedthehiddenreser- voirofobjectswiththesameisotopecompositionastheECs but different chemical composition, that was postulated by Dauphas (2017) toexplaintheEarth.Theoppositemass-dependentisotopic fractionationof Siin theEarth andECs maybe a naturalconse- quence oftheformation ofthefirstcondensates,asdiscussed by Kadlagetal.(2019).
Pushedfurther,thegeneticrelationshipbetweentheEarthand the ECs illustratedin thispaper can alsohelp to understandthe smalldifferencesintheirrespectiveNd,MoandRuisotopiccom- positions.The Earthhasan endmemberisotopic composition rel- ativetoknownmeteorites,slightlyenriched inisotopesproduced bythes-processwithrespecttotheECs(seeBurkhardtetal.,2016 andBouvierandBoyet,2016forNd;Burkhardtetal.,2014forMo andFischer-Gödde andKleine,2017 forRu). If, for some reason, thematerial that condenseddirectly intheRCRis enriched ins- process isotopes relative to the solar-composition grains coming intotheRCRoncethe temperaturehasdecreased, wecan under- stand this difference. In fact, in this case the first planetesimals andtheresidual condensateswouldhavethesame proportionof s-processisotopesbut,asshowninSect.3.2,theEarth,ECandOC meteorites incorporated increasing fractions of solar-composition material,thus explaining-atleastqualitatively- therelative rank- ingofs-processenrichment/deficiencyobservedintheseobjects.
andsolar-compositiongrainstomaketheECsandOCs,theseme- teoritesaremadeofchondrulesandnotgrains. Chondruleforma- tionisstillnotfullyunderstood(Krotetal.,2018)andpresumably the mixingwe invokeoccurred atthe levelofchondrule precur- sorsandweretransformedinthehigh-temperatureeventsthatled tochondruleformation.Ourelementalandisotopicconsiderations shouldneverthelessholdeveninthismorecomplexscenario.
The relationship between the first condensed material dis- cussed in this paper and the refractory materials (CAIs, AOAs) found in mostly in the CCs is more elusive. It wouldbe tempt- ing to identifyCAIswitha fractionof themineralscondensed at T1,500 Kthatescaped incorporationinthefirst generationof planetesimalsandsomehowreachedtheouterdisk.ButCAIsalso carry isotopicanomalies(forinstanceinNdorMo)relatedtothe p- andr-processes,which arenot observedintheEarth, ECsand OCs. However, Ebert et al. (2018) claim to have identified a re- fractorycomponentisotopicallydistinctfromCAIsinOCs.Thefirst condensed material discussed in this paper would rather corre- spondtothisrefractorycomponentratherthanCAIs.
6.4. Protoplanetarydiskpropertiesandgraindynamics
Although our work does not specify where the RCR was lo- cated, the fact that the first planetesimals haveto be a primary componentoftheEarthsuggeststhat thesequenceofeventsde- scribed in thispaper happened at∼1 AU. Thisimplies that the disk at ∼1 AU was originally hotter than 1,400 K. Viscous-disk models (Bitschetal., 2015)suggestthat thetemperatureat1 AU was initiallylower,butthesemodels neglecttheheatreleasedby the accretion ofgas from the interstellar medium onto the disk, whichwaspresumablyvigorousatearlytimes(P. Hannebelle,pri- vatecommunication).So,ourmodeldoesnotseemunreasonable, butitpointstoadiskmuchmorecomplexthanthoseusuallyen- visioned.
As long asthe infall ofgas onthe inner disk isvigorous, the temperature remains very high. Forinstance, Baillié etal.(2019) find atemperature largerthan 1,500 Kup to 2 AU fromtheSun for the first 105 y. Thus, in this timeframe, only the gas vis- cously spreading beyond2AU wouldcool andcondensate. Then, when the infall wanes, the temperature in the inner disk starts to decrease andcondensation can occur locally, producinga sec- ond condensation front moving towards the star. The fractional condensation discussed in this paper would correspond to this second condensationfront. This view oftwo condensation fronts couldexplainthedifferencebetweenCAIsandthenon-CAIrefrac- tory component of Ebert et al. (2018), ifthe isotopic properties oftheinfalling gaschangedovertime,asinvokedinNanneetal.
(2019) to explaintheisotopicradialheterogeneity oftheprotoso- lardisk.3Similarly,ifthegaschangedofchemicalcomposition,the highlocalC/OratiorequiredtoexplainCr-abundances canbeex- plained aswell. Indeed,filaments ofgasareobservedtofallonto protoplanetary disks (Alves et al., 2019), in some cases carrying a differentC/Ocomposition (Segura-Cox,private communication).
Moreover, therapid dropoftemperatureto ∼850 Kfollowed by slowcooling,thatourmodelrequirestoendtheresidualconden- sationbeforethe condensationofNa,couldbe duetothetransi- tionfromadiskdominatedbyarapidlywaninginfallofmaterial from the ISM to a diskdominated by its own viscous evolution.
Admittedly,thisscenarioisspeculative,butitisnotimplausible.
3 SeeJacquet,2019,foradiscussionofthepossibilitythatCAIsformedrelatively farfromtheSunfromthepointofviewof10Beproduction.
mix with solar-composition grains to form eventually the NCCs.
However, theparent bodiesofthese meteoritesformed relatively late, after about2–3 My (Sugiura and Fujiya, 2014). How grains could survive in the disk for so long despite their tendency to migratetowardstheSunisan open problemthatthisworkdoes nothelptosolve.Possibleexplanationsinvolveturbulentdiffusion counteracting radial drift near the midplane of the disk (Ciesla, 2007), reducedor reversed radial drift due to the partial deple- tion of gas in the inner disk (Ogihara et al., 2018), recycling of materialindiskwindsorjets(Ciesla, 2009), lock-upinplanetesi- malsandlaterreleaseascollisionaldroplets(Johnsonetal.,2015).
Westressthatinourmodelwedonotneedthatallresidualcon- densatessurvive.IfthetotalmassofplanetesimalswithNCC-like compositionswas small, only a tiny fraction of residual conden- satesmayhavesurvived.
6.5.Closingremarks
Insummary,uptonowthegreatlydifferentratiosamongmajor refractory elements inthe Earthand in non-carbonaceous chon- driteshavechallengedourunderstandingoftheformationofinner SolarSystembodies.Althoughseveralunknownsremain,wehave shownthattheaccretionofafirstgenerationofplanetesimalsdur- ingthecondensationsequenceofrefractoryelementsandthecon- sequent formationofresidual condensatesare keyprocesses that contributetothesolutionofthisproblem.
Declarationofcompetinginterest
Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.
Acknowledgements
WethankC. Burkhardt, T.Kleine,E.YoungandN.Dauphasfor valuablesuggestionson anearlierversion ofthismanuscript. We thank in particular C. Alexander for an open discussion on our respective models and B. Fegley and K. Lodders for an in depth critical assessment of our results during their visit to Nice and their historical perspective on this long-studied subject. The re- viewsfromtwo anonymousrefereeshavealsohelpedtoimprove themanuscriptandclarifytheresults.
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