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O2-andCO-RichAtmospheresforPotentiallyHabitableEnvironmentsonTRAPPIST-1Planets1RenyuHu1,2,LukePeterson1,3,andEricT.Wolf41JetPropulsionLaboratory,CaliforniaInstituteofTechnology,Pasadena,CA911092DivisionofGeologicalandPlanetarySciences,CaliforniaInstituteofTechnology,Pasadena,CA911253NorthwesternUniversity,Evanston,IL602014LaboratoryforAtmosphericandSpacePhysics,DepartmentofAtmosphericandOceanicSciences,UniversityofColorado,Boulder,CO80303renyu.hu@jpl.nasa.govShorttitle:TheO2-CORunawayAbstractSmallexoplanetsofnearbyMdwarfstarspresentthepossibilitytofindandcharacterizehabitableworldswithinthenextdecade.TRAPPIST-1,anultracoolMdwarfstar,wasrecentlyfoundtohavesevenEarth-sizedplanetsofpredominantlyrockycomposition.Theplanetse,f,andgcanhavealiquidwateroceanontheirsurfacegivenappropriateatmospheresofN2andCO2.Particularly,climatemodelshaveshownthattheplanetseandfcansustainagloballiquidwaterocean,for≥0.2barCO2plus1barN2,or≥2barsCO2,respectively.Theseatmospheresareirradiatedbyultravioletemissionfromthestar’smoderatelyactivechromosphere,andtheconsequenceofthisirradiationisunknown.Hereweshowthatchemicalreactionsdrivenbytheirradiationcanproduceandmaintainmorethan0.2barO2and0.05barCOiftheCO2is≥0.1bar.TheabundanceofO2andCOcanrisetomorethan1barundercertainboundaryconditions.BecauseofthisO2-COrunaway,habitableenvironmentsontheTRAPPIST-1planetsentailanO2-andCO-richatmospherewithcoexistingO3.TheonlyprocessthatwouldpreventtherunawayisdirectrecombinationofO2andCOintheocean,areactionthatisfacilitatedbiologically.OurresultsindicatethatO2,O3,andCOshouldbeconsideredtogetherwithCO2astheprimarymoleculesinthesearchforatmosphericsignaturesfromtemperateandrockyplanetsofTRAPPIST-1andotherMdwarfstars.1.IntroductionTheeraofcharacterizingtemperateandrockyexoplanetshasbegun.Ground-basedsurveyshavefoundtemperateplanetshostedbyMdwarfstarsliketheTRAPPIST-1planetsandLHS1140b(Gillonetal.2017;Dittmannetal.2017).TheK2missionandtheTransitingExoplanetSurveySatellite(TESS)arefindingafewtenstransitingandtemperateplanetsaroundnearbyMstars(e.g.,Sullivanetal.2015).Orbitingsmallstars,theseplanetsprovideanacceleratedpathtowardfindingandcharacterizingpotentiallyhabitableworlds.TheTRAPPIST-1planetsalreadyhavetransmissionspectrameasuredbyHubble(deWitetal.2018;Zhangetal.2018).With>7timesmorecollectingareaandinfraredinstruments,theJamesWebbSpace

1©2019.CaliforniaInstituteofTechnology.Governmentsponsorshipacknowledged.

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Telescope(JWST)willbecapableofprovidingamoredetailedlookintotheatmosphereofthesecoldexoplanets(Beichmanetal.2014).AkeyfactorthatimpactstheatmosphericcompositionsofrockyplanetsaroundMdwarfstarsisthestellarultraviolet(UV)irradiation.UVradiationdissociatesCO2intoCOandO,butthedirectrecombinationofthetwoproductsisslow.TwoOproducedthencombinetoformO2.IntheSolarSystem,theCO2atmosphereofMarsisstabilizedprincipallybycatalyticalcyclesofOHandHO2thatrecombineCOandO2(McElroy&Donahue1972;Nairetal.1994),whilethatofVenusisadditionallystabilizedbychlorinespecies(McElroyetal.1973).IfthestarisanMdwarf,itsirradiationisstronginthefar-UV(FUV)bandpassbutweakinthenear-UV(NUV)bandpass(Franceetal.2013).BecauseFUVradiationdissociatesCO2,andNUVradiationamplifiesthecatalyticalcyclesofOHandHO2,aliquid-water-oceanplanetofanMdwarfinclinestoaccumulateCOandO2intheatmosphere.UsingthespectrumoftheMdwarfGJ876,atmosphericphotochemistrymodelshavepredictedanO2mixingratioupto5%inanN2-dominatedatmospherewith0.05barCO2(Tianetal.2014;Domagal-Goldmanetal.2014;Harmanetal.2015).AtmosphericphotochemistrymodelshavealsoshownthatmassiveO2andCOwouldbeproducedfromCO2-dominatedatmospheresofdesiccated–andhenceuninhabitable–rockyplanetsofMdwarfstars(Gaoetal.2015).ClimatemodelsoftheplanetTRAPPIST-1e,f,andgindicatethattheyneedmorethan0.05barCO2tosustainagloballiquidwaterocean,sincetheplanetshavelosttheirprimordialhydrogenenvelopesduetoX-rayandextreme-UVirradiation(Bourrieretal.2017;Bolmontetal.2017).Foranatmospherewith1barN2andvariedabundanceofCO2ontheplanete,icewouldcover57%oftheplanetat0.1barCO2,andthecoveragedropsquicklytonearlyzeroat≥0.2barCO2(Wolf2017).Ontheplanetf,≥2barsCO2arerequired(Wolf2017;Turbetetal.2018).SubstitutingCO2withCH4orNH3asthemaingreenhousegaswouldbeunlikelytosustainthehabitability,fortheirmuchweakergreenhouseeffectandtendencytoformphotochemicalhazesthatcauseananti-greenhouseeffect(Turbetetal.2018).ThephotochemicallifetimeofCH4couldhoweverbequitelongonTRAPPIST-1planetsfortheweakerNUVradiation(e.g.,Rugheimeretal.2015).ToinvestigatetheeffectofthestellarirradiationonthishighCO2abundance,weuseourphotochemistrymodel(Huetal.2012;Huetal.2013)todeterminethesteady-statecompositionoftheatmospheresunderirradiation.Thephotochemistrymodelusestheatmosphericpressure-temperatureprofilesgeneratedbythe3Dclimatemodel(Wolf2017),whichwascalculatedforvariedpartialpressuresofCO2.Wefindthatmorethan0.2barO2and0.05barCOareproducedinthesteadystateiftheCO2partialpressureis≥0.1bar.TheabundanceofO2andCOcanrisetomorethan1barforgreaterCO2partialpressures,whichconstitutesan“O2-COrunaway”.Thepaperisorganizedasfollows.Wedescribeourmodels,includingthe3DclimatemodelinSection2,presenttheconditionsandthechemistryoftheO2-COrunawayinSection3,discussitsclimateimplications,feedback,andgeologiccontextinSection4,andconcludeinSection5.

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2.Methods2.1PhotochemistryModelThephotochemistrymodelusedinthisstudy(Huetal.2012;Huetal.2013)hasbeenvalidatedbycomputingtheatmosphericcompositionsofpresent-dayEarthandMars,sincetheoutputsagreedwiththeobservationsofmajortracegasesinEarth'sandMars'atmospheres.Themodelhasalsobeenusedtodeterminethephotochemicaloxygenbuildupinabioticatmospheres(Huetal.2012;James&Hu2018).Forthelatterpurpose,themodelhasbeencomparedwithotherphotochemistrymodelindetailandwehavefoundgoodagreement(Gaoetal.2015;Harmanetal.2018).Thephotochemistrymodelsolvestheone-dimensionalchemical-transportequationfor111O,H,C,N,andSspeciesincludingsulfurandsulfuricacidaerosols.ThefullspeciesandreactionlistcanbefoundinHuetal.(2012).Themodelseekstobalanceproductandlosstermsfromallchemicalandphotochemicalreactionsforeachgasateachaltitudelevel.Wetypicallydonotassumephotochemicalequilibriumforanygas;so,unlessotherwisestated,allgasesareincludedinthefullchemical-transportcalculation.Thesystemisconsideredasconvergedtoasteadystateiftheminimumvariationtimescaleisgreaterthan,forinstance,theageoftheSolarSystem(1017s).InthemodelsthatfeaturetheO2-COrunaway,theambientpressurechangesinthesimulationbecausetheproducedO2andCOmeaningfullycontributetothepressure.Ourphotochemistrymodelself-consistentlycalculatestheeffectofthechangingambientpressureonthekineticrates.Sincethephotochemistrymodelsolvedthecontinuityequationofnumberdensities(Huetal.2012),thetotalnumberdensityofeachlayerisobtainedbysummingthenumberdensitiesofallmoleculesinthatlayer.Assuch,thetotalnumberdensity,andthusthepressure,ofeachlayerisupdatedaftereachtimestepping.Thechangingpressureaffectstheratesoftermolecularreactions,becausetheyareproportionaltothetotalnumberdensity,andalsoaffectstheratesofphotolysisviaradiativetransferintheatmosphere.Theseeffectsareself-consistentlycalculatedineachtimestep.Inparticular,animportanttermolecularreactionisthedirectcombinationbetweenCOandOintheatmosphere,CO+O+M®CO2+M,anditsrateincreaseswiththeambientpressure.ThisfeedbackloopeventuallylimitsthesizeoftheatmospherewhentheO2-COrunawayisstrong.WeadopttheeddydiffusioncoefficientderivedfromthenumberdensityprofilesoftracegasesonEarth(Massie&Hunten1981).Theeddydiffusioncoefficientischaracterizedbyahighvalueintheconvectivetroposphere,aminimumcorrespondingtothetropopause,andanincreasingvaluewithsmallernumberdensitiesinthenon-convectivestratosphere.Whentheambientpressureincreases,theeddydiffusioncoefficientasafunctionofaltitudeisunchanged.Thisensuresvigoroustransportintheatmosphereandpreservesthesensitivityoftheeddydiffusioncoefficientontheconvectivenatureoftheatmosphere.Therecouldbe

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additionaleffectsofthechangingpressureontheeddydiffusioncoefficient,andwethuscautionthattheresultsmaybedependentontheassumptionoftheeddydiffusion.Tosimulatetheeffectoflightning,weadoptaterrestrialproductionrateofNOfromlightning,6´108cm-2s-1(Schumann&Huntrieser2007),whichisalreadygreaterthanthemajorityoftheparameterspaceexploredpreviouslyforN2-CO2-H2Oatmospheres(Wongetal.2017;Harmanetal.2018).Inaddition,itisfoundthatinanatmospheremoreO2-richthanEarth’satmosphere,theNOproductionratefromlightningcanbehigher,upto~109cm-2s-1(Harmanetal.2018).Wealsoconsiderthishigherproductionrateinasensitivitystudy.

ThestellarspectrumofTRAPPIST-1hasnotbeenmeasuredinUV.Therefore,weusetheUVspectrumofGJ876obtainedbytheMUSCLESprojectastheproxy(Franceetal.2016).ThesurveyusesHubbleobservationsintheUVtoreconstructintrinsicstellarLyman-aemissions.Thevisiblespectrumisobtainedfromground-basedobservations,andtheinfraredspectrumisfromthePHOENIXstellaratmospheremodels.GJ876,anM5VstarofTeff~3100K,isoneofthecloseststarstoTRAPPIST-1(Teff~2600K)intheMUSCLESsample.AsshowninFig.1,wescalethespectrumintheUVwavelength(<300nm)bythemeasuredLyman-afluxofTRAPPIST-1(Bourrieretal.2017,afactorof0.135withrespecttoGJ876,

Fig.1:Stellarspectrausedinthisstudy.AllspectraarescaledbytheirbolometricluminositywithrespecttoTRAPPIST-1.ThespectrumofGJ876isobtainedbytheMUSCLESproject,whichusesHubbleobservationsintheUVtoreconstructtheintrinsicstellarLyman-aemissions(Franceetal.2016).ThespectrumofTRAPPIST-1atwavelengths>300nmisthesameasthescaledGJ876spectrum,butatwavelengths<300nmadifferentscalingaccordingtothemeasuredLyman-afluxisapplied.ThespectrumofADLeo,amoreactiveMstar,isfromSeguraetal.(2005).TheLyman-areconstructionwasnotperformedonthespectrumofADLeo.

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Youngbloodetal.2016),andthatinthevisiblewavelength(>300nm)bythemeasuredbolometricluminosityofTRAPPIST-1(VanGrooteletal.2018,afactorof0.0428withrespecttoGJ876,vonBraunetal.2014).Inaddition,weexploreinasensitivitystudyaspectralshapeintheUVasADLeo,anactiveM4.5Vstar.Fig.1showsthatthespectralshapeofADLeohasalargerFUV/NUVratio,buttheFUVfluxmaybeinaccurateastheLyman-areconstructionwasnotperformed.Lastbutnotleast,ourmodelensurestheredoxfluxbalanceoftheatmosphereandtheocean.Theconvergenceofthephotochemistrymodelitselfensuresthebalanceoftheredoxbudgetoftheatmosphere.However,thisdoesnotensurethattheresultsarerealisticonplanets,asthereisnoknownabioticwaytodepositreducingspeciesatthebottomoftheocean.Wethereforeenforcethebalanceoftheredoxbudgetoftheoceanbyrequiringthenettransferoftheredoxfluxbetweentheatmosphereandtheoceantobezero(Domagal-Goldmanetal.2014;Harmanetal.2015;James&Hu2018).Inpractice,thisbalanceisachievedbyincludingapseudoreturnfluxofhydrogen.Ifwefindanettransferoftheredoxfluxfromtheatmospheretotheoceaninaconvergedsolution,weincludethisnetfluxasareturnfluxofhydrogenfromtheoceantotheatmosphereandrelaunchthesimulation.Werepeattheprocessuntiltheimbalanceisnolargerthan1%oftheoutgassingredoxflux.Thisway,ourresultssatisfytheredoxbalanceforboththeatmosphereandtheocean.2.2OutgassingandDepositionWeusethevolcanicactivityrateofpresent-dayEarth,andtheper-massoutgassingratecalculatedformid-oceanridgebasalts(Gaillard&Scaillet2014)tocalculatethegasoutgassingrate.Theoutgassingrateis1.5´109cm-2s-1forCO,H2,andSO2,and1.5´108cm-2s-1forH2S(seeJames&Hu(2018)fordetails).TRAPPIST-1emayhaveatidalheatingfluxcorrespondingto1~10timesgeothermalheatflux(Lugeretal.2017;Papaloizouetal.2017).Wehaveperformedanadditionalsetofsimulationassuming10timeshighervolcanicoutgassingrateandfoundnonoticeabledifferenceintheO2orCOpartialpressure.Themodelhasafullsulfurchemistrynetwork(Huetal.2013),andwefindthattheoutgassedH2SandSO2iseitherrainedoutdirectlyoroxidizedtoH2SO4.TheH2SO4isthenrainedout.Theoutgassingrate,evenatthe10times,isnothighenoughtoproduceaH2SO4aerosollayerintheatmosphere.ThestandardmodelassumesadepositionvelocityofzeroforO2,andincludesadepositionvelocityofeitherzeroor10-8cms-1forCO.ThenonzerovalueforCOcomesfromassumingaqueousformationofformate(CO+OH-àCOOH-)astheratelimitingsteptoremoveCO(Kharechaetal.2005).Otherreactionsactingasaratelimitingstepwouldleadtoevenlowerdepositionvelocities(Harmanetal.2015),andthusthezerovalueforCOisincludedasanotherend-memberscenario.WefindthattheexactabundanceofO2versusCOintheO2-COrunawayscenariosisquitesensitivetothechoiceofthedepositionvelocityofCO(Section3.1).

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Inadditiontothestandardmodel,wehaveperformedadditionalsimulationstoevaluatetheeffectofpotentialsinksforO2intheocean.(1)Adepositionvelocityof10-8cms-1forO2wouldbepossibleforthepotentialrecombinationofO2andCOinhydrothermalflowthroughthemid-oceanridges(Harmanetal.2015).Weobservednonoticeablechangestotheresultswhenadoptingthisdepositionvelocity.(2)AsecondpotentialsinkofO2isFe2+inputintheoceanfromcrustformation.WedescribethetesttoincludethissinkinSection3.1.(3)AsalimitingscenarioweconsiderthepossibilitythatdirectrecombinationofO2andCOoccursrapidlyinthesurfaceocean.ThiswouldenabletherapiddepositionofbothO2andCO,andwealsodescribeitsimpacttotheresultinSection3.1.ForthescenarioswithsubstantialO2buildup,O3hasasubstantialmixingratioatthesurface,andthereforecanhaveasubstantialdepositionfluxontothesurface.ThiswouldmakethemodelresultssensitivetothechoiceofthedepositionvelocityofO3.SomeofthepreviousstudiesassumeO3tobetheshort-livedspeciesinphotochemicalequilibrium(Harmanetal.2015;Harmanetal.2018),thusremovingtheneedtospecifyadepositionvelocity.OnEarth,thedepositionvelocityofO3isverydifferentbetweenthelandandtheocean.Asaslightlysolublegas,O3’sdepositionvelocityovertheoceanislimitedbythemasstransferrateintheliquidphase(Broecker&Peng1982).UsingthetypicalmasstransfercoefficientandtheHenry’slawcoefficientforO3,thedepositionvelocityisapproximately10-3cms-1,andthisvalueisconsistentwiththemeasurementsoverEarth’socean(Hardacreetal.2015).ThesurfaceresistanceofO3isconsiderablysmalleroverEarth’sland,andthemeasureddepositionvelocityistypicallyontheorderof0.3cms-1.Whilethisvalueisalsovalidfordeserts(Hardacreetal.2015),thelowerresistanceismostlikelyduetotheprevalenceofbiosphereonEarth.Wethereforeadoptthevalueof10-3cms-1inthestandardmodel,andexploreavalueof0.1cms-1inasensitivitystudy.ThestandardvalueisthesameasusedinTianetal.(2014).2.3ClimateModelingandTemperature-PressureProfilesToinitializethephotochemicalmodel,weusethesubstellarhemispheremeanverticalprofilegeneratedbythe3Dclimatemodel(Wolf2017)inthisstudy.ThescenariosusedinthisstudyaresummarizedinTable1.Wefixthenumberdensityofwatervaporatthebottomoftheatmosphereaccordingtothe3Dmodel,andallowwatervaportocondenseoutasthetemperaturedropsasaltitude.Thetopoftheatmosphereisassumedtobe0.1Pa,correspondingtodifferentaltitudesbetweenthescenariosduetodifferenttemperaturesandmeanmolecularweights.ThemassandtheradiusofeachplanetarethemeasuredvaluesfromGrimmetal.(2018).Table1:Startingscenariosofthisstudyandtheirkeyclimatecharacteristicsbasedonthe3DmodelofWolf(2017).

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IceFraction

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TRAPPIST-1e 1bar None 227 86% 0.0018 88TRAPPIST-1e 1bar 0.0004

bar241 80% 0.0037 84

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254 73% 0.0056 84

TRAPPIST-1e 1bar 0.1bar 274 57% 0.0138 83TRAPPIST-1e 1bar 0.2bar 285 18% 0.0213 82TRAPPIST-1e 1bar 0.4bar 303 0% 0.0407 71TRAPPIST-1e 1bar 1bar 333 0% 0.1001 73TRAPPIST-1f None 1bar 227 100% 0.0007 56TRAPPIST-1f None 2bar 289 2% 0.0067 59TRAPPIST-1f None 5bar 335 0% 0.0444 66WhentheO2-COrunawayoccurs,O2andCOcontributemeaningfullytothetotalatmosphericpressure.Newlyforthiswork,wehaveconductedseveraladditional3Dclimatemodelsimulationstotestofclimateeffectsofthisincreasedatmosphericpressure.TheradiativeeffectsofO2andCOareprimarilyfeltindirectlythroughtheircontributiontothetotalatmosphericpressure,andsubsequentpressurebroadeningofCO2absorptionfeatures,whichcanhaveasignificantwarmingeffectonclimate(Goldblattetal.2009).Aspresentlyconfiguredour3DmodelhandlesonlyN2,H2O,andCO2,andthereforewehavesubstitutedN2asthebroadeninggasinthesesimulations.Whilethissubstitutioninthe3Dmodelintroducessomeuncertainty,still,wecangainausefulestimateoftheclimateconsequencesofaddingsignificantamountsofaradiativelyinactivebroadeninggas.WediscusstheclimatefeedbackinSection4.2.3.Results3.1TheO2-CORunawayThesteady-stateabundanceofO2jumpsby7–8ordersofmagnitudeto0.2–2baronTRAPPIST-1ewhentheCO2abundanceincreasesfrom0.01to0.1bar(Fig.2,thicklines).TheabundanceofCOalsoincreasesby4–5ordersofmagnitudeto>0.05bar.ThespreadoftheresultantabundancesofO2andCOiscausedbytheuncertaintiesintheirdepositionvelocities.Aswestartthecalculationfrom1barN2and0.1~1barCO2,thesteady-stateatmospherehasO2andCOasmaincomponents,aswellasasubstantialabundanceofO3.Wethuscallthisphenomenon“theO2-COrunaway.”TheabundanceofO2continuestograduallyincreasewithmoreCO2,buttherunawayispartiallystabilizedbythefactthatahigheratmosphericpressuremakesthedirectrecombinationreactionbetweenCOandOfaster.ForTRAPPIST-1e,theconditionfortheO2runawaycoincideswiththeconditionforaglobalocean,

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indicatingthatahabitableenvironmentontheplanetnecessarilyentailsanO2-andCO-richatmosphere.ForTRAPPIST-1fandg,moreCO2isrequired,andthusthesameresultappliesqualitatively.

Figs.3and4andTable2showtheverticalprofilesofkeymoleculesandtheredoxfluxesofthescenariosbeforeandaftertheO2-COrunaway.TheredoxbalancesoftheatmosphereandtheoceanarewellbalancedforthemodelsbeforeandaftertheO2-COrunaway,andtheremainingimbalancesareduetosubtledifferenceintheH2mixingratioonthegroundandthatatthehomopause.Thewatervaporprofilecalculatedbythe1Dphotochemistrymodelagreeswellwiththemeanwatervaporprofilecalculatedbythe3Dclimatemodel(seeSection4.2).AftertheO2-COrunaway,O2isessentiallywell-mixedintheatmosphere,andthemixingratioofO3peaksat~1mbar(Fig.3).AftertheO2-COrunaway,mostoftheHOx(OHandHO2)speciescombinetoformthe“reservoir”moleculeH2O2,andtheabundanceofthefreeradicalOHisextremelylow(Fig.4).ThisexplainstheinabilityoftheOH-HO2catalyticcycletorecombineCOandO2.Fig.4alsoshowsthataftertheO2-CO

Fig.2:Modeledicefractionandcolumn-integratedabundancesofO2,CO,andO3versustheabundanceofCO2.ThicklinesarethestandardmodelsthatincludeknownsurfacesinksofO2andCO,andtheshadedareasbetweenthethicklinesdenotethespreadoftheresultsduetothedepositionvelocityofCOrangingfromzeroto10-8cms-1.ThenonzerodepositionvelocityofCOleadstohigherabundanceofO2andlowerabundanceofCOthanthezerodepositionvelocity.ThinlinesarethemodelsthatadditionallyassumeadirectrecombinationreactionofO2andCOintheocean.O2andCObecomemaincomponentsoftheatmospherewhenpCO2is≥0.1bar;forTRAPPIST-1ethisjumpisroughlycoincidentwiththerequirementofagloballiquidwaterocean.

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runaway,mostofthereactivenitrogenspeciescombinetoformHO2NO2abovethepressurelevelof0.1bar,thereservoirspeciesfornitrogen.WewilldiscussthebehaviorsofnitrogenphotochemistryinSection3.2.

OnemightaskwhethertheO2-COrunawaydependsontheassumptionsoftheboundaryconditions,particularlythelackofrapidsurfacesinksforO2andCO.WehaveexploredtheimpactsofgeochemicalsinksofO2andCOontheiratmosphericabundances,andtheO2-COrunaway.Thegeochemicalsinksareexpressedinthephotochemistrymodelasthevaluesforthedepositionvelocity.Conceptually,the

Fig.3:MixingratioprofilesofbackgroundgasesandoxygenspecieswithouttheO2runaway(solidlines,1barN2with0.01barCO2)andwiththeO2-COrunaway(dashedlines,1barN2with0.1barCO2).ThedepositionvelocityiszeroforO2andis10-8cms-1forCO.AftertheO2-COrunaway,O2becomesthedominantgasoftheatmosphere,andasubstantialO3layerforms.

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transferfluxfromtheatmospheretothesurfaceis𝜙 = 𝑣dep_max +𝑛- −/0123 = 𝑣dep𝑛-,

where𝑣dep_maxand𝑣depisthemaximumandeffectivedepositionvelocitiesofthegas,𝑛-isthegas’snumberdensityatthesurface,𝑀-isthemolalityinthesurfaceocean,𝛼istheHenry’sLawcoefficient,and𝐶isaunitconversionconstant.Theeffectivedepositionvelocitythusdependsonhowquicklytheoceancanprocessthedepositedmoleculeanddrive𝑀-awayfromtheequilibriumvalue.

AmajorpotentialsinkforO2istheFe2+inputtotheoceanfromcrustalformation.TheO2canoxidizeFe2+intheoceanandcauseBandedIronFormation(BIF,6FeO+O2®2Fe3O4).OnEarth,theestimatedrateofironoutputduringtheHamersleyBIFsinthelateArcheanis~3´1012molyr-1,or1.1´1010cm-2s-1(Holland2006).AssumingthisentireoutputofironisoxidizedtoFe3O4intheoceanbyO2,ithastwo

Fig.4:MixingratioprofilesofreactivehydrogenandnitrogenspecieswithouttheO2runaway(solidlines,1barN2with0.01barCO2)andwiththeO2-COrunaway(dashedlines,1barN2with0.1barCO2).ThedepositionvelocityiszeroforO2andis10-8cms-1forCO.

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effects:(1)thiswouldcorrespondtoanadditional8´109cm-2s-1equivalentHinfluxtotheatmosphere,doublingtheH2mixingratioaccordingtotheredoxbalance;(2)thiswouldbeasinkof𝜙max=2´109cm-2s-1forO2.Howtoimplementthislimitingsinkinthephotochemistrymodel?ForO2undertypicalconditions,themaximumdepositionvelocity𝑣dep_max=1.4´10-4cms-1.This𝑣dep_maxisdeterminedbythetwo-filmmodelofmasstransferbetweentheatmosphereandtheocean(Broecker&Peng1982)andisrelatedtothepistonvelocityandissensitivetothesolubilityofthegas,thewindspeed,andthetemperature(Domagal-Goldmanetal.2014;Harmanetal.2015).Therefore,whenthesurfacenumberdensity𝑛-issmall,therateofdepositionissmallerthanthelimitingsinkduetoBIF,and𝑣depshouldbecloseto𝑣dep_max.When𝑛-islarge,thedepositionfluxislimitedby𝜙max.WethereforeimplementthelowerboundaryconditionforO2duetoBIFasfollows:if𝑣dep_max𝑛- < 𝜙max,ironoxidationeffectivelyremovesO2intheocean,andthen𝑣dep = 𝑣dep_max;if𝑣dep_max𝑛- > 𝜙max,thedepositionvelocityislimitedbytherateofBIF,or𝑣dep = 𝜙max/𝑛-.Afterimplementingthisboundaryconditionandperforminganothersetofsimulations,wefindthattheformerconditionismetbeforetheO2-COrunaway,andthelatterconditionismetaftertheO2-COrunaway.InthecasesaftertheO2-COrunaway,theinclusionofBIFleadstoadecreaseoftheO2columnabundanceby<10%.WethereforeconcludethatBIFdoesnotsubstantiallyimpacttheonsetoftheO2-COrunaway.WenotethattherateofironproductionduringtheearlyArchean(andpresumablyonaterrestrialexoplanet)maybe20-foldhigherthantheHamersleyBIFs(Kasting2013).Hereweconsideritsimpact.The0.1-barCO2case(i.e.,theonsetoftheO2-COrunaway)hasanO2numberdensityof5.5´1019cm-3atthebottom,thefulldepositionofwhichwouldhaveafluxof7.7´1016cm-2s-1,about4´107largerthanthefluxintheHolland(2006)estimate.Thereforea20-foldincrease,evenifitoccurs,wouldnotmateriallychangeourresults.Additionally,weconsideralimitingscenariowithdirectrecombinationofO2andCOoccurringrapidlyinthesurfaceocean.InthiscasetheeffectivedepositionvelocitiesofO2andCOapproachtheir𝑣dep_max,whicharemainlycontrolledbysolubilitiesintheocean(1.2´10-4cms-1forCOand1.4´10-4cms-1forO2,Domagal-Goldmanetal.2014).TheO2-COrunawayispreventedinthiscase,andtheirabundancesmaxoutat10-3–10-4bar(Fig.1,thinlines).ThisreactionisperformedbyaerobicCO-oxidizingbacteriaonEarth(King&Weber2007),andisthusconceivableonanexoplanetwithliquidwaterandabundantO2andCOonthesurface.Table2:RedoxfluxesofrepresentativeatmosphericmodelsforTRAPPIST-1e(1).Model 𝒗dep(CO)=1E-8cms-

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𝒗dep(O2)=0

𝒗dep(CO)=1.2E-4cms-1𝒗dep(O2)=1.4E-4cms-1

𝒗dep(CO)=0𝒗dep(O2)=0

CO2 0.01bar 0.1bar 0.01bar 0.1bar 0.01bar 0.1bar

12

EscapeH -3.1E+8 -2.9E+9 -3.1E+8 -7.1E+8 -3.1E+8 -1.5E+9H2 -5.4E+9 -2.8E+9 -5.4E+9 -5.0E+9 -5.4E+9 -4.2E+9Total -5.7E+9 -5.7E+9 -5.7E+9 -5.7E+9 -5.7E+9 -5.7E+9OutgassingH2 3.0E+9 3.0E+9 3.0E+9 3.0E+9 3.0E+9 3.0E+9CO 3.0E+9 3.0E+9 3.0E+9 3.0E+9 3.0E+9 3.0E+9H2S 9.0E+8 9.0E+8 9.0E+8 9.0E+8 9.0E+8 9.0E+8NO(2) -1.2E+9 -1.2E+9 -1.2E+9 -1.2E+9 -1.2E+9 -1.2E+9Total 5.7E+9 5.7E+9 5.7E+9 5.7E+9 5.7E+9 5.7E+9DryandWetDepositionO2 7.9E+11 O3 3.4E+9 2.7E+8 3.4E+8HO2 2.9E+5 1.5E+8 1.4E+7H2O2 5.8E+7 1.1E+10 4.7E+9CO -2.0E+6 -1.1E+10 -9.1E+9 -8.1E+11 CH2O -2.8E+6 -7.8E+5 -2.8E+6 CHO2 -2.4E+6 -2.4E+6 H2S -1.1E+8 -9.0E+8 -1.1E+8 -3.7E+8 -1.1E+8 -8.5E+8H2SO4 1.0E+7 1.7E+7 9.9E+6 1.0E+7 NO 1.1E+8 1.6E+8 1.1E+8 NO2 1.7E+6 4.0E+8 2.7E+6 1.9E+7 1.7E+6 1.8E+8NO3 1.3E+9 5.4E+6 2.4E+7N2O5 1.2E+9 2.4E+5 1.3E+7HNO 5.1E+8 4.5E+8 5.1E+8 HNO2 2.6E+7 1.3E+8 5.8E+7 1.8E+9 2.6E+7 1.6E+9HNO3 3.6E+6 1.1E+5 9.7E+6 1.4E+7 3.6E+6 5.0E+4HNO4 2.2E+6 1.7E+7 3.0E+7Total 5.4E+8 -5.0E+9 -8.5E+9 -4.1E+9 5.5E+8 6.0E+9ReturnH2FluxH2 -5.5E+8 5.0E+09 8.5E+9 4.1E+9 -5.5E+8 -6.1E+9OverallFluxBalance

1.0E+4 1.1E+6 1.1E+7 -7.9E+6 8.6E+5 -4.5E+6(1)TheredoxfluxisexpressedastheequivalentofunitHinfluxtotheatmosphere.H2O,CO2,N2,andSO2aredefinedasredoxneutral.Forexample,depositionofaCOmoleculewouldcreatearedoxfluxof-2,anddepositionofaO3moleculewouldcreatearedoxfluxof+6.

13

(2)TheNOfluxisincludedtosimulatelightningproductionofNO.

InadditiontothesinkofO2,thephotochemistrymodeltakesotherinputparameterssuchastheNOproductionratefromlightning,thestellarspectrum,andthedepositionvelocityofO3.OnemightaskwhethertheseparameterssignificantlybearsupontheO2-COrunaway.WehavetestedthesensitivityofthemodelontheseparametersusingTRAPPSIT-1easthetestcase(Fig.5).First,wefindthatincludingaterrestrialrateofNOproductionbylightningreducestheresultingO2partialpressurebyonlyafactorof~2insomecases,andtheexactvalueofthelightningproductionrateneartheterrestrialratehaslittleimpact(Fig.5,Panela).Thislackofsensitivityhastodothenitrogenphotochemistry,whichwillbediscussedinSection3.2.Second,wefindthattheonsetoftheO2-COrunawayismildlysensitivetothestellarspectralshape.ThereislittledifferencebetweenthestandardmodelandthemodelusingtheGJ876’sspectrum.WhenusingtheADLeo’sspectrum,however,theO2-COrunawayrequiresahigherpartialpressureofCO2,~0.2bar(Fig.5,Panelb).ThissensitivityreaffirmsthepointthattheO2-COrunawayisdrivenbythehighFUV/NUVratiooftheirradiationoflateMdwarfs.TheADLeo’sspectrumhasalowerFUV/NUVratiocomparedtotheGJ876’sspectrumortheassumedTRAPPIST-1spectrum,andthereforeitislessabletodrivetheO2-COrunaway.Third,changingtheO3depositionvelocityfromthestandardvalue(10-3cms-1)toahighervalue(10-1cms-1)onlyhassomeimpacttothecaseof0.1barCO2,andoverallitdoesnotaffecttheonsetoftheO2-COrunaway.Insum,theO2-COrunawayappearstoberobustagainstreasonableuncertaintiesinthelightningrate,stellarspectrum,anddepositionvelocities.3.2NitrogenPhotochemistryonMdwarfs’PlanetsOurphotochemistrymodelsshowthatnitrogenchemistryintheatmosphereinitiatedbylightningcannotpreventtheO2-COrunaway.Lightningmainlyproduces

Fig.5:SensitivityoftheonsetoftheO2-COrunawayonthelightningrate,thestellarspectralshape,andthedepositionvelocityofO3.ThesensitivitystudiesareperformedonthemodelsofTRAPPSIT-1e,andtheresultsfromvariedparametersareshownwithrespectivelinestyles.Thesolidlinesarefromthestandardmodel.TheonsetoftheO2-COrunawayisnotsensitivetothelightningrateorthedepositionvelocityofO3,andismildlysensitivetothespectralshape.

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(a) NO production rate by lightningdashed: 0dotted: 109 cm-2 s-1

(b) Stellar spectral shapedashed: GJ 876dotted: AD Leo

(c) O3 deposition velocitydashed: 0.1 cm s-1

14

NOinanN2-CO2-O2atmosphere(Wongetal.2017;Harmanetal.2018;Rimmer&Helling2016).ReactivenitrogenspeciesfacilitatecyclesofOHandHO2inEarth’sstratosphereandhavebeensuggestedtoreducetheabundanceofaccumulatedO2inCO2-richplanetaryatmospheresbymanyordersofmagnitude(Harmanetal.2018).AmaincatalyticcycleenabledbyreactivenitrogenspeciesisNO+HO2®NO2+OH,NO2+hv®NO+O,whichisfollowedbyCO+OH®CO2+H.Ourmodelindicatesthattheeffectoflightning,however,islimitedtowithinafactorof~2.ThisisbecausemostofthereactivespeciesislockedinthereservoirmoleculesHO2NO2andN2O5(Fig.4),andthuscannotparticipateinthecatalyticcycles.ThesereservoirmoleculesarephotodissociatedbyNUVirradiationinEarth’sstratosphere,butthisphotodissociationisseverelylimitedonanMdwarf’splanet.HO2NO2alsodissociatesthermallyinthetroposphere,butthedissociationinthestratosphereappearstobemoreimportantforenablingthecatalyticcycles.OurmodelincludesphotodissociationofHO2NO2viaovertuneandcombinationbandsinthenearinfrared(Roehletal.2002)whereanMdwarf’semissionisstrong,butfindsthatthetotalphotodissociationrateatthetopoftheatmosphereisstillmorethananorderofmagnitudelessthanthataroundaSun-likestar.Additionally,thereservoirmoleculesareefficientlyrainedoutfromtheatmosphere.IfwedonotincludeHO2NO2orN2O5inthemodel,wewouldreproducetheorders-of-magnitudeeffectbylightning.Thedetailofnitrogenphotochemistryisdescribedinthefollowing.Harmanetal.(2018)foundthatthesteady-stateabundanceofO2wouldbereducedbymanyordersofmagnitudebyincludinglightningproductionofNO.Harmanetal.(2018)howeverdidnothaveHO2NO2orN2O5intheirchemicalnetwork.Hereweperformasetofmodelswith1barN2and0.05barCO2,thesameasHarmanetal.(2018),withonemodelusingourchemicalnetworkandtheotherwithoutHO2NO2orN2O5.TheresultsareshownincomparisoninFig.6.Tobecomparable,themodelshereareforahypothetical1-Earth-radiusand1-Earth-massplanetinthehabitablezoneofGJ876.Theboundaryconditionsarethesameasthestandardmodelspreviouslydescribed.BecausetheresultsareinsensitivetothespectralshapechangingfromtheassumedTRAPPIST-1toGJ876,themodelspresentedinFig.6canalsobeinterpretedinthecontextoftheTRAPPIST-1models(Figs.2-5)asacaseinthemiddleoftheO2-COrunaway.IfN2O5andHO2NO2(sometimescalledHNO4)arenotincludedinthechemicalnetwork,themixingratioofO2wouldindeedbereducedbymanyordersofmagnitude(Fig.6,dashedlines).TheO3wouldbealmostcompletelyremoved.ThisresultisconsistentwithHarmanetal.(2018)intermsoftheeffectoftheNOandNO2cycleandingeneralwiththebasicunderstandingofterrestrialatmosphericchemistry,thattheNOandNO2cyclehelpreduceO3.NotethattheamountofO2nearthesurfaceisstillmuchhigherthanthatinHarmanetal.(2018),whichmaybe

15

duetodifferentchoicesofspeciesinphotochemicalequilibrium,anddifferentboundaryconditionsassumed(Section4.1).WhenN2O5andHO2NO2areincludedinthechemicalnetwork,theresultsaredramaticallydifferent.Weseethat(1)mostofthenitrogenotherthanN2orN2OarelockedintheformofHO2NO2inthestratosphere,andtheN2O5reservoirisalsosignificant(Fig.6,solidlines,alsoinFig.4,dashedlines);(2)summingthereactivenitrogenspecies(nitrogenspeciesotherthanN2orN2O),themixingratioissmallerthanthecasewithoutN2O5orHO2NO2;and(3)themixingratioofO2remainsconstantthroughouttheatmosphereratherthanbeingreducedbymanyordersofmagnitude.

Fig.6:Atmosphericmodelswith1barN2and0.05barCO2,includingaNOsourceof6´108moleculecm-2s-1atthesurfacemimickingtheeffectoflightning(solidlines),andthesameNOsourcebutwithoutN2O5orHO2NO2inthechemicalnetwork(dashedlines).ThesemodelsusethestellarspectrumofGJ876,correspondingtoHarmanetal.2018).Theeffectoflightningislimitedwhenthereservoirmoleculesareincludedinthechemicalnetwork.

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16

WhydoesincludingN2O5andHO2NO2inthechemicalnetworkhavesuchalargeeffect?Inthestratosphere,HO2NO2isformedbythefollowingcombinationreactionHO2+NO2+MàHO2NO2+ManddestroyedbyphotolysisHO2NO2+hvàHO2+NO2HO2NO2+hvàHO+NO3andreactionwithOHHO2NO2+OHàH2O+NO2+O2Similarly,forN2O5,itsformationisbycombinationofNO2andNO3,anditsdepletionisbyphotolysis.HO2NO2andN2O5areimportantspeciesinEarth’satmospherebuttheydonotovertakeNOorNO2asthemainreactivenitrogenspecies.Undertheconditionsthatcorrespondtopresent-dayEarth’smid-latitude,ourmodelpredictedthemixingratioprofilesofNO,NO2,N2O5,HNO3,andHO2NO2inthemiddleatmospherethatarefullyconsistentwithmeasurementsfromballoons(Senetal.1998;Hu2013).OnaterrestrialplanetofMdwarfstars,however,theUVirradiationfluxthatdrivesthephotolysisofHO2NO2andN2O5ismorethanoneorderofmagnitudelower(Table3),andthereforethesespeciescanaccumulatetoahigherabundance,overtakingNOorNO2asthemainreactivenitrogenreservoir.ThisiswhatweseeinthesolidlinesofFig.6.WehaveincludedthephotodissociationofHO2NO2viaovertoneandcombinationbandsinthenearinfrared(Roehletal.2002)inourcalculations,becausethenear-infraredirradiationonaplanetinthehabitablezoneofMdwarfstarsiscomparabletothatofSun-likestars.Table3indicatesthatwhilethenear-infrareddissociationcontributesdominantlytothetotaldissociationrate,andtotaldissociationrateisstillmorethanoneorderofmagnitudelessthanthevalueforSun-likestars.Table3:Top-of-atmospherephotolysisrates(Jvalues)ofHO2NO2andN2O5onEarthandonTRAPPIST-1e.ThecontributionfromovertoneandcombinationbandsofHO2NO2inthenearinfraredtotheJvaluesforTRAPPIST-1eisalsoshown.Reaction JEarth(s-1) JTRAPPIST-1e(s-1) Inwhichcausedbynear

infraredirradiationHO2NO2+hvàHO2+NO2

1.83´10-4 9.66´10-6 6.28´10-6

HO2NO2+hvàHO+NO3

4.89´10-5 8.90´10-7 0

N2O5+hvàNO3+NO2

4.82´10-5 6.56´10-7 0

N2O5+hvàNO3+NO+O

1.45´10-4 2.52´10-6 0

Additionally,morenitrogeninHO2NO2andN2O5leadstomorerapidremovalofreactivenitrogenfromtheatmosphere.Withoutthesespecies,theonlyeffectiveremovalpathwayofreactivenitrogenisthedepositionandrainoutofHNO,HNO2,

17

andHNO3.ItiswellknownthatHO2NO2andN2O5arehighlysolubleorreactiveinwaterandrainoutveryefficiently.Also,heterogeneousreactionsofN2O5onandwithinatmosphericaerosolsorclouddropletsfurtherfacilitaterainout(Wangetal.2017).Therefore,formationofthesespeciesleadstomorerapidremovalandreductionofthetotalreactivenitrogenmixingratio,asweseeinFig.6.Finally,wepointoutthattheatmospherehasasubstantialamount(1ppb)ofN2Oproducedabiotically.TheproductionpathisN2+O(1D)+M®N2O+MThekineticrateofthisreactionismeasuredrecently(Estupinánetal.2002)andthisreactionisnottypicallyincludedinphotochemistrymodelsofplanetaryatmospheres.AgainbecauseofthelowNUVirradiation,thisabioticN2Ocanaccumulateto1ppbintheatmospheresofTRAPPIST-1planets.ThelongerlifetimeofN2OinplanetaryatmospheresaroundMstarshasbeensuggestedpreviously(Seguraetal.2005).Notably,thisN2OisthesourceofNOandNO2intheupperatmosphere(Fig.6),viaN2O+O(1D)®NO+NOThissourceofNOexistswithoutanylightningevents.ItisthereforenecessarytoalsoincludeN2OinthephotochemicalmodelofrockyandpotentiallyhabitableplanetsaroundMdwarfstars.4.Discussion4.1ComparisonwithPriorStudiesTofurtherconfirmthattheO2andCObuildupwefoundisnotamodelartifact,wecomparewithtwopriorstudiesthatstudiedN2-CO2atmospheresofterrestrialplanetsinthehabitablezoneofMdwarfstars(Tianetal.2014;Harmanetal.2015).Thetwostudiesbuiltmodelsforahypothetical1-Earth-radiusand1-Earth-massplanet,having1barN2atmospherewith0.05barCO2.NotethatthelevelofCO2theyassumedislessthanthelevelofCO2requiredforglobalhabitabilityonTRAPPIST-1e.BothstudiesusedthehabitablezoneofGJ876astherepresentativecase,andappliedthesamemethodtomaintaintheredoxbalanceofboththeatmosphereandtheocean(i.e.,thepseudoH2flux).Forcomparison,wesetupamodelofa1-Earth-radiusand1-Earth-massplanet,having1barN2atmospherewith0.05barCO2,atthe0.21-AUorbitaldistancefromtheMstarGJ876.Wesetupthesamepressure-temperatureprofileasTianetal.(2014),i.e.,thesurfacetemperatureof288Kandthestratospheretemperatureof180K.Weusethesameprofileoftheeddydiffusioncoefficientfromterrestrialmeasurements,adoptedbyTianetal.(2014).Whilethesefactorsarenotexplicitlystated,wesuspectthattheyaretreatedthesamewayasinHarmanetal.(2015).Weusethesameemissionratesastheseworks:theemissionrateofH2is1010cm-2s-1,andthatofothergasesiszero.NotethatourmodelshaveamoreexpandedchemicalnetworkincludingHO2NO2andN2O5,andthechoicesofspeciesinphotochemicalequilibriumaretypicallydifferentbetweenphotochemicalmodels.

18

ThemaindifferencebetweenTianetal.(2014)andHarmanetal.(2015)isinthedepositionvelocities.Weadoptthedepositionvelocitiesthateachworkused.InTianetal.(2014),thedepositionvelocitiesofCOandO2are10-6cms-1,andO3asalong-livedspecieshasadepositionvelocityof10-3cms-1.Fig.7showsourresultsinthiscase.TheresultsaresufficientlyconsistentwithTianetal.(2014)intermsofthemixingratiosofCOandO2,aswellasthepeakmixingratioofO3.

Harmanetal.(2015)assumedadepositionvelocityof10-8cms-1forCO,andzeroforO2,andassumedO3tobeashort-livedspecies.TheamountofO2inourresultisconsistentwithHarmanetal.(2015),howevertheamountofCOinourresultisafactorofafewgreater(Fig.8).ThedifferencemaybeduetothefactthatthemodelofHarmanetal.(2015)had15speciesassumedtobeinphotochemicalequilibrium,whileourmodeldoesnothaveany.NotethattheO2columnabundanceinbothcases,assuming0.05barCO2,fallsbetweenthevaluefor0.01barCO2and0.1barCO2inourTRAPPIST-1emodels(Fig.2).Thiscomparisonshowsthatthe0.05barCO2casethatthepreviousstudieshaveassumedhappenstobeinthetransitionintotheO2-COrunaway.AsmallincreaseintheCO2partialpressurewillleadtoalargeincreaseintheaccumulationofphotochemicalO2.ComparingFig.7andFig.8,wefindthatassumingO3tobeoneofthespeciesinphotochemicalequilibrium,ornot,introducessubstantialvariationtothemodelresults.O3mayhavesubstantialabundanceatthesurface,anditsdepositionmaycontributetotheoverallredoxbalanceoftheatmosphere(Table2).4.2ClimateFeedbackoftheO2-CORunaway

Fig.7:ResultsusingthesameparametersasTianetal.(2014).

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AsphotochemicallyproducedO2andCObecomemainconstituentsintheatmosphere,theycontributemeaningfullytothetotalpressure.O2hasnostronginfraredabsorptionbands,andCOabsorptionoccursonlyattheshouldersoftheplanetarythermalemissionspectra.TheirprimarycontributiontoradiationisthroughpressurebroadeningofCO2absorptionlinesandRayleighscattering,withthepressurebroadeningeffectbeingthedominantofthetwo(Goldblattetal.2009).Severaladditional3DclimatemodelsimulationsareconductednewlyforthisworktotesttheeffectsofincreasedbroadeninggaspartialpressuresontheclimateofTRAPPIST-1e,summarizedinTable4.3DsimulationsareconductedforTRAPPIST-1ewith0.1barand0.2barCO2,andwithbroadeninggaspartialpressuresof1.5,2,and4barsrespectively.Table4:Newclimatescenariosmodeledforthisstudyandtheirkeyclimatecharacteristics.Planet N2 CO2 Tsurf

globe(K)IceFraction

TRAPPIST-1e 1bar 0.1bar 274 57%TRAPPIST-1e 1.5bar 0.1bar 286 12%TRAPPIST-1e 2bar 0.1bar 291 0.3%TRAPPIST-1e 4bar 0.1bar 320 0%TRAPPIST-1e 1bar 0.2bar 285 18%TRAPPIST-1e 1.5bar 0.2bar 297 0%TRAPPIST-1e 2bar 0.2bar 308 0%TRAPPIST-1e 4bar 0.2bar 332 0%

Fig.8:ResultsusingthesameparametersasHarmanetal.(2015).

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Theresultsofthe3DclimatemodelswithincreasedatmosphericpressureareshowninFig.9.Usinga3Dclimatemodel,wecanself-consistentlyincorporatetheeffectsofpressurebroadeningandRayleighscattering,alongwithresultantclimatologicalfeedbacks.Increasingthebackgroundpressurebyupto4foldsyieldsincreasestotheglobalmeansurfacetemperaturebyafewtensofK;eventhoughsignificant,thisdoesnotchangethegeneralassessmentregardinghabitabilityforatmosphereswith≤0.2barCO2.However,forhigherbackgroundpressuresproducedbylargerCO2amounts,thecombinedeffectsmaycauseTRAPPIST-1ebecomingtoohottobereasonablyhabitable.Inaddition,O3isagreenhousegaswithhaveanabsorptionbandinthemiddleoftheplanetarythermalemissionspectra(9.6µm).Atexpectedconcentrations,however,itscontributiontothegreenhouseeffectisdwarfedbythatofCO2andH2O(Kiehl&Trenberth1997),andthuswouldnotsignificantlyraisethesurfacetemperature.GiventheO2runawayandtheclimatemodels,weconcludethatforTRAPPIST-1etoremaingloballyhabitableitmusthavepCO2inasomewhatnarrowrangebetween0.01and0.2bar.OnemightwonderifsubstitutingO2/COwithN2intheclimatemodelisreasonable.O2/COandN2havemeanmolecularweightswithin~15%,specificheatswithin~10%,andneitherhavestrongabsorptionbandsintheplanetarythermalemissionspectra.BothO2andN2arediatomicmoleculesandthusdonothavevibrationalorrotationalabsorptionmodes,andthusarenotconventionalgreenhousegases.TheabsorptionfeatureofCOat~100µmisswampedbyH2Orotational-vibrationabsorptionbands.ThefeatureofCOat~5µmmayshowthroughbothCO2andH2O,butthisspectralregionislocatedwhereboththermalemittedandincidentstellarradiationarerelativelysmall.Inaddition,insufficientlydenseatmosphereseachmolecularpairfeaturescollisioninducedabsorption(CIA)intheinfraredwhichcanaffectclimate.But,inmoistatmospheres,asmodeledhere,O2-O2CIAat6.4µmisswampedbytheH2Ofeatureinthissamespectralregion(Hopfneretal.2012),andN2-N2CIA,whichaffectswavelengthslongwardof~30µm,isswampedbyH2Orotational-vibrationabsorptionbands(Wordsworth&Pierrehumbert2013).Intotal,theradiativeeffectsofO2,CO,andN2areprimarilyfeltindirectlythroughtheircontributiontothetotalatmosphericpressure,andsubsequentpressurebroadeningofCO2absorptionfeatures,whichcanhaveasignificantwarmingeffect

Fig.9:GlobalmeansurfacetemperatureofTRAPPIST-1eversustheabundanceofCO2(x-axis)andthebroadeninggasamount(legend).Thetemperatureiscalculatedin3Dclimatemodelsimulations,withtheH2Oabundanceandthecloudfeedbackself-consistentlymodeled(Wolf2017).WeconsiderincreasestothetotalpressurebyincreasingtheN2backgroundamount,ratherincludingO2orCOexplicitlyintheclimatemodel.Increasingthebackgroundpressureresultsinmeaningfulincreasesinthemeansurfacetemperature.

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onclimate(Goldblattetal.2009).Collisionsbetweenmoleculesshiftsabsorptionfromlinecenterstowardthewings,withtheendresultbeingmoretotalradiationbeingabsorbed.IncreasingthetotalpressureoftheatmospherealsoincreasesRayleighscattering,whichwouldacttocooltheplanet,counteractingtheabovediscussedeffectofpressurebroadening.However,theincreaseingreenhouseforcingfromenhancedpressurebroadeningdominatesovertheincreaseinreflectionduetoenhancedRayleighscatterings(Goldblattetal.2009).NotethattheRayleighscatteringcross-sectionsforO2,CO,andN2arealsoquiteclose(Thalmanetal.2014).COhasanabsorptionbandat~2.3µm,andthisbandcontributestonear-infraredabsorptionofstellarradiationfromTRAPPIST-1.However,thenear-infraredabsorptionofCO2andH2Owillbemoresignificant.Thus,substitutingN2forO2andCOinourmodelshouldnotgiverisetoalargeerrorinthermalorstellarforcings.

OuratmosphericchemistrymodelalsopredictsthattheO2-richatmospheresonTRAPPIST-1planetsshouldhaveasignificantO3layer(Fig.3),andthisisconsistentwithpreviousmodelsofO2-richplanetsfoundaroundM-dwarfstars(Seguraetal.2005;Meadowsetal.2018).ThatO3isalsoabsentfromour3Dclimatemodel.However,notethatbecauseM-dwarfstarsemitseveralordersofmagnitudelessradiationinthenear-UVregion(l≥200nm),astratosphericO3layerwouldhavelittleradiationtoabsorb,andwouldnotformastratosphericinversion.Indeed,simulationsofO2-richplanetsaroundM-dwarfstarsindicatethatthestratospherictemperatureswouldremaincold(Seguraetal.2005;Meadowsetal.2018).WhileO3isagreenhousegas,withhaveanabsorptionbandat9.6µm,atexpectedconcentrationsitscontributiontothegreenhouseeffectisdwarfedbythatofCO2andH2O(Kiehl&Trenberth1997),andthusisnotasignificantdriverofclimatechange.Basedontheabovediscussions,wefeelthatsubstitutingN2forO2andCO

Fig.10:Globalmeantemperatureandwaterprofilesof3DclimatemodelsassumingvariedbackgroundN2partialpressureforTRAPPIST-1e.Thewatervaporprofilesarelargelyconsistentwiththeprofilespredictedbyour1Dphotochemistrymodel(Fig.3).Thestratosphereremainscoldandwater-depletedwhenmorethan1barofN2isassumed.

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a b c

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willnotradicallyaltertheresultantclimatesinour3Dmodel,andprovidesusefulestimatesforclimatechangeforTRAPPIST-1eunderthickeratmospheres.Finally,webrieflydiscuss“thefeedbackofthefeedback”:theeffectofthechangedtemperatureprofileaftertheO2-COrunawayontotheatmosphericphotochemistryitself.Fig.10showsthemeanpressure-temperatureandwaterprofilesfromthe3DclimatemodelsassumingvariedpartialpressureofN2.Thesimilarityoftheseprofilesisstriking:thestratosphere’stemperatureandwatervaporabundancestaylow,andonlythelowestlayersoftheatmosphereexperiencehighertemperaturesaftertheO2-COrunaway.Assuch,eventhoughnewphotochemicalsimulationswerenotperformedwiththenewclimatestudies,thechangeinthetemperatureprofileanditsimpactontheatmosphericchemistryislikelylimitedtothebottomlayersoftheatmosphere,andthusunlikelytosignificantlyaffecttheO2-COrunaway.4.3GeologicContextfortheO2-CORunawaySilicateweathering,ifitoccursonarockyplanet,helpskeepingpCO2inadesirablerangethatisconsistentwithaliquidwaterocean(Walkeretal.1981).TheO2-COrunaway,togetherwiththeenhancedwarmingduetopressurebroadening,increasesthesensitivityofthesurfacetemperatureonpCO2.ThisincreasedsensitivitywouldallowsilicateweatheringtomaintainpCO2intherequirednarrowrange.AnotherquestioniswhethertheO2-COrunawaystateissustainable.OurphotochemistrymodelsassumefixedcolumnabundancesofCO2,andthereforeimplyappropriateratesofvolcanicoutgassingthatmaintainthefixedabundances.Fig.11showstheimpliedCO2outgassingrateforvariedassumptionsofthedepositionvelocities.Weseethatinthestandardmodels,aswellasthemodelsincludingtheBandedIronFormation(BIF)asthesinkforO2,theimpliedCO2outgassingrateoftherunawayscenariosisclosetotheoutgassingratebyridgevolcanismonpresent-dayEarth(Fig.11,blackandbluelines).Inthosecases,theO2-COrunawaystateiswellsustainablebyreasonablerateofreplenishmentfromtheplanetaryinterior.However,ifafixeddepositionvelocityforO2isused,evenassmallas10-8cms-1presumablyduetorecombinationinhydrothermalflows,averylargeCO2outgassingratewouldberequiredtosustaintherunawaystate(i.e.,outoflimitonFig.11,redlines).Isthisscenariorealistic?Infact,theimpliedCO2outgassingratedoesnotnecessarilycomefromtheinterioroftheplanetas“new”

Fig.11:OutgassingrateofCO2impliedbytheCO2partialpressure,forvariedassumptionsofthedepositionvelocities(cms-1).TheoutgassingratebyridgevolcanismonEarthis0.4~1´1010cm-2s-1(Sleep&Zahnle2001).WhentheCO2partialpressureissmall,asmallnegativevaluefortheoutgassingrateisimplied;thisisbecauseafixedoutgassingrateofCOisassumed.

10-4 10-3 10-2 10-1 100

CO2 Partial Pressure [Bar]

0

1

2

3

4

5

CO2 O

utga

ssing

Rat

e [cm

-2 s-1

]

1010 TRAPPIST-1 e

Vdep(CO) = 1E-8, Vdep(O2) = 0Vdep(CO) = 1E-8, Vdep(O2) = 1E-8Vdep(CO) = 1.2E-4, Vdep(O2) = 1.4E-4Vdep(CO) = 1E-8, Vdep(O2) = BIF

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CO2;instead,theveryrecombinationprocessinhydrothermalflowsthatconsumesO2willproducesCO2.TheO2-COrunawaystatewouldthereforebesustainableviacyclingthroughthedeepocean.Lastly,whenthesurface-oceanrecombinationofCOandO2isassumed,theO2-COrunawaydoesnotoccur(Fig.2),butalarge“outgassingrate”isstillrequiredforpCO2>0.1bar.Thisoutgassingratecanbesustainedbytheproductoftherecombinationitself.Inall,theO2-COrunawayappearstobesustainablefromageochemicalpointofview,andthesustainabilitymayinvolvereplenishmentofCO2fromtheplanetaryinterior,orcyclingofCO,O2,andCO2throughthedeepocean.Assuch,theO2-andCO-richatmospheremodeledheredoesnotrequireanyplanetaryoutgassingoutsideoftypicalgeologicalregimes;nordoesitrequireahighlyoxidizedordrieduppermantle,presumablyproducedbylossofhydrogenintospaceoveralongactiveperiodoftheMdwarfs(Lugar&Barnes2015;Tian&Ida2015;Bolmontetal.2017).TheatmospheremodeledherehasO2andCOco-existingatlargeabundances,differentfromthepredictedmassiveO2atmospheresfromaccumulativehydrogenlossthatwouldhavelittleCO(Bolmontetal.2017;Lincowskietal.2018).5.ConclusionWeuseanatmosphericphotochemistrymodeltostudytheeffectofstellarUVradiationonvariedabundanceofCO2ontherockyplanetsinthehabitablezoneofthelateMdwarfTRAPPIST-1.OurmodelsshowthatforasmallabundanceofCO2,anatmospherewithO2andCOasmaincomponentswouldbethesteadystate.This“O2-COrunaway”isrobustagainstthenitrogencatalyticalcyclesfromlightning,reasonableuncertaintiesinthestellarspectrum,aswellasvariousgeochemicalsinksforO2andCO,includingtheBandedIronFormation.FortheplanetsTRAPPIST-1e,f,andg,sincetheyrequiresizableabundanceofCO2tobehabitable,themodelspresentedhereimplythatvirtuallyallhabitablescenariosoftheTRAPPSIT-1planetsentailanO2-richatmosphere.TheO2-COrunawaycanonlybepreventedbyassumingadirectrecombinationofO2andCOinthesurfaceocean,whichwouldprobablyrequirebiochemistry.TheO2-COrunawaymechanismdescribedherealsoappliestotemperateandrockyplanetsofotherlow-temperatureMdwarfstars,afewtensofwhichareexpectedtobediscoveredbytheTESSmission(Sullivanetal.2015).Thisisbecausethecauseoftherunaway,thestrongFUVandweekNUVirradiation,appliestomanymoderatelyactiveMdwarfstars(Loydetal.2016).ThecalculationspresentedherenotonlyshowthatthespectralfeaturesofO2andO3cannotberegardedasrobustsignsofbiogenicphotosynthesis(Tianetal.2014;Domagal-Goldmanetal.2014;Harmanetal.2015),butalsoshowthatO2andCOarelikelydominantgasesonhabitableplanetsofMdwarfstars.Thesegaseshavespectralfeaturessuitablefordetectionwithhigh-resolutionspectroscopy(Snellenetal.2010;Lovisetal.2017).TheabsorptionfeaturesofO2,O3,CO,andCO2,aswellasthecollision-inducedabsorptionfeaturesofO2(Lincowskietal.2018;Misraetal.2014),shouldtherefore

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