THE FAINT YOUNG SUN PROBLEM Georg Feulner Received Se - PDF document

EarthSystemAnalysis,PotsdamInstituteforClimateImpactResearch,Potsdam,Germany.Correspondingauthor:G.Feulner,EarthSystemAnalysis,PotsdamInstituteforClimateImpactResearch,POBox601203,D-14412Potsdam,Germany.(feulner@pik-potsdam.de) Copyright2012bytheAmericanGeophysicalUnion.ReviewsofGeophysics,50,RG2006/20121of298755-1209/12/2011RG000375Papernumber2011RG000375 star.ApplyingtheseprinciplestotheSun,itbecameclearthattheluminosityoftheSunhadtochangeovertime,withtheyoungSunbeingconsiderablylessluminousthantodaytodayHoyle,1958;,1958].1958].6]Accordingtostandardsolarmodels,whennuclearfusionignitedinthecoreoftheSunatthetimeofitsarrivalonwhatiscalledthezero-agemainsequence(ZAMS)4.57Ga(1Ga=10yearsago),thebolometricluminosityoftheSun(thesolarluminosityintegratedoverallwavelengths)wasabout30%lowerascomparedtothepresentepochepochNewmanandRood,1977].Thelong-termevolutionofthebolometricsolarluminosity)asafunctionoftimecanbeapproximatedbyasimpleformula[,1981]
¼ 11þ 251 =3.85Wisthepresent-daysolarlumi-nosityand=4.57Gyr(1Gyr=10years)istheageoftheSun.Exceptforthefirst0.2GyrinthelifeoftheyoungSun,thisapproximationagreesverywellwiththetimeevolutioncalculatedwithmorerecentstandardsolarmodels[e.g.,Bahcalletal.,2001];seethecomparisoninFigure1.1.7]Notethatsolarmodelshadbeenunderintensescrutinyforalongtimeinthecontextofthesolarneutrinoprob-anapparentdeficiencyofneutrinosobservedinter-restrialneutrinodetectors[,1995]thatisnowconsideredtoberesolvedbyamodificationofthestandardmodelofparticlephysics[MohapatraandSmirnov,2006]ratherthantobeanindicationofproblemswithsolarmod-els.Furthermore,thetimeevolutionoftheSunsluminosityhasbeenshowntobeaveryrobustfeatureofsolarmodelsmodelsNewmanandRood,1977;Bahcalletal.,2001].ThusitappearshighlyunlikelythatthepredictionoflowluminosityfortheearlySunisduetofundamentalproblemswithsolarmodels.(Slightlymodifiedsolarmodelsinvolvingalargermasslossinthepastwillbediscussedinsection4.)4.)8]Inawaytherobustnessoftheluminosityevolutionofstellarmodelsisnotsurprising,sincethegradualriseinsolarluminosityisasimplephysicalconsequenceofthewaytheSungeneratesenergybynuclearfusionofhydrogentoheliuminitscore.Overtime,heliumnucleiaccumulate,increasingthemeanmolecularweightwithinthecore.Forastable,sphericaldistributionofmass,twicethetotalkineticenergyisequaltotheabsolutevalueofthepotentialenergy.Accordingtothisvirialtheorem,theSunscorecontractsandheatsuptokeepthestarstable,resultinginahigherenergyconversionrateandhenceahigherluminosity.Thereseemsnopossibilityforescape[,1981,p.28]:gradualincreaseinluminosityduringthecorehydrogenburningphaseofevolutionofastarisaninevitableconse-quenceofNewtonianphysicsandthefunctionaldependenceofthethermonuclearreactionratesondensity,temperatureandcomposition.composition.9]Inadditiontothisslowevolutionofthebolometricsolarluminosityovertimescalesofyears,theSunexhibitsvariabilityonshortertimescalesofuptotoFröhlichandLean,2004].Thisvariabilityinsolarradiationisamanifestationofchangesinitsmagneticactivityrelatedtothesolarmagneticfieldcreatedbyamagnetohydrody-namicdynamowithintheSun[WeissandTobias,2000].ThebolometricsolarluminosityisdominatedbyradiationinthevisiblespectralrangeoriginatingfromtheSunsloweratmospherethatshowsverylittlevariationwithsolaractivityactivityFröhlichandLean,2004].Forthepresent-daySun,for Figure1.EvolutionofsolarluminosityoverthefourgeologiceonsforthestandardsolarmodeldescribedinBahcalletal.[2001](solidline)andaccordingtotheapproximationformula[1981](dashedline)giveninequation(1).FEULNER:THEFAINTYOUNGSUNPROBLEM2of29 3.8Ga,althoughtheexactendofthatperiodisnotresolvedinthegeologicalrecord.Irrespectiveofthesemattersofdefinition,itisimportanttorealizethattheArchean,themainfocusofthisreview,spansaverylongperiodoftimeinthehistoryofEarth.Earth.20]TentativeevidenceforliquidwaterontheearlyEarthcanbefoundintheHadean.NorocksareknownfromtheHadeanduetotheexponentialdecreaseofpreservationwithage,yetsomeinformationonthesurfaceconditionsduringthoseearliertimescanbederivedfromthemineralzircon)preservedfromtheHadeaninyoungerrocksrocksHarrison,2009].Indeed,zircongrainsmayprovideevi-denceforliquidwaterevenbeforetheArchean,asearlyas4.2Ga[Mojzsisetal.,2001;Wildeetal.,2001;Valleyetal.,2009].2009].21]Note,however,thattheenvironmentinwhichthisHadeanoceanexistedwasconsiderablydifferentfromtheArchean(forareviewofthefollowingoutlineofeventssee,Zahnleetal.[2007]).TheEarthwasformedbygravi-tationalaccretionofsmallerbodies(planetesimals)formedinthenebulasurroundingtheyoungSun.ThelargeimpactformingtheMoonoccurredafter50Myrtowardtheendoftheaccretionperiod.Afterthisevent,Earthwasenshroudedinrockvaporfor1000years.Astronggreenhouseeffect(causedbylargeamountsofcarbondioxideandwatervapordegassingfromthemantle)andtidalheatingbythestilltightlyorbitingMoonkeptthesurfacecoveredbyamagmaoceanforafewmillionyearsaftertheMoon-formingimpact.Thenthecrustsolidifiedandahotwateroceanwithtemperaturesof500Kformedunderadenseatmosphere100barofcarbondioxide.Thecarbondioxideintheatmospherewasthensubductedintothemantleovertimescalesof10years,beforetheLateHeavyBombard-ment(3.8Ga)setthestagefortheArcheaneon.Itisthusclearthattheprocessesresultinginaliquid-wateroceanintheHadeanareconsiderablydifferentfromtheArchean,sotheywillnotbediscussedfurtherinthisreview.review.22]GeologicevidenceforliquidsurfacewaterduringtheArcheanismostlybasedonsedimentaryrocklaiddowninavarietyofaqueousconditionsupto3.5Gaandpossiblyasearlyas3.8Ga,andthereisnoevidenceforwidespreadglaciationsduringtheentireArchean(see(seeWalker[1982],andWalkeretal.[1983];formorerecentoverviewsofArcheangeologyingeneralsee,e.g.,Fowleretal.al.Erikssonetal.[2004],andBennetal.[2006]).Telltalesignsofliquidwaterincludepillowlavasthatareformedwhenlavaextrudesunderwater,ripplemarksresultingfromsedimentdepositionundertheinflu-enceofwaves,andmudcracks.cracks.23]Furthermore,thereisevidenceformicrobiallifeintheArcheanderivedfrommicrofossilsorstromatolites/microbialmatsinrocksofagesbetween2.5and3.5GyrGyrBarghoornandSchopf,1966;AltermannandKazmierczak,2006].AlthoughalllifeonEarthisbasedontheexistenceofliquidwater[e.g.,,2001],themereexistenceoflifeisonlyapoorcontraintonicecover.Theearlyevidenceofphotosyntheticcyanobacteriaandstroma-tolites,however,constitutesfurtherevidenceforanearlyEarthnotpermanentlycoveredbyice(oratleastforcontin-uouslyice-freeregionsintheoceans).Onecould,inprinci-ple,imaginephotosyntheticlifeunderathinicecoverinthetropicsofasnowballEarthaspostulatedbybyandinvestigatedinPollardandKasting[2005,2006].Laterstudieshaveindicated,however,thaticecoverwouldhavebeentoothickeveninthetropics[Warrenetal.,2002;,2006;WarrenandBrandt,2006],makingsuchascenariounlikely.unlikely.24]Insummary,therearemultiplelinesofindependentevidencesuggestingtheexistenceofliquidwateronEarthsurfaceduringtheArchean,whentheSunwasconsiderablyfainterthantoday.2.3.OceanTemperatureDuringtheArcheanArchean25]Itisoneofthekeycharacteristicsofwaterthatitremainsliquidoveraratherwiderangeoftemperatures,sothequestionarisesofhowwarmtheArcheanclimateactu-allywas.TheconstraintsonandestimatesofArcheanoceantemperaturesdiscussedbelowaresummarizedinFigure2.2.26]UpperlimitstoArcheanclimatetemperaturescanbemainlyderivedfromtwolinesofargument.First,evaporitemineralscanbefoundinthegeologicalrecordbackto3.5Ga,andsincemanyofthesewereoriginallyprecipitatedintheformofgypsum(CaSOO),whichisconvertedtoanhy-drite(CaSO)attemperaturesabove58Cinpurewater(andatlowertemperaturesinseawater),temperaturescannothavebeenhigherthanthisvalue[Holland,1978,1984;Walker1982].Second,thecontinuedpresenceoflifeandthetypicalheattoleranceoflivingorganismscanbeusedtoestimateanupperlimitintherangeof4040Walker,1982]..27]Inconflictwiththeseupperlimitsfromevaporitesandthecontinuedpresenceoflife,lowvaluesoftheisotoperatioin3.5to3.0Gachertswereinterpretedbysomeresearchersasevidenceofahotclimatewithoceanictemperatureof555KnauthandEpstein,1976;KarhuandEpstein,1986;KnauthandLowe,2003;RobertandChaussidon,2006].Thereisalotofdebate,however,abouthowstronglyoxygenisotoperatiosactuallyconstraintemperatures.Ithasbeenargued,forexample,thatthesedatacouldreflectalowOofancientseawaterratherthanahotclimate(see,e.g.,Walker[1982],KastingandOno[2006],KastingandHoward[2006],Kastingetal.[2006],andJaffrésetal.[2007]fordiscussions).AnalternativeexplanationforchangesinisotoperatiosduringthePrecam-brianhasbeenputforwardbyvandenBoornetal.[2007],whoarguethatthedatamightreflectmorewidespreadhydrothermalactivityontheancientseafloor..28]InlightofthisdiscussionthereappearstobenostrongargumentinfavorofahotArcheanclimate.Indeed,arecentanalysiscombiningoxygenandhydrogenisotoperatiosindicatesoceantemperaturesbelow40Cforasampleof3.4Gaoldrock[Hrenetal.,2009].Blakeetal.al.analyzedd18Oisotopecompositionsofphosphatesin3.23.5GyroldsedimentsandinterpretedthehighOfoundintheirsamplesasbeingindicativeoflowoceanictempera-turesintherange26C.ThesetemperaturesareclosetoFEULNER:THEFAINTYOUNGSUNPROBLEM4of29 48]Thesolarwind,however,isknowntohavebeenstrongerfortheyoungSunbecauseofthehighersolaractivityinthepast(seesection3).Dependingontheassumedmass-losshistory,ayoungSunwithaninitialmass4%higherthantodaywouldbebrightenoughtoexplainthepresenceofliquidwateronMars3.8Ga[Sackmannand,2003],andaninitialmassof6%higherthantodaymakestheSunasbrightastoday4.5Ga,althoughthesolarluminositywouldstilldropbelowtodayslevelsduringtheArchean[Guziketal.,1987;SackmannandBoothroyd2003].Inadditiontothedirectincreaseinenergyinputduetothehighersolarluminosity,EarthwouldalsobeclosertoamoremassiveSunonitsellipticalorbit,furtherenhancingthewarmingeffect,withthesemi-majoraxisattimeinverselyproportionaltothesolarmassmassWhitmireetal.,1995] 49]However,therearelimitstothemassoftheearlySun.AweakupperlimitcanbederivedfromthefactthatathighersolarluminositiesEarthwouldhaverunintoarun-awaygreenhouseeffect(seeGoldblattandWatsonWatsonforarecentreview).Ifthesolarluminositywerebeyondacertainthreshold,theincreasedevaporationofwaterwouldresultinacceleratingwarming.Eventually,alloceanwaterwouldbeevaporatedandlosttospacebyphotodissociationandhydrodynamicescape,aprocessthatisbelievedtoberesponsibleforthelackofwaterintheatmosphereofVenusVenusIngersoll,1969;RasoolanddeBergh,1970].1970].50]Ithasbeenestimatedthata10%increaseinsolarfluxcouldhaveledtorapidlossofwaterfromtheearlyEarth[,1988].Takingintoaccountthemass-luminosityrelationinequation(4),thechangeinEarthsemi-majoraxisduetosolarmasschangefromequation(5)andthesecularevolutionofsolarluminosityfollow-ingequation(1),thiscorrespondstoa7%increaseinsolarmass[Whitmireetal.,1995],sohighmasslosscouldmaketheArcheanunsuitableforlife.life.51]Furthermore,ithasbeensuggested[GuzikandCox1995]thatanextendedmasslossoftheearlySuncanberuledoutusinghelioseismology,thestudyoftheSuninteriorstructureusingresonantoscillations[Deubnerand,1984].SolvingthefaintyoungSunproblemwouldrequirethattheSunremainedatleastafewpercentmoremassivethantodayover1or2billionyears,whilehelio-seismologylimitstheenhancedmasslosstothefirst0.2GyroftheSunslife[GuzikandCox,1995].Amoreextendedperiodofmasslossleadstochangesinthedistributionofheavierelementsbelowthesolarconvectionzone,resultingindifferencesbetweencalculatedandobservedoscillationfrequencies.GuzikandCoxsmodeloftheinterioroftheSunhasbeencriticizedbySackmannandBoothroydBoothroydhowever,whoclaimthatmodelswithinitialmassesupto7%higherthantodayarecompatiblewithhelioseismologi-calobservations.observations.52]MuchmorestringentlimitstoamoremassiveyoungSuncanbeinferredfromobservationsofmasslossinyoungstarssimilartotheSun[,2004;Woodetal.,2005].Observationsofothercoolstarsshowthattheylosemostoftheirmassduringthefirst0.1Gyr[MintonandMalhotra2007].Mostimportantly,theobservedsolaranalogsexhibitconsiderablylowercumulativemass-lossratesthanrequiredtooffsetthelowluminosityoftheearlySunSunMintonandMalhotra,2007].ThesolutiontothefaintyoungSunproblemthereforeseemstolieintheotherparameterscontrollingEarthssurfacetemperature,forexample,theconcentrationofgreenhousegasesintheearlyatmosphere,ratherthaninamodificationofthestandardsolarmodelinvolvinghighermass-lossrates.5.ENHANCEDGREENHOUSEEFFECTEFFECT53]Intodaysclimate,thetemperatureofEarthstropo-sphereisincreasedduetotheabsorptionoflong-waveradiationfromthesurfacebyatmosphericgaseslikewatervapor,CO,andmethane(CH).ThisgreenhouseeffecteffectMitchell,1989]hasanaturalandananthropogeniccom-ponent.ThenaturalgreenhouseeffectisthecauseforglobalaveragetemperaturesabovethefreezingpointofwaterovermuchoftheEarthshistory,whiletheanthropogeniccom-ponentresultingfromthecontinuingemissionofgreenhousegasesbyhumanityisresponsiblefortheobservedglobalwarmingsincethe19thcentury[IntergovernmentalPanelonClimateChange,2007].2007].54]Therefore,oneobviouspossibilitytoexplainawarmearlyatmospheredespitealowerinsolationisanenhancedwarmingeffectduetoatmosphericgreenhousegaseslikeammonia(NH),CH,orCO5.1.AmmoniaAmmonia55]AmmoniaisaverypowerfulnaturalgreenhousegasgasWangetal.,1976]becauseithasastrongandbroadabsorptionfeatureatmcoincidentwiththepeakinblackbodyemissionfromEarthssurface.AmmoniaseemedanattractivesolutiontothefaintyoungSunprobleminearlystudiesforanumberofhistoricreasons.Indeed,intheiroriginalpaperonthefaintyoungSunproblem,Saganand[1972]suggestthatanammoniagreenhousecouldhavecompensatedthelowersolarirradiancetokeepEarthoceansfromfreezingover.over.56]Historically,thechoiceofgreenhousegaseslikeNH(andCHdiscussedinsection5.2)asgreenhousegaseswasmotivatedbythreearguments:theassumptionthattheearlyatmospherewasreducing,theapparentrequirementofareducingatmospherefortheproductionoforganicmole-cules,andthewidespreadglaciationsatthebeginningoftheProterozoic.Thesehistoricargumentswillbeexploredinthethe57]TheviewheldatthattimethatEarthsearlyatmo-spherewasreducingiscloselylinkedtotheoriesofplanetaryformation.Earthwasformedbyaccretionofsmallerbodies(planetesimals)formedinthesolarnebula[,1990]andmayhaveformedaprimaryatmospherefromgases(predominantlyhydrogen)presentinthenebula.ThisFEULNER:THEFAINTYOUNGSUNPROBLEM8of29 whichhadearlierbeennotedby[1966];usingmodelsforthephotochemistryofammonia,theydemon-stratedthattheSunsultravioletradiation(whichwasmuchmoreintenseduringtheArchean;seesection2.1)wouldhavedestroyedthisamountofNHviaphotodissociationinlessthanadecade.TheyconcludethatcontinuousoutgassingofammoniafromtheEarthsinteriorwouldhavebeenrequiredtomakeanNHgreenhouseduringtheArcheanwork.work.64]Investigatingthisbalancebetweenoutgassingandphotochemicaldestruction,[1982]estimatedsteadystateammoniaformationratesfortheearlyEarthandcon-cludedthatabioticsourcescouldhavebeensufficienttosustainmixingratiosofthathavebeenarguedtoberequiredfortheevolutionoflifeintheoceanbasedontherapiddecompositionofasparticacidintheabsenceofammonium(NH)andtheassumptionthatasparticacidisnecessaryforlifetooriginate[BadaandMiller,1968].However,theammoniumresupplyratesderivedin[1982]areinsufficienttoprovidesubstantialgreenhousegreenhouse65]ItshouldalsobenotedthatammoniaishighlysolublesolubleLevineetal.,1980]andthusquicklyrainedoutoftheatmosphereanddissolvedasNHintheoceans[,1982].Sustainingatmosphericpartialpres-suresofammoniaintherangerequiredtooffsetthefaintyoungSunrequires0.110%oftheatmosphericnitrogentobedissolvedintheocean(C.Goldblatt,privatecommuni-cation,2011).2011).66]Duetotheseproblems,ammoniahadfallenoutoffavorasthedominantgreenhousegasintheArcheanatmosphere.Morerecently,SaganandChybaChybarevivedtheideaofanArcheanammoniagreenhousebypointingoutthatanearlyatmospherecontainingnitrogen)andCHwouldformanorganichazelayerproducedbyphotolysis.ThislayerwouldblockultravioletradiationandthusprotectNHfromphotodissociation.Othersshowed,however,thattheexistenceofsuchalayerwouldleadtoaneffectbecauseitblockssolarradiationfromreachingthesurfacebutallowsthermalradiationtoescapetospace[McKayetal.,1991,1999].Highhumidityhasbeenshowninexperimentalstudiestofurtherenhancethiscoolingeffectofaerosols[Hasenkopfetal.,2011].Furthermore,thesizedistributionofthehazeparticlescouldhavelimitedthelayersshieldingfunctionagainstsolarultravioletradiation[Pavlovetal.,2001],althoughlabora-toryexperimentssuggestparticlesizesthatmakethehazeopticallythickintheultravioletyetopticallythinintheoptical[Traineretal.,2006].2006].67]Theammoniastorytookanunexpectedturnrecently,Uenoetal.[2009]suggestedthatcarbonylsulfide(OCS)atpartspermillionvolume(ppmv)levelscouldexplainthedistributionofsulfurisotopesingeologicalsam-plesfromtheArcheanandcouldshieldNHagainstultra-violetradiation.Detailedphotochemicalmodelingshows,however,thatsuchhighconcentrationsofOCSareunlikelybecauseOCSisrapidlyphotodissociatedintheabsenceofultravioletshieldingbyozone[Domagal-Goldmanetal.al.68]Asanadditionalargumentagainstthecoolingeffectsofhazelayers,WolfandToon[2010]demonstratedinageneralcirculationmodelwithsize-resolvedaerosolsthatthefractalstructureoftheaerosolparticlesformingthehazedrasticallydiminishestheantigreenhouseeffect.SuchfractalparticlesgiveagoodfittothealbedospectrumofTitan,thelargestmoonofSaturn,whichhasadenseatmospherewithanopaqueorganichazelayer[Danielsonetal.,1973;andPollack,1980,1983;McKayetal.,1991].Inaddition,Hasenkopfetal.[2011]showedthattheaerosolparticlesinthehazecouldhaveledtotheformationofshort-livedandopticallythincloudswithaloweralbedothantodayclouds,hencedecreasingtheircoolingandincreasingtheirwarmingeffect.(Note,however,thatcloudeffectsaloneareinsufficienttoeffectivelycounteractthefaintyoungSun;seesection6.)6.)69]Insummary,ammoniamaynotbecompletelyoutofthegameasapossiblesolutionofthefaintyoungSunproblemafterall,althoughpotentialproblemswiththehazeshieldingandthehighsolubilityofammoniaappeartomakeandCOmorelikelycandidates.5.2.MethaneMethane70]GiventheproblemswithammoniaasagreenhousegasintheArchean,someresearchersturnedtoCHasapotentialwarmingagentfortheArcheanclimate.climate.71]Themainadvantageofmethaneascomparedtoammoniadiscussedinsection5.1aboveisthatCHphotolyzedconsiderablyslowerthanNH,becauseitrequiresultravioletlightofmuchshorterwavelengths145nm)wheretheSunemitslessradiation.Indeed,pho-tochemicalmodelsshowthatevenunderthemoreintenseultravioletradiationemittedbytheyoungSun,thelifetimeofCHinaterrestrialatmospherelowinCOisoftheorderof10to10years[,1986],incontrasttolessthan10yearsforNHNH72]TherearetwoeffectsconstrainingtheallowedparameterspaceforamethanegreenhouseontheearlyEarth,though.First,dependingontheassumedatmosphericmeth-anepartialpressure,acontributionfromothergreenhousegasestothewarmingwillberequired,withcarbondioxidebeingthemostnaturalchoice.Asdiscussedinsection5.3below,geochemicaldatafromancientpaleosolssetanupperlimittotheatmosphericcarbondioxidepartialpressureofatmost0.03barduringtheLateArchean.Scenarioswithlowmethanepartialpressurescouldbeinconflictwiththisconstraint,unlessotherforcingscontributetowarming.warming.73]Second,photochemicalmodelsshowthatanorganichazestartstoformathighCHratios[Kastingetal.1983].Asdiscussedabove,anorganichazelayerexhibitsanantigreenhouseeffectbecauseitreflectssolarradiationbackintospacewhilebeingtransparenttooutgoinginfraredradiation[McKayetal.,1991,1999].Thishazewouldthuscooltheplanet,effectivelylimitingthegreenhousewarmingachievablebymethaneintheearlyatmosphere.EarlierphotochemicalmodelingindicatedthatorganichazeshouldformintheprimitiveatmosphereatCHratioslargerthan1[,1986;Pavlovetal.,2001].RecentlaboratoryFEULNER:THEFAINTYOUNGSUNPROBLEM10of29 parameterspacewheresufficientwarmingcanbeprovidedwithoutcoolingbyorganichazeandwithoutconflictwiththepaleosolconstraintson.Notethat,dependingontemperature,theupperlimitsoncarbondioxidepartialpressurecouldbeevenlower(seeFigure6andthediscus-sionbelow).Itislessclearhowtighttheconstraintfromhazeformationisinrealityas,ontheonehand,hazecouldbeformedatevenlowerCHmixingratios[etal.,2004,2006]butcouldexhibitadecreasedanti-greenhouseeffectduetothefractalnatureoftheaerosolparticlesformingthehazelayer[WolfandToon,2010];seethediscussioninsection5.1above.above.77]TherecentmodelcalculationsbyHaqq-Misraetal.[2008]takingintoaccounttheantigreenhouseeffectof(nonfractal)organichaze(whichstartstoformatCHmixingratiosof0.1intheirmodel,inagreementwiththelaboratoryresultsdiscussedabove)andadditionalwarmingbyethane(C)areshowninFigure4b.Accordingtothesesimulations,aLateArcheanCOsolutiontothefaintyoungSunproblemappearstobemorecomplicatedthanpreviouslythoughtbecauseorganichazeformationsetsinathighermethanepartialpressureswhilehighcarbondioxidepartialpressuresareruledoutbypaleosolconstraints,yieldinginsufficientwarmingtoexplaintheabsenceofglaciationintheLateArchean.Thisstronglydependsonthestillsomewhatobscurepropertiesoforganichazelayersintheearlyatmosphere,however,andothergasesbesidesCOandCHmighthavecontributedtothewarming.warming.78]Finally,althoughmethaneisconsiderablymorestablethanammonia,itiscontinuouslydepletedbyphotolysisandreactionswithhydroxyl(OH)radicals.ThusitisinterestingtoaskwhatconstraintsonArcheanmethanefluxesandatmosphericconcentrationscanbederived.derived.79]BeforediscussingestimatesofatmosphericmethaneconcentrationsduringtheArchean,wetakeabrieflookatthemethanebudgetoftodaysatmosphere.Themethanecon-centrationinthepresent-dayatmosphereisabout1.8ppmv,havingincreasedfrom0.7ppmvinpreindustrialtimesduetoanthropogenicmethaneemissionsfromagricultureandindustrialprocesses[Forsteretal.,2007].Methanesourcestodayamounttoamethanefluxofabout600Tgyr(1Tg=g)[Denmanetal.,2007].Intheliterature,estimatesforArcheanmethanefluxesareoftencomparedtothispresent-dayflux(frequentlyandinaccuratelyevencalledthebiologicalflux).Thisisofcourseavalidorder-of-magni-tudecomparisoninprinciple,butitshouldbekeptinmindthatmorethan60%oftodaysmethanefluxisfromanthro-pogenicsources(includingindustrialprocessesandemis-sionsrelatedtofossilfuels),andabout90%oftheremainingnaturalfluxoriginatesfromecosystemsthatwerenotpresentduringtheArchean,i.e.,wetlands,termites,wildanimals,andwildfires[Denmanetal.,2007].2007].80]Today,methaneispredominantlyproducedbiologi-cally.IntheArchean,threesourcesofmethanehavecon-tributedtotheatmosphericbudget:impactsfromspace,geologicalsources,andanaerobicecosystems[2005];seeFigure5foranoverview.overview.81]Veryhighmethanefluxesfromcometaryimpactsof500Tgyrat3.5Gaand5000Tgyrat3.8GahavebeenestimatedbyKressandMcKay[2004]basedonimpactratesderivedin[1990].However,moremodestCHproductionratesappearmorelikely.[2005]esti-matesanmethanefluxfromimpactsatthebeginningoftheArchean3.8Gaof20Tgyr.Usingthenonlinearrela-tionbetweenmethanesourcefluxandatmosphericconcen-trationbasedonphotochemicalmodelinggivenin[2005]andbasedonPavlovetal.[2001],thiscorrespondstoavolumemixingratio7ppmv.ppmv.82]Theorderofmagnitudeofgeologicalmethanesour-cesintheArcheancanbederivedfromthepresent-dayabiogenicmethaneflux.Thecurrentfluxfrommineralalterationatmid-oceanridges,emissionsfromvolcanoes,andgeothermalsourcesbasedonthemostrecentdatahasbeenestimatedtobe2.3TgyryrEmmanuelandAgue2007],sufficienttosustain1ppmvaccordingto[2005].IntheEarlyArchean,thisfluxcouldhavebeenafactorof5to10largerduetothefastercreationofseaflooronearlyEarth[,2005],resultinginanatmosphericmixingratioof7ppmv.ppmv.83]Therefore,lowconcentrationsoftheorderof10ppmvofmethaneintheatmospherecouldhavebeensustainedfromabiogenicsourcesintheEarlyArchean.Laterintime,aftertheoriginoflifeandbeforethefirstmajorriseinatmosphericoxygen,muchlargermethaneconcentrationscanbeachievedfrombiologicalsources.Biologicalmethaneproductiontodayisaccomplishedbymethanogenicbacteria(ormetha-nogensforshort)thatarebelievedtohavearisenveryearlyintheevolutionoflife[WoeseandFox,1977].Theirmetabo-lismisbasedonavarietyofmetabolicpathways[1998].ThetwomostimportantnetreactionsareOandand84]Assumingthatmethanogensconvertedmostofthehydrogenavailableintheatmosphere[Kraletal.,1998;Kastingetal.,2001]andusinganestimatedhydrogenmixingratioof(1,Archeanmethanemixingratiosof5001000ppmvcouldbeplausible.Moreelaboratesimulationswithacoupledphotochemistry-ecosystemmodelessentiallyconfirmtheseearlyestimates,withatmo-sphericmethanemixingratiosintherange1001000ppmvforreasonableatmospherichydrogenfractions[etal.,2005].ItshouldbenotedthatourunderstandingofArcheanecosystemsisnaturallyratherlimited,sotheseestimatesshouldbetakenwithagrainofsalt.salt.85]Nevertheless,fromtheseargumentsonecanconcludethatmethanemixingratiosintheArcheanatmosphereofupto1000ppmvappearplausible;seeFigure5.ComparingthistotheresultsfromclimatemodelsimulationsfortheLateArcheanpresentedinFigure4,itisobviousthattheseareinsufficienttoprovideenoughwarminggiventhepaleosolconstraintsoncarbondioxidepartialpressuresduringthattime.Evenifhighermethanefluxesshouldhavebeenachieved,hazeformationlimitsthewarminginaLateFEULNER:THEFAINTYOUNGSUNPROBLEM12of29 88]Thisprecipitatedcalciumcarbonateisthenpartlydepositedinsedimentsatthebottomoftheoceans.Thesedimentsontheseafloorarethentransportedviathemotionsofplatetectonics.Atsubductionzones,mostofthecarbondioxideisreturnedtotheatmosphereviaarcvolca-nism,whilesomeisincorporatedintotheEarthsmantle,dependingonthecompositionofthesedimentsandtem-perature[KerrickandConnolly,2001;,2002].Quiteremarkably,thebasicprinciplesoftheinorganiccarboncyclewerealreadydiscoveredbyseveralscientistsinthe19thcentury(see[1995]andBernerandMaasch[1996]fordiscussionsofthisearlyhistoryofideasabouttheinorganiccarboncycle).cycle).89]Thesilicate-weatheringcycleispartofanegativefeedbackloopbecausetheweatheringrateremovingCOfromtheatmosphereincreaseswithgrowingatmosphericconcentrationsandrisingtemperatures(andviceversa),whilethevolcanicemissionofCOcanbeassumedtoberoughlyconstantovergeologicaltime(whenaveragedoversufficientlylongtimescalestosuppressthelargevariationscausedbyindividualeruptions)orpossiblydecreasingovertimegovernedbychangesingeothermalheatflowandvolcanicactivity.activity.90]FollowingtheinitialworkoncarbondioxideintheArcheanatmosphere,one-dimensionalradiative-convectiveclimatemodelswereusedtoestimatetheamountofCOnecessarytokeepEarthfromfreezing(seealsoFigure6).Forsolarluminositiesof=0.75representativefortheEarlyArchean,thesemodelssuggestthatcarbondioxidepartialpressuresof0.3bar(ormorethan1000timesthepreindustrialvalueof0.00028bar)arerequiredtoreachglobalaveragesurfacetemperaturessimilartotoday,i.e.,288K,whereaspartialpressuresof0.1bar(about300timesthepresent-dayvalue)aresufficientfortheLateArchean[Owenetal.,1979;Kastingetal.,1984;KiehlandDickinson,1987;vonParisetal.,2008].2008].91]Atemperatureof288Kwouldpresumablycorre-spondtoaworldwithsmallicecapssimilartoourpresentclimate,thelimitofcompletefreezingisoftensetatameansurfacetemperatureof273K,thefreezingpointofwater.Carbondioxidevaluesrequiredtoreachthistemperatureare Figure6.ComparisonofempiricalestimatesofcarbondioxidepartialpressuresduringthePrecambrianandclimatemodelresultsforanaverageglobalsurfacetemperatureof288Kassumedtoberequiredtopreventglobalglaciationasafunctionofrelativesolarluminosity(solidblackline).Theresultsforaglobalmeantemperatureof273Kareindicatedbythedashedblackline.Calculationsarebasedonaone-dimensionalradiative-convectiveclimatemodel[vonParisetal.,2008].GeochemicalestimatesforatmosphericCOpartialpressuresatdifferentepochsareindicated[Ryeetal.,1995;Hessleretal.,2006;Rosingetal.,2010;Drieseetal.,2011];seethetextfordetails.Atemperatureof298Kisassumedincaseanexplicitdependenceoftheestimatesonenvironmentaltemperatureisavail-able.InadditiontotheArcheanandPaleoproterozoicestimates,fourMesoproterozoicestimatesareshownforcomparison:alowerlimitderivedfromacarbonisotopeanalysisofmicrofossilsdatingback1.4Ga[KaufmanandXiao,2003],a1.2Gaupperlimitinferredfrominvivoexperimentsofcyanobac-terialcalcification[KahandRiding,2007],andtwoestimatesfrom[2006].ThedottedlineshowsthepreindustrialCOpartialpressureof2.8bar.Theconversionfromsolarluminosity(bottomscale)toage(topscale)followstheapproximationgiveninequation(1).ModifiedandupdatedafterafterFEULNER:THEFAINTYOUNGSUNPROBLEM14of29 carbonatesrequiresCOpartialpressuresofabout10timespreindustriallevelsforthesameenvironmentaltemperatureof298KasintheRosingetal.[2010]study[Hessleretal.,2004].04].98]Despitetheuncertaintiesdiscussedabove,geochem-icaldatathereforesuggestthatCOpartialpressureswerelikelysmallerthanafewhundredtimespreindustriallevelsintheLateArcheanandEarlyProterozoic,meaningthatcarbondioxidealonewouldmostlikelyhavebeenunabletoprovideenoughwarmingduringthesetimes(seeagainFigure6).InthiscontextitshouldbekeptinmindthatallmodelingstudiesthatdeterminetheCOlimitnecessarytowarmtheearlyEarthrelyonone-dimensionalmodelsneglectingmanyimportantfeedbackmechanismsliketheice-albedofeedback.Afurthercomplicationarisesfromuncertaintiesinradiativetransfercalculationsforatmo-spheresrichincarbondioxide[Halevyetal.,2009;Wordsworthetal.,2010].Theproblemarisesbecausethewingsofabsorptionlineprofilesandtheparametersgov-erningthecontinuumabsorptionofCOarepoorlycon-strainedbyempiricaldataforthehighCOpartialpressuresusedincalculationsofthefaintyoungSunproblem.Wordsworthetal.[2010],forexample,suggestthattheradiativetransfercalculationsusedinmanyearlierstudiesoverestimatetheCOabsorptionintheearlyatmospherewhencomparedtoaparametrizationthatmostaccuratelyreflectspresentlyavailabledata.data.99]Itthereforeremainstobeseenwhethercarbondiox-ideconcentrationsinagreementwithgeochemicalevidencearesufficienttooffsetthefaintyoungSun.5.4.OtherGreenhouseGasesGases100]OthergreenhousegaseshavebeensuggestedtocontributetowarmingearlyEarth.Forexample,Cexpectedtoforminanatmospherecontainingmethaneandexposedtoultravioletradiation[Haqq-Misraetal.,2008].IthasbeenshownthatethanecancontributetoanArcheangreenhouse[Haqq-Misraetal.,2008],althoughtheeffectisnotlargeascanbeseeninFigure4.Warmingbynitrousoxide(NO)hasbeensuggested[,2007],butNOisrapidlyphotodissociatedintheabsenceofatmosphericoxygen[Robersonetal.,2011],makingitanunviableoptionfortheArchean.Furthermore,OCSatppmvlevelshasthepotentialtooffsetthefaintyoungSun[Uenoetal.2009],butitappearsveryunlikelythatOCSconcentra-tionshigherthanpartsperbillionvolume(ppbv)levelcouldhavebeenmaintainedduetophotodissociationlosseslossesDomagal-Goldmanetal.,2011].2011].101]Althoughnitrogenisnotagreenhousegasinitself,ahigherpartialpressureofatmosphericnitrogenduringtheArcheanwouldamplifythegreenhouseimpactofothergasesbybroadeningofabsorptionlines[Goldblattetal.2009].DespitethefactthatthisadditionalwarmingispartlycompensatedbyincreasedRayleighscatteringofshort-waveradiation[Halevyetal.,2009],modelcalcula-tionsshowthatitcouldcauseawarmingby4.4CforadoublingoftheNconcentration[Goldblattetal.,2009].NitrogenoutgassedquicklyonearlyEarth,sotheatmo-sphericnitrogencontentlikelyequaledatleastthepresent-dayvalue.Sinceallnitrogeninthemantletodaymusthavebeenprocessedthroughtheatmosphere,thereservoirsinthecrustandmantleappearsufficientlylargetoexplainhigheratmosphericconcentrationsandthusawarmerArcheanArcheanGoldblattetal.,2009].Notethatarecentstudyoffossilraindropimprintslimitstotalairdensity2.7Gatolessthantwicetodayslevel,withthemostlikelyvaluesimilartothepresent-daydensity[Sometal.,2012].5.5.SummarySummary102]Insummary,anenhancedgreenhouseeffectargu-ablystillseemsthemostlikelysolutiontothefaintyoungSunproblem.Carbondioxideandmethanearethemostobviouscandidates,althoughtheycouldfaceseverediffi-cultiesintermsofgeochemicalconstraintsandlowpro-ductionrates,respectively,andtheirrespectivecontributionremainsuncertain.AmmoniaappearslesslikelythanCOandCHbecauseitwouldhavetobeshieldedagainstpho-todissociationbyultravioletradiationandbecauseitwouldbewashedoutbyrain.rain.103]Afinalassessmentofgreenhousegaswarmingintheearlyatmosphere,however,iscomplicatedbyuncertaintiesintheradiativetransferfunctionsandthelackofspatiallyresolvedandfullycoupledclimatemodelsfortheearlyEarthcomprisingthefullrangeoffeedbacksintheEarthsystem.Finally,otherclimaticfactorslikechangesincloudcovercouldinprincipleatleasthavecontributedtoawarmingoftheArcheanEarth.6.CLOUDSINTHEARCHEANATMOSPHERETMOSPHERE104]Cloudsexhibittwocompetingeffectsontheclimate.Ontheonehand,clouds,andinparticularlowclouds,reflectsolarradiationbackintospace,thusincreasingthealbedoandcoolingtheclimate.Ontheotherhand,thewatervaporwithinthecloudsabsorbsandreemitslong-waveradiationfromthesurfaceandhencewarmstheplanet(see,e.g.,[1972,andreferencestherein],aswellas[2005],forarecentreview).review).105]Thewarmingeffectofadecreasedcloudcover(resultinginaloweralbedoandhenceanincreaseinabsorbedsolarradiation)ontheearlyatmospherehasbeensuggestedasapossibleoffsettothefaintyoungSunaspartofanegativefeedbackloopinwhichlowertemperaturesdecrease(low-level)cloudinessduetoareductionincon-vectiveheatingandthusincreasetheamountofabsorbedsolarradiation,counteractingtheinitialcooling[,1979;Rossowetal.,1982].ThishypothesishasbeenconsideredanunlikelysolutionforthefaintyoungSunproblemforalongtime,however,becausetheearlyEarthwasbelievedtobeevenwarmerthantoday(presumablyresultinginahighercloudcoverduetoincreasedevapora-tionandthushigherreflectivityoftheatmosphere),althoughmorerecentstudiesindicateamoretemperateArcheancli-mate(seethediscussioninsection2.3).Inanycase,thepreciseeffectofcloudfeedbackforwarmingorcoolingtheearlyEarthremainsuncertain.Morerecently,Rosingetal.[2010]arguedthattheArcheanwascharacterizedbylargerclouddropletsandshortercloudlifetimes,effectivelyFEULNER:THEFAINTYOUNGSUNPROBLEM16of29 obliquitynottoodifferentfromthepresentvaluesincetheformationofEarth.Earth.114]TidalfrictioncausesEarthsrotationtoslowdownandtheMoontomovefurtherawayfromEarthovertimetimeWilliams,2000].Forexample,Earthsrotationperiodat4Gahasbeenestimatedtobejust14h[Zahnleand,1987].Usingasimpleone-dimensional(zonallyaveraged)energybalancemodeltoestimatetheeffectsofashorterdaylengthonclimate,Kuhnetal.[1989]findthattheeffectisimportantforthePrecambrianclimatesinceitincreasesthetemperaturegradientbetweenequatorandpoles.Thisisduetothefactthatmidlatitudeeddiesthataremostlyresponsiblefortheheattransportstronglydependonrotationrate;atfasterrotationrates,theseeddiesbecomesmallerinsizeandthuslessefficientintrans-portingheatpoleward.Ithasbeenshownthattherateofmeridionalheattransportisproportionalto1/1/Stone,1972],whereistheCoriolisparameterdependingonEarthsrotationrateandlatitude.Thiseffectcould,inprinciple,preventlow-latitudeglaciation.Note,however,thatthereisarunawayeffectassociatedwithice-albedofeedbackthatpushestheplanetintoasnowballEarthregimeonceabouthalfofitssurfaceiscoveredwithice;seethediscussionbelow.below.115]Studiesusinganatmosphericgeneralcirculationmodelcoupledtoasimpleoceanwithoutheatcapacitysug-gestedthatfastrotationcoulddecreaseglobalcloudcoverbyabout20%foradaylengthof14handthusresultinariseoftheglobalmeanairtemperatureof2K[Jenkinsetal.,1993;,1993].Inthesemodelexperiments,thedecreaseincloudinessisduetoaweakerHadleycellandthusreducedconvectionandcloudformationinequatoriallatitudesandlargersubsidenceinmidlatitudesagainreducingcloudcover.Afollow-upstudywithfixedseasurfacetemperaturesfailedtoshowtheeffect,however,andfoundasmallincreaseinglobalcloudcover[,1996].1996].116]Sensitivitystudiescarriedoutwithatmosphericgen-eralcirculationmodelsfordifferentrotationperiodsdemon-stratetheimportanceoftherotationrateforthestructureandstrengthoftheatmosphericcirculation[,1988;NavarraandBoccaletti,2002]:withincreasingrotationrate,theHadleyandFerrelcellsbecomegenerallynarrowerandweaker,thepolarcelltendstosplitintosmallercells,andthetemperaturegradientbetweenthepolesandtheequatorincreases.Howthesechangesinteractwiththeocean,how-ever,hasstilltobedemonstratedwithfullycoupledmodelsusingageneralcirculationoceanmodule.7.2.ContinentalAreaArea117]AfurtherstrikingdifferencebetweentheArcheanworldandthepresent-dayEarthisthefractionofthesurfacecoveredbycontinents.DuringtheArchean,thelandareahasbeenestimatedtocompriseonlyabout10%oftodaycontinentalarea[,1981].Earliermodelsforconti-nentalgrowthyieldedwidelydiverginggrowthcurvesforcontinentalvolume(see,e.g.,[1985]and[2009]foranoverview),butrecentwork[Belousovaetal.Dhuimeetal.,2012]basedontheisotopiccomposi-tionofzirconsprovidesmuchbetterconstraintsontheevolutionofcontinentalvolume,whichisillustratedinFigure7.Whilecontinentalvolumehasgrownto70%bytheendoftheArchean,itappearslikelythatasmallerfractionofEarthssurfacewascoveredbylandduringtheEarlyArchean,whichaffectedboththealbedoandheattransportprocessesintheEarthsystem.system.118]TheloweralbedoduetothesmallercontinentalareahasbeensuggestedseveraltimesasanimportantfactorfortheenergybudgetoftheArcheanclimate[Schattenand Figure7.Examplesforrecentresultsonthegrowthofthevolumeofcontinentalcrustovertimederivedfromisotopicdata[Belousovaetal.,2010;Dhuimeetal.,2012].FEULNER:THEFAINTYOUNGSUNPROBLEM18of29 analyzedfluidinclusionsin3.2Gadepositsinterpretedasmid-Archeanhydrothermalventsandfoundchlorinecon-centrations1.65largerthantoday,buttheseformationshavelaterbeenreinterpretedasQuaternaryspringdeposits[andByerly,2003].2003].124]TotaloceansalinityisofinterestfortheArcheanclimatesystembecauseitcouldinprincipleinfluencethethermohalineoceancirculation[Kuhlbrodtetal.,2007].Hayetal.[2006]observedthatforpresent-daysali-nitiesofthedensityofseawaterchangesonlyweaklywithtemperaturewhenapproachingfreezingpoint,requiringanenhancementofthesaltcontentbyseaiceformationorevaporationtomakeseawaterdenseenoughtosinktothesinterior.Foranoceanwithsalinitiesabovethedensityincreaseswithfallingtemperature.Therefore,anenergy-consumingphasetransitionduringdeepwaterfor-mationwouldnotberequired,whichcouldyieldastrongerthermohalinecirculation.ThisclaimhasbeenrefutedinamodelingexperimentbyWilliamsetal.[2010],however,whichinfactshowsaweakermeridionaloverturninginanoceanmodelwithtwicethepresent-daysalinityandtodaytopography.Thephysicalreasonsfortheseconflictingassessmentsofcirculationstrengthforhigheraveragesalinityremainunclear,however,andtheinfluenceofglobalsalinityonoceancirculationcertainlymeritsfurtherstudy.study.125]TidalactivitywashigherduringtheArcheanduetothesmallerorbitoftheMoon,whichaffectsmixingintheoceanandthus,inturn,oceancirculationandmarineheattransport[MunkandWunsch,1998].Botheffectsshouldbeexploredinmoredetailwithstate-of-the-artoceangeneralcirculationmodels.7.4.SummarySummary126]RotationalandcontinentaleffectsarethusimportantforassessingthewarmingeffectsontheArcheanclimate.ItislikelythattheycannotsolvethefaintyoungSunproblemontheirown,forwhichanenhancedgreenhouseeffectonearlyEarthappearstoberequired.Theinfluencesoffasterrotationanddifferentcontinentalconfiguration,however,areimportantforunderstandingtheenergybudgetanddynamicsoftheArcheanclimatesystem,soanyconvincingdemonstrationsofsolutionsinvolvingenhancedlevelsofgreenhousegaseswillrequiresimulationswithfullycoupledstate-of-the-artclimatemodelsincludingtheseeffects.8.CONCLUSIONSANDFUTUREDIRECTIONSDIRECTIONS127]Afterfourdecadesofresearch,thefaintyoungSunproblemindeedrefusestogoawayawayKasting,2010,p.687].Toalargeextent,thisiscertainlyduetothestilllimitedknowledgeoftheconditionsonearlyEarth,althoughthelastdecadeshaveseenconsiderableprogress,andsomepara-metersarenowbetterconstrainedthantheyusedtobeinthepast.Nevertheless,improvedconstraintsonatmosphericcompositionduringtheArcheaneonwouldobviouslybeextremelyimportant,althoughcertainlychallengingtoobtain.Despitethedifficultiesinvolved,therehavecertainlybeenremarkableadvancesingeochemistryinrecentyears.Note,forexample,thatmostofthegeochemicalconstraintsonArcheanandProterozoiccarbondioxidepartialpressuresshowninFigure6werederivedwithinthelastdecade.Thereisthusreasontobehopefulincontinuedprogressinthisarea.area.128]Inadditiontobetterdata,however,improvementsintheeffortsonmodelingtheEarthsclimateduringtheArcheanareurgentlyneeded,asonotherimportantpro-blemsindeeptimepaleoclimatologylikeclimatechangesassociatedwithmass-extinctionevents[,2009]orgreenhouseclimatesofthepast[Huberetal.,1999].ManysuggestedsolutionstothefaintyoungSunproblem,espe-ciallythoseinvolvingcontinentaloralbedoeffects,requirespatiallyresolvedclimatesimulations,ratherthantheone-dimensionalorsimpleenergybalanceatmosphericmodelstraditionallyusedinstudiesofthefaintyoungSunproblem,andfullcouplingtostate-of-the-artoceanandseaicemod-els.Finally,thefullrangeoffeedbackmechanismshastobeexploredindetail.detail.129]ThereareseveralchallengesinallmodelingeffortsoftheArcheanclimate.First,therearestillconsiderableuncertaintiesinkeyclimatecharacteristicslikegreenhousegasconcentrationsorcontinentalconfiguration.TheseparameteruncertaintieshavetobeproperlyquantifiedusingensemblesimulationsoftheArcheanclimatesystem.Becauseoftheirhigherspeed,thisistraditionallythedomainofintermediate-complexityclimatemodels[Claussenetal.al.130]Second,essentiallyallofthemorecomprehensiveclimatemodelsaretosomeextenttunedtopresent-daycli-mateconditions.Tobeabletoapplythemtotheearlysclimateandobtainmeaningfulresults,theyhavetoproviderobustresultsforaclimatestatethatisconsiderablydifferentthantoday.Notonlyforthisreason,theemphasisinallclimatemodelingeffortsforthefaintyoungSunproblemshouldlieinimprovingourunderstandingofthephysicalprocessescharacterizingtheArcheanclimatesys-tem.Finally,itwouldbeadvisabletosimulatetheArcheanclimatewithseveralmodelsusingdifferentapproachestobeabletocomparemodelresults.results.131]Giventhecontinuedinterestthisimportanttopicenjoys,thenextdecademightbringusclosertofinallyansweringthequestionofhowwateronearlyEarthcouldhaveremainedliquidunderafaintyoungSun,certainlyoneofthemostfundamentalquestionsinpaleoclimatology.NOTATIONsemi-majoraxisofEarthsellipticalorbitcalciumcarbonateOgypsumOformaldehydeSdimethylsulfidecarbondioxideFEULNER:THEFAINTYOUNGSUNPROBLEM20of29 Proterozoic:GeologicaleonlastingfromtheendoftheArchean2.5yearsagoto542yearsago.Protoplanetarydisk:Rotatingdiskofdensegasanddustsurroundinganewlyformedstar.Geologicalperiodspanningthelast2.6Radiativeforcing:Changeinnetirradiance(downwardminusupward)attheupperlimitofthetroposphere,thuscharacterizingchangesintheenergybudgetofthesurface-tropospheresystem.Measureofthedissolvedsaltcontentofoceanwater,usuallyexpressedaspartsperthousand.Solaranalogs:Starswithphysicalandchemicalcharac-teristicssimilartotheSun.Solarconstant:TotalradiativeenergyperunittimeandunitareaincidentonaplaneperpendiculartothedirectiontotheSunandatthemeandistancebetweenSunandEarth.Solarluminosity:Radiativeenergyperunittimeemit-tedbytheSun.Solarwind:Streamofchargedparticles(mostlyelec-tronsandprotons)originatingintheSunsupperatmosphere.Standardsolarmodel:Numericalmodelofthestruc-tureandevolutionoftheSunbasedonfundamentalequa-tionsofstellarphysicsandconstrainedbytheobservedphysicalandchemicalcharacteristicsofthepresent-daySun.Stromatolites:Lithified,sedimentarystructuresgrow-ingviasedimenttrappingbymicrobialmats.Thesupernatantwatercolumnisthewateroverlyingsedimentedmaterial.Thermohalinecirculation:Large-scaleoceancurrentsdrivenbydensitygradientsduetoheatandfreshwaterfluxesattheoceansurface.Troposphere:ThelowermostlayerofEarthsatmosphere.Zero-agemainsequence(ZAMS):Positionofstarsinabrightness-colordiagramthathavejuststartednuclearfusionofhydrogentoheliumintheircores.cores.132]ACKNOWLEDGMENTS.Itisapleasuretothankthetworeviewers,ColinGoldblattandJamesKasting,aswellastheEditor,MarkMoldwin,fortheircommentsthathelpedtoimprovethisreviewpaperconsiderably.Furthermore,IwouldliketothankHendrikKienertfornumerousdiscussionsandhelpfulcommentsonearlierdraftsofthemanuscript.IamgratefultoAlisonSchlumsforproofreadingandtoGritSteinhöfel-Sasgenforbackgroundinformationonbandedironformations.ThisresearchhasmadeuseofNASAsAstrophysicsDataSystemBibliographicServices.Services.133]TheEditoronthispaperwasMarkMoldwin.Hethankstworeviewers,JamesKastingandColinGoldblatt.Abbot,D.S.,A.Voigt,andD.Koll(2011),TheJormungandglobalclimatestateandimplicationsforNeoproterozoicglaciations,J.Geophys.Res.,D18103,doi:10.1029/2011JD015927.Abelson,P.H.(1966),ChemicaleventsontheprimitiveEarth,Proc.Natl.Acad.Sci.U.S.A.,13651372,doi:10.1073/Altermann,W.,andJ.Kazmierczak(2003),Archeanmicrofossils:AreappraisalofearlylifeonEarth,Res.Microbiol.617,doi:10.1016/j.resmic.2003.08.006.Bada,J.L.,andS.L.Miller(1968),Ammoniumionconcentrationintheprimitiveocean,,423425,doi:10.1126/Bada,J.L.,C.Bigham,andS.L.Miller(1994),ImpactmeltingoffrozenoceansontheearlyEarth:Implicationsfortheoriginoflife,Proc.Natl.Acad.Sci.U.S.A.,1248Bahcall,J.N.,M.H.Pinsonneault,andS.Basu(2001),Solarmodels:Currentepochandtimedependences,neutrinos,andhelioseismologicalproperties,Astrophys.J.,990Barghoorn,E.S.,andJ.W.Schopf(1966),MicroorganismsthreebillionyearsoldfromthePrecambrianofSouthAfrica,,758763,doi:10.1126/science.152.3723.758.Barron,E.J.(1984),Ancientclimates:InvestigationwithclimateRep.Prog.Phys.,15631599,doi:10.1088/0034-Beerling,D.,R.A.Berner,F.T.Mackenzie,M.B.Harfoot,andJ.A.Pyle(2009),MethaneandtheCH-relatedgreenhouseeffectoverthepast400millionyears,Am.J.Sci.,97Bekker,A.,H.D.Holland,P.-L.Wang,D.Rumble,H.J.Stein,J.L.Hannah,L.L.Coetzee,andN.J.Beukes(2004),Datingtheriseofatmosphericoxygen,,117120,doi:10.1038/Belousova,E.A.,Y.A.Kostitsyn,W.L.Griffin,G.C.Begg,S.Y.OReilly,andN.J.Pearson(2010),Thegrowthofthecon-tinentalcrust:ConstraintsfromzirconHf-isotopedata,,457466,doi:10.1016/j.lithos.2010.07.024.Benn,K.,J.-C.Mareschal,andK.C.Condie(Eds.)(2006),ArcheanGeodynamicsandEnvironmentsGeophys.Monogr.,vol.164,320pp.,AGU,Washington,D.C.,doi:10.1029/Berner,R.A.(1995),A.G.Högbomandthedevelopmentoftheconceptofthegeochemicalcarboncycle,Am.J.Sci.495,doi:10.2475/ajs.295.5.491.Berner,R.A.,andK.A.Maasch(1996),ChemicalweatheringandcontrolsonatmosphericOandCO:FundamentalprincipleswereenunciatedbyJ.J.Ebelmenin1845,Geochim.Cosmochim.,16331637,doi:10.1016/0016-7037(96)00104-4.Berner,R.A.,A.C.Lasaga,andR.M.Garrels(1983),Thecarbonate-silicategeochemicalcycleanditseffectonatmo-sphericcarbondioxideoverthepast100millionyears,J.Sci.(7),641683,doi:10.2475/ajs.283.7.641.Blake,R.E.,S.J.Chang,andA.Lepland(2010),PhosphateoxygenisotopicevidenceforatemperateandbiologicallyactiveArchaeanocean,,10291032,doi:10.1038/Boothroyd,A.I.,I.Sackmann,andW.A.Fowler(1991),OurSun.Earlymasslossof0.1solarmassandthecaseofthemissingAstrophys.J.,318329,doi:10.1086/170361.Budyko,M.I.(1969),TheeffectofsolarradiationvariationsontheclimateoftheEarth,,611619,doi:10.1111/j.2153-Buick,R.(2007),DidtheProterozoicCanfieldOceancausealaughinggasgreenhouse?,,97100,doi:10.1111/Caldeira,K.,andJ.F.Kasting(1992),SusceptibilityoftheearlyEarthtoirreversibleglaciationcausedbycarbondioxideclouds,,226228,doi:10.1038/359226a0.Cameron,A.G.W.,andW.R.Ward(1976),TheoriginoftheLunarSci.,120Canfield,D.E.(2005),Theearlyhistoryofatmosphericoxygen:HomagetoRobertM.Garrels,Annu.Rev.EarthPlanet.Sci.36,doi:10.1146/annur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