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ModelingpN2ThroughGeologicalTime:ImplicationsforPlanetaryClimatesandAtmospheric

Biosignatures

E.E.Stüeken1,2,3,4*,M.A.Kipp1,4,M.C.Koehler1,4,E.W.Schwieterman2,4,5,B.Johnson6,R.Buick1,4

1.Dept.ofEarth&SpaceSciencesandAstrobiologyProgram,UniversityofWashington,Seattle,WA98195,USA2.Dept.ofEarthSciences,UniversityofCalifornia,Riverside,CA92521,USA3.DepartmentofEarth&EnvironmentalSciences,UniversityofStAndrews,StAndrewsKY169AL,Scotland,UK4.NASAAstrobiologyInstitute’sVirtualPlanetaryLaboratory,Seattle,WA981195,USA5.Dept.ofAstronomyandAstrobiologyProgram,UniversityofWashington,Seattle,WA98195,USA6.SchoolofEarth&OceanSciences,UniversityofVictoria,Victoria,BCV8P5C2,Canada*correspondingauthor(evast@uw.edu)

Astrobiology,Volume16,Number12,doi:10.1089/ast.2016.1537Abstract Nitrogen is amajor nutrient for all life on Earth and could plausibly play a similar role in extraterrestrialbiospheres.ThemajorreservoirofnitrogenatEarth’ssurfaceisatmosphericN2,butrecentstudieshaveproposedthatthesizeofthisreservoirmayhavefluctuatedsignificantlyoverthecourseofEarth’shistorywithparticularlylowlevelsintheNeoarchean–presumablyasaresultofbiologicalactivity.WeusedabiogeochemicalboxmodeltotestwhichconditionsarenecessarytocauselargeswingsinatmosphericN2pressure.ParametersforourmodelareconstrainedbyobservationsofthemodernEarthandreconstructionsofbiomassburialandoxidativeweatheringindeeptime.A1-Dclimatemodelwasusedtomodelpotentialeffectsonatmosphericclimate.Inasecondsetoftests,weperturbedourboxmodeltoinvestigatewhichparametershavethegreatest impactontheevolutionofatmosphericpN2andconsiderpossibleimplicationsfornitrogencyclingonotherplanets.Ourresultssuggestthat(a)ahighrateofbiomassburialwouldhavebeenneededintheArcheantodrawdownatmosphericpN2tolessthanhalfmodernlevels,(b)theresultingeffecton temperature couldprobablyhavebeencompensatedby increasing solar luminosityandamildincrease inpCO2, and (c) atmosphericoxygenation couldhave initiateda stepwisepN2 rebound throughoxidativeweathering.Ingeneral,lifeappearstobenecessaryforsignificantatmosphericpN2swingsonEarth-likeplanets.OurresultsfurthersupporttheideathatanexoplanetaryatmosphererichinbothN2andO2isasignatureofanoxygen-producingbiosphere.

1.Introduction Lifeasweknowitisimplausiblewithoutnitrogen.Itisanessentialmajornutrientforalllivingthingsbecauseitisakeycomponentofthenitrogenousbasesinthenucleicacidsthatstore,transcribe,andtranslategeneticinformation, a necessary ingredient of the amino acidsconstitutingtheproteinsresponsibleformostcellularcatalysisandatthecoreoftheATPmoleculethatistheprincipalenergytransferagentforbiologicalmetabolism.Asnitrogen’scosmicabundanceisonlyslightlylessthanthatofcarbonandoxygenand because it condenses atmoderate distances in circum-stellardisks, itshouldhavebeenavailabletootherpotentialexoplanetary biospheres. However, N2 gas, the most likelynitrogenspeciesnearplanetarysurfacesinthehabitablezone,is nearly inert at standard conditions because of the very

strongtriplebondinN≡N.Lightningcanbreakthisbondandcombine nitrogen with other atmospheric species, but onEarththisprocesshasbeenrelativelyinefficient(BoruckiandChameides,1984;Navarro-Gonzalezetal.,2001).Muchmoresignificant for removing N2 from Earth’s atmosphere ismicrobialN2fixationtoammonium,areactioncatalyzedbytheenzyme nitrogenase. Today, most of this fixed nitrogen isreturnedtotheatmosphereviathebiogeochemicalnitrogencycle,aseriesofmicrobiallymodulatedredoxreactions thatultimately transform organic nitrogen back to gaseous N2.Thus, life’s demand for nitrogen regulates its atmosphericabundance. Though N2 is not a greenhouse gas itself, itsatmosphericpartialpressureaffectsplanetaryenvironmentalconditions. Higher N2 pressure can enhance greenhouse

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warmingbypressurebroadeningtheabsorptionbandsofsuchgases as water vapor, CO2, CH4, and N2O (Goldblatt et al.,2009).Hence, thepartialpressureofN2 indirectly influencessurface temperature and thus habitability.Moreover, a lowtotalatmosphericpressureofallgasescombinedweakensthecold-trapforwatervaporatthetropopause(WordsworthandPierrehumbert,2014).WhereN2isamajoratmosphericconstituent,adropinpN2canmakethetropopausecold-trapleaky(ZahnleandBuick,2016),allowingwatervaporintotheupperlayersoftheatmospherewhereitcaneitherremainasvapor,perhapsincreasingoverallgreenhousewarming(Rind,1998; Solomon et al., 2010; Dessler et al., 2013) (but for acontraryviewseeHuangetal.,2016),orfreezeashigh-altitudeice clouds in polar regions, warming the high latitudes andmaking planetary climate more equable (Sloan and Pollard,1998). Thus, planetary habitability is dependent, at least inpart,onatmosphericnitrogenlevels. Thoughweknownexttonothingabouttheevolutionof the biogeochemical nitrogen cycles on other planets, wenowhaveabetterresolvedpictureofthebehaviorofnitrogenthroughEarth’shistory(Aderetal.,2016;Stüekenetal.,2016;Weissetal.,2016).Itseemsthat(1)microbialnitrogenfixationevolvedveryearlyinEarth’shistorysuchthatanitrogencrisisfor the primordial biosphere was averted (Stüeken et al.,2015a; Weiss et al., 2016), (2) the partial pressure ofatmospheric N2 has fluctuated through time to a greaterdegreethanpreviouslyanticipated (Sometal.,2016), (3)anaerobicnitrogencyclearosebeforetheGreatOxidationEventat~2.35Ga(Garvinetal.,2009;GodfreyandFalkowski,2009),(4)duringthemid-Proterozoicaerobicandanaerobicnitrogencyclingwas spatially separatedunder lowoxygen conditions(Stüeken, 2013; Koehler et al., in press), and (5) a modernnitrogencyclewithwidespreadaerobicactivitydidnotariseuntil the late Neoproterozoic (Ader et al., 2014). The mainconstraintsonthesedevelopmentswereevidentlybiologicalevolutionandredoxchangesinEarth’ssurfaceenvironments,principallytheoxygenationstateoftheatmosphereandocean(Stüeken et al., 2016). Other Earth-like planets may haveevolved along somewhat similar pathways with respect tonitrogencycling,providedthattheyalsooriginatedEarth-likelife.Ifso,thenatmosphericswingsinpN2maybeacommonfeatureofterrestrialinhabitedplanets. Inthepresentstudy,weinvestigatedthediversityofterrestrialplanetarynitrogencyclesbymodelingtheevolutionof Earth’s atmosphericN2 reservoir.We then perturbed themodel toexamineseveralahistoricalextremescenarios thatcouldariseonEarth-likeexoplanets,definedhereasplanetswith a silicate rock mantle and iron core (empirically < 1.6Earth radii in size, Rogers, 2015), an orbit within theconservative limits of the habitable zone (Kopparapu et al.,2013),andasimilarvolatilecontenttoEarth.Thisconservativedefinition prescribes a high molecular weight atmospheredominated by N2, CO2, and H2O rather than H2 (cf.

Pierrehumbert and Gaidos, 2011; Seager, 2013). Afterexploring a range of variables, we concluded that somecombinationsofN2abundancewithothergasescouldactasextraterrestrial biosignatures, others could be “falsepositives,” and yet others may indicate that a planet isuninhabited. Overall, our results suggest that an anaerobicbiospherecangreatlyfacilitatetheremovaloflargeamountsofN2fromaplanetaryatmosphere.2.Modelsetup2.1.Biogeochemicalnitrogenboxmodel Weusedthe IseeStella softwaretoconstructaboxmodel of the global biogeochemical nitrogen cycle (Fig. 1),tracking total nitrogen. Boxes included the atmosphere,pelagic marine sediments deposited on oceanic crust,continental marine sediments deposited on continentalshelvesandinepeiricseas,continentalcrust,andthemantle.Continentalmarinesedimentsweredefinedtobecomepartofthe continental crust after100millionyearsand from thereonwards were subjected to metamorphism, which returnsnitrogen to theatmosphere.Similarly,we letpelagicmarinesedimentsaccumulatefor100millionyearsbeforetheyweresubjected to subduction, metamorphism, and volcanism.These timescales were based on the observation that C/Nratiosinsedimentaryrocksolderthanabout100Myrbecomemorevariablewithhigheraveragevalues(Algeoetal.,2014).Thetwosinksofnitrogenfromtheatmospherewereburialinpelagic sediments and burial in continental sediments withproportions of ~1:25 (Berner, 1982). The sources ofatmospheric nitrogen were volcanic and metamorphicdegassingofsubductedpelagicsediments,metamorphismofcontinental crust, oxidative weathering of continents, andmantleoutgassing.Denitrificationwasnotexplicitly includedas a source, because we did not track the marine nitrogenreservoir.

Themodelwasrunin1million-yeartime-stepsfrom4.5Gatopresent.Differentialequationslistedintheappendixwere solvedwith the Eulermethod. The chosen step size ismuch lower than the residence time of nitrogen in ourmodeled reservoirs (>100 Myr), which eradicatescomputational artifacts that can result in mass imbalances.Theinitialabundancesofnitrogeninthemantle,continentalcrust, and sedimentswere set such that the concentrationswere the same, assuming that any disequilibrium inconcentrations observed today is due to biogeochemicaloverprinting. The rock masses and modern nitrogeninventoriesweretakenfromtheworkofJohnson&Goldblatt(2015).The initialabundanceofatmosphericN2 isunknown.We tuned the model such that the final atmospheric N2abundanceafter4.5billionyearsequaledthemodernamountof 2.87·1020 mol, defined as one time present atmosphericnitrogen(PAN)(JohnsonandGoldblatt,2015).

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Amore detailed description of how rate constantswerederivedisgivenintheappendix.FollowingtheworkofBerner (2006b), nitrogen burial was parameterized throughbiomassburial (i.e., organic carbon).Although thisapproachneglects the origin and radiation of biological nitrogenmetabolismsover Earth’s history (Stüeken et al., 2016), it ispreferred because (a) it avoids major uncertainties aboutmetabolicratesindeeptime,and(b)itissufficientfortrackingthe total nitrogen sink from the atmosphere. As furtherdiscussed below (Section 4.1), additional nitrogen burialthroughadsorptiononclaymineralsisnegligiblecomparedtotheorganicnitrogenfluxintosediments.Usingthisapproach,we calculated modern nitrogen burial from the modernvolcanic CO2 outgassing flux of 6·10

18 mol/Myr (Marty andTolstikhin, 1998), assuming that 22% (forg = 0.22) ofvolcanogenicCO2isburiedasorganiccarbonintheabsenceofland plants (pre-Devonian) (Krissansen-Totton et al., 2015),and that the C/N ratio of post-diageneticmarine biomass is

approximately10(GodfreyandGlass,2011;Algeoetal.,2014).Thisgaveanitrogenburialfluxof1.32·1017mol/Myr,equalto~1.5% of modern biological N2 fixation (8.64·10

18 mol/Myr)(Gallowayetal.,2004).Wethenmodulatedthisfluxindeeptimeinthreedifferentways.First,wetookintoaccountseculartrendsinforgasinferredfromthecarbonisotoperecord(“Forgmodel”)(Krissansen-Tottonetal.,2015).Uncertaintiesinthisrecord, resulting from potentially underrepresentedcarbonate reservoirs (Bjerrum and Canfield, 2004; Schrag etal., 2013) and the variance in δ13C values at any given timepoint, are discussed below. Second, we assumed a gradualdecline in CO2 outgassing from the Hadean to themodern,followingtheparameterizationofCanfield(2004,Equ.2)(“Forg+Heatflowmodel”).Bymassbalance,higherCO2outgassingintheearlierPrecambrianimplieshigherburialfluxesofbiomassand with it nitrogen. Uncertainties and caveats of thisapproacharediscussedbelow.Third,wetestedfortheeffectsof additional two-fold increases in CO2 input, and hence

Figure1: Schematicof thenitrogenmodelfor theEarth.All fluxesexceptforburialofnitrogenfromtheatmosphere intosedimentsaredependentonthereservoirsize.Fluxeswithdashedarrowsareimplementedastime-variable,exceptinour"basemodel"(Fig.2a).

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nitrogenburial,duringsuperplumeevents (Abbottand Isley,2002)(“Forg+Heatflow+Superplumemodel”).ThismodeldidnotincludepotentialN2additionthroughenhancedvolcanism,which we will discuss separately. In all of these models,oxidativeweatheringwas implementedas a functionofpO2throughtime(Lyonsetal.,2014)withareactionorderof0.5,that is, proportional to (pO2)

0.5 (Chang and Berner, 1999;Boltonetal.,2006).

Ina separate setofmodels,we testedhypotheticalscenariosforEarth-likeplanetswithoutanybiosphereandananoxicatmosphere,orwithacompletelyanaerobicbiosphere

thatdoesnotexperienceoxygenationevents.OurdefinitionofEarth-likeplanetsincludesanorbitwithinthehabitablezonewhere liquidwatercanbestableatthesurface,aswellasarockycompositionandavolatileinventorysimilartothoseofEarth (Section1). Thisdefinition is admittedly limited,but itallows us to identify with greater confidence a subset ofparameters that canplay a critical role in thehistoryof thenitrogencycle.WeassumedabioticnitrogenburialwasdrivenbyNH4

+adsorptiononclaymineralsafterabioticN2reductionintheatmosphere.RatesweretakenfromtheworkofStüeken(2016) fortwoextremeend-memberscorrespondingtohigh

Figure2:ReconstructingnitrogenburialoverEarth’shistory.ArrowsmarkpN2valueinferredforproxies(Martyetal.,2013;Sometal.,2016).(a)Basemodel.Nburialisheldconstant,calculatedastheproductofvolcanicCO2outgassing,thepre-Devonianorganicburial fraction(forg)of0.22,andthe inverseoftheRedfieldC/Nratioof10. (b)Forgmodel.Nburial ismodulatedbysecularchangesinforgas inferredfromthecarbonisotoperecord(Krissansen-Tottonetal.,2015).(c)Forg+Heatflowmodel.CO2outgassing isassumedtohavedeclinedgradually fromtheHadeantothemodernwithdecreasingheatflow from Earth’s interior, as described by Canfield (2004). Carbon burial andwith it nitrogen burial is changed inproportion.Mantleoutgassingismodulatedinthesameway.(d)Forg+Heatflow+Superplumesmodel.AdditionalpulsesofCO2outgassingareassumedduringintervalsofsuperplumesasrecordedintherockrecord(AbbottandIsley,2002).Solidblackline=usingbestestimatesforallparameters;dashedlines=mostextremeuncertaintyintervalifallparametersareoffinthesamedirection(excludinguncertaintiesinRedfieldratioandmodernCO2outgassing,AppendixA3);greyshadedarea=moreplausibleuncertaintyintervalwithnarrowerrangeofvaluesforthemetamorphicrateconstant(mostsensitivevariable,seeAppendixA3).

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andlowestimatesofabioticN2fixationratesfortheArcheanEarthandseawaterpHof5and8,respectively(seeAppendixA1.1).Forillustration,theseburialfluxesareequalto1.4·10-1and 1.7·10-5 times the modern nitrogen burial describedabove.We did not test abiotic burial under oxic conditionsbecauseinthatcaseNH4

+productionwouldlikelybelowandnitrogenburialtrivial.Forthe"bioticanoxic"scenario,weusednitrogenburialratesequalto1-10%ofthemodernbiologicalN2 fixationrate. Inboththeabioticandbioticanoxicmodel,oxidativeweatheringwasswitchedoff.

Rate constants for oxidative weathering,metamorphism, erosion, subduction, volcanism, andoutgassingwere calculated as the ratio ofmodern fluxes tomodernreservoirsizes(seeAppendixfordetails).Wefurtherperformed simple order-of-magnitude estimates ofcatastrophic events, such as impacts and large volcaniceruptions, to test whether these could affect our overallconclusions(Section3.3)

2.2.Modelingeffectsongreenhousegases&globalclimate

Weselectedthemostextremeend-membersofourEarthmodeltodeterminepotentialeffectsonEarth’sclimate.Asshownbelow,thetimescalesoverwhichvariationsinpN2can occur exceed those of the carbonate-silicate feedbackcycle (Walker et al., 1981). Hence, changing pN2 alone isunlikely to cause rapid climate changes, because pCO2 can

rapidly re-adjust to keep surface temperaturesmore or lesssteady. We therefore decided to calculate the requiredchanges in pCO2 that would counterbalance the effects ofvaryingpN2.WeusedaniterativeapproachtodeterminethepCO2necessarytomaintaina278Kgloballyaveragedsurfacetemperature (TGAT), equivalent to the estimated globallyaveraged temperatureduring the last glacialmaximum.Thislimit was chosen because geological evidence suggests thattheArcheanwascool(Hrenetal.,2009;Blakeetal.,2010)butnotpermanentlyglaciated (Young,1991;deWitandFurnes,2016). As input values, we used the changes in nitrogenabundance shown in Section 3 (Fig. 2) and changes in solarluminosity from3.5Ga to 2.4Ga. To do this,weused a 1Dradiativeconvectivemodelthatwasrecentlyusedtocalculatehabitablezoneboundaries(Kastingetal.,1984;Kastingetal.,1993; Kopparapu et al., 2013) and characterize the surfacetemperature of a hypothetical Archean Earth with a globalhydrocarbon haze (Arney et al., 2016).We chose a surfacealbedo of Asurf = 0.32, which is a tuning parameter used toreproducethetemperatureofmodernEarth(Kopparapuetal.,2013; Arney et al., 2016). Our atmospheric compositionconsistedofonlyN2,CO2,H2O,andCH4,where thepN2wastakenfromourmodeloutput(Table1)andCH4wasfixedatpCH4=0.001(fCH4,fCO2,fN2andthetotalsurfacepressureP0wereadjustedself-consistentlyforchangesinpCO2).TheH2Oprofiles were calculated using a relative humidity profile

Table1:ClimateresponsetochangesinatmosphericN2.Inputdataaretheage,thecorrespondingrelativesolarluminositytakenfromBahcalletal.(2001),atmosphericN2[PAN]calculatedfromourboxmodel,andanassumedconstantbackgroundlevelof1000ppmvCH4.PartialN2pressure(pN2)wascalculatedastheproductoftotalN2inunitsofPANandthemodernpN2of0.78bar.OutputparametersareTGAT(globalaveragesurfacetemperature),pCO2,andP0(totalaveragesurfacepressure,i.e.,sumofallgases).Line1=startingconditionsat3.5Ga;line2=changingPANwithconstantluminosityandconstantpCO2(takenfromline1);line3=changingPANandluminositywithconstantpCO2; line4=changingPAN,luminosityandpCO2.ParametersarecalculatedsuchthattheTGATat(1)and(4)convergesto278K.

line Age[Ga]

Rel.SolarLuminosity

N2[PAN]

pN2[bar]

pCO2[bar]

pCH4[bar]

P0[bar]

TGAT[K]

Forg+Heatflowmodel: 1 3.5 0.769 0.61 0.476 0.046 0.001 0.523 278.02 2.4 0.769 0.42 0.328 0.046 0.001 0.375 274.73 2.4 0.831 0.42 0.328 0.046 0.001 0.375 282.44 2.4 0.831 0.42 0.328 0.018 0.001 0.346 278.0

Forg+Heatflow+Superplumesmodel,lowerlimit:1 3.5 0.769 0.54 0.421 0.056 0.001 0.480 278.02 2.4 0.769 0.08 0.062 0.056 0.001 0.119 264.83 2.4 0.831 0.08 0.062 0.056 0.001 0.119 270.64 2.4 0.831 0.08 0.062 0.160 0.001 0.223 278.0

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assuming a surface relative humidity of 80% (Manabe andWetherald,1967).Thesolarluminosityat3.5and2.4Ga(0.769and0.831)wasfoundthroughinterpolationofTable2intheworkofBahcalletal.(2001).WefocusedonthepCO2requiredto maintain a TGAT > 278 K, noting that significantly lowertemperatures(TGAT<273K)mayallowsomeopenoceans,buta 3D model would be needed to capture their additional

complexities (see Appendix A5 for limitations of ourapproach).Table1showsasummaryofourresults.WealsoindicatethesurfacetemperatureifpCO2wasnotadjustedtomaintainTGAT=278K,butwasmaintainedatthepCO2valueat3.5 Ga, and if both the pCO2 and solar luminosity weremaintainedatthe3.5Gavalues.Table2showssimilarresultsasTable1,but foramorepermissive initialandfinalTGATof273 K. This illustrates the sensitivity of the required pCO2adjustmenttocompensateforpN2drawdownasafunctionofthechoiceofreferencetemperature.

3.Results3.1.Nitrogenburialconstrainedbycarbonburial Wetestedfourdifferentmodelsfortheevolutionofnitrogenburialthroughgeologictime(Fig2).Inourbasemodel(Fig.2a),nitrogenburialwasheldconstantatitsmodernflux.Each subsequent iteration incorporates an additionalparametertotheNburialrecordand,thus,showsadditionalatmospheric N drawdown. Sensitivity tests are presented inSectionA3.ThemajorityoftheuncertaintyrangeillustratedinFig.2derivesfromuncertaintiesaboutratesofnitrogenlossduringcontinentalmetamorphism.

3.1.1.ForgmodelInthefirsttest,thebasemodelwasmodifiedbyscaling

nitrogen burial as a function of forg (organic carbon burialfraction). This did not significantly change the evolutionarytrendoftheatmosphericnitrogenreservoirpredictedbythebase model, as forg has been relatively invariant throughgeologictime(Fig2b).Duringthelargestburialeventindicated

bythecarbonisotoperecord,theLomagundiEventatca.2.3-2.1 Ga, forg temporarily exceeds 0.3 (Precambrian baseline~0.15-0.2).However,eventhisincreaseinorganicburialaloneappears to be insufficient to significantly deplete theatmosphericN2reservoirbymorethan~0.02PAN.Thismodelshowsaslowdepletionoftheatmosphericnitrogenreservoirduring the Archean (from 1.0 to 0.81 PAN), and relativelyconstantatmosphericnitrogenduringtheProterozoic(range0.78to0.82PAN).ModernatmosphericnitrogenlevelsarenotattaineduntillateinthePhanerozoic.3.1.2.Forg+HeatFlowmodel

WhenwescalenitrogenburialproportionallytotheamountofCO2outgassing(Canfield,2004),ourmodelshowsasignificant drawdown of atmospheric nitrogen during theArchean,reachingaminimumof0.44PAN(=0.35barN2) intheearliestPaleoproterozoic, immediatelypriortotheGreatOxidation Event (GOE, Fig 2c). Fixed nitrogen is principallyburied and stored in continental sediments and continentalcrust,whichreachamaximumof1.7×themoderncontinentalreservoir size at this time (SectionA2).During theGOE, theatmospheric nitrogen reservoir rebounds due to enhancedoxidativeweatheringofthecontinents,butthisreboundstopsaftertheGOEandatmosphericnitrogenremainslowat0.59-

Table2:ClimateresponsetochangesinatmosphericN2.SameasTable1,butforafiducialTGATof273.2Katlines(1)and(4).DifferencesfromTable1areinbold.

line Age[Ga]

Rel.SolarLuminosity

N2[PAN]

pN2[bar]

pCO2[bar]

pCH4[bar]

P0[bar]

TGAT[K]

Forg+Heatflowmodel: 1 3.5 0.769 0.61 0.476 0.020 0.001 0.497 273.22 2.4 0.769 0.42 0.328 0.020 0.001 0.348 270.63 2.4 0.831 0.42 0.328 0.020 0.001 0.348 278.44 2.4 0.831 0.42 0.328 0.005 0.001 0.333 273.2

Forg+Heatflow+Superplumesmodel,lowerlimit:1 3.5 0.769 0.54 0.421 0.024 0.001 0.446 273.22 2.4 0.769 0.08 0.062 0.024 0.001 0.087 261.13 2.4 0.831 0.08 0.062 0.024 0.001 0.087 266.24 2.4 0.831 0.08 0.062 0.118 0.001 0.181 273.2

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0.65 PAN (= 0.47-0.51 bar N2) until the NeoproterozoicOxidationEvent(NOE).AtmosphericN2rapidlyrisesduringtheNeoproterozoic and Paleozoic in response to a furtherenhancementofoxidativeweatheringwiththesecondriseofO2. The later Phanerozoic shows a slow gradual increase inatmosphericN2.Asdiscussedbelow,weconsiderthismodelthe most plausible mechanism for explaining a Neoarcheanpressure minimum of 0.23 ± 0.23 bar as determined from

basalticamygdales(Sometal.,2016).3.1.3.Forg+HeatFlow+Superplumesmodel Scaling up N burial by a factor of 2 during plumeintervals (Abbott and Isley, 2002) resulted in a small butnoticeable effect on the atmospheric nitrogen reservoir (Fig2d). The effect is most pronounced during the longestsuperplumeeventinthegeologicrecord,whichisthoughttohavelastedfrom2.775to2.696Ga.Atmosphericnitrogenisdrawndownto0.42PAN(=0.33barN2)by2.69Gainthewake

of this event,which is also consistentwith basalt amygdalepaleobarometryestimatesfor2.7Ga(Sometal.,2016).

Totesttheplausibilityofgreaterburialenhancementfactors, we explored the range from 1× to 10× burialenhancement during plume intervals. A 10× burialenhancement factor for superplume intervals caused theatmosphericnitrogenreservoirtobecomeentirelydepletedinthe Neoarchean (0.0 PAN at 2.71 Ga), which is implausible

becauseitwouldhavedriventhebiospheretonearextinctionbyremovingamajornutrient,orcouldhaveinducedaglobalglaciation, for which there is no geological evidence at thistime. We thus deemed 10× too extreme of a burialenhancementfactor.Valueslessthan10×andgreaterthan1×areplausible,butgivenavailabledata, it isdifficulttoderiveaccurate constraints. It is also quite possible that differentplume events affected organic burial by different factors.Furthermore,asnotedinSection3.3,nitrogenoutgassingfromthe mantle may have been more pronounced during

Figure3:HypotheticalevolutionofatmosphericN2onextrasolarplanets.(a)AbioticanoxicplanetwherenitrogenburialisdrivenbyNH4

+adsorptiononclayminerals.Highburialrate=1.5·1016mol/Myr,lowburialrate=2.2·1012mol/Myr(Stüeken,2016). (b)Biologicalanoxicplanetwithoutoxidativeremineralizationandweathering.NitrogenburialiscalculatedastheproductoftheproductivityfactorandthemodernbiologicalN2fixationrateonEarthof8.6·10

18mol/Myr(Gallowayetal.,2004). (c)Biologicalanoxicplanetwithextinctionofthebiosphereuponatmosphericloss. (d)Anoxicbiologicalburialandextinctionasinpanelcwithandwithoutburialoncontinentalcrust.Theburialfluxissetequalto4%ofmodernbiologicalN2fixation(dashedlineinddescribesthesamescenarioasdashedlineinc).Notechangeinscaleonx-axis.

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superplumeevents,offsettingtheeffectofenhancedcarbonburial.Thiseffectwasnotconsideredinourmodel.Allofthesecomplications make assessing the impact of plumes on theatmosphericnitrogenreservoirratherdifficult.Still,itisworthnotingthat,evenwitha2×burialenhancement,effectsontheatmosphericnitrogen reservoir fromplumeeventsare smallduetotheirshortduration.

3.2. Atmospheric nitrogen evolution on abiotic and anoxicworlds3.2.1Abioticanoxicplanets In thehypothetical scenarioof a completely abioticEarth-like planet in the habitable zone of another star withplausible abiotic nitrogen burial rates (Stüeken, 2016), theatmosphericnitrogenreservoirincreasedslightlyfrom1.0PANto 1.14 -1.22 PANafter 4.5 billion years,with noperiods ofatmosphericN2drawdown(Fig.3a).Catastrophiceventssuchasplumeswouldhavelittleeffectonsuchaplanetbecause,asfurtherdiscussedbelow(Section3.3.2),mostofthenitrogenliberatedby suchevents on Earth is likely sourced from thecrust that has been enriched in nitrogen due to biologicalburial. On an abiotic planet, the crust would be relativelydepletedinnitrogen.Thesensitivityofthesetrendstochangesin surface and deep Earth nitrogen fluxes is given in theappendix (Section A4). Overall, we find no plausiblemechanismthatcouldcause largeswings inpN2,apart fromthepossibilityofatmosphericerosion(e.g.,Mars,Section4.3)orfreeze-outofN2onplanetsfaroutsideofthehabitablezone(e.g.,Pluto).Althoughthismodeledscenarioishypothetical,itemphasizesthepotentialimportanceoflifefortheevolutionoftheglobalnitrogencycle. 3.2.2Bioticanoxicplanets Our results forahypotheticalEarth-likeplanetwithan anaerobic biosphere suggest that, under the rightconditions, biological nitrogen drawdown can have a majoreffect on the evolution of atmospheric pN2 through time.Nitrogenburialratesequalto0.1and0.04timesthemodernN2 fixationratesequesteratmosphericnitrogento0PANby4.1 Ga and 2.9 Ga respectively (Fig. 3b). Theminimum fluxrequiredtoreach0PANwithin4.5billionyearsisroughly0.03timesmodern biological N2 fixation, or 2 times themodernnitrogen burial flux. As in the case of our “Forg + Heatflow”model above,most of this nitrogen is stored in continentalsedimentsandcrust.Afluxof0.01timesmodernbiologicalN2fixationdoesnotcompletelydrawdownatmosphericN2,butleadstoasteadystateof~0.84PAN(Fig.3b).Amoredetailedsensitivity analysis of these simulations is presented in theSection A4. When other parameters are set to their mostconservative values (i.e., minimizing N2 sequestration), afixationfluxof~0.13timesmodernwouldbeneededtodrawdown atmospheric N2 to 0 PAN. Again, this scenario ishypothetical, but in comparison to our Earth model, it

emphasizestheimportantinfluenceofatmosphericoxygenonthenitrogencycle. It is conceivable that a biosphere would go extinctwhen the atmospheric N2 reservoir becomes depleted andtriggersaglobalglaciation,atleastifbiologicalN2drawdowndoes not slow down dramatically aspN2 approaches 0 PAN(e.g.Klingleretal.,1989).Ofcourse,inreality,biogeochemicalfeedbacks that were not considered in our model maymaintainalow,butnon-zero,N2reservoirintheatmosphere,andthebiospheremaynotnecessarilygoextinctasevidencedbyextremeglacialeventsonEarth.Weneverthelessexploredthiscaseinourmodel,becauseitprovidesanestimateofhowfastpN2canrecoveronananoxicplanetintheabsenceofanEarth-likeatmosphericoxygenationevent(cf.Figs.2c,2d).Ourresultsshowthatinthiscasetheburiednitrogenwouldreturnmuch more slowly through continental metamorphism anderosion than it does with oxidative weathering. Wedetermined the recovery timeof atmosphericpN2after it iscompletely sequestered by switching off biological nitrogenfixation once atmosphericN2 reached 0 PAN.With nitrogenburialfluxesof10%and4%modernN2fixation,ittakes2.76Gaand2.62billionyearsrespectivelyforatmosphericnitrogenvaluestorecoverto1.0PAN,assumingthatthebiospheredoesnotrecoverduringthattime(Fig.3c).Thisismuchslowerthanthe increases inpN2 thatoccurred inourmodelsovera fewhundredmillionyearsaftertheGOEandNOEonEarth,whichhighlights the linkage between pO2 and pN2 that is furtherdiscussedbelow(Section4.3). Toassesstheeffectsofcontinentalcrust(themajornitrogenrepositoryinourmodels),weranaseparatemodelwhere all burial was directed to pelagic sediments, that is,continents were bypassed to mimic a planet without anequivalentof continental crust.Burial fluxeswerearbitrarilyset to 4% times the modern fixation rate. Under theseconditions,pN2drawdownto0PANismuchslower(Fig.3d),because nitrogen in pelagic sediments has a much shorterresidencetimethanincontinentalsedimentsandcrustandisreturned relatively rapidly through subduction zonemetamorphismandvolcanism.However,onceatmosphericN2hasbeensequesteredinthemantle,itdoesnotrecover,evenoverabillion-yeartimescale.Althoughthismodeldescribesapurelyhypotheticalscenarioofplatetectonicsintheabsenceof continents, it demonstrates that a relatively shallownitrogen repository akin to continental crust with anintermediate residence time between that of pelagicsedimentsandthemantlegreatlyfacilitateslargeatmosphericpN2swingsoverhundredsofmillionsofyears,assuggestedforthePrecambrianEarth(Sometal.,2016).3.3.Catastrophicevents

Planetsareperiodicallysubjecttocatastrophiceventsthroughout their history.Weperformedorder-of-magnitudecalculations to test whether such events could affect

9

atmosphericN2reservoirsand,hence,ouroverallconclusions.Possible events considered here include asteroid or cometimpacts, superplume volcanism as an N2 source, and large-scaleplanetaryresurfacing.3.3.1.Impacts

Therearethreewaysimpactscouldaffecttheamountofnitrogeninaplanetaryatmosphere:directnitrogenadditionfromthebolide,atmosphericerosionwithlossofN2tospace,and release of buried nitrogen through crustal heating. Avariety of asteroids have substantial nitrogen contents. Themost volatile rich are carbonaceous chondrites, which have1235ppmnitrogenonaverage(WassonandKallemeyn,1988;JohnsonandGoldblatt,2015).IfallnitrogenwerereleasedasN2 upon impact, then a hypothetical 3.2·1021 kg ofcarbonaceous chondrites could contribute one PAN. Such amass is about 0.05% of Earth’s mass, and is approximatelyequivalent to the once proposed total mass of late heavybombardmentmaterial(Wetherill,1975).ImpactslaterintheArchean, post-dating the late heavy bombardment, wouldhavebeenseveralordersofmagnitudesmallerthan0.05%ofEarth’s mass (Johnson and Melosh, 2012), and hence thisnitrogen source was most likely trivial for atmosphericevolution.

ImpacterosionhasbeenproposedasanexplanationforthethinatmosphereofMars(MeloshandVickery,1989),butmorerecentcalculationssuggestthatthismechanismmayhavebeenlesseffectivethanpreviouslythought(Manningetal., 2009). The effect would further decrease with moremassiveplanets thanMars; it is not generally considered tohavebeensignificantonearlyEarth.ItisthusprobablynotamajornitrogensinkonmosthabitableEarth-likeplanets.

Large scale crustal heating resulting from impactscould add some nitrogen to the atmosphere (Wordsworth,2016). Current estimates of nitrogen in continental crustsuggestamassof1.7·1018kg,or0.5PAN(Goldblattetal.,2009;JohnsonandGoldblatt,2015).DuringthelateArchean,whenatmosphericpN2mayhavebeenaslowas0.44PAN(Section3.1.2),thecontinentalreservoirmayhavebeenaslargeas1.7times the present continental reservoir, though nitrogenconcentrations in continental crust rocks through time arepoorly constrained (Section A2). The nitrogen contained inoceanic crust and lithosphere is relatively minor (~0.57 to0.67·1018 kg N) (Johnson and Goldblatt, 2015). To raiseatmospheric pN2 by more than 0.1 PAN through crustalmelting,more than 5% of the continental crustwould haveneededtomeltintheNeoarcheanandmorethan20%inthemodern. We consider this unlikely, because there is nogeologicalevidenceofsuchlarge-scalecrustalmeltingevents.We note, however, that some rock types, such as lowercontinentalcrustandtheoceanic lithosphericuppermantle,arepoorlycharacterized.Therearesuggestionsthatpartsofthemantlemaycontainsubstantialnitrogen(Lietal.,2015),

andifasignificantfractionofthemantleexperiencedmelting,then large quantities of nitrogen could be added to theatmosphere.3.3.2.Superplumes

Superplumeeventsrepresentanothertypeofmantlemelting that may contribute to changes in atmospheric N2.While typical mantle melts (i.e., MORB) have a very lownitrogen content of ~1 ppm (Marty, 1995; Marty andZimmermann, 1999.; Johnson and Goldblatt, 2015), sparsedata from continental basalts show higher concentrations.BasaltsfromtheAbitibiregionhave6ppmnitrogen(Honma,1996),ColumbiaRiverbasalthas34ppm(BCR-1,Govindaraju,1994), and recent Antarctic basalts around 60 to 100 ppm(Greenfield, 1991). Assuming that most nitrogen will degasduringeruption,theseconcentrationssuggestthatsubstantialnitrogencouldhavebeenreleasedduringfloodbasalteruptiveevents.

Fluidinequilibriumwithbasalticmeltunderoxidizingconditions(fO2=∆NNO+3)hasapproximately104timesmorenitrogen than the melt itself (Li et al., 2015). Assuming allnitrogencontainedinthefluiddegasses,aneruptionof3·1018kg basalt (equivalent to the Siberian Traps) with ~30 ppmnitrogenremaininginthebasaltsuggestsareleaseof1·1018kgnitrogen, or 0.25 PAN. While measurements of nitrogen inflood basalts are quite rare, making this speculative, thissimple calculation hints that these events could influenceatmosphericN2content.However,itisimportanttonotethatsuperplumes inoceanicplateswould likelyhavebeenmuchless effective, given thatmarine basalts tend to havemorethan one order ofmagnitude less nitrogen than continentalflood basalts (see above); the latter likely assimilate andliberatenitrogenfromcontinentalcrust.Anexceptionmaybeoceanic superplumes that pass through parts of themantlethatareenriched innitrogendue toa subductionoverprint.Lamproites and lamprophyres, which are volcanic rocksresulting from the melting of enriched mantle, are notablynitrogen-rich(10sppm)(Jiaetal.,2003),suggestingthatsuchplume events could potentially liberate large amounts ofnitrogenintotheatmosphere.Nitrogencouldalsohavebeenliberated by plumes that sampled the lower mantle, whichaccording to some estimatesmay be nitrogen-rich (Johnsonand Goldblatt, 2015). However, both the nitrogenconcentrationofthelowermantleandthetransportpathwaysof material from such great depth (>660 km) are highlyuncertain, making this mechanism difficult to evaluate.Anothercomplicationinpredictingtheeffectofsuperplumesindeeptimecomesfromthepossibilitythattheredoxstateofmagmas may have increased over time, and under morereducing conditionsmagmatic nitrogenmay have been lessvolatile(Liboureletal.,2003;Kadiketal.,2011;Roskoszetal.,2013;MikhailandSverjensky,2014).

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3.3.3.PlanetaryresurfacingIf superplume events are extended to a planetary

scale,asissuggestedtohavehappenedonVenus,evenmorenitrogencouldbereleased.TheareaoftheSiberiantraps,tocontinuetheaboveexample,is2.5·106km2,orabout1/200thof the surface of Earth. Multiplying the above estimate fornitrogenreleasedduringSiberianTrapvolcanismby200yieldsanitrogenoutputof2·1020kg,or~50PAN.Again,wenotethatthis is a highly speculative estimate, but it does suggest thepossibility of substantial additions of nitrogen to theatmosphere via large scale volcanism on other planetarybodies that contain substantial amounts of nitrogen in thecrust. Overall, catastrophic events could havemoremarkedeffectsonplanetswherethecrustisnitrogen-enriched,which,asnotedabove(Section3.1.2,3.2.2),ismorelikelytobethecase on planets with a large biosphere that transfersatmosphericnitrogentocrustalrepositories.4.Discussion4.1.TheevolutionofatmosphericpN2onEarth Although many parameters in the globalbiogeochemical nitrogen cycle are uncertain and potentialreconfigurations of Earth’s interior are not taken intoconsiderationforlackofquantitativeconstraints(MikhailandSverjensky,2014),ourresultsallowustodrawseveralbroadconclusions under the assumption of persistent tectoniccyclingthroughEarth’shistoryasfollows:1.Theresultsfromourbasemodel(Fig.2a),wherenitrogenburial is held constant through time while oxidativeweathering follows atmospheric pO2, show that theoxygenationoftheatmospherealonecouldprobablynothavecaused the large swings in atmospheric pN2 that weresuggestedbySometal. (2016).Changes in theatmosphericnitrogen reservoir by more than ~0.1 PAN most probablyrequireachangeinnitrogenburialovertime.2. Variations in nitrogen burial by up to a factor of 2.9, asinferredfromtherecordofrelativeorganiccarbonburial(forg),areinsufficienttocausesignificantswingsofmorethan~0.2PANinatmosphericN2(Fig.2b).Evenifweuseforgvaluesfromtheupperendoftheuncertaintyrange(Krissansen-Tottonetal.,2015),theatmosphericN2reservoirdoesnotdropbymorethan0.3PAN.Ifforgwassmallerthanassumed,duetoagreaterproportionofcarbonateformationinoceaniccrustorwithinsediments (BjerrumandCanfield,2004;Schrag etal.,2013),thisvariablewouldhaveeven lesseffectonatmosphericN2.Toreachatmosphericpressuresoflessthan0.5barat2.7Ga(Sometal.,2016),whilemaintainingpressuresof0.5-1.1barN2 at 3.5Ga (Marty et al., 2013), nitrogenburialmust havebeenmarkedlyhigherintheearlierArcheanthanit istoday.Therearethreepossiblescenariostoincreasenitrogenburial:(i) subduction was more efficient than it is today and

metamorphic devolatilization was suppressed; (ii) nitrogenwasburiedpreferentiallyrelativetocarbon;(iii)theabsoluteorganic carbon burial fluxwasmuch higher, andwith it theburial of carbonate, such that forg did not change. It isconceivablethatsubductionwasfasterintheArchean(optioni),butoursensitivitytests(SectionA3)showthatshorteningtheresidencetimeofnitrogeninpelagicsedimentsbyafactorof2hasminimaleffectsontheatmosphericreservoir(<0.01PAN),becausethebulkofsedimentarynitrogenisrecycledviametamorphism.MetamorphicdevolatilizationmayhavebeenenhancedintheArcheanwhenthegeothermalgradientwasperhapssomewhathigherthantoday(CondieandKorenaga,2010; Cartigny and Marty, 2013), but variations in thisparameteralsohaveminimal influenceontheoutputofourmodel(SectionA3).Theeffectsofmorerapidsubductionandenhanced devolatilization may have more or less canceledeachotherwithoutanetincreaseofnitrogendrawdown.

Preferential nitrogen burial (option ii) couldpotentially occur through adsorption of NH4

+ onto clayminerals.Boatman&Murray(1982)experimentallyderivedarelationship between the amount of NH4

+ adsorbed on clayand the dissolved NH4

+ concentration in solution. For adoubling of the total nitrogen burial flux, the adsorbedconcentration would have to match the concentration oforganic nitrogen. Shale samples of sub-greenschistmetamorphicgradetypicallyhavenitrogenconcentrationsinthe range of 100-1000 ppm with C/N ratios around 40,suggesting that most nitrogen is derived from organics(Stüekenetal.,2016).ToachievethisconcentrationthroughNH4

+ adsorption alone would require a dissolved NH4+

concentrationof3-30mM,whichis30-300timeshigherthantheNH4

+concentrationof themodernBlackSea (~100μM,BrewerandMurray,1973),and100-1000higherthanmodernmarineNO3

-levels(~30μM,Sverdrupetal.,1942).Suchhighammonium abundances are also inconsistent with thenitrogen isotope record, which suggests that N-limitedecosystemsdominatedbybiologicalN2fixationwereinitiatedin the Mesoarchean at 3.2 Ga (Stüeken et al., 2015a) andpersisteduntil theGOEat~2.35Ga(Stüekenetal.,2016).Alarge reservoir of dissolved NH4

+ should have resulted inisotopic fractionations of up to 27‰associatedwith partialNH4

+assimilationintobiomass(Hochetal.,1992;Pennocketal., 1996), which is not observed. Moreover, due to theextreme energetic cost of splitting the N≡N triple bond,nitrogen fixation should have been suppressed rather thanexpressed where ammonium was readily available as anutrient. Enhanced nitrogen burial through adsorption isfurther inconsistent with the record of C/N ratios, becausesignificant addition of adsorbed NH4

+ would requireconsistentlylowerC/NratiosintheearlierPrecambrian,whichisoppositetoobservations;C/Nratiostendto increasewithincreasing age due to preferential nitrogen loss during low-grademetamorphism(Stüekenetal.,2016).NH4

+adsorption

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toclayslikelydidoccurduringdiagenesis,whereNH4+inpore

waterscanbecomeenrichedtoseveralmMbydegradationoforganicmatter(e.g.Rosenfeld,1979;BoudreauandCanfield,1988), but in that case the adsorbed nitrogen is simplyreturnedtothesedimentfromwhichitwasderivedanddoesnotleadtoexcessnitrogenburial.EnhancedNH4

+adsorptionin theArcheanocean is thereforeunlikely tohave caused adrawdown inatmosphericN2. Instead,we find itmore likelythat absolute organic carbon burial, and with it organicnitrogenburial,weresignificantlyhigher(optioniii).3.EnhancedvolcanicCO2outgassingintheearlierPrecambriancould explain greater nitrogen burial if accompanied byincreased burial of both organicmatter and carbonate. Theobserved constancy of forg could have been maintainedthroughcarbonatizationofoceaniccrustasalargecarbonatesink (Nakamura and Kato, 2004). Organicmatter burial waslikely concentrated under anoxic waters along continentalmargins where sedimentation rates were high. Such anenhancedbiomassburialfluxwouldhaveledtoanincreaseinnitrogen burial and can thus explain the observation of lowNeoarchean pN2 (Fig. 2c). Following the formulation ofCanfield(2004)forahigherheatflowandproportionallyhighervolcanic fluxes in deep time, this scenario increases thenitrogenburial fluxby40-80%(dependingon theexactage)relative to our early Paleozoic base value, or 3.4-1.9 timesabovetheforg factoralone,throughoutmostoftheArchean.We note that the assumption of a higher Archean CO2 flux(Canfield, 2004; Zahnle et al., 2006)hasbeen challengedbystudiesarguingforagradualincreaseinCO2outgassingfromthe Archean into the Proterozoic, concurrent with latecontinentalgrowth(Holland,2009;Leeetal.,2016).However,ifvolcanicCO2emissionswerelowerintheArcheanthantheyaretoday,absolutecarbonburialwouldhavebeenlowerandwith it theburialofnitrogen.LowArcheanCO2fluxeswouldonlybecompatiblewithhighnitrogenburial if forghadbeenmuchhigherthangenerallyassumed.AhighArcheanCO2fluxthusremainsthemostplausiblemechanisminourmodeltoexplainadeclineinpN2from0.5-1.1barat3.5Gato<0.5barat 2.7 Ga, as suggested by paleobarometers (Marty et al.,2013;Sometal.,2016).Wewill thereforeproceedwiththisassumption, noting that the Archean CO2 flux requiresadditionalconstraintstoderiveamoreaccuratetrajectoryforpN2.

Wefurthernotethatahigherabsoluteburialfluxoforganic carbon would constitute a source of oxygenequivalents that would have needed to be balanced byreductants to maintain anoxic surface conditions in theArchean (Kasting, 2013). Proposed fluxes of possiblereductants (H2, CO, H2S, Fe

2+) range over an order ofmagnitude (reviewed by Zahnle et al., 2006; Holland, 2009)andcouldthereforeplausiblycovertheeffectofcarbonburial.Reductantfluxesmayindeedhavebeenhigherthanpreviously

suggested during the earlier Archean if new evidence for asecularincreaseintheredoxstateofEarth’smantleistakenintoaccount(Nicklasetal.,2015).A2-to-4-foldhighercarbonburialfluxdoesthereforenotnecessarilyviolateredoxbalancemodels.

IfwecalibrateourmodelwiththeresultsofSometal.(2016),whoinferredanatmosphericpressureof<0.5barfrom the relative sizes of vesicles in basalt flows, then thelowerpartofouruncertaintyrangeinFig2cismorelikelytobecorrectthantheupperpart.Inthiscase,ourmodelpredictsthelowestatmosphericpressureintheNeoarcheanandtwostepwise increases across the Paleoproterozoic andNeoproterozoicoxidationevents,whenoxidativeweatheringprogressively shortens the residence time of nitrogen incontinentalsedimentsandcrust.Ourpredictionof~0.6PAN(=0.47barN2) in theMesoproterozoic is testablewith furtheranalysesofvesiclesizesinProterozoiclavaflows.4.Theeffectofsuperplumesisdifficulttoassess;theycouldhave led to either more rapid nitrogen recycling throughcrustal melting or slightly enhanced nitrogen drawdownthroughcarbonburial.Thebalancemayfurtherdependontheredoxstateofmagmaswhichmayhavechangedovertimeinfavor of progressively more N2 degassing (Mikhail andSverjensky,2014).Overall,reconfigurationsofthedeepEartharecurrentlypoorlyconstrained,but thesecouldpotentiallyhavesignificanteffects,beyondthescopeofourmodel.4.2. Climatic effects of atmospheric pN2 changes in theArchean Significant changes of >0.1 PAN in our modeledatmospheric N2 abundances occur over several hundredmillion-year time scales (Fig. 2c,d). Although atmosphericpressure affects the greenhouse efficiency of otheratmospheric gases like CO2 through pressure broadening(Goldblattetal.,2009)andcanthereforetheoreticallycausechangesinsurfacetemperature,thesetimescalesaresolongthatanyresultingtemperaturechangecouldbebalancedbythe carbonate-silicate feedback cycle, which has a responsetimeontheorderofafewhundredthousandyears(Sundquist,1991). As pN2 declines, greenhouse warming decreases,causingtheplanettocool.However,withlowertemperatures,silicateweatheringbycarbonicacidslowsdown,whichlowersthesinkfluxofatmosphericCO2fromtheatmosphere(Walkeret al., 1981). CO2 would thus build up and balance thetemperaturechangecausedbythedropinpN2. Table1showstherequiredresponseinpCO2toourcalculateddropinpN2intheArchean.Thesecalculationsalsotakeintoaccounttheincreasingsolarluminosity,whichwarmstheplanetandthereforeleadstoasteadydecreaseinpCO2.Insum,theeffectofrisingsolarluminosityoverpowerstheeffectofdecliningpN2from3.5Gato2.7Gainournominalmodelscenario (Fig. 2c), and hence pCO2 would have needed to

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decreasetomaintainastablesurfacetemperatureof278K.IfpCO2 did not respond, then surface temperature wouldincreasebyabout4degreesoverthistimeintervalduetotheincreaseinsolarluminosity,despitethedropinpN2.Itisonlyincasesofextremenitrogenburial,thatis,atthelowerlimitof our uncertainty interval in the model with an additionalsuperplume (Fig. 2d, excluding potential effects of crustalmelting), that the decline in pN2 would cause surfacetemperaturetodropbyaround7.5degrees.Thisdropcouldhavebeencounterbalancedbyathree-tofive-foldincreaseinpCO2.Wenote thatallofourcalculatedvalues forpCO2 fallwithin, or very close to, the range of late Archean CO2pressuresinferredfromtherockrecord(0.003-0.15barat2.5Gaand0.004-0.75bararound2.7Ga,Sheldon,2006;Drieseetal., 2011; Kanzaki and Murakami, 2015). Although theseestimatesvarywidely,thisagreementsuggeststhatourmodelresults are not unrealistic. Overall, plausible changes inatmosphericpN2 as inferred fromourmodel are unlikely tohave resulted inmassive climatic perturbations. (We notethat a requirement for globally averaged temperaturesapproachingmodernvalues(~288K)orhigherthroughouttheArcheanwouldbehardtoreconcilewiththemostrestrictiveconstraintsonpCO2frompaleosolsevenwithouttheclimaticimpactoffallingpN2,whichisthewell-knownFaintYoungSunParadox. For all butourmost extreme scenarios, fallingpN2wouldonlynegligiblyexacerbatethisproblem.)4.3.N2inextraterrestrialatmospheres Geological and potential biological processes onother planets may differ markedly from those on Earth, asmightthe initialvolatile inventory.Ourresultscanthereforeonly provide qualitative trends, but they may neverthelessserve as useful guidelines in evaluating measurements ofatmosphericpN2inexoplanetaryatmospheres(Schwietermanet al., 2015b). At the very least, our approach allows us toisolate selected variables that have the potential to play amajorroleintheevolutionofaplanet’snitrogencycle. Most importantly, nitrogenburial under completelyabioticandanoxicconditionsonanEarth-likeplanetwithinthehabitable zone is likely to be trivial compared to mantledegassing,andhenceanuninhabitedEarth-likeplanetwithasignificant nitrogen inventory is unlikely to ever show lowatmospheric N2 pressures (Fig. 3a). This conclusion may beviolatedinafewcasesasfollows:(a)Onyoung,veryhot(>1000K),reducingplanets,N2mayberapidly reduced to NH3 and dissolved in a magma ocean(Wordsworth,2016).Thisscenariocouldprobablyberuledoutby inferring the planetary temperature throughmeasurements of infrared emission, examination of theplanet’satmosphericscaleheighttodetermineH2abundance,and/orobservationsofthehoststartoprovideanestimateoftheplanet’sage.

(b)AtmosphericpN2maybepermanentlylowonplanetsthathave lost their atmosphere by erosion and where theoutgassingrateisatleastanorderofmagnitudelowersothatthe atmosphere cannot be replaced (e.g.,modernMars). Inthiscase,however,theabundanceofotheratmosphericgaseswouldalsobeverylow,andtheplanet’spropensitytoloseitsatmosphere could be inferred from direct or indirectmeasurementsofitsmassandradiusandthereforeitssurfacegravity.(c)NitrogenburialcouldbemoreeffectiveifabioticN2fixationbyvolcanism,lightning,orimpacts(KastingandWalker,1981;Kasting, 1990; Navarro-González et al., 1998;Mather et al.,2004)isatleastanorderofmagnitudehigherthanestimatedfor early Earth. If the pH of the ocean on such a planet issignificantly higher than 5, then even larger fixation rateswouldbe required,becauseotherwise fixedNH4

+ (producedafterconversionofNO3

-toNH4+viahydrothermalreduction)

(Brandesetal.,1998)wouldbereturnedtotheatmosphereasNH3gasinsteadofadsorbingontomineralsurfaces(Stüeken,2016).NH3gasquicklydissociatesback toN2underUV light(Kuhn and Atreya, 1979). So far, a theoretical basis forunusually high extraterrestrial lightning rates is lacking.Enhanced volcanic activity may be detectable remotelythrough time-dependent observations of sulfate aerosolsthroughtransmissionspectroscopy(Misraetal.,2015).(d) Planets may have had a large compositional deficit ofnitrogen after the initial period of accretion and enhancedatmospheric erosion by stellar UV light (Lichtenegger et al.,2010;Wordsworth and Pierrehumbert, 2014). This scenariomaybedetectablethroughtheabundanceofothervolatilesinthe planet’s atmosphere or measurements of the nitrogenabundanceinthehoststar(e.g.Breweretal.,2016).(e) Planets with a markedly lower oxygen fugacity in theirmantlecomparedtothatofEarthmaynotdegasN2,becausemantlenitrogenmaybe stableasNH3and thus less volatile(MikhailandSverjensky,2014;Lietal.,2015).ButsuchplanetsmaybediscernablebythepresenceofCOratherthanCO2intheiratmospheres.

Forplanetsthatdonotfallwithinthehabitablezone,andthusarenotcoveredbyourmodelresults,otherscenarioscouldapply.Forexample,planetsthatareclosertothehoststarthanthehabitablezonethatlackasurfaceocean,suchasVenus, would show insignificant nitrogen burial, and henceatmosphericN2would increaseas themantledegasses.Thiseffect would be enhanced on planets with a high oxygenfugacitywhereN2outgassingisfavoredoverNH3retention,asproposed for early Venus (Wordsworth, 2016). Planets farbeyondthehabitablezonemayhavelowatmosphericpN2iftemperatures drop low enough for N2 to become liquid orsolid, such as on modern Pluto and possibly ancient Titan(McKay et al., 1993; Lorenz et al., 1997). Hence, pN2 canfluctuateabiotically insuchextremecases,butforEarth-like

13

planetswithinthehabitablezoneasconsideredinourmodel,abioticN2drawdownismuchlesslikely. AbiosphereonacompletelyanoxicEarth-likeplanetcanpotentiallyhavesubstantialeffectsonatmosphericN2(Fig.3b). A nitrogen burial flux equivalent to a few percent ofmodern biological N2 fixation rates (without oxidativeremineralization)maybesufficienttodepletetheatmosphereofN2 ifmantleoutgassing rates are comparable to thoseofEarth.Intheabsenceofoxidativeweathering,theonlysteadyreturnfluxesofburiednitrogenbacktotheatmospherewouldbe metamorphism, volcanism, and mantle outgassing, andpossiblycatastrophicevents(Section3.3.2).Itisimportanttonote,however,thatburialratesmaybesignificantlydifferenton planets that lack a surface reservoir equivalent tocontinentalcrustonEarth (Fig.3d),which isable to takeupand release atmospheric N2 on hundred-million-yeartimescales.

Overall, our results strengthen the conclusion thatthesimultaneouspresenceofsignificantamountsofbothN2andO2may be a biosignature and indicative of a biospherewith oxygenic photosynthesis (Schwieterman et al., 2015b;Krissansen-Tottonetal.,2016)(Fig.4).Asshownabove,alargeanaerobic biosphere that never "invents" oxygenicphotosynthesis can draw down N2 to relatively low levels.Hence,bothO2andN2wouldbelow.Atmosphericerosionandthe possibility of an unusually low mantle fugacity can beevaluatedindependentlyinsuchascenario(e.g.,Mars).OnacompletelyabioticplanetorbitinginthehabitablezoneaSun-likestar,O2canbuildupabiotically,butprobablyonlyunderthe condition that non-condensible gases (including N2) arepresent in low amounts (Wordsworth and Pierrehumbert,

2014). According to thismodel,water froma surfaceoceanwouldbeabletoentertheupperatmospherewhereitwouldbephotolyzedbyUV,causingtheHtoescapeandOtobuildupaftersurfacesinksforoxidantsaredepleted.Inthiscase,N2must start and remain low, otherwise theprocess is halted.Hence,highlevelsofabioticO2wouldnotco-existwithathickN2 atmosphere. (Though note the likelihood that abiotic O2maybesubstantiallyhigherforplanetsorbitingMdwarfstarsdue to other mechanisms not applicable to solar-type hoststars (e.g. Harman et al., 2015; Luger and Barnes, 2015). Ahigh-O2-low-N2scenarioisdifficulttocreatebiologicallygiventhe strong tendency of oxidative weathering and increasingoxygenfugacityinthemantletoreleaseN2totheatmosphere.An inhabited planet whose biosphere invents oxygenicphotosynthesis could eventually transition to oxidativeweathering, thereby initiating rapid recycling of buriednitrogenfromcontinentalcrustasonearlyEarth(e.g.Fig.2c).ThisisthusperhapstheonlycasewherebothN2andO2reachhighrelativeabundancesintheatmosphere.Insummary,(1)a planet with high pN2 and no O2 probably has either nobiosphere(e.g.,Venus)oraverysmalland/oryoungbiosphere(e.g., first life on the Hadean Earth) that is incapable oftransferring large quantities of nitrogen to the crust, (2) aplanetwithO2butnoN2maybeuninhabited,(3)aplanetwithneitherO2norhigh(modern)abundancesofN2mayhostananaerobic biosphere as exemplified by Archean Earth,providedthatatmosphericerosioncanberuledout(cf.Mars),and(4)aplanetwithbothsignificantN2andO2suggeststhepresence a biosphere powered at least in part by oxygenicphotosynthesisasonmodernEarth.LowtotalN2onananoxicplanet (case3)maybeaweakbiosignature,whichcouldbeconfirmedthroughthedetectionofotherbiosignaturegasesorsurfacefeatures(e.g.DesMaraisetal.,2002;Pilcher,2003;Domagal-Goldmanetal.,2011;Schwietermanetal.,2015a).

5.Conclusion Thewiderangeofuncertaintiesinallourmodels,inparticularaboutanythingrelatedtopossiblereconfigurationsof Earth’s mantle (Mikhail and Sverjensky, 2014), prohibitsfirmconclusions.Nevertheless,ourresultsallowustoisolateafewkeyparametersfortheevolutionofaplanet’snitrogencycle and to formulate hypotheses about the evolution ofatmosphericN2reservoirsonEarthandotherplanets.Someof thesehypothesesmaybetestablewithmoreconstraintson nitrogen fluxes and with additional measurements ofgeologicalproxiesforatmosphericpressure(Sometal.,2012;Martyetal.,2013;GlotzbachandBrandes,2014;Kiteetal.,2014;Sometal.,2016)(seeKavanaghandGoldblatt,2015forpossiblecomplications). To first order, our results suggest that the greatestvariabilityinatmosphericpN2overthehistoryofaplanetcanbe achieved if the planet is inhabited, if biomass burial ishighlyvariable,and/orifitexperiencesoxygenationeventsor

Figure4:Plausible interpretationsofobservedN2andO2abundances in exoplanetary atmospheres. Quantitativeconstraints on cutoffs for "low" and "high" abundanceswould need to be evaluated based on measurements ofother gases and comparisons to other planets in theobservedsystem.

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large-scale crustalmelting. Other abiotic scenarios could beenvisionedthatcouldpotentiallyleadtopN2fluctuations,suchasN2freeze-outoratmosphericloss,butmanyofthesecaseswould likely be discernable through other observations, inparticulartheorbitoftheplanetandtheabundancesofothergases.Onaninhabitedplanet,variationinbiomassburialcanresult from changes in the supply of metabolic substratesincludingCO2 (asonEarth, Fig. 2c,d) andN2 (as inpotentialexoplanets, Fig.3b). In thecaseofEarth,enhancedbiomassburialintheArchean,followedbyastepwiseshorteningofthecrustal residence time across the Paleoproterozoic andNeoproterozoic increases in oxidative weathering, couldexplain the drawdown and recovery of atmospheric N2inferred fromabundancesofN2 in fluid inclusions at 3.5Ga(Marty et al., 2013) and the size distribution of basalticamygdalesat2.7Ga(Sometal.,2016).Wenotethatthereisnoindependentevidenceofenhancedburialofbothorganiccarbonand carbonate in theArchean,because totalorganiccarbon(TOC)andcarbonatecontentsofArcheansedimentaryrocksarenotknowntobeparticularlyhigh.Thisdiscrepancymaysuggestthatlargeamountsofcarbon-richsedimentsandcarbonatedbasaltshavebeensubductedandlost.Ifoneweretorejectourhypothesisofenhancednitrogendrawdownintocontinental crust as a temporary reservoir, then anotheralternative possibility for explaining a low Neoarchean N2pressure(Sometal.,2016)wouldbeamuchlowerinitialpN2valueintheearlyArchean,followedbyamarkedincreaseinmantledegassingatsometimebetweentheNeoarcheanandthemodern.Atestwithour“Forg”modelsuggeststhatsuchatrajectorycouldbeachievedifthemantledegassingratewereanorderofmagnitudehigherthroughoutEarth’shistorythanthought (Busignyetal.,2011).However, thisscenariowouldbe inconsistentwithproposedN2pressuresof0.5-1.1barat3.5 Ga (Marty et al., 2013). There is also no evidence for amajortransitioninthestyleorrateofmantleoutgassing.Butifsuchatransitionoccurred,itcouldconceivablyberelatedtoproposed changes in the mantle’s redox state (Mikhail andSverjensky, 2014; Nicklas et al., 2015; Aulbach and Stagno,2016).Furtherresearchisneededtoevaluatethispossibility. Lastly, our results may have some practicalimplicationsforobservationsofextrasolarplanets.Despiteallthe uncertainties in ourmodels, our results suggest that ananaerobic biosphere can – under Earth-like geologicalconditions – remove significant amounts of N2 from theatmosphere.Ifmultipleterrestrialplanetsaroundanotherstarstartedoutwithsimilarvolatilecontents,butoneofthemhasasignificantlyloweratmosphericN2abundance,thenthismaypotentially serve as a biosignature. Measurements of othergasesmaybenecessarytoruleoutatmosphericerosionasonMars. In contrast, a planetwith an oxygenic biosphere thatstimulates oxidative weathering could maintain anatmosphererichinbothN2andO2,similartothepost-ArcheanEarth.Ourresultsthussupporttheideathatthecombination

of N2 and O2 in an exoplanetary atmosphere may be asignature of a biosphere that is capable of oxygenicphotosynthesis (Wordsworth and Pierrehumbert, 2014;Schwietermanetal.,2015b;Krissansen-Tottonetal.,2016).Acknowledgements

WethanktheNASApostdoctoralprogram(EES;EWS),the NSF Graduate Research Fellowship program (MAK), theNSF FESD program (grant number 1338810, subcontract toRB),theNSERCDiscoveryprogram(BJ),theNASAExobiologyprogram (grant NNX16AI37G to RB) and the NAI VirtualPlanetary Laboratory at the University of Washington(solicitation NNH12ZDA002C and Cooperative AgreementNumber NNA13AA93A; EWS, RB) for financial support. WethankJimKastingandtwoanonymousrefereesfornumeroushelpfulcommentsthatimprovedthemanuscript.ReferencesAbbott,D.H.andIsley,A.E.(2002)Theintensity,occurrence,and

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Appendixto:

ModelingpN2throughGeologicalTime:ImplicationsforPlanetaryClimatesandAtmosphericBiosignatures

E.E.Stüeken1,2,3,4*,M.A.Kipp1,M.C.Koehler1,E.W.Schwieterman2,4,5,B.Johnson6,R.Buick1,4

1.Dept.ofEarth&SpaceSciencesandAstrobiologyProgram,UniversityofWashington,Seattle,WA98195,USA2.Dept.ofEarthSciences,UniversityofCalifornia,Riverside,CA92521,USA3.DepartmentofEarth&EnvironmentalSciences,UniversityofStAndrews,StAndrewsKY169AL,Scotland,UK4.NASAAstrobiologyInstitute’sVirtualPlanetaryLaboratory,Seattle,WA981195,USA5.Dept.ofAstronomyandAstrobiologyProgram,UniversityofWashington,Seattle,WA98195,USA6.SchoolofEarth&OceanSciences,UniversityofVictoria,Victoria,BCV8P5C2,Canada*correspondingauthor(evast@uw.edu)A1.Detailedmodeldescription

Theboxesincludedtheatmosphere,pelagicmarinesedimentsdepositedonoceaniccrust,continentalmarinesedimentsdepositedoncontinentalshelves,continentalcrust,andthemantle.Wedidnotincludeoceaniccrustasaseparatebox,becausenitrogenthatistakenupintooceanicbasaltduringalterationisthoughttobederivedfromsediments(Halamaetal.,2014)andwasthereforealreadyaccountedforbypelagicdeposition.Nitrogenburialremovesnitrogenfromtheatmospherewhilemetamorphism,volcanism,andmantleoutgassingreturnnitrogen.AsensitivityanalysesofourmodelispresentedinSectionsA3andA4.A1.1.Nitrogenburial

Inmostofourmodels,theNburialfluxwascalculatedbasedonorganicCburial,consistentwiththeapproachofBerner(2006b).ThetotalvolcanicCO2fluxtoday(FCO2(modern))is~6·1018mol/Myr(range4·1018mol/Myrto10·1018mol/Myr)(MartyandTolstikhin,1998).IntheearlyPaleozoic,priortotheevolutionoflandplants,~22%ofthatfluxwasburiedasorganiccarbon(forg(Paleozoic))(Krissansen-Tottonetal.,2015).(LandplantsareexcludedtomakeourmodelapplicabletoallofEarth’shistory).Multiplyingthesenumbersyieldsanorganiccarbonburialfluxofaround1.3·1018mol/Myr.AveragealgalbiomasshasaC/Nratioofaround7((C/N)algal)(GodfreyandGlass,2011),whilemarinesedimentsfromthelastfewmillionyearsdisplayanaverageC/Nratioof~13(Algeoetal.,2014).Weassumedameanvalueof10andcalculatedaNburialfluxof1.3·1017mol/Myr.Holdingthisvalueconstantthroughtimeconstitutesour‘basemodel’(Fig.2a).Themodernnitrogenburialflux(Fbuial)isthuscalculatedas:

Fburial(modern)=FCO2(modern)*forg(Paleozoic)*(C/N)algal (Equ.A1)Wethenusedtherecordoforganiccarbonburial(forg(t))tocalculatenitrogenburialindeeptime(Fburial(t)).Inafirst

test,weheldCO2input(FCO2)constantatthemodernvalueandusedthecarbonisotoperecord(Fig.A1)(Krissansen-Tottonetal.,2015)tomodulatethepre-Devonianorganicburialfractionof~0.22,i.e.thevariableforginEqu.(A1)becameafunctionoftime((forg(t)).Thiswastermedthe‘Forg’model(Fig.2b).

Inasecondtest(‘Forg+Heatflow’),weassumedhigherCO2inputinthePrecambrian,assuggestedbyahottermantle,fasterplatetectonicsandmorevigorousvolcanism(SleepandZahnle,2001).ThismadeFCO2inEqu.(A1)afunctionoftime(FCO2(t)).GreaterCO2inputwouldhaveraisedtheburialfluxesofbothorganiccarbonandcarbonatewithoutleavingasignatureintheδ13Crecord.WeusedtheparameterizationofCanfield(2004,Equ.2),whichpredicts~3timeshigherCO2inputat4Gyrand~2timeshigherinputat2.7Gyr.

Inathirdtest(‘Forg+Heatflow+Superplumes’),weincreasedCO2inputandhencenitrogenburialevenfurtherduringintervalsofplumevolcanism.WeincreaseNburialbyafactorof2duringeachdiscreteplumeevent,whosetimingwasdeterminedfromthecompilationofAbbotandIsley(2002).Inmathematicalterms,thetimedependenceofForg(t)wasthuschangedslightlyrelativetothe‘Forg+Heatflow’model.Thefactorof2burialenhancementwassuggestedforthemid-

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Cretaceouseruptionsofoceanicplateausandrelatedcontinentalbreakup(CaldeiraandRampino,1991),andthusmaynotbeapplicabletosuperplumeevents.Wethereforealsotestedlargerburialenhancementvaluestodeterminemaximumplausibleeffectsonthenitrogencycle(seeSection3.1.3).

Inaseparatesetofmodels,weexploredtheeffectsofnitrogenburialonacompletelyabioticplanetandonananoxicplanetwithasmallbiosphere.Inbothcases,oxidativeweatheringwasturnedofftomimictheabsenceofbiogenicO2.NitrogenburialfluxesonanabioticplanetweretakenfromStüeken(2016)andkeptconstantthroughtime.Nitrogencanbefixedabioticallybylightning,impactshockheatingandvolcanism,whichgenerateNO3

-(KastingandWalker,1981;Kasting,1990;Navarro-Gonzálezetal.,1998;Matheretal.,2004).HydrothermalcirculationcanconvertNO3

-toNH4+

(Brandesetal.,1998),whichcaninturnbeburiedinsedimentsbyadsorptiontoclayminerals(BoatmanandMurray,1982).AbioticnitrogenburialinsedimentsdependsonthepHofseawater,becausedissolvedNH4

+dissociatestovolatileNH3+H+

withapKaof9.25atstandardconditions(Lietal.,2012),whichlowersthefluxofNH4+intosedimentswithincreasingpH.

Wechosetwoendmembers,oneatpH5withanN2fixationfluxof1011mol/Myr,andoneatpH8withanN2fixationfluxof

1010mol/Myr.TheseendmemberscorrespondtoNH4+burialfluxesof1.5·1016mol/Myrand2.2·1012mol/Myr,respectively

(Stüeken,2016).

FigureA1:ReconstructionofForgusedinourmodel(Krissansen-Tottonetal.,2015).ForgisdefinedasthefractionofCO2thatisburiedasorganiccarbonratherthancarbonate.

Forananoxicbiologicalplanet,wecalculatednitrogenburialfromthemodernbiologicalN2fixationrateof

8.68.6·1018mol/Myr(Gallowayetal.,2004),multipliedbyaproductivityfactorthatwasvariedfrom1%to10%.Weassumedthatrecyclingoffixednitrogenbacktotheatmospherewouldbenegligibleintheabsenceofoxygen,becausesulfateandironoxidesarenotstrongenoughoxidizersofammoniumundermostenvironmentalconditions(Stüekenetal.,2016).WhenatmosphericpN2droppedtozero,weranseparatetestswherethebiospherewasturnedoffatthatpoint,mimickinganextinction.ForallabioticandanoxicbiologicalmodelrunstheinitialN2inventoryoftheatmospherewassetequalto1.0PAN.Allotherparameters(metamorphism,subduction,etc.)werekeptatEarthconditions.Thisisofcourseasimplification,becausetheseparameterscouldbemarkedlydifferentonotherplanets,buttestingawiderparameterspaceisbeyondthescopeofthispaper.Ourchoseapproachallowsustoisolatetheeffectoflifeandoxygen.

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A1.2.Shelfversuspelagicburial

Inallourbiologicalmodels,weassumedthat96.2%ofbiomassburialoccurredoncontinentalshelves,while3.8%occurredinpelagicsedimentsintheopenocean,i.e.inaratioof25.3(Berner,1982).Burialinthetworeservoirsarethusdefinedas:

FburialContinent=Fburial*0.962 (Equ.A2)FburialPelagic=Fburial*0.038 (Equ.A3)

whereFburialisdefinedasinEqu.(A1)orkeptconstantasintheabioticandanoxicmodels.Today,continentalshelvesaremajorlocalesofcarbonburialbecauseproductivityisstimulatedbynutrientsfrom

landandsedimentationratesarehigh(Berner,1982).BothfactorswouldalsohavebeenvalidinthePrecambrian.Furthermore,continentalshelvesintheArcheanwouldhavebeenrelativelymoreanoxicthantoday,soalargerproportionoffixedcarbonandnutrientsmayhavebeenretainedinsteadofbeingtransportedintotheopenocean.AsshownbyLyonsetal.(2014),Archeanshalesingeneral,includingthosefromcontinentalmargins(e.g.EigenbrodeandFreeman,2006),commonlyhaveTOClevelsofseveralpercent,equivalenttothoseofNeogeneanoxicbasinsandhigh-productivityareas.Theseconcentrationsaresignificantlyhigherthantheaverageof~0.6%ofmoderncontinentalshelves(Berner,1982).ItisthereforeconceivablethatorganiccarbonburialoncontinentalshelvesintheArcheanwasproportionallyhigherthanitistoday,attheexpenseofpelagicsediments.

Ontheotherhand,therelativeproportionsofpelagicandshelfburialmayhavechangedwithcontinentalgrowth(Fig.A2),butthiseffectislikelyminor,becauseshelfareawouldhavegrownrelativelyfasterthancontinentalmass.First,thesurface/volumeratioisgenerallylargerforsmallerobjects,andsecond,withlesstotalcontinentalmass,thelikelihoodofcollisionswouldhavebeensmaller,meaningthatthenumberoflandmassesandtherelativelengthofcontinentalmarginswaslikelyhigherthantoday.Furthermore,ithasbeenproposedthatcontinentalreliefincreasedovertime(ReyandColtice,2008).Ifso,thenalargerproportionoflandmassesmayhavebeenfloodedinthepast,makingshelfarealarger,relativetocontinentalmass.Itcouldattimeshavebeenevenlargerthantoday.Lastly,thetotalvolumeofseawatermayhavebeenhigherintheArchean(Popeetal.,2012),andmid-oceanridgesmayhavebeenlonger(Hargraves,1986),whichwouldfurtherincreasesealevelandshelfarea.Giventhenumberofuncertaintiesabouttheevolutionofcontinentalvolume,continentalrelief,oceanvolumeandnutrientdistributionintheocean,wedecidedtokeepthepelagicburialfractionconstantthroughtime.

FigureA2:EvolutionofcontinentalvolumethroughtimeasproposedbyDhuimeetal.(2012).Shelfareawouldhavebeenproportionallyhigherforsmallercontinentsbecauseofthehighersurface/volumeratioofsmallerobjectsandbecause

22

continentswouldlikelyhaveexistedasalargernumberofsmalllandmasseswithpotentiallylowerreliefandhighersealevelandoceanvolumethantoday.A1.3.Oxidativeweathering Continentalmarinesedimentsandcontinentalcrustweresubjectedtooxidativeweatheringinourmodel.Wefirstcalculatedarateconstant(Rwx)basedonthemodernnitrogenweatheringflux(FwxCont(modern))relativetothemoderncontinentalnitrogenreservoir(Mcontinent(modern)).Nitrogenweatheringattimetinthepast(Fwx(t))wasthencalculatedastheproductbetweentherateconstantandthenitrogenreservoirincontinentalcrust(Mcontinent(t)).Thesameratelawwasappliedtocontinentalmarinesediments.ThisfluxwasfurthermodulatedinproportiontoatmosphericpO2withareactionorderof0.5(ChangandBerner,1999;Boltonetal.,2006).Overall,thisledtothefollowingexpressionsforoxidativeweatheringofcontinentalcrustandshelfsediments: FwxCont(t)=Rwx*Mcontinent(t)*pO2(t)

0.5 (Equ.A4) FwxSed(t)=Rwx*McontSed(t)*pO2(t)

0.5 (Equ.A5)ThemoderncontinentalreservoirMcontinent(modern)wasassumedtobe1.21·1020mol(JohnsonandGoldblatt,2015).WeusedseveraldifferentsourcestodeterminethemodernweatheringrateRwx.Kump&Arthur(1999)andBerner(2006a)reportweatheringfluxesfororganiccarbon.DividingthosebyaC/Nratioof10andthecontinentalnitrogenreservoirfromaboveyieldsweatheringrateconstantsforNof0.00829Myr-1and0.0018Myr-1,respectively.Sleep&Zahnle(2001)reportaweatheringfluxforcarbonate,butnotorganiccarbon.Assumingacarbonatetoorganiccarbonratioofabout4:1inthecrust(Berner,2004)andproportionalweatheringfluxes,assupportedbylong-termstabilityincarbonisotopes(Krissansen-Tottonetal.,2015),thisyieldsanitrogenweatheringconstantof0.00351Myr-1,inbetweentheprevioustwoestimates.Alternatively,onecouldusethemodernriverinefluxofnitrogentotheocean(Gallowayetal.,2004;Algeoetal.,2014),whichyieldsaweatheringrateconstantof0.01478Myr-1to0.01657Myr-1.However,themodernfluxislikelystronglyaffectedbymodernlandvegetationandthereforeunlikelytobeapplicabletothePrecambrian.Wethereforechose0.00351Myr-1asamediumvalue. AsshownbyMontrossetal.(2013),oxidativeweatheringgeneratesnitratethatiswashedintotheoceanwhereitissubjecttodenitrificationtogetherwiththemarinenitratereservoir.Inourmodel,whichiscalibratedbycarbonburial,thiscontributionoffixednitrogentothemarinebiosphereisindirectlyaccountedforinthenetremovalfluxofnitrogenfromtheatmospherethroughburial.Whateverisnotremoved,ispracticallyreturnedtotheatmospherebydenitrification.Theoxidativeweatheringfluxisthereforedirectedtotheatmosphereinourmodel.

FigureA3:EvolutionofatmosphericpO2throughtimeusedinourEarthmodels.ThereconstructionofpO2istakenfromLyonsetal.(2014).OxidativeweatheringscaleswiththepO2withareactionorderof0.5(ChangandBerner,1999;Boltonetal.,2006).

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Indeeptime,weassumedthatoxidativeweatheringscaledwithatmosphericpO2withareactionorderof0.5

(ChangandBerner,1999;Boltonetal.,2006).WeusedthemostrecentreconstructionofpO2(t)byLyonsetal.(2014)(Fig.A3).Inthisreconstruction,pO2was10

-5timespresentatmosphericlevels(PAL)intheArchean(before2.5Gyr),itincreasedto10-3PALat2.5Ga(Kendalletal.,2015),thentomodernlevels(1PAL)duringthe“oxygenovershoot”inthePaleoproterozoic(2.3-2.2Gyr).Itreturnedto1%PALintheMesoproterozoic(2.0-0.9Gyr),androseagaintomodernlevelsbetween0.8Gyrand0.6Gyr.Transitionsbetweenthephaseswereimplementedaslinearinlogarithmicscale.

A1.4.Continentalerosionandmetamorphism Similartooxidativeweathering,thefluxesforcontinentalerosion(Ferosion)andinthepastattimetwerecalculatedastheproductbetweenthecontinentalsedimentreservoir(McontSed)attimetandafixedrateconstantthatwascalibratedwiththemodern.Theerosionfluxprimarilyincludesturbiditesthattransportmaterialfromthecontinentalshelvestothedeepoceanwhereitcanbesubducted.Toestimatethisfluxforthemodern(Ferosion(modern)),wecalculatedthedifferencebetweennitrogenaddedtopelagicsedimentsbybiologicalproductivitytoday(5.7·1015mol/Myr,i.e.3.8%ofallnitrogenthatisburiedglobally,withvolcanicCO2=6·10

18mol/Myr,forg=0.25,andC/N=10)andthetotalamountofnitrogenthatleavespelagicsedimentsviasubduction(5.42·1016mol/Myr)andmetamorphism(1.63·1017mol/Myr)(Beboutetal.,1999;Busignyetal.,2003;Busignyetal.,2011).Theresultingerosionalfluxof2.12·1011mol/Myrwasconvertedintoarateconstant(Rerosion)of0.001785Myr-1.Thiserosionalfluximpliesthatpelagicproductivitymakesupabout0.7%ofthetotalamountofnitrogeninoffshoremarinesediments,whichfallsnearthelowerendoftherangeof1-16%derivedfromamassbalanceoforganiccarbon(BauerandDruffel,1998).Wethereforeconsideredthisthelowerlimitandtestederosionratesupto10timeshigher.Theoverallequationfortheerosivefluxis: Ferosion(t)=McontSed(t)*Rerosion (Equ.A7)Applyingasimilarerosivefluxfromthecontinentalcrustintocontinentalsediments,asmayoccurinrapidlyerodingregionsthatescapeoxidativeweathering,hasminimaleffectonthecalculatedreservoirssizes(<0.01PAN).

Nitrogenincontinentalsedimentsultimatelygetsincorporatedintocontinentalcrust(“maturation”)withalagtimeof100millionyears(TSed,tested50-200millionyears).Duringthislagtime,anygivenparcelofnitrogenthatenteredthisreservoirthroughburialissubjecttooxidativeweathering(SectionA1.3)anderosionforthedurationofthelagtimeTsed.The‘maturation’fluxfromcontinentalsedimentstocontinentalcrustwasthusdefinedas:

Fmaturation(t)=FburialPelagic(t-Tsed)-[Rwx*FburialPelagic(t-Tsed)+Rerosion*FburialPelagic(t-Tsed)]*Tsed (Equ.A8)Oncethenitrogenreachedthecontinentalcrust,itsubjectedtometamorphism.Byanalogytootherfluxes,thecontinentalmetamorphicflux(FcontMetam)attimetwascalculatedastheproductbetweenthecrustalreservoir(Mcontinent)arateconstant(RcontMetam)derivedfromthemodern.Therateconstantforcontinentalmetamorphism(RcontMetam)wascalculatedfromthefluxoforganiccarbonmetamorphism(4·1017mol/Myrto6·1017mol/Myr)(WallmannandAloisi,2012),aninitialC/Nratioof10forunmetamorphosedorganicmatter(GodfreyandGlass,2011;Algeoetal.,2014)andtheassumptionthatnitrogenescapes2timesfasterthancarbon.Thisapproachyieldedarateconstantof0.000829Myr-1fornitrogenmetamorphism.Overall,thecontinentalmetamorphicfluxwasexpressedas: FcontMetam(t)=Mcontinent(t)*RcontMetam (Equ.A9)

TheassumptionoftwotimesfasternitrogenescaperelativetocarbonisbasedontheobservationthatC/Nratiosingreenschisttogranulitefaciesrocksdisplayamedianof15(Stüekenetal.,2015andreferencestherein).Themedianincreasesto27ifalldatapointsfromtheAravalliGroupwereexcluded,whichtendstohavelowerC/Nratiosonaveragecomparedtoothergeologicalunits(Papineauetal.,2009;Papineauetal.,2013).Usinganaverageratioofaround20comparedtoaninitialratioof10wouldthussuggest2timesmorenitrogenlossrelativetocarbon.ThisnumberisalsosupportedbytheaverageC/Nratioof10-30fortotalcontinentalcrust(1.1-4.0·1021molCand1.2·1020molN)(Hunt,1972;Berner,2004;JohnsonandGoldblatt,2015).Therefore,weuseda2xfasternitrogenlossfactorinourpreferredmodel.ItistruethatC/Nratiosoflow-grademetamorphicrockscanbeashighas100-200(Stüekenetal.,2015andreferencestherein),however,atveryhighgradeorduringpartialmelting,relativelymorenitrogenisprobablyretainedinsilicatemineralswhilekerogenispreferentiallylost.Anoverallhigherlossrateof2xfornitrogenovercarbonthereforeseemsmostappropriate.Asupperandlowerlimits,weconsideramaximumuncertaintyintervalforthisnumberfrom1xto10x,correspondingto

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scenarioswherenitrogenlossoccursatthesamerateascarbonloss,or10timesfastertoexplainC/Nratiosupto100.Thisupperlimitislikelytoohightobearealisticglobalestimate,butwasincludedforthoroughnessinourmodels.AmorelikelylimitcanbederivedfromtherangeofmedianC/Nratiosof15-30,correspondingto1.5xto3xfasternitrogenlossrelativetocarbon.Weusedthisrangetoarriveatourpreferreduncertaintyinterval. A1.5.Subductionzonemetamorphism,volcanism&nitrogensequestrationinthemantle

Pelagicsedimentsweresubjectedtosubductionaftertheir100millionyeartransittime(Tpel)(testedrange50-200millionyears).Thefateofnitrogeninthesesedimentswasdesignatedaseither(1)metamorphicdegassing(returnedtotheatmosphereduringmetamorphicdevolatilization,FpelMetam),(2)volcanism(returnedtotheatmosphereduringarcvolcanism,Fvolc),or(3)subduction(transferredtothemantle,Fsub).Therelativemagnitudesofthesefluxesarepoorlyconstrained,soweassembledvaluesfromtheliteratureandconductedasensitivitytesttoarriveatourpreferredvalues.Itisimportanttonotethatweappliedthesametransittimetoallthreefluxes,i.e.weassumedthatvolcanism,metamorphismandfurthersubductionalloperateatthesametime,althoughinrealitymetamorphismwouldstartseveralmillionyearsearlier.Asshowninoursensitivityanalysisbelow,thetransittimehasminimaleffectontheatmosphericN2budget,andthereforethissimplificationdoesnotviolateourconclusion.

Metamorphicdevolatilizationinsubductionzonesconstitutesasignificantnitrogenlossprocess(BeboutandFogel,1992;Bebout,1995).Inasuiteofmetasedimentaryrocksrangingfromlow-tohigh-gradeanalyzedbyBeboutandFogel(1992),rocksofamphibolitefacieswereshowntohavelost~80%(fpelMetam)oftheoriginalnitrogencontentasestimatedusingmarinesedimentsandrocksoflawsonite-albitefacies.Wethereforeexploredtherangefrom70%to90%forfpelMetam,ourmetamorphicdegassingparameter.Inmathematicalterms,themetamorphicdevolatilizationfluxfromsubductedmarinesedimentsisthusdefinedas: FpelMetam(t)=FburialPelagic(t-Tpel)+Ferosion(t-Tpel)*fmet (Equ.A10)

Thenitrogenremainingaftermetamorphicdegassingeitherreturnstotheatmosphereviaarcvolcanismoritgetssubductedintothemantle.Therelativeproportioningbetweenthesetwofluxesonaglobalscaleisdifficulttoassess.Estimatesrangingfrom100%recyclingtotheatmosphere(Elkinsetal.,2006)to<20%recycling(Mitchelletal.,2010)havebeenproposedformodernarcsettings,withlocaltemperature-pressureregimesappearingtocontributetothelargedisparitiesbetweendifferentsubductionzones(Halamaetal.,2014).Busignyetal.(2011)proposeda20%/80%partitioningofvolcanism/subduction(fvolc/fsub)asaglobalbudgetbasedonacompilationofseveralindependentstudiesofsubductionzoneinputandoutputfluxes.Tobethorough,weexploredthefullrangefrom0%/100%to100%/0%volcanism/subductionpartitioninginoursensitivitytests.Thefluxesforvolcanismandsubductionarethusdefinedas:

Fvolc(t)=FburialPelagic(t-Tpel)+Ferosion(t-Tpel)*(1-fmet)*fvolc (Equ.A11)Fsub(t)=FburialPelagic(t-Tpel)+Ferosion(t-Tpel)*(1-fmet)*fsub (Equ.A12)

Thetestswereconductedonourbasemodelwithoutanyperturbationstonitrogenburialincluded.Thefirstcriterionthatwesoughtinthemodeloutputswasaseculartrendofnitrogenaccumulationinthemantle.Allmodelswith90%metamorphicdegassingdidnotmeetthiscriterion.Ofthe70%and80%metamorphicdegassingscenarios,allthosewithlessthan30%subductionalsodidnotshowsecularmantlenitrogensequestration.Fromtheremainingscenarios,weelected70%metamorphicdegassing,20%/80%volcanism/subductionasourpreferredmodelbecause(1)itwasthebestfittotheglobalvolcanism/subductionestimatefromBusignyetal.(2011),and(2)itbestrepresentedtheproposedstabilityofPhanerozoicpN2.A1.6.Mantleoutgassing EstimatesformantleoutgassingofnitrogenonthemodernEarth(Fout(modern))rangefrom1.4-8.8·1015mol/Myr(Bebout,1995;Tajika,1998;Sanoetal.,2001;Busignyetal.,2011).Weadoptedavalueof7.1·1016mol/Myr,sincerecentstudieshavefavoredthehigherendoftheaforementionedrange(e.g.Busignyetal.,2011).WethendividedbythesizeofthemodernmantleNreservoir(1.7·1021molnitrogen,Mmantle(modern))(JohnsonandGoldblatt,2015)tocalculateanoutgassingrateconstant(Rout=4.15·10

-6Myr-1).Mantleoutgassingattimetinourmodel(Fout(t))wasthencalculatedbymultiplyingtherateconstantbythesizeofthemantlereservoirateachtimet:

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Fout(t)=Mmantle(t)*Rout (Equ.A13)Wedidnotvarytherateconstantasafunctionofgeologictimeinthebasemodel.InmodelswherenitrogenburialwasscaledbyenhancedCO2outgassing(followingCanfield,2004,discussedabove),themantleoutgassingrateofnitrogen(Rout(t))wasscaledbythesamefactorundertheassumptionthatoutgassingofCO2andN2wouldfollowthesamefirst-ordertrends.Testrunsinwhichmantleoutgassingwasnotscaledbythesamefactorasburialshowedlittledeviationfromthemodelsthatincludedoutgassingmodulation,sincemantleoutgassingisa~1-2orderofmagnitudesmallerfluxthannitrogenburial.A1.7.Differentialequationsforreservoirevolution

Usingthefluxesasdefinedabove,wecalculatedtherateofchangeofeachnitrogenreservoir(Mi)inourmodel(Equs.A14-A18).Reservoirsareinmolesofnitrogen,fluxesinmolespermillionyears.

Atmosphere:dMatm/dt=Fout+Fvolc+FpelMetam+FcontMetam+FwxCont+FwxSed-FburialSed-FburialPelagic (Equ.A14)

Continentalsediments:dMcontSed/dt=FburialContinent-Ferosion-FwxSed-Fmaturation (Equ.A15)Continentalcrust:dMcontinent/dt=Fmaturation-FcontMetam-FwxCont (Equ.A16)Pelagicsediments:dMpel/dt=FburialPelagic+Ferosion-FpelMetam-Fvolc-Fsub (Equ.A17)Mantle:dMmantle/dt=Fsub-Fout (Equ.A18)ThedifferentialequationsweresolvedbytheEulermethod.Initialreservoirsizesweredefinedsuchthatthenitrogenconcentrationwasequalinallreservoirs(seemaintext,Section2.1).Theinitialatmosphericnitrogencontentwasadjustedsuchthatthefinalresultsforthemodernwasequalto1.0PAN,exceptintheabioticandanoxicmodels,wheretheinitialvaluewassetto1.0PAN.A2.Evolutionofthecontinentalnitrogenreservoir Continentalmarinesedimentsandcontinentalcrustarethemajorrepositoriesofburiednitrogeninmostofourmodels.Fig.A4illustratesthenitrogencontentofcontinentsascalculatedinour“Forg+Heatflow”model(Fig.2b),whichisthemostplausiblemodelforreconstructinglowNeoarcheanpressuresasinferredbySometal.(2016).ThecontinentalreservoirisalmostamirrorimageofatmosphericN2.Ourcalculatedvalueformoderncrustiswithinafactorof2.2oftheamountestimatedbyJohnson&Goldblatt(2015),basedonnitrogenconcentrationsindifferentrocktypesandfractionalrocktypeabundancestakenfromWedepohl(1995).Giventherangeofuncertaintiesinbothourmodelandtheestimatesonmodernabundances,ourresultsareinfairlygoodagreement.

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FigureA4.Nitrogencontentofthecontinentalcrustthroughtime.NitrogenaccumulatesinthecontinentalcrustasprogressiveorganicburialsequestersNinthisreservoir.ThelateArcheanspikeincontinentalnitrogencorrespondstonitrogendrawdownatthistime.OurpreferredmodelpredictsamoderncontinentalcrustNreservoirsizeof5.4×1019mol(i.e.0.45timesthemoderncontinentalreservoir;uncertaintyinterval2.6-7.9×1019,i.e.0.21-0.66timesthemodern),whichiswithinafactorof2.2oftheestimateof1.2×1020molbyJohnsonandGoldblatt(2015).

A3.SensitivityanalysisforEarthmodels Wetestedeachvariableindividuallytoassessitsimpactonouroverallconclusions(Fig.A5andA6).Thecurvesarecomparedtoour“Forg+Heatflow”model,whichweconsiderthemostrealistic.Formostvariables,changesofinputvalueswithinouruncertaintyintervalhaveminimaleffect(<0.01PAN)ontheresults.Thisincludescontinentalerosionintopelagicsediments(Fig.A5e),thefractionofpelagicmetamorphism(Fig.A5h),thefractionofvolcaniclossfrompelagicsediments(Fig.A6a),andtheresidencetimesofsedimentsoncontinentalshelves(Fig.A6b)andinthedeepocean(Fig.A6c).Theinitialvalueofpre-DevonianForg(Fig.A5c)hasaminoreffect.AsshownbyKrissansen-Tottonetal,(2015),thevalueisuncertainandpossiblyvariable,butmostlikelywithintherangeof0.20-0.22.Thisrangeimpartsanuncertaintyof~0.06PANontheNeoarcheanpN2minimumwithnoeffectonourconclusions.

Forthepelagicburialfraction,wetestedarangefrom1%to30%.TheupperendofthisrangewouldonlyapplyintheHadeanandearliestArchean,whencontinentalshelfspacemayhavebeenlower(Fig.A2),andifmodernshelfareais‘maxedout’intermsofcarbonburial,suchthatwithsmallercontinentsandconstantcarbonburial,moreburialoccurredinpelagicsediments.However,asnotedabove,highArcheanTOClevelsinmarineshalessuggestthatArcheanshelveswereprobablycapableofholdinglargeamountsofcarbon.Furthermore,shelfareagrewproportionallyfasterthancontinentalmass.Asmalleruncertaintyrangeforthepelagicburialfractionisthereforemoreplausible.Arangeof1-10%(basevalue=3.8%,Berner,1982)givesanuncertaintyofonly0.08PANontheNeoarcheanN2minimum(Fig.A5d).

Foroxidativeweathering,theuncertaintyisontheorderof0.2PANforweatheringrateconstantsbasedonorganiccarbonweathering(seeabove).AlargerrateconstantleadstoamoredramaticN2risewiththePaleoproterozoicGreatOxidationEventandarelativelyhigheratmosphericN2pressureintheMesoproterozoic.Evenwiththelowerlimitontherateconstant,NeoarcheanpN2wouldstilldroptoaround0.54PAN,equivalentto0.42barofpressure.

LargeruncertaintiesresultfromchangesintheinitialCO2outgassingrate(Fig.A5a),theC/Nratioofmarinebiomass(Fig.A5b),andthecontinentalmetamorphicrateconstant(Fig.A5g).RegardingC/Nratios,thereissofarnoevidencethattheymayhavechangedoverthecourseofEarth’shistory.Wechoseavalueof10asameanbetweenthecanonicalRedfieldratioof7(GodfreyandGlass,2011)andobservedC/Nratiosof13inmarinemud(compilationbyAlgeoetal.,2014).Intherangeof10-13,theeffectonatmosphericN2isaround0.1PANintheNeoarchean.IfC/Nratiosweresignificantlydifferent

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thantoday,thenthismaypotentiallyhaveanimpactonourresults,assuggestedbyonemodelrunwheretheC/Nratiowassetto20throughoutEarth’shistory(Fig.A5b).IntheabsenceofevidenceforchangesinC/Nratios,wedonotconsiderthisparameteranyfurtherinthediscussionoftemporalchangesinpN2.

OurmodernCO2outgassingrateof6·1018mol/Myrwastakenfromthemostexhaustiveandmostwidelyquoted

studyonthissubject(MartyandTolstikhin,1998).Theauthorsquotearangefrom4-10·1018mol/Myr.AhighervalueleadstoamoredrasticArcheanN2drawdowninourmodel(Fig.A5a).ComparingthestudybyMarty&Tolstikhin(1998)tomorerecentcompilationsofCO2fluxes(e.g.Kerrick,2001;Berner,2004,page59;Fischer,2008)showsthattheirestimatesareatthemiddletoupperend.Theupperlimitof10·1018mol/MyrbyMarty&Tolstikhin(1998)maythereforebetoohigh.Withthemorerealisticrangeof4-8·1018mol/MyrtheeffectontheuncertaintyofatmosphericN2intheNeoarcheanisaround0.3PAN.Usingthelowerlimitof4·1018mol/MyrforthemodernCO2flux,NeoarcheanpN2woulddropto0.59PAN,or0.46bar,comparedto0.42PAN(0.33bar)withabasevalueof6·1018mol/Myr.BecausesomeofourmodelsarealreadybasedonhighervolcanicCO2fluxesintheearlierPrecambrian,wechosenottoconsiderchangesinthemodernCO2fluxintheuncertaintyintervalofFig.2inthemaintext.TheuncertaintyabouttheevolutionofCO2outgassingover4.5billionyearsislikelylarger(thoughunconstrained)thantheuncertaintyofthemodernflux.

Thelargestimpactresultsfromchangesinthecontinentalmetamorphicrateconstant(Fig.A5g).Ifnitrogenwereescaping10xfasterthancarbon,thentheNeoarcheanpN2minimumwouldessentiallydisappear(0.81PAN,0.63barat2.7Ga).Asnotedabove,suchahighmetamorphicrateisunlikelygivenC/Nratiosof10-30foraveragecontinentalcrustandhighgrademetamorphicrocks.Withamorerealisticuncertaintyrangeof1.5-3timesfasternitrogenloss,theuncertaintyonatmosphericpN2isroughly0.2PANintheNeoarchean,withamaximumvalueof0.56PAN(0.44bar)at2.7Ga.

Insummary,ArcheandrawdownofatmosphericN2remainsplausible,giventhelargeuncertaintyaboutmanyofourinputvariables.OurmodelsdoalmostcertainlynotprovideaccuratereconstructionsofpN2throughtime,buttheycanconvincinglydemonstratethatsignificantswingscouldhaveoccurredunderareasonablesetofconditions.

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FigureA5:Sensitivitytests,firstbatch.Parameterswerechangedindividuallywhilekeepingallotherparametersequaltobasevalues.Calculationsarebasedonthe“Forg+Heatflow”model.

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FigureA6:Sensitivitytests,secondbatch.Parameterswerechangedindividuallywhilekeepingallotherparametersequaltobasevalues.Calculationsarebasedonthe“Forg+Heatflow”model.A4.Sensitivityanalysisforhypotheticalextraterrestrialmodels

WetestedthesensitivityofpN2evolutioninourhypotheticalextraterrestrialscenariosbyvaryingparametersthatwereshowntohavethemostimpactinourEarthmodels.OurextraterrestrialmodelsuseestimatesofmodernbiologicalfixationandabioticfixationasabasevalueforthefluxofnitrogenoutoftheatmosphereinsteadofusingCO2outgassingratesandC/Nratios.Thoseparametersarethereforenotrelevantforsensitivitytests.Oxidativeweatheringisalsoturnedoffforthesescenarios.Sobesidesvaryingthetotalnitrogenfixationrate,wetestedthesensitivitytometamorphicrates,erosion,andsedimentresidencetimeswiththesameparameteruncertaintiesasinSectionA3.SimilartoourEarthmodel,atmosphericpN2turnedouttobemostsensitivetovariationsincontinentalmetamorphism.AsshowninFig.A7,the

30

differenceintheevolutionoftheatmosphericN2reservoirbetweenthepreferredscenarioandthelowerandupperlimitsincreasesastherateoftotalnitrogenfixationincreases.A0.5and5timeschangeinthecontinentalmetamorphismratedoesnotgreatlyaffectthepN2evolutioninourpurelyabioticscenarios(~0.002PANforthelowabioticburialrate,and~0.06PANforthehighburialrate).Thesedifferencesincreaseto>0.3PANstartingat1%oftheestimatedmodernbiologicfixationflux.Asnotedinthemaintext,completeN2drawdownattheupperuncertaintylimitwouldrequireaburialfluxequalto~13%ofmodernbiologicalN2fixation.

FigureA7:Sensitivitytestsforanoxicandabioticmodels.Theuncertaintyrangeisprimarilycontrolledbyouruncertaintyincontinentalmetamorphism.A5.Additionalnotesonthe1Dclimatemodel

Wefocusedoureffortsonconditionsthatwouldmaintaingloballyaveragedtemperatures(TGAT)>278K(Table1)andTGAT>273K(Table2).WhileaTGATbelow273Khasoftenbeenassumedtoresultinaglobalsnowballduetorunaway

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glaciationin1Dradiativeclimatemodelingstudies(Domagal-Goldmanetal.,2008;Haqq-Misraetal.,2008),recent3DGlobalCirculationModeling(GCM)hasshownthataTGATbelow273Kwouldnotnecessarilyresultinglobalicecover.Forexample,Wolf&Toon(2013)foundthatasubstantial(>50%)openoceanfractionispossiblewithTGAT≥260K.Additionally,Charnayetal.(2013)foundthataTGATaslowas248Kcanresultinan50°wideice-freewaterbeltattheequator(seetheirFigure9).While1Dclimatestudiescanbesufficienttocalculategloballyaveragedtemperaturesgivenasolarluminosity,atmosphericcomposition,andsurfacealbedo,theycannotbythemselvesdeterminewhethertheplanetsuccumbstoanicecoveredstate.

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