SEMI-ANALYTICMODELINGOFSTELLARPOPULATIONSINASTROPHYSICALSIMULATIONSByBrianDavidCrosbyADISSERTATIONSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeofAstrophysicsandAstronomy{DoctorofPhilosophy2016ABSTRACTSEMI-ANALYTICMODELINGOFSTELLARPOPULATIONSINASTROPHYSICALSIMULATIONSByBrianDavidCrosbyUnderstandinggalaxyformationisanenduringquestionsinastrophysics.Galaxiesaresystemsrichininterestingphysicalprocesses,andthevastrangeoftimesandenvironmentsinwhichgalaxiesformandevolveawealthofchallenges.Oneoftheprimarydrivingforcesingalaxiesistheinteractionofstellarpopulationswiththeirsurroundings.Thenatureofthisinteractiondrivestheevolutionofbothcomponents,andtheresultingbehaviorhasaprofoundimpactontheobservableuniverse.InthisdissertationIdiscusstheresultsofmodelingthisinteractioninavarietyofcontextsusingsemi-analyticmethodsinconjunctionwithhigh-performancenumericalsimulationstobridgethehugedynamicrangesspannedbytheseprocesses.WiththesetechniquesIexploretheenvironmentsinwhichPopulationIIIstarsform,studyingthetransitiontochemically-enrichedstarformation,andquantifyingthechangingenvironmentandassemblyhistoryofthedarkmatterhaloswhichhostPopula-tionIIIstarsinauniverseofincreasinglychemicalcomplexity.Chemicalenrichmentinhighredshiftproto-galaxiesisinvestigatedbycouplingsemi-analyticmodelsofstarformationandfeedbacktocosmologicalN-bodysimulations.Theresultingelementalabundanceratiosarecomparedtothoseobservedinmetal-poorstarsandsatellitesystemsoftheMilkyWay,withthecomparisonconstrainingthenatureofPopulationIIIstars,galaxyformationathighredshift,andthetransitionfrommetal-freetochemicallyenrichedstarformation.Ensem-blesofsemi-analyticmodelsrepresentinginternalgalacticprocessesareusedtodevelopanewformalismforrepresentinggalaxiesincosmologicalsimulationsofgalaxyclusters.Thismethodisusedtoinvestigategalaxyformationinaclusterenvironmentandtheinteractionbetweenclustergalaxiesandtheintraclustermedium.Theinteractionbetweenstellarpop-ulationsindiskgalaxiesandthedcircumgalacticmediumisstudiedinsimulationsofidealizeddiskgalaxies.Theinterplayofstellarfeedbackandthedevelopmentofmultiphasegasinthecircumgalacticmedium,andinturntheofthismultiphasegasfallingbackontothestellardiskisinvestigated.ACKNOWLEDGMENTSThisworkwasmadepossiblebythegeneroushelpandsupportofmanyindividualsandorganizations.InvaluableassistanceandguidanceatMichiganStateUniversitywasprovidedbyDr.BrittonSmith,Dr.DevinSilvia,Dr.MeganDonahue,andDr.MarkVoit.Iwouldliketoacknowledgethehelpprovidedbycollaboratorsatotherinstitutions,includingDr.MatthewTurk(NationalCenterforSupercomputerApplications),Dr.OliverHahn(ObservatoiredelaC^oted'Azure),Dr.JasonTumlinson(SpaceTelescopeScienceInstitute),andDr.TimothyBeers(UniversityofNotreDame).SpecialthanksgoestoDr.JackBurns(UniversityofColorado)forprovidingmewithspaceandsharinghisinsightwhileIwasworkingattheUniversityofColoradoBoulder.AssistancefromHilaryEgan,Dr.SamSkillman,andDr.NathanGoldbaumallcontributedtothiswork.Finally,Iwouldlikeextendmyutmostthankstomythesisadvisor,Dr.BrianO'Shea,withoutwhomnoneofthiswouldhavebeenpossible.TheworkpresentedinthisdissertationwascompletedwiththesupportoftheDepart-mentofPhysicsandAstronomyasMichiganStateUniversity,andwassupportedinpartbyNASAthroughgrantsNNX09AD80G,NNX12AC98G,NNX15AP39G,andHubbleTheoryGrantsHST-AR-13261.01-AandHST-AR-14315.001-A.AdditionalsupportwasprovidedbytheNationalScienceFoundationthroughgrantsAST-0908819,PHY-1430152,andAST-1514700,theLANLInstituteforGeophysicsandPlanetaryPhysics,andMSU'sInstituteforCyber-EnabledResearch.ComputationalresourcesandwereprovidedbyExtremeSci-enceandEngineeringDiscoveryEnvironment(XSEDE),whichissupportedbytheNationalScienceFoundation,MSU'sInstituteforCyber-EnabledResearch,andispartoftheBlueWatersproject,whichajointsupportedbytheNSF(awardnumberACI-1238993)ivandthestateofIllinois,usingNSFPRACACI-1514580.ThesimulationandanalysisworkinthisdissertationwouldhaveneverbeencompletedwiththeEnzoandytcodes,whicharedevelopedbyaglobalcommunityofresearcherswhosegenerouscontributionstothesecodesmadethisresearchpossible.vTABLEOFCONTENTSLISTOFTABLES....................................xLISTOFFIGURES...................................xiChapter1Introduction...............................11.1PopulationIIIStarFormation..........................11.2GalacticChemicalEvolution...........................41.3GalaxyClusters..................................81.3.1Overview.................................81.3.2TheIntraclusterMedium.........................81.3.3ClusterGalaxies.............................101.3.4BrightestClusterGalaxy.........................101.4TheCircumgalacticMedium...........................111.4.1Overview.................................111.4.2Observations...............................131.4.3StarFormationandFeedback......................151.5Structureofthisdissertation...........................18Chapter2LiteratureReview............................212.1PopulationIIIStarFormation..........................212.1.1FormationEnvironment.........................212.1.2PopIIIStellarCharacteristics......................222.1.3TransitiontoChemically-EnrichedStarFormation...........252.2GalacticChemicalEvolutionandNear-FieldCosmology............262.2.1ObservationsofMetal-PoorStars....................282.2.2TheoryandSimulation..........................292.3GalaxyClusters..................................312.3.1Observations...............................312.3.2TheoryandSimulation..........................332.4TheCircumgalacticMedium...........................362.4.1NeutralHydrogenGas..........................372.4.2WarmIonizedandWarm-HotGas....................382.4.3HotHaloGas...............................392.4.4RecentObservations...........................392.4.5Precipitation-RegulatedFeedback....................41Chapter3PopulationIIIStarFormationInLargeCosmologicalVolumes:HaloTemporalAndPhysicalEnvironment............433.1Introduction....................................433.2Simulations....................................47vi3.2.1Enzo....................................473.2.2HaloFindingandMergerTreeCreation................483.3ModelDescription................................513.3.1Overview.................................513.3.2PopulationIIIStarFormation......................523.3.3ChemicallyEnrichedStarFormation..................563.3.4LymanWernerFluxDetermination...................583.3.5HaloGasEjection.............................613.4Results.......................................653.4.1Overview.................................653.4.2StarFormationRates...........................673.4.3PopulationIIIStarFormationHaloMassLimit............703.4.43:5h1MpcBoxStarFormationRates.................733.4.5HaloEnvironment............................773.5Discussion.....................................843.5.1ComparisontoObservation.......................843.5.2ComparisontoOtherWork.......................843.5.3ImplicationsforPopulationIIIModeling................863.5.4LimitationsandFutureWork......................863.6SummaryandConclusions............................913.7Acknowledgments.................................92Chapter4TracingTheEvolutionOfHigh-RedshiftGalaxiesUsingStel-larAbundances.............................934.1Introduction....................................934.2ModelDescription................................984.2.1Overview.................................984.2.2PopulationIIIStarFormation......................1014.2.3ChemicallyEnrichedStarFormation..................1034.2.4GasandMetalEjection.........................1064.2.5ChemicalEvolution............................1074.3StellarYields...................................1124.3.1YieldsofAGBStars...........................1134.3.2YieldsofSNeII..............................1144.3.3YieldsofSNeIa..............................1144.4Results.......................................1154.4.1ComparisontoObservations.......................1164.4.2FittingSeveralAbundancesSimultaneously..............1244.5Discussion.....................................1284.5.1TheModel.................................1284.5.2ComparisontoObservations.......................1314.5.3PopulationIIIStellarYields.......................1344.5.4PossibleConstraintsfromHydrodynamicalSimulations........1374.5.5LimitationsandFutureWork......................1384.6SummaryandConclusions............................140vii4.7Acknowledgments.................................142Chapter5TowardsRealisticSimulationsofGalaxyClusters:GalaxyPar-ticles....................................1435.1Motivations....................................1435.2Methods......................................1455.2.1IntroducingGalaxyParticles.......................1455.2.2ParticleCreation.............................1465.2.2.1HaloFinding..........................1465.2.2.2MassAssignment........................1475.2.2.3OtherParticleAttributes...................1485.2.3FeedbackandEvolution.........................1485.2.3.1StarFormation.........................1495.2.3.2StellarFeedback........................1505.2.3.3RamPressureStripping....................1525.2.4Particle-HaloAssociation.........................1535.2.5GalaxyParticleGrowthandMerging..................1555.3SimulationSetup.................................1565.4PreliminaryResults................................1575.4.1GalaxyPopulation............................1585.4.2ICMProperties..............................164Chapter6ThermalInstabilitiesandPrecipitationintheCircumgalacticMedium..................................1696.1Motivations....................................1696.1.1Observations...............................1696.2Methods......................................1716.2.1StarParticles...............................1726.2.2Formation.................................1726.2.3FeedbackandEvolution.........................1756.3SimulationSetup.................................1776.3.1GalaxyCharacteristics..........................1796.3.2StarParticleParameters.........................1806.3.3ChemistryandCooling..........................1806.4PreliminaryResults................................1816.4.1CGMThermalandKineticProperties.................1816.4.2CGMChemicalProperties........................185Chapter7ConclusionsandFutureWork....................1947.1Conclusions....................................1947.2FutureWork....................................1957.2.1PopulationIIIStarFormation......................1957.2.2GalacticChemicalEvolution.......................1977.2.3GalaxyClusterSimulationsWithGalaxyParticles..........1987.2.4ThermalInstabilitiesandPrecipitationintheCircumgalacticMedium200viiiBIBLIOGRAPHY...................................202ixLISTOFTABLESTable3.1:Modelparameterswiththeirvalue,therangetested,andabriefdescription..............................52Table4.1:ModelParameterswithTheirFiducialValues,theRangeTested,andaBriefDescription............................99Table4.2:ImplausibilityandJointProbabilityValuesWhenFittingtheOb-servedIndividual[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]DistributionsFromtheSEGUEDataSetatz=6......................119Table4.3:ImplausibilityandJointProbabilityValuesWhenFittingtheOb-servedIndividual[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]DistributionsFromtheFrebelDataSetatz=6.......................120Table4.4:ImplausibilityandJointProbabilityValuesWhenSimultaneouslyFittingMultipleElemental-AbundanceDistributionsatz=6....127xLISTOFFIGURESFigure3.1:Thecumulativehalodarkmattermassfunctionforallfoursimulationvolumesatz=15(dashedline)andz=10(solidline).PlottedinblackistheanalyticpredictionfromtheWarrenmassfunction(Warrenetal.,2006).Thereisgoodagreementbetweenthehalomassfunctionsinthesimulationsovertheredshiftsofinterestinthisproject...................................50Figure3.2:ThethreeIMFsconsideredinthisworkareSalpeter(violet,solidline),Kroupa(blue,dashedline),andChabrier(red,dot-dashedline),overamassrangeof0:08Mto260M.Theintegratedareaundereachofthecurvesisthesame.TheSalpeterIMFemphasizeslowmassstars,theKroupaIMFemphasizesintermediatemassstars,andtheChabrierIMFisbythefarthemosttop-heavyofthethree,emphasizinghighmassstars.......................64Figure3.3:Thestarformationrate(SFR)densitiesforallfoursimulationsforourchoiceofparameters.Thethick,solidlineshowsthetotalSFRdensity,thedashedlineisthechemicallyenrichedSFRdensity,andthethin,solidlineisthePopulationIIISFRdensity.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.Allfoursimulationsshowverygoodagreementdespitetestingtwotvolumesandallbeingcreatedfrominitialconditionsgeneratedwithtrandomseeds...........66xiFigure3.4:Thestarformationrate(SFR)densityinMyr1Mpc3asafunc-tionofredshiftforvariationsinIMF,starformation,andLyman-Werner(LW)photonescapefraction.PanelAshowstheef-fectofvaryingtheIMF,PanelBshowstheofvaryingthestarformation,andPanelCshowstheofvaryingtheLWphotonescapefraction.Inallpanels,thePopulationIIISFRdensityisplottedinthin,solidlines,thechemicallyenrichedSFRdensityisplottedindashedlines,andthetotalSFRdensityisplottedinthick,solidlines.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.InPanelA,thetotalandcompo-nentSFRdensitiesforthethreeIMFsarenearlyindistinguishable.PanelBshowstheSFRdensityusingaSalpeterIMFandvaryingthestarformation.IncreasingthestarformationincreasesthebetweenthePopulationIIIandchemicallyenrichedSFRdensities,drivingPopulationIIIstarformationdownandchemicallyenrichedstarformationup.InPanelC,changestotheLWphotonescapefractionhaveasmallonthechemicallyenrichedSFRdensity,anddecreasingtheescapefractionincreasesthePopulationIIISFRdensityatlatetimes.Inallcases,chemicallyenrichedstarformationrapidlydominatesPopulationIIIstarforma-tionbyseveralordersofmagnitude,butPopulationIIIstarformationcontinuesatverylowlevelsfortheentiretyofthesimulation.....69Figure3.5:PanelAshowsthevariationinstarformationrate(SFR)densityinMyr1Mpc3asafunctionofredshiftforallcombinationsofparametersinourmodel.ThemeanPopulationIIISFRdensityisplottedasablacksolidline,andtheaveragechemicallyenrichedSFRdensityisplottedasablackdashedline.ThemaximumrangespannedbythePopulationIIIandchemicallyenrichedSFRdensitiesareshownbythelightredandlightblueshadedregions,respec-tively.Thedarkshadedregionsshowthe68percentin-tervalsaroundthemean.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.PanelBshowstheratioofthechemicallyenrichedSFRdensitytothePopulationIIISFRdensityasafunctionofredshiftforallparametercombinations,withtheblacklineshowingtheaveragevalueandtheshadedregionshavingthesamemeaningasinPanelA.Toaidininterpretation,dashedlinesareshownatlevelscorrespondingtochemicallyenrichedtoPopulationIIIstarformationrateratiosof1and1000.......71xiiFigure3.6:ThePanelAshowstheproperLyman-Werner(J21)andPanelBshowstheminimummassthresholdforPopulationIIIstarformationasafunctionofredshift,plottedforthethreeinitialmassfunctions(IMF)withastarformationof0:04aswellasforaSalpeterIMFwithstarformationof0:008and0:2.TheSalpeter,Kroupa,andChabrierIMFsareindistinguishableinthisplot.Forcomparison,inPanelBthemassthresholdwithoutaccountingforradiativefeedbackisshowninblack,andismuchlower,particularlyoncechemicallyenrichedstarformationbecomethedominantcom-ponentofthestellarmassinthesimulation.TheminimumhalomassforPopulationIIIstarformationisdependentonJ21,andasaresultPanelAcloselymirrorsthebehaviorofPanelB.Simultaneously,J21isdependentonthestellarmassinthesimulation,andwillthetrendsofthetotalstarformationratedensityinFigure3.4...72Figure3.7:Thestarformationrate(SFR)densityinMyr1Mpc3asafunc-tionofredshiftforvariationsinIMF,starformation,andLyman-Werner(LW)photonescapefraction.PanelAshowstheef-fectofvaryingtheIMF,PanelBshowstheofvaryingthestarformation,andPanelCshowstheofvaryingtheLWphotonescapefraction.Inallpanels,thePopulationIIISFRdensityisplottedinthin,solidlines,thechemicallyenrichedSFRdensityisplottedindashedlines,andthetotalSFRdensityisplottedinthick,solidlines.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.Inallcases,chemicallyenrichedstarformationrapidlydominatesPopulationIIIstarformationbyseveralordersofmagnitude,butPopulationIIIstarformationcontinuesatlowlevelsfortheentiretyofthesimulation...............74Figure3.8:SameasFigure3.5,thoughappliedtoa3:5h1Mpcbox.PanelAshowsthevariationinSFRdensityinMyr1Mpc3asafunctionofredshiftforallcombinationsofparametersinourmodel.ThemeanPopulationIIISFRdensityisplottedasablacksolidline,andtheaveragechemicallyenrichedSFRdensityisplottedasablackdashedline.ThemaximumrangespannedbythePopulationIIIandchemicallyenrichedSFRdensitiesareshownbythelightredandblueshadedregions,respectively.Thedarkshadedregionsshowthe68percentintervalsaroundthemean.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.PanelBshowstheratioofthechemicallyenrichedSFRdensitytothePopulationIIISFRdensityasafunctionofredshiftforallparametercombinations,withtheblacklineshowingtheaveragevalueandtheshadedregionshavingthesamemeaningasinPanelA.Toeaseviewing,dashedlinesareshownat1and1000.......75xiiiFigure3.9:Thedistancetothenearestneighboringhalo,originatingfromPopu-lationIII(red)andchemicallyenriched(blue)halos.PanelAshowsthedistributionofdistancesatz=18,PanelBshowsthedistri-butionatz=14,andPanelCshowsthedistributionatz=10.Atearlytimestheenvironmentsarealmostindistinguishable,butastimepassesthechemicallyenrichedhalosbecomemoreclusteredandPopulationIIIforminghalosbecomeincreasinglyspreadout.ThehistogramsarenormalizedtoallowforthecomparisonofthemuchmorenumeroussetofchemicallyenrichedhalostothesetofPopula-tionIIIhalos...............................78Figure3.10:ThedistancefromhalosformingPopulationIIIstarstothenearestchemicallypristinehaloofanymass(red)andtothenearestchemi-callyenrichedhaloofanymass(blue).ThechemicallypristinehalosdonotneedtobemassiveenoughtoformaPopulationIIIstar.PanelAshowsthedistributionofdistancesatz=18,PanelBshowsthedistributionatz=14,andPanelCshowsthedistributionatz=10.HaloshostingPopulationIIIstarformationaremuchclosertootherchemicallypristinehalosthantochemicallyenrichedhalos......79Figure3.11:ThedistancefromPopulationIIIstarforminghalostothenearestotherPopulationIIIstarforminghalo(red)andnearestchemicallyenrichedhaloofanymass(blue).PanelAshowsthedistributionofdistancesatz=18,PanelBshowsthedistributionatz=14,andPanelCshowsthedistributionatz=10.Theneareststarforminghalosarealmostentirelychemicallyenriched,andPopulationIIIstarforminghalostendtoforminisolationfromoneanother.TakenwithFigure3.10,thisplotindicatesthatPopulationIIIstarforminghalosaregenerallysurroundedbychemicallypristinehalosthatarenottlymassivetoformaPopulationIIIstar............80Figure3.12:ThehalocorrelationfunctionsforPopulationIIIhalos(red)andchemicallyenrichedhalos(blue),andtheunbiaseddarkmatterden-sity(violet).PanelA,B,andCshowthecorrelationfunctionsatz=18,14,and10,respectively.Errorbarsareplottedforallpoints,butaregenerallynotvisible.AtalltimeschemicallyenrichedhalosaremoreclusteredthanPopulationIIIstarforminghalos...82xivFigure3.13:Anexampleoftherateofgrowthofhalostotheirmassatz=10:73.Eachhaloisnormalizedtoitsmass,andeachlinerepresentsanindividualhalo.Timeisshownonthehorizontalaxis,withtbeingastheamountoftimesincethestarinthesimulationformed.Red,dashedlinesshowthe10mostmassivechemicallyenrichedhalosandblue,solidlinesshowthe10mostmas-sivechemicallypristinehalos.All10chemicallypristinehalosareplotted,thoughtheirverysimilargrowthatlatetimesmakesthemoverlapinthisChemicallyenrichedhalosexperiencefastergrowthatearlytimes,whilethechemicallypristinehalosthathostPopulationIIIstarsgrowslowlyatearlytimes,remainingbelowthemassrequiredforstarformation.Growthinchemicallypristinehalosoccursrapidlyatlatetimes,immediatelypriortostarformation...83Figure4.1:ThethreeIMFsconsideredinthisworkareSalpeter(violetsolidline),Kroupa(bluedashedline),andChabrier(reddot-dashedline),overamassrangeof0:08260M.Theintegratedareaundereachofthecurvesisthesame.TheSalpeterIMFemphasizeslow-massstars,theKroupaIMFemphasizesintermediate-massstars,andtheChabrierIMFisbythefarthemosttop-heavyofthethree,emphasizinghigh-massstars.................................111Figure4.2:The[C/Fe]-[Fe/H]distributionatz=6asmodeledwithaChabrierIMF,achemicallyenrichedSFEof0:2,anLWphotonescapefractionof1,andaredshiftofreionizationofzreion=7.Theshadedregioninthecenterpanelshowsthedistributionofstellarmassinoursimu-lationin[C/Fe]-[Fe/H]spacewiththeshadethefractionofstellarmassatthatpairofabundances.Darkblueregionshavethelargestfractionofthestellarmass,whilelightblueregionshavelessstellarmass.SEGUEdataareplottedinred,andtheFrebeldatasetisplottedinyellow.Observationaldataarebinnedin0:25dexincrements,withthebinmeanshownasacontinuousline,the68%intervalshownasathickline,andthemaximumandmin-imumextentofthedatasetshownasthinlines.Thetopandrighthistogramsshowthedistributionsofstellarmassineither[Fe/H](top)or[C/Fe](right).Simulateddataareshowninblue,SEGUEdatainred,anddatafromFrebelinyellow.Thissetofparametersmaximizesthejointprobabilityforthecombinedof[Mg/Fe]and[C/Fe]intheSEGUEdataandminimizestheimplausibilityforthesameabundancesintheFrebeldata...................122xvFigure4.3:The[Mg/Fe]-[Fe/H]distributionatz=6forthesamemodelpa-rametersasshowninFigure4.2,withallcoloringandweightingthesameasinthatThissetofparametersmaximizesthejointprobabilityforthecombinedof[Mg/Fe]and[C/Fe]intheSEGUEdataandminimizestheimplausibilityintheFrebeldata.......123Figure4.4:[Zn/Fe]-[Fe/H]distributionatz=6asproducedbyamodelusingaChabrierIMF,achemicallyenrichedSFEof0:2,andaredshiftofreionizationof7.ObservationaldatafromFrebelareshowninyellow,binnedin0:25dexincrements.Themeanineachbinisplottedalongwiththe68%intervals(thickverticallines)andmaximumandminimumextentofobservedabundancedataineachbin.ThismodelproducesthelowestimplausibilityvaluewhenallFrebelabundancessimultaneously........................125Figure4.5:[Ca/Fe]-[Fe/H]distributionatz=6asproducedbyamodelusingaChabrierIMF,ahighchemicallyenrichedSFEof0:2,andaredshiftofreionizationof7.Themajorityofobservedstarsmatchthesimulatedmetallicitydistributionfunction,butthequalitativebehavioratlowvaluesof[Fe/H]strongly.EnrichmentfromPopulationIIIstarsdrasticallyunderproducesCainrelationtoFe,establishinginitialabundancesforchemicallyenrichedstarformationfarbelowthosethatareobserved.............................133Figure5.1:Thenumberofgalaxyparticlesasafunctionofredshift.Theparticleformsatz=3:2.Majormergereventsoccuratz=1:501:42,z=1:341:27,andz=1:000:92...............158Figure5.2:Aslicethroughthecentralregionofthesimulationdomainatz=0:6showingthegastemperaturewiththelocationsofgalaxyparticlesoverplottedinblack.Galaxyparticlesdonotdisplaytheexcessivecentralclusteringseeninpreviouscosmologicalsimulationsofgalaxyclusters..................................160Figure5.3:Themassofstarsingalaxyparticlesasafunctionofredshift.....161Figure5.4:Thestellarmassfunctionforgalaxyparticlesatz=0:6.Thema-jorityofthestellarmassiscontainedinonlyafewgalaxyparticles,contributingtotheexcessivestellarmassseeninFigure5.3......163xviFigure5.5:Aprojectionthroughthecentralregionofthesimulationdomainatz=0:6showingthemetaldensityweightedbythegasdensitywiththelocationsofgalaxyparticlesoverplottedinblue.Aburstofstarformationandtheassociatedchemicalenrichmentcanbeat+5Mpcalongthey-axisand5Mpcalongthez-axis.Theremnantofanotherburstcanbeseenat+3Mpcalongthey-axisand+4Mpcalongthez-axis..............................165Figure5.6:Aslicethroughthecentralregionofthesimulationdomainatz=0:6showingthegasmetallicity.Thelocationsofgalaxyparticlesareoverplottedinred.Similartowhatisseeninobservations,theenrichmentoftheICMisveryuneven,andtheoveralllevelofICMenrichmentisingoodagreementwithobservations..........166Figure5.7:Thespherically-averagedradialofgasmetallicityinthegalaxyclusteratz=0:6.Thedistributionislesscentrallyconcentratedtheothersimulationtechniques,inbetteragreementwithobservations,butthecentralvalueisafactorof23largerthanobservedvalues.168Figure6.1:Aprojectionofgastemperatureweightedbygasmetaldensity815MyrafterthestartoftheREsimulation.Thecentral120kpcofthesimulationareshown,andthegalaxydiskisbeingviewededge-on.Filamentsandcloudsofcold,enrichedgascanbeseenbothaboveandbelowthedisk.Thesecloudsarefallingbacktowardsthedisk..183Figure6.2:Aprojectionofthecomponentofgasvelocitynormaltotheplaneofthedisk,weightedbygasmetaldensity,815MyrafterthestartoftheREsimulation.Thecentral120kpcofthesimulationareshown,andthegalaxydiskisbeingviewededge-on.Theenriched,coldgasinthecentralregionsoftheplumesoriginallydrivenoutwardsbystellarfeedbackarefallingbackontothedisk.................184Figure6.3:Thedistributionofgasmassintemperature-velocityspaceintheREsimulation.Toshowgasmotiontowardsandawayfromthegalaxy,onlythecomponentofvelocitynormaltotheplaneofthediskisused.Thedatashownisforaregionofgas240kpcwideand100kpctallextendingupwardsabovethegalaxy,withthebottomedge30kpcabovethegalaxymidplane....................186Figure6.4:AprojectionoftheOVInumberdensityinthecentral360kpcoftheLRsimulationafter320Myr.Thediskisviewededge-on.......187Figure6.5:SameasFigure6.4,butshowingtheprojectedCIVnumberdensity.Theplumesarestillpropagatingoutwards,buttheCIVdistributiondoesnotextendtoaslargeofradiiastheOVIdistribution......188xviiFigure6.6:SameasFigure6.4,butshowingtheprojectedMgIInumberdensity.MgIIisbeingdrivenintothehalogas,butitisnotreachingasgreatofaradialextentasOVIorCIV....................189Figure6.7:RadialoftheOVInumberdensitythroughouttimeintheLRsimulation.Eachlinerepresentsattime,rangingfromthestartofthesimulation(yellow,leftmostline)to320Myr(darkestviolet,rightmostline)in5Myrincrements...............190Figure6.8:RadialoftheCIVnumberdensitythroughouttimeintheLRsimulation.Eachlinerepresentsattime,rangingfromthestartofthesimulation(yellow,leftmostline)to320Myr(darkestviolet,rightmostline)in5Myrincrements...............192Figure6.9:RadialoftheMgIInumberdensitythroughouttimeintheLRsimulation.Eachlinerepresentsattime,rangingfromthestartofthesimulation(yellow,leftmostline)to320Myr(darkestviolet,rightmostline)in5Myrincrements...............193xviiiChapter1Introduction1.1PopulationIIIStarFormationAsthestarstoformintheuniverse,PopulationIII(PopIII)starsareinherentlyinterestingobjects.Theywerethesourcesofthelightintheuniverse,beginningthereionizationoftheirsurroundings.PopIIIstarsinitiatedthechemicalenrichmentoftheuniverse.NucleosynthesiswithinPopIIIstarsandduringthesupernovae(SNe)thatarepresumedtohaveendedtheirlivesandbegantotransformtheprimordialproductsoftheBigBang(hydrogen,helium,andtraceamountsoflithiumandberyllium)tothecurrentmyriadofelements.Despitetheirintegralroleintheevolutionoftheuniverse,wehaveaveryincompletepictureofPopIIIstars.NoPopIIIstarshavebeenobserved,relegatingthepursuitofanunderstandingoftheircharacteristicstotherealmoftheory,simulation,andinferencefromobservationsoflow-metallicitystars.WhilethelackofdirectobservationsprecludesofPopIIIstellarproperties,theirapparentabsenceatz=0,combinedwiththeirprimordialcompositioncanprovidesomeinsightintothePopIIIinitialmassfunction(IMF).AsnoPopIIIstarshavebeenobservedinthecurrentuniverse,sub-SolarmassPopIIIareveryunlikely.Thelackofmetals1fundamentallychangesthenatureofcoolingintheprotostellarcloud,suppressingfragmentationandnecessitatingalargermassinorderfor1Theconventioninastronomyisto\metals"tobeanyelementsotherthanhydrogenandhelium.1coolingviamolecularhydrogentoenablegravitationalcollapse(Abeletal.,2002).TheseconstraintssuggestthatPopIIIstarslikelyhadalargercharacteristicmassthanthatofsubsequentgenerationsofmetal-enrichedstars,andweremorelikelytoformeitherinisolationorgroupsofafew(Turketal.,2009)owingtomonolithiccollapseoftheprotostellarcloud.Theprocessofformingstarsfromprimordialhydrogenandheliumgasfrommetal-enrichedstarformation,wheretheintroductionofdustandmetalstlyalterthepropertiesoftheprotostellarcloud,whichfragmentsreadily,formingstarsinpopulationsofhundredsoreventhousands(e.g.,Brommetal.(2001);Bromm&Loeb(2003);Smithetal.(2009);Meeceetal.(2014)).WhilethesedeductionsprovidesomebroadqualitativeinsightintoPopIIIstars,theo-reticalinvestigationisnecessarytofurtherelucidatethenatureoftheseobjects,thespatialandtemporalenvironmentsinwhichtheyexisted,andtheroletheyplayedinhighred-shiftgalaxyformation.Theintricaciesofstellarformationandevolutionmakeadetailedanalyticapproachintractable,requiringrecoursetosimulations.Thegravitationally-bounddarkmatterstructures(referredtoashalos)thathostPopIIIstarformationaresubstan-tiallylargerthanthestar-formingcloud,butcomparableenoughinsizethatonlyasinglecloudformsinagivenhalo.Owingtothisco-evolution,thepropertiesofthepre-stellarcloudarecloselyrelatedtothehaloformationhistory(O'Shea&Norman,2007).Giventheimportanceofhaloformationhistory,PopIIIstarformationmustbestudiedinacosmo-logicalcontext,wheretheevolutionofhalosthroughaccretionofmassandmergingwithotherhaloscanbetracked.Finitecomputationalresourcesrequirethatsimulationsmakeabetweencosmologicalvolumeandsimulationresolution.ProperlymodelingPopIIIstarformationrequiresmultiphysicssimulationsthathavehighspatialandtemporalresolution,andhencearecapableofsimulatingonlyasmallnumberofhalosinsmallcos-2mologicalvolumestypicallynotmorethanafewhundredkpconaside(e.g.,Abeletal.(2002);Brommetal.(2002);O'Shea&Norman(2007);Turketal.(2009)).Simulationsofhighredshiftgalaxyformationencompasslargervolumes,butarelimitedtoresolvingonlyasmallnumberofhaloobjects.Theyarethereforeincapableofresolvingtheintricaciesofstarformation(e.g.,Ricottietal.(2002b);Wiseetal.(2012b,a);Chenetal.(2014);Xuetal.(2016)).Themostadvancedcurrentsimulationsareresolvingapproximately1000haloobjects(O'Sheaetal.,2015),andwhilethisisasitimprovement,itstillprovidesonlyweakstatisticalpower.ThesetechnicallimitationshamperourunderstandingtheroleofPopIIIstarsingalaxyformation.Simulationsarecapableofresolvinglargenumbersofhigh-redshiftprotogalaxies,butcannotresolvethePopIIIstar-formingclouds,providingveryweakstatisticsonthenatureofthePopIIIstellarpopulationasafunctionoftimeandenvironment.havebeenmadetogaininsightintoPopIIIstarformationenvironmentsandstellarcharacteristicsbyconstructingmockhalopopulationsthroughanalyticmethodssuchastheextendedPress-Schechterformalism(Wise&Abel,2005)andcouplingittoapre-scriptionforstarformation(Trenti&Stiavelli,2009).Whilethesemodelsarecapableofinvestigatingsomestatisticsofthepopulation,theylackthecrucialinformationofthehaloformationhistory,andareunabletodirectlyinvestigatethenatureofindividualPopIIIstars.Amorepromisingmethodistosimulatelargecosmologicalvolumes,resolvingindi-vidualhalosataresolutionappropriateformultiphysicssimulations.CurrentsimulationareabletoresolvethousandsofhalosthatarepotentiallycapableofhostingPopIIIstarformation(O'Sheaetal.,2015),butthesesimulationsarestillincapableofresolvingthestarformingclouditself.Asaresult,thenatureofPopIIIstarsinthesesimulationsmustbesetbyhand,littleunderstandingoftheiractualproperties.Byself-consistently3identifyingwhichhaloswillbecapableofhostingPopIIIstarformationacrossarangeoftimesandenvironments,arepresentativesampleofPopIIIstar-forminghaloscanbecre-ated,enablingmorerealistichigh-resolutionsimulationsofthePopIIIformationprocess.ThisimprovedsetofsimulationscanyieldmuchmorestringentconstraintsonthenatureofPopIIIstars,theirIMF,andtheroletheyplayinhighredshiftgalaxyformation.1.2GalacticChemicalEvolutionHowtheuniversetransitionedfromtheprimordialnucleosyntheticproductsoftheBigBangtothecurrentproliferationofelementsisalong-standingquestioninastrophysics.Inbroadterms,thisprocessiswellunderstood:PopulationIIIstarsinitiatechemicalenrichmentthroughtheexpulsionofenrichednucleosyntheticproductsintotheISM,andthispollutedmaterialisincorporatedintosubsequentgenerationsofmetal-enrichedstars.Thiscycleofstarformation,chemicalenrichmentwithinstars,andejectionofenrichedmaterialtotheISMformsthefoundationofgalacticchemicalevolutionmodels.Thesuccessofcosmologyarguesforthescenarioofhierarchicalstructureforma-tion,withsmallgravitationallyboundhalosrepeatedlymergingtogethertocreateever-largerboundstructures.TheMilkyWayistheresultofthesmallerstructuresthathavemerged;itschemicalandkineticstructureencodesthehistoryofeverythingthatmergedtoformit(Feltzing&Chiba,2013).Ifthemostmetal-poorstarspreservearecordofthechemicalabundancesoftheirenvironmentatthetimeoftheirformation(Freeman&Bland-Hawthorn,2002;Beers&Christlieb,2005),studyoftheoldest,mostmetal-poorstarsintheMilkyWay,apracticetermed\GalacticArcheology,"canprovideinsightintothenatureoftherststarsandtheevolutionofhigh-redshiftgalaxies(Frebel&Norris,2015).4Observationofmetal-poorstarsintheMilkyWayiscomplementarytothedirectstudyofhigh-redshiftgalaxyformation.Observationsofhigh-redshiftstructurehaveprogressedtothepointofobservingobjectsatz˘11(Oeschetal.,2016),providingadirectviewoftheseearlygalaxies.Theseimpressiveobservationsareneverthelesslimitedbytheinherentinobservingaveryfaintstructureanddeducingitscharacteristics.Observationsofthemostmetal-poorstarsintheMilkyWaycarryatsetofadvantagesanddisad-vantages.Spectroscopicobservationsofindividualstarsallowforprecisiondeterminationsofabundancesinamannerthathigh-redshiftobservationscannotaccomplish,givingcrucialinsightsintothestellarpopulationsthatprecededthatstar'sformation.Theseobservationsarelimitedbythefactthatmostdetailsofthegalaxyinwhichtheyformarelostduringthemergerprocess.AnalysisofthestellarhalooftheMilkyWayinkinematicphasespacehasmadestridesinstellarstreamsandpopulationsfromdisruptedandmergingstructures(Feltzing&Chiba,2013;Ivezicetal.,2012),butthelongandcomplicatedpro-cessofmergersthatbuilttheMilkyWayhasinevitablywipedawayalargeamountofthisinformation.Thecumulativebuildupofchemicalcomplexitythroughsuccessivegenerationsofstel-larformation,nucleosynthesisinstars,andenrichmentoftheISMsuggeststhatthemostmetal-poorstarsarealsotheoldeststars.Whilethisrelationshipgenerallyholdstrue,itissomewhatindirectatthelowestmetallicities(e.g.,Smithetal.(2015)).Lowmassstarsareextremelylong-lived,andobservationsoftheseobjects,bothinisolationandaspopulations,caninformourunderstandingoftheirenvironmentsatthetimeinwhichtheywereformed.Inparticular,lowmass,lowmetallicitystarsenablethestudyofstarandgalaxyformationathighredshifts,andthesestarsconnecttheirpresentenvironmentswiththesystemsinwhichtheyformed.Galacticarcheologyhasgrowninscope,encompassingnotonlysolitary5starsintheMilkyWayhalo,buttheoldstellarpopulationsresidingtheMilkyWaydwarfgalaxies(Tolstoyetal.,2009)aswell.Astheyformedveryearly(Bovill&Ricotti,2009),dwarfspheroidal(dSph)andultra-faintdwarf(UFD)galaxiesthathavebeenaccretedbytheMilkyWayprovideaconnectionbetweencosmologicalstructureformationandstarsintheGalactichalo.Studyoftheelementalabundancepatternsofthesemetal-poorsystemsandMilkyWayhalostarsthatformedinsituallowsforcomparisonbetweentheseenvironmentsatthetimeinwhichtheyformed.ComparisonbetweencosmologicalsimulationsofstructureformationandobservationsofdwarfgalaxiesdrawsaconnectionbetweentheseobjectsandthebuildingblocksoftheMilkyWay,especiallytheGalacticmetal-poorhalo(Mateo,1998;Belokurov,2013;Pila-Detal.,2014).Inconjunctionwiththis,observationsoftheAndromedagalaxyshowthatglobularclustersareassociatedwithstellarstreamsinthehalo,linkingthesestructureswiththeaccretionofcapturedgalaxies(McConnachieetal.,2009).Thus,themostmetal-poorhalostars,inglobularclusters,dSphgalaxies,andultra-faintdwarfgalaxies,representtracersoftheearliestaccretioneventstheMilkyWay'sformationhistory.Thechemicalabundancesofthestarsinthesesystemsencapsulatethecumulativeoftheirformationandevolution,rangingfromtheinitialchemicalenrichmentofprimordialmaterialbyPopIIIstarsandSNe,totheassemblyoftheproto-galaxies(Bromm&Yoshida,2011),tothenatureoftheISMwhenthechemicallyenrichedstarsformed,tothecosmologicalstructureformationprocesseswhichassembledtheMilkyWayandresultedinthesesystemsresidingintheGalactichalo.PatternsandintheelementalabundancesofstarsintheGalactichalo,dSphgalaxies,andUFDsarguesformultiplechannelsofstarformation(Jietal.,2014,2016)athigh-redshift.Forexample,whilestarsinallofthesesystemshaveequivalentlylowoverall6metallicities,carbon-richstarsareobservedinthehaloandultra-faintdwarfs,butnotdSphgalaxies.WhiledSphgalaxiesandUFDshavesimilaroverallstellarmetallicitiesrangesof4<[Fe/H]<0,UFDsarecomparativelydetinstarswith[Fe/H]<1:5(Kirbyetal.,2008),suggestingatruncatedchemicalenrichmenthistory.Inmanycases,halostarshaveelevatedabundancesofneutron-captureelementsrelativetodSphandUFDgalaxies(Frebeletal.,2010b,2014;Gilmoreetal.,2013;Ishigakietal.,2014),thoughotherUFDs,suchasReticulumII,showmassiveenchancementofr-processelementalabundances,suggestingenrichmentthroughrareeventssuchasneutronstar-neutronstarmergers(Jietal.,2016).Theseindicatedisparitiesintheformationhistoriesandenvironmentsoftheseobjects,buttheirsimilaritiescanbeequallytelling.Forexample,starsinboththehaloanddwarfsystemshavesimilarlightelementabundances(Frebeletal.,2010b),suggestingthattheinitialenrichmentoftheenvironmentsinwhichtheyformedwasdrivenbymassivestars.Asthesemetal-poordwarfsystemshavebecomeresidentsoftheMilkyWayhalowecanusetheirpresencetoassesstheformationoftheMilkyWayintheparadigmofcosmology.HowdidtheseobjectscometoresideintheGalactichalo?Dotheycarrysignaturesintheirelementalabundancepatternsthatareuniquetothegalaxies(Frebel&Bromm,2012)?CansimulationscouplingcosmologicalstructureformationtomodelsofgalacticchemicalenrichmentreproducetheabundancesobservedintheMilkyWaydwarfgalaxies?Ifso,canthesesimulationsbeusedtoconstrainhigh-redshiftstarformationprocesses,orstellarandSNenucleosyntheticyields?Dotheabundancepatternsinmetal-poorstellarpopulationsintheMilkyWayinformourunderstandingofthegalaxies?Andcanweextendthisallthewaybacktotheearlieststars,constrainingthePopIIIIMFandthenatureoftheSNewhichendedtheirlives?71.3GalaxyClusters1.3.1OverviewGalaxyclustersarethelargestgravitationallyboundobjectsintheuniverse.Theyarecom-posedofthreeprimarycomponents:theclustergalaxies,theintraclustermedium(ICM),andadarkmatterhalo.Thedarkmatterhaloisthemostmassivecomponent,andformsthegravitationalpotentialwellwhichdrivesthedynamicsofthecluster.TheICMisahot,plasmainwhichtheclustergalaxiesreside,andmakesupthemajorityofthebaryonicmassinthecluster.Thegalaxiesthemselvesnumberinthehundredstothousands,aregenerallyredellipticals,whichthemselvesgenerallyhavelowstarformationrates.Intotalgalaxyclustershavemassesontheorderof10141015Mandradiiofapproximately25Mpc(Kravtsov&Borgani,2012).Asthemostmassiveboundstructuresintheuni-verse,galaxyclustersarealsothemostrecentlyvirializedobjects,owingthethehierarchicalgrowthofstructureincosmology.Theirpositiononthetipofthehalomassfunctionmakesthemincrediblysensitivetocosmologicalparameters,andenablesclusterstobeusedasuniqueenvironmentsinwhichtoexplorecosmology.Galaxyclustersarealsointerestingenvironmentsforgalaxyformationandevolution,andforthepurposesofthisdissertation,wewillforgoafulldiscussionofthedarkmatteraspectofclustersandtheircosmologicalim-plications,insteadfocusingonthegalaxypopulation,theICM,andtheinteractionsbetweenthem.1.3.2TheIntraclusterMediumCharacterizedbyaverageparticledensitiesofn'103cm3,typicaltemperaturesof30100106K,andmagneticdsofafewG,theICMisahot,low-densityenvironment8(Sarazin,1988).DespitetheverylowdensityoftheICM,itcontainsthemajorityofthebaryonicmassinthecluster,accountingforapproximately8090%ofbaryonicmass,withthebalanceresidingintheclustergalaxies(Kravtsov&Borgani,2012).Thegasmassfractioninclustersisobservedtoincreasewithincreasingclustermass(Gonzalezetal.,2013).TheaveragemetallicityoftheICMisroughly0:3Z(Leccardi&Molendi,2008),increasingintheclustercoretovaluesof0:45Z(Leccardi&Molendi,2008)to0:45Z(Matsushita,2011),anddecliningwithradiusto0:1Zintheoutskirts(Simionescuetal.,2010,2011).ThemetalcontentoftheICMcomprises7080%ofthemetalcontentoftheentirecluster.Additionally,themetallicitydistributionintheICMisveryinhomogeneous(Simionescuetal.,2010,2011).Thesubstantiallevelofchemicalenrichmentindicatesthatfeedbackfromthestellarpopulationsinclustergalaxiesisoccurring.LikelymethodsoffeedbackareSNe-drivenwindsandrampressurestrippingofenriched,lowdensityISMgasontheoutskirtsofclustergalaxies(Domainkoetal.,2006;Kapfereretal.,2007).OfparticularinteresttoastrophysicistsisthenatureoftheICMinthecoresofgalaxyclusters.4070%ofclustersare\cool-core"clusters(e.g.,Sandersonetal.(2006);Chenetal.(2007);Johnsonetal.(2009)),characterizedbyacentraltemperaturethatisonly3040%oftheclustervirialtemperature(Ikebeetal.,1997;Lewisetal.,2002;Petersonetal.,2003).Identifyingandunderstandingtheexactmechanismsthatgiverisetocoolcoresareenduringchallengesinastrophysics.Byvirtueofexistinginabouthalfofallclusters,coolcoresstronglysuggestthatheatingandcoolingprocessesarenearlybalancedinthecentralregionofgalaxyclusters.Feedbackfromacentralenginesuchasactivegalacticnuclei(AGN)isthecurrentlyfavoredmechanismwithwhichtoheattheICMandbalanceradiativecooling(McNamara&Nulsen,2007,2012).91.3.3ClusterGalaxiesGalaxiesinclustershostthemajorityofthestellarpopulationingalaxyclusters,withasmallportionoftheclusterstellarmassresidingoutsideofgalaxiesandproducingthefaintintraclusterlight(ICL).Galaxiesinclustersfromgalaxiesintheinseveralways,perhapsmosttlybytheirmorphologiesandstarformationrates.Inhigh-densityenvironments,galaxiesevolvemorerapidly,atrendborneoutinclusters,asbyz=0thegalaxypopulationiscomprisedprimarilyofredellipticalswithverylittleongoingstarformation.Thebaryonicmassingalaxiesisonlyabout10%ofthemassintheICM,andthismassratioisastrongfunctionofclustermass.Moremassiveclustersarelesstatconvertinggasintostars,withthemostmassiveclusters(M5002'1015M)havingMstars=Mgas'0:05andgalaxygroups(M500'1013M)beingcomparativelymoret,withMstars=Mgas'0:2(Gonzalezetal.,2013).1.3.4BrightestClusterGalaxyWithinthegalaxypopulationofanygivenclusterisauniqueobject,thebrightestclustergalaxy(BGC).BCGsdisplayseveraldistinguishingcharacteristicsthatmakethempartic-ularlyintriguing.Theyareamongthelargestgalaxiesintheuniverse,andareremark-ablyuniformfromclustertocluster.AllBCGshaveapproximatelythesamestellarmass,Mstar'1011:5M,independentofthemassofthecluster.SeveralpropertiesofBCGsstronglysuggestco-evolutionwiththeclusterasawhole.Theyareubiquitouslylocatedatthecentersofclusters,alignedwiththeX-rayemissionpeak,andaregenerallyalignedwiththeprinciplerotationaxisofthecluster.BGCsdisplayconsistentmorphologyfrom2M500istobethemasswithinaradiusenclosingaregionwithanaveragedensitythatis500timesthecosmologicalcriticaldensity.10clustertocluster.Theyaregenerallylarge,gas-poorellipticalgalaxieswithextendedenvelopes.AusefulquantityforcharacterizingthegasingalaxyclustersisKkBTn2=3e;(1.1)termed\entropy"inastrophysicalcontexts(Voit,2005),wherekBisBoltzmann'sconstant,Tisthetemperature,andneistheelectrondensity.ThequantityKisdirectlyrelatedtostandardthermodynamicentropyperparticle,s,ass=kBlnK2=3+s0;(1.2)wheres0isaconstantwhichdependsonlyonfundamentalconstantsandthemixtureofparticlemassesinthegasbeingconsidered.Inthecaseofadiabaticmonatomicgas,KistheconstantofproportionalityintheequationofstateP=Kˆ5=3g.ActivestarformationinBCGsonlyappearstooccurinclusterswithcentralICMentropiesK0<30keVcm2,lowerthaninclusterswithnon-starformingBCGsthathavecentralentropiesK0>30keVcm2(Cavagnoloetal.,2008;Rayetal.,2008;eretal.,2012).1.4TheCircumgalacticMedium1.4.1OverviewAstheinterfacebetweentheintergalacticmedium(IGM)andthedenseISMofthegalacticdisk,thecircumgalacticmedium(CGM)isthebridgebetweencosmologicalstructurefor-mationandgalaxyevolution.MaterialfromtheIGMisdepositedintheCGMviadirect11accretionandthroughrampressurestrippingofthegasinsatellitegalaxiesthatfallintothegalactichalo.Thissupplyofgascoolsandfeedsthegalacticdisk,fuelingstarformation.Inturn,materialthathasbeenenrichedthroughstellarnucleosynthesisisoftenreturnedtotheCGM,drivenfromthediskbystellarwindsandSNemechanicalfeedback.TheCGMcancontainuptohalfthebaryonsinagalaxyandamassofmetalssimilartothatoftheISMandgreaterthantheamountcurrentlyresidinginstars(Peeplesetal.,2014).Despiteitscrucialroleingalaxyevolution,manyofthephysicalprocessesthatgovernthebehavioroftheCGMarepoorlyunderstood,andonlyrecentlyhaveobservationsbeguntoelucidatetherichcomplexityofthisgalacticcomponent.TheCGMisamultiphasebodyofgassurroundinggalaxies,extendingfromthedenseISMofthedisktoapproximatelytheradiusofthedarkmatterhalo.AgeneralfeatureoftheCGMappearstobeincreasingtemperatureanddegreeofionizationwithincreasingradius.Hot,roughlyvirial-temperaturegasisfoundeverywhereintheCGM,withdiscontinuouscloudsoflow-temperaturegasresidingclosertothecenterofthedarkmatterhalo.Observationsindicatethatthislow-temperaturegasisapproximatelycontainedwithinr500(Liang&Chen,2014;Werketal.,2014),theradiuswithinwhichtheaveragedensityisafactor500greaterthenthecriticaldensity,ˆcrit3.Thephysicalmechanismsmediatingthetransitionbetweentheseregionsisnotwellunderstood.TheCOS-Halossurvey(Werketal.,2014),inobservingahighlyionizedstateofoxygen,OVI,foundacoveringfractionof80%extendingtoaradiusof150kpc.Similarly,Liang&Chen(2014)foundasubstantialdropintheCIVcoveringfractionatapproximately70%ofthedarkmatterhaloradiusofgalaxies,withnoionictransitionsfrommetalsdetectedbeyondthisradius.Hydrogen,ontheotherhand,3Thecriticaldensityisthedensityrequiredforthegeometryoftheuniversetobeinthecasethatthecosmologicalconstant,iszero.Inpracticeitistobeˆcrit=3H28ˇG,whereHistheHubbleparameterandGisthegravitationalconstant.12wasdetectedwellbeyondthefulldarkmatterhaloradius,withacoveringfractionof60%.inthecoveringfractionoflow-andhighly-ionizedspeciesasafunctionofradiusindicateseitherthattheCGMbecomesincreasinglyionizedatlargerradii(Liang&Chen,2014),orthatthelow-ionizedgasismorepronouncedatsmallerradii.Indwarfgalaxies,thecoveringfractionofCIVdropsfromnearlyunitywithin0:2Rvirto60%at0:4Rvir,to0beyond0:5Rvir(Bordoloietal.,2014).GrowthoftheCGMoccursthroughaccretionofmaterialfromtheIGM.Somesimulationshavesuggestedthataccretioncanoccurdirectlyalongcosmicts,withmaterialfromtheIGMwingintotheCGMwithoutbeshock-heated(e.g.,Keresetal.(2005);Brooksetal.(2009)).Anotherpositedaccretionmethodisoneinwhichgasbeyondthevirialradiuscollapsesroughlysphericallyandfallsintothehalo,gettingshockheatedintheprocess(e.g.,White&Rees(1978);White&Frenk(1991)).AmannerofexternallysuppliedgrowthoftheCGMisthroughtheaccretionandsubsequentrampressurestrippingofsatellitegalaxies(e.g.,Putmanetal.(2003b);Grcevich&Putman(2009).Cosmologicalsimulationsshowthatroughly40%ofLgalaxieshosta<0:1Lsatellite(Tollerudetal.,2011),atrendthatisinagreementwithobservationsfromSDSS(Liuetal.,2011).1.4.2ObservationsKnowledgeofthegasandmetalcontent,aswellthetemperaturestructure,ionizationstate,andmultiphasenatureoftheCGM,comesprimarilyfromopticalandUVobservations.Coolgas,withtemperaturesT<104K,istracedbyobservationsofneutralhydrogenvia21-cmemission.Thiscoolgasgenerallyresidesinstructuresknownashigh-velocityclouds(HVCs),whicharethedensest,coldestcomponentoftheCGM.HVCsaretheremnantsofaccretedmaterial,originatingfrombothtaryaccretionfromtheIGMandthecannibalization13andsubsequentrampressurestrippingofaccretedsatellitegalaxies.Warmandwarm-hotgas,tohavetemperaturesintherange104K<T<106K,isobservedinabsorptionofvariousionspecies.OfparticularusefulnessaretheionsSiII,SiIII,CII,CIII,andCIV,aswellasOVI.CIVtracksphotoionizedgasatT'4104Kandtraceschemicallyenrichedgasinandaroundstarformingregions,andthehighionizationstateofoxygen,OVI,alongwithotherlithium-likeions,tracegasat3105K.Finally,hotgasistohavetemperaturesT>106K.ThisregimecanbeseenabsorptionintheculttoobservespeciesOVIIandOVIII(Williamsetal.,2005;Wangetal.,2005),andcanalsobeseeninX-rayemissionobservations.RecentobservationalcampaignshaveexposedmoredetailsofthestructureoftheCGMaroundgalaxiesofvarioussizes,atarangeofredshifts,andwithvaryingdegreesofstarformation.TheCOS-Halossurvey(Tumlinsonetal.,2013;Werketal.,2014)observedthecool,photoionizedgassurrounding44approximatelyLgalaxies.Theyfoundgasvolumedensitiesatlargeradiithatweresubstantiallylowerthanpreviousestimates,goinghandinhandwithobservationsoftheincreasingdegreeofionizationatlargeradii,owingtothediminishedcapabilityofthegastoself-shieldagainstextragalacticUVradiation.Under-scoringtherelationshipbetweentheCGMandstarformationinthegalacticdisk,astrongcorrelationwasfoundbetweenabsorptionofhighlyionizedOVIandthestarformationrate.Additionallytheythatcool,lowionizationstategasintheCGMaccountsforaminimumof25%ofthebaryonsinanLgalaxy,andthattheadditionofhot,highlyionizedgascanraisethatfractionsuchthatitcouldbringthetotalbaryoncontentofLgalaxiesintoagreementwiththecosmicbaryonfraction,potentiallyresolvingthe\miss-ingbaryons"problemingalaxies.ThecomplementaryCOS-Dwarfssurvey(Bordoloietal.,2014)observedtheCGMaround43lowmassgalaxies,andfoundasimilarrelationshipbe-14tweenionizedspeciesintheCGMandtheamountofstarformationinthediskaswasfoundinCOS-Halos,withhigherlevelsofCIVabsorptioncorrelatingwithhigherstarformationrates.CIVabsorptiondeclineswithradius,andthecoveringfractionwithin0:5Rvirissub-stantiallylargerinstar-forminggalaxiesthaninnon-star-forminggalaxies,reinforcingthenotionthatstarformationinthediskandthestateofthemultiphaseCGMareinextricablylinked.ComparisonoftheCOS-DwarfsdatawithsimulationsindicatesthatstrongwsarenecessarytoproducetheobservedmetalcontentoftheCGM;rampressurestrippingofaccretedsatellitesalonewouldbet.1.4.3StarFormationandFeedbackMostspiralgalaxieshaveastarformationrateof0:55Myr1.Sustainingthislevelofstarformationnecessitatestheaccretionoflowmetallicitygasintothediskatroughlyhalfthisrate.SeveralpathwayshavebeenproposedforthisgastotransitionfromtheCGMtothedisk,withoneofthehistoricallyfavoredmethodsbeing\quietaccretion"atthedisk-halointerface(Putmanetal.,2009,2012).Quietaccretionpositsthatwarmhalogascoolsandintegratesintothediskimmediatelynearthediskboundary,anddrawsitsnamefromthepresentinobservingit.Infact,theevidenceforquietaccretionleansheavilyondeducingwhatisplausiblyhappeningbasedonwhatisnotobservedratherthaninterpretingwhatcanbedirectlyseentobeoccurring.MaterialaccretedinthismodelwouldenterthediskviaparcelsofCGMgasthathavenotspatialorkinematicfromthegasalreadyinthedisk,substantiallyhamperingourabilitytodetectit.Thequietaccretionmodelhastheadvantageofprovidinganaturalexplanationforseveralotherwisetointerpretobservations,suchashighredshiftgalaxiesthatshowhighlevelsofstarformationandprominentwsfromthedisk,butnotobviousaccretion(Erb,2008;Shapley,2011;15Steideletal.,2010).Thereisalsoevidencefortheaccretionofcloudsascoherentstructures,withneutralHfeaturesobservedintheMilkyWaydiskthatarespatiallyandkinematicallyconnectedtothedisk.HobservationsofthewarmionizedgasintheMilkyWayalsoshowwalongthegalacticpoles.CirculationofthegasintheCGM,withhotgasfromthehalobuoyantlyrisingtogreaterdistancesaboveandbelowthedisk,pairedwiththedescentofgraduallycoolinghothalogas,couldalsoprovideastepinthediskfuelingprocess,whilehelpingtointerpretobservationsofgasatgreaterdistancesfromthediskthatlagsthelargergalaxyrotationrate(Marinaccietal.,2011).Accretionfromthehaloisnottheonlysourceofgasavailabletofuelstarformation.Recyclingofenriched,processedstellarmaterialcanreturngasandmetalstotheISMtobeincorporatedintofuturegenerationsofstars.Inparticular,AGBstarsreturn3050%oftheirmasstotheISM(Wachteretal.,2002).Thisrecyclingofmaterialcanfuelongoingstarformationwhilediminishingtheneedforthegassupplyinthedisktobeexternallyreplenished.Thecycleofstellarnucleosynthesis,ejectiontoandenrichmentoftheISM,andsubsequentstarformationunderpinsthetheoryofgalacticchemicalevolution.Themetal-licityoftheISMandgalacticstellarpopulationsiselevatedsubstantiallybeyondprimordiallevels,indicatingthatthisisoccurring.StellarandISMmetallicitiesanddeuteriumabun-dancesindicatethatrecyclingmustbesupplementedwithadditionallowermetallicitygasinordertoreconcilestarformationhistoriesandobservedenrichmentlevels.StarformationingalacticdisksisthereforefueledbyacombinationoflowermetallicitygasaccretedfromthehaloandtherecyclingofenrichedmaterialreturnedtotheISMbycurrentandpaststellarpopulations.ThemetalcontentandkinematicsoftheCGMindicatethatstellarfeedbackplaysaroleinthestateandevolutionoftheCGM.X-rayandgamma-raybubblesextendingalongthe16polesoftheMilkyWayareconsistentwithfeedbackfromanAGN-drivenw.StellarwindsandSNe-drivenwsservetodepositchemicallyenrichedhighentropymaterialinthehalogas.ThemetalliccontentoftheCGMcannotbeexplainedonlythroughenrichmentviatidaldebrisandrampressurestrippingofthegasfromaccretedsatellites.StrongwsfromthediskarerequiredtoboththecurrentlyobservedstarformationratesandCIVcoveringfractionsinsub-Lgalaxies(Bordoloietal.,2014).Inanaccountingofthemetalsproducedinastar-forminggalaxy,2025%ofthetotalmetalsproducedingalaxieswithstellarmassesfrom1091011:5MresideinthestellarandISMcomponentsofthedisk,whileatleast40%oftheproducedmetalscanbeobservedwithinaradiusof150kpc,suggestingthatstellarfeedbackisdepositingenrichedmaterialintheCGM.Distinctfromthesestrongws,acycleknownasthe\galacticfountain"inwhichmaterialisdrivenfromthediskbySNe,adiabaticallyexpandsabovethedisk,coolsradiatively,andfallsbacktothediskispositedtobeoccurring(Shapiro&Field,1976;Bregman,1980).Thiscycleissupportedbybothsimulationsandobservations.Thekinematics,locations,andmorphologyofintermediatevelocityclouds(IVCs)intheCGM,areinagreementwiththismodel.IVCmetallicitiesareroughlysolarandtheirdustcontentissimilartothatoftheISMinstarformingregions,lendingsupporttotheideathattheyoriginatedinthedisk.Whilewidespreadacrossthedisk,thereachofthegalacticfountainisrelativelysmall,extendingonlyafewkpcaboveandbelowthedisk(deAvillez,2000;deAvillez&Breitschwerdt,2005).Recenttheoreticalworkinvestigatingprecipitationasthedrivingforcebehindthede-velopmentofmultiphasegasintheCGM,itsroleinfuelingstarformationinthedisk,andhowitcanproduceaself-regulatingfeedbackresponse(fromeitherSNeoracentralenginesuchasanaccretingblackholeorAGN)hasyieldedanevenmorehighlyintertwinedpictureofthestarformingregionsofgalaxiesandtheCGM(Voitetal.,2015a).Multiphasegas17precipitatesoutoftheCGMbasedontheratioofthecoolingtime,tcool,tothefree-falltime,t.Simulationsofgalaxiesshowthiscriticalratiotobeapproximatelytcool=t=10.Belowthisthreshold,coldcloudsprecipitateoutofthehotCGMgasandchaoticallyaccreteontheAGN,triggeringfeedback(Gasparietal.,2012,2013,2015;Li&Bryan,2014a,b).ThisfeedbackinturnexpandstheCGMgas,increasingtcoolsuchthattcool=t>10,haltingfurtherprecipitationandaccretion.Thereissubstantialobservationalevidencesupportingthismodel,asitreproducesthedeclineinstarformationratewithchemicalenrichmentlevel(Ellisonetal.,2008;Mannuccietal.,2010),theabundanceatwhichfurtherchemicalenrich-mentwillsaturate,thestarformationhistoriesofgalaxiesasfunctionofgalaxymass,thegalaxymass-metallicityrelationship(Gravesetal.,2009;McConnachie,2012),theFaber-JacksonandTully-Fisherrelations(Faber&Jackson,1976;Tully&Fisher,1977)betweengalaxystellarluminosityandgalaxygravitationalpotential,andeventhenon-detectionoflow-ionizationcloudsbeyondr500(Liang&Chen,2014).1.5StructureofthisdissertationTheinteractionbetweenstarsandtheirenvironmentisfundamentaltomanyprocessesinastrophysics.Amyriadofphysicalprocessesgovernthisco-evolution;thesesystemsarehighlycoupledandnon-linear,makingapurelyanalyticapproachintractable.Relevantphysicalprocessesoccuronavastrangeofspatialandtemporalscales,andlimitedcomputa-tionalresourcesprohibitexplicitlysimulatingtheentiretyofthesesystems.Thisdissertationpresentsanexplorationoftheinteractionbetweenstellarpopulationsandtheirsurround-ingsinavarietyofenvironments,utilizingsemi-analyticmodelingtechniquesinconjunctionwithlarge-scalenumericalsimulationstobridgethesescalesandencapsulatethebehavior18ofphysicalprocessesoperatingonscalessmallerthanthesimulationresolutionlimit.Thestructureofthisdissertationisasfollows:Chapter2presentsareviewoftherelevantliteratureinallofthesesystemsandestablishesthecurrentstateoftheTheremainderofthisdissertationisbroadlyorganizedintochaptersbasedontheenvironmentinwhichtheinteractionbetweenstarsandtheirsurroundingsisbeingstudied.Chapter3isworkthatwaspreviouslypublishedinCrosbyetal.(2013)andinvestigatestheformationenvironmentofPopIIIstars.CosmologicalstructureformationaswellasphotodissociatingradiationandchemicalenrichmentfromPopIIIandchemicallyenrichedstarsimpactstheabilityofahalotohostPopIIIstarformation.Theseareself-con-sistentlytrackedandfromthisadescriptionofPopIIIstarformationratesandenvironmentsasafunctionoftimeisconstructed.Chapter4waspreviouslypublishedinCrosbyetal.(2016)andpresentstheresultsofresearchinvestigatingtheelementalabundancedistributionofstellarpopulationsinhigh-redshiftproto-galaxiesandcomparingthemtotheobservedelementalabundancedistri-butionsofMilkyWaydwarfgalaxies.ThisworkisanextensionofthemodeldevelopedinChapter3,andincludesamultiphasemodelofgasandmetaltransportingalaxies,withstarformationandfeedbackprocessescoupledtostellarnucleosyntheticyields.WiththismodelIproducesyntheticstellarelementalabundancedistributionsandcomparethemtoobser-vationsoflow-metallicitystars,providingconstraintsonthecharacteristicsofhigh-redshiftstarformation,galacticchemicalevolution,andstellarnucleosyntheticyieldcalculations.InChapter5thesemi-analytictechniquesdevelopedintheprevioustwochaptersareappliedtogalaxyclusters.TheGalaxyParticleformalismisisdeveloped,inwhichanindi-vidualparticlerepresentsanentiregalaxy.Agalaxyparticleisan\activeparticle"suchthateachparticleisanensembleofsemi-analyticmodelsrepresentinginternalgalacticprocesses19thatoccuronscalesmuchsmallerthantheresolutionelementofthesimulationinwhichtheareused.Galaxyparticlespossessanextendedspatialextent,allowingfortheinteractionsbetweenthegalaxiesandtheICMtobeself-consistentlymodeled.Theadditionofgalaxyparticlestocosmologicalgalaxyclustersimulationscreatesmuchmorerealisticclusters,withgalaxypopulationsandICMpropertiesthatareinbetteragreementwithobservationsthanpreviousgalaxyclustersimulations.Chapter6investigatestheroleplayedbystellarpopulationsindiskgalaxiesinthedevel-opmentofachemicallyenrichedmultiphasegasintheCGMofdiskgalaxies.Thethermal,chemical,andkineticstateoftheCGMischaracterized.ThesesimulationsbegindevelopingaframeworkwithwhichtoassesswhetherprecipitationintheCGMcansupplygasforstarformationinthedisk,andgiverisetoself-regulatingstarformationandfeedbackinthesegalaxies.Finally,Chapter7summarizestheconclusionsofthisdissertationandlaysoutdirectionsforfutureworktoextendthesegs.20Chapter2LiteratureReview2.1PopulationIIIStarFormationPopulationIII(PopIII)starsweretheluminoussourcesinuniverse,andinitiatedtheprocessofchemicalenrichmentthattransformedtheuniversefromasimplecompositionofH,He,andtraceamountsofLianddeuteriumtothecurrentwealthofelements.Owingtotheirearlyformationtimesandinferredshortlifetimes,noPopIIIstarshaveeverbeenobserved,andunderstandingtheirnaturehasbeenalongstandingandvexingchallengeinastrophysics.Ofprimaryinterestareseveralaspectsoftheseobjects:whatwastheircharacteristicmass,andwhatwastherangeanddistributionsofmassesofthePopIIIstars?Didtheyforminisolation,orinmultiples?Inwhatenvironmentsdidtheyform,andoverwhattimespan?DidtheirownfeedbackenhanceorsuppressfurtherPopIIIformation,andwhatprocessesmediatedthetransitiontolowmass,chemicallyenrichedmodesofstarformation?2.1.1FormationEnvironmentInthebroadeststrokes,thestarsarethoughttohaveformedindarkmatter(DM)minihalosofmass˘106Matredshiftsz˘3020(Couchman&Rees,1986).These21minihaloshavevirialtemperatures(Tvir)ofapproximatelyTvir'2103KMh106(2=3)1+z20;(2.1)whereMhisthemassoftheminihalo.Thesetemperatureswillbewellbelow104K,theminimumtemperaturefortcooling1ofthegasviaatomichydrogen.Instead,thegasmustrelyonmolecularhydrogencooling(Saslaw&Zipoy,1967).Silk(1977)andRees&Ostriker(1977)identhattherelationbetweenthecoolingtimetcoolandthedynamicaltimetdyn=r3=(GM)wascrucialtoidentifyingobjectsthatwouldcollapse,namelythosethattheRees-Ostriker-Silkcriterion,tcool<tdyn.Withthesebasicrequirementsasguides,aswellastherarityofpeakscapableofproducingsuchfromthecolddarkmatter(CDM)powerspectrum,Yoshidaetal.(2003)foundthathalosincapableofbeingmaintainingthermalsupportagainstgravitationalcollapsegenerallyhadamolecularhydrogenfractionfH2˘104,andthattheseobjectsareprimarilyspatiallyclustered.Movingintotherealmofself-consistentcosmologicalsimulations,Fuller&Couchman(2000)foundthatcollapsesetinwhenfH2&5104.SimulationsbyO'Shea&Norman(2007)idenathresholdmassforcollapseof2105M,andfoundthatthenatureofthestar-formingcloudwascloselytiedtotheformationhistoryoftheDMhaloinwhichitiscontained.2.1.2PopIIIStellarCharacteristicsUnderstandingtheIMFofPopIIIstarspresentsaremarkablechallenge,asfollowingtheevolutionofastar-formingcloudallthewaytothecreationofathelstellarobject1Inthecontextofastrophysicalgases,\cooling"isgenerallytoberadiationprocessthatactinginisolationwouldreducethethermalcontentofthegas.22(orobjects)iscomputationallyprohibitiveformanyreasons:theincreasingdensityascol-lapseproceedsnecessitateseversmallertimesteps,keepingtheobjectalwaysoutofreach.Withincreasingdensitycomesincreasingopticalthicknessofthegas,butthisdoesnothappenuniformly,necessitatingcostlyradiativetransportcalculations.Thecollapsinggasislargely(butnotsolely)composedofmolecularhydrogenwhichhasmanynarrowab-sorptionlines,andasaresulttheopacityisastrongfunctionoftheH2fractionandlocalvelocitystructure.Computingtheimpactoftheseconditionsrequiresmulti-frequencyra-diationtransportcalculationsacrossawiderangeofdensities,renderingsimulationsofthefullevolutionofthesecollapsingsystemsinfeasible.UncertaintiesintheH2formationrateproducevastlytoutcomesbasedontheassumedmodel(Turketal.,2011a).Atthehighdensitiesreachedduringcollapse,magneticandnon-idealMHDbecomeimportantandcannolongerbeneglected(Xuetal.,2008).Oncefusionbegins,theinter-actionoftheradiationoftheprotostaranditsaccretiondiskmustbeproperlymodeledtodeterminewhenaccretionceases,establishingthemassofthePopIIIstar(Tan&McKee,2004;McKee&Tan,2008).Thelackofobservablemetal-freestarssuggeststhatlonglived,lowmassPopIIIstarsarehighlyunlikely,butasidefromthatinferredconstraint,thecharacteristicmassandfunctionalformoftheIMFislargelyunknown.PioneeringworkbyBrommetal.(1999,2002)attemptedtoconstrainthePopIIIIMFthroughaseriesofsimulationsstartingwithidealizedhalosatz=100.Theauthorsfoundcollapsingregionsofapproximately103M,whichtheysuggestcouldresultinPopIIIstellarmassesinexcessof100M.AsimilarendeavorbyAbeletal.(2000,2002)alsoaimedtoconstrainthePopIIIIMF,butwithsimulationsbeginningfromcosmologicalinitialconditionsatz=100.TheiralsoindicatedacharacteristicPopIIIstellarmassofapproximately100M.McKee&Tan(2008)23usedsemi-analytictechniquestoconsidertheofradiativefeedback(aprocessnotincludedintheworkofBrommetal.(1999,2002)andAbeletal.(2000,2002))fromtheformingPopIIIstarontheaccretiondiskthatissupplyingitwithmaterial,andfoundthatradiativeevaporationcouldhaltaccretionandresultinanuppermasslimitof140M.Thesemodelsweretestedinaradiation-hydrodynamicssimulationsbyHosokawaetal.(2011),theofthemechanismandfurtherloweringtheupperlimit,withastellarmassof43M.ThisupperlimitcouldpotentiallyexplainthelackofobservednucleosytheticsignaturesfrompairinstabilitySNe(PISNe),thepresumedfateofextremelymassivestarswithmasses130<M=M<240.ThisworkwascarriedastepfurtherinHosokawaetal.(2012),wheretheyconsideredtheformationofthesecondgenerationofstarswithprimordialcomposition,butnowinthepresenceofUVradiativefeedbackfromPopIIIstarswhichhadformedearlier.Theyfoundthisscenarioproducedevenlowermassstars,withfeedbackstoppingaccretionwhenthestarhadreachedasmassof17M.Stacyetal.(2012)similarlytestedtheuenceofprotostellarradiationonthesurroundingaccretiondisk,andfoundthatthedevelopmentofthebinarysystemlowermassesthansimulationswhichdonotincluderadiativefeedback,resultinginanestimatedmassoftheprimarystarofapproximately30M.ThefunctionalformoftheIMFhasprovenmuchmoretoconstrain,butasuiteofsimulationsbyGreifetal.(2011)indicatesthatthemassfunctionisnearlyinlogNlogMspace.Abeletal.(2000,2002)advancedtheideathatPopIIIstarsformedinisolation,withmonolithiccollapsewinningoutoverfragmentationprocesses.Incontrast,Brommetal.(1999,2002)foundthatPopIIIstarstendedtoforminsmallmultiplesystemsofupto5distinctobjects.IdealizednumericalexperimentsbyMachidaetal.(2008)studiedtheconditionsrequiredforfragmentationofrotatingsphericalclouds.Ofthecharacteristics24exploredinthisstudy,fragmentationwasfoundtobethemostsensitivetorotation.Theyfoundthataratioofrotationaltogravitationalenergy,0,of106wasttoinducefragmentation.Thisvalueis0islowerthanthatpredictedforPopIIIstar-formingclouds,suggestingthatfragmentationandtheformationofPopIIImultiplesystemswasacommonoutcome.Turketal.(2009)providedanexampleofthefragmentationofaPopIIIstar-formingcloudintoadistinctbinarysystem.SubsequentworkonthetopicbyStacyetal.(2010)supportedthisthoughthePopIIImultiplicitythatmanifestsinthatworkoriginatedfromfragmentationintheaccretiondiskthatformedaroundtheinitiallycollapsedPopIIIprotostar,ratherthanfromthenear-simultaneouscollapseoftwodensitypeaksasoccurredinTurketal.(2009).Similarinvestigations,withsimilars,wereundertakenbyClarketal.(2011b)andGreifetal.(2011),bothofwhichusedsink-particlestorepresenttheopticallythickregionsoftheprotostar.Inbothstudies,multiplicityoriginatedfromfragmentationoftheaccretiondisk,thoughthenatureoftheresultingPopIIImultipleswerestronglydependentonthedetailsofthesink-particlealgorithm.Stacy&Bromm(2013)endeavoredtoconstrainthecharacteristicsofPopIIImultiplesystems,andfoundabinaryfractionof35%,semi-majororbitalaxesupto3000AU,andalog-normaldistributionoforbitalperiodswithaslightpeakat900yrs.Approximatelyhalfoftheprotostarswhichformarelosttomergerswithlargerprotostars,andhalfofthesurvivingprotostarsareejectedfromtheirorbits.2.1.3TransitiontoChemically-EnrichedStarFormationThepresenceoftheheavyelementsproducedinPopIIISNefundamentallychangesthephysicsandchemistryoftheISM,alteringthenatureofstarformation.Atomicandionizedmetalspecies,aswellasdust,providenewavenuesofcooling,andenablecollapseand25fragmentationofstar-formingcloudsonsmallerscales.Omukai(2000)advancedtheideathatthereexistsametallicitythresholdabovewhichstarformationtransitionsfromthehighmassregimeofPopIIIstarformationtotheformationoflowmassstars.TheideaofacriticalmetallicityZcritwasfurtheredbyBrommetal.(2001),dingthatmetallicitiesgreatthan5104Zledtomuchgreaterdegreesoffragmentation,indicatingthetransitiontoalow-massmodeofstarformation.ThevalueofZcritvariesdependingonthemodelbeingused.Onemodeladvocatesthatcoolingviastructurelinesistheprimarydriverwithincreasingmetallicity,withZcrit'103:5Z(Brommetal.,2001;Smithetal.,2009;Safranek-Shraderetal.,2010).Asecondcategoryofmodelsproposesthatdustisthecrucialcomponentmediatingthetransition(Schneideretal.,2006;Schneider&Omukai,2010),andenablesfragmentationatmuchlowervaluesofZcritthanstructurecooling.However,Dopckeetal.(2013)thatthereisnocriticalmetallicitybelowwhichfragmentationcannotoccur.Nevertheless,theyadistincttransitioninthemassesofcloudsthatcollapsebelow105Z,becausebelowthismetallicitythetimescaleforfragmentationislongerthanthetimescaleforaccretion.Meeceetal.(2014)studiedtheideaofacriticalmetallicityinaseriesofsimulationsoffragmentationandcollapseinhighredshifthalos,bothwithandwithoutdust.Theyfoundtentativesupportfortheideaofacriticalmetallicity,butthatthemagnitudeoftheismuchlessthanhadbeenpreviouslysuggested.2.2GalacticChemicalEvolutionandNear-FieldCos-mologyGalacticchemicalevolutionmodelsprovidetheparadigmbywhichweunderstandthebuildupofchemicalcomplexityintheUniverse.Theoverallpictureiswellestablished:stars26expelnucleosyntheticproductsintotheISM,whichissubsequentlyincorporatedintolatergenerationsofchemicallyenrichedstars.Freeman&Bland-Hawthorn(2002)positedthatthisprocessofchemicalenrichmentcanbecoupledwithmodelsofcosmologicalstructureformation,andthatinturnstarsintheMilkyWaycaninformourunderstandingofthehigh-redshiftuniverse.Theycoinedtheterm\nearcosmology"todescribethisapproach,layingthefoundationfordevelopmentofthisTheviabilityofcosmologyhingesontheideathatstarspreservearecordofthechemicalabundancesoftheenvironmentatthetimewhentheyformed.Theideaof\galacticarcheology"wasputforthbyBeers&Christlieb(2005),whichsoughttostudytheoldest,mostmetal-poorstarsintheMilkyWayhalo.\Dwarfgalaxyarcheology"isanextensionofgalacticarcheologyfocusingonobservationsofthestellarpopulationsinMilkyWayultra-faintdwarfanddwarfspheroidalgalaxies(Belokurov,2013).Inparticular,dwarfgalaxyarcheologyseekstoinvestigatesmall-scale,high-redshiftgalaxyformationandandassociatedmetal-mixingandchemicalevolutionprocessesbycomparingtheabundancepatternsofthesesystemswithothermetal-poorstarsintheMilkyWayhalo.Galacticarcheologyandcosmologybothexploittheinverserelationshipbe-tweenstellarlifetimeandmass:thelowestmassstarslivethelongest,andhencethestudyoflowmass,lowmetallicitystarsintheMilkyWayhalocanprovideainsightintothehigh-redshiftgalaxiesinwhichthesestarsformed.Thechemicalsignaturesofthestars,andpotentialforusingmodernchemicalabundancepatternstoprobethenatureofthesestars,isdiscussedinKarlssonetal.(2013)andthereferencestherein.ThereviewbyFeltzing&Chiba(2013)discusshowthechemicalandkineticstructureoftheMilkyWayencodesthehistoryofalltheobjectsthatmergedtoformit,andalongwithIvezicetal.(2012)summa-rizestheidenofstreamsandpopulationsintheMilkyWaythroughtheanalysisof27thestellarhaloinkinematicphasespace.2.2.1ObservationsofMetal-PoorStarsFrebeletal.(2010b)observedsixmetal-poorstarsintheUrsaMajorIIandComaBerenicesdwarfgalaxies,allwithmetallicities3:2<[Fe/H]2<2:3,andwhichtheyfoundtohaveabundancepatternsoflight,alpha,andiron-peakelementswhichwereverysimilartothoseinMilkyWayhalostars.Furthersearchesforextremelymetal-poorstarsintheMilkyWayhaveresultedinthediscoveryofeightstarswith[Fe/H].4:5,sevenofwhicharehavestronglyenhancedcarbonabundancesrelativetosolarlevels(seeFrebel&Norris(2015)forthefulllistandassociatedreferences).Metallicitydistributionfunctionsfor86extremelymetal-poorstarswith[Fe/H]<3:0werecreatedbyYongetal.(2013)usinghigh-resolution,highsignaltonoise(S/N)observations.Thisworkshowedthatthefractionofstarsthatarecarbon-enhanced([C/Fe]>1:0)increaseswithdecreasing[Fe/H].Below[Fe/H]=4:5,allobservedstarsarecarbon-enhanced.Placcoetal.(2014)undertookasimilarstudy,seekingtoquantifythefrequencyofcarbon-enhancementinextremelymetal-poorstars.Theyusedhigh-resolutionabundancedataavailableintheliteratureandtookintoaccountdecreasedsurfaceabundancesofcarboninredgiantbranchstars,asimilartrendtoYongetal.(2013),withthefractionofcarbon-enhancedstarsincreasingas[Fe/H]decreased,butwithslightlyhighercarbon-enhancedfractions.Thedetectionofstarswith[Fe/H]<3:0indwarfgalaxysystemsbeganwithKirbyetal.(2008)discovering15suchobjectsin8ultra-faintdwarfsystems.Theyfoundthestarsinultra-faintdwarfsaretinstarswith[Fe/H]<1:5whencomparedtostarsinthe2Weadoptthestandardconvention[X/Y]=log10(NX=NY)log10(NX=NY).ThisshowsthelogratioofquantitiesXandYscaledtotheSolarratios.28MilkyWayhalo.SubsequentobservationsbyNorrisetal.(2008)oftheBootesIultra-faintdwarffoundastarwithaninferred[Fe/H]=3:4basedonthestrengthoftheCaIIKline.tofthemethodbywhichthe[Fe/H]valueofastarwasinferredinlow-metallicitysystemsbasedontheCIItripletbyStarkenburgetal.(2010)ledtothediscoveryofstarswith[Fe/H]'4:0intheSculptor(Frebeletal.,2010a)andFornax(Tafelmeyeretal.,2010).Frebeletal.(2010b)collectedspectraofsixmetal-poorstarsintheUrsaMajorIIandComaBerenicesultra-faintdwarfgalaxies,andfoundageneralsimilarityinthelightelementabundancepatternsbetweenthesestarsandthoseintheMilkyWayhalo.Ishigakietal.(2014),inobservingotesI,foundthatithadlowerabundanceofneutron-captureelementsthanmetal-poorstarsintheMilkyWayhalo,butrecentobservationsbyJietal.(2016)indicatethatthismightbeanartifactofweakstatisticsstemmingfromasmallsamplesize,andamassiveenhancementofr-processelementsintheReticulumIIultra-faintdwarf.Alternately,theeventsthatproducethisr-processenhancementmayoccurlongafterstarformationends,oraresutlyrarethatthisinfrequencypairedwiththesmallstellarpopulationsinultra-faintdwarfsmayprecludetheseeventsfromoccurringineverysystem.2.2.2TheoryandSimulationManygroupshaveendeavoredtounderstandtheformationofmetal-poorstarsthroughthe-oreticalandcomputationalinvestigations.Thesemi-analyticmodelsofFontetal.(2006)constructedmergerhistoriesforseveralgalaxiesresemblingtheMilkyWayusingamethodbasedontheextendedPress-Schechterformalism(Lacey&Cole,1993)andfollowedtheevo-lutionofelementalabundancesofalphagroupelementsaswellasirontotrackthechemicaldistributionofgalactichalosandtheirsatellites.Theyfoundthatmanyobservedabundancepatterninhalostarsanddwarfgalaxiesarisenaturally,andthattheelementalabundance29distributionscanserveasdirectprobesoftheaccretionhistoryofagalaxy.Salvadorietal.(2010)modeledthespatialmetallicitydistributionofstarsintheMilkyWaybycombiningsemi-analyticmodelsforstarformationinasingle-phaseISMwithN-bodysimulationsofstructureformation.Theytrackedironabundanceasaproxyfortotalmetallicity,ndingthatmoreenrichedstarsarepreferentiallylocatedintheinnerregionsofthegalaxy,andthattheouterhaloregionsarethebestareastosearchformetal-poorstars.Tumlinson(2010)usessemi-analyticchemodynamicalmodelingofhigh-redshiftstarformationtoinvestigatethedegreetowhichstarsintheMilkyWayhalotheenvironmentinwhichtheyformedbefore,during,andaftertheepochofreionization.HismodelproducessimulatedgalaxiesthatresembletheMilkyWaystellarmass,metallicitydistribution,luminosityfunction,andpopulationofsatelliteanddwarfgalaxies.IncontrasttoSalvadorietal.(2010),Tumlinson(2010)thatthemostmetal-poorstarsresideontightlyboundorbitsinthebulgeofthegalaxy,butdonotoriginatethere,andinsteadareformedathighredshift(z>6)andaccretedbythegalaxy.Komiya(2011)constructedamergerhistoryreplicatingtheMilkyWayusingextendedPress-SchechterformalismandtracksevenelementalabundanceswhilefocusingonyieldsfromSNeratherthanincludingotherstellarenrichmentchannels.Theyusethismodelinconjunctionwiththespatialandabundancedistributionofmetal-poorstarsintheMilkyWaytoprobethePopIIIIMF,andthattheobservationsofextremelymetal-poorstarsarebestreproducedbyapopulationofmassivestars,withacharacteristicmassofapproximately10M.Kobayashi&Nakasato(2011)coupleasemi-analyticmodelofstarformationwithN-bodycosmologicalsimulationsofaMilkyWay-likegalaxy.Intracking13elements,theyreproducethegeneraldisk,bulge,andhaloabundances,butduetolimitedresolutionandalatesimulationinitialtimeofz=24,theydonotresolvestarformationandchemicalevolutioninMilkyWaysatellitesandthedwarfgalaxypopulation.30DeBennassutietal.(2014)evaluatedseveralphysicalconditionsthatcouldmediatethetransitionbetweenPopIIIandchemicallyenrichedmodesofstarformationandfoundthatatlyhighratioofdusttogasinthegalacticmediumproducedthebestagreementwiththeobservedMilkyWaymetallicitydistribution.Theyfoundthatacriticaldust-to-gasratiowasdistinguishedfromtheothertransitioncriteriainvestigatedinthatworkbybeingtheonlycriterionthatreproducedboththecarbon-enhancedandcarbon-normalmetal-poorstellardistributionsobservedintheMilkyWayanditssatellites.Cooke&Madau(2014)investigatedtheoriginofcarbon-enhancedmetal-poorstarsbyconsideringtheinterplaybetweentheenergyofPopIIISNeandthemassofthehaloinwhichtheseexplosionsoccur.Theyascenarioinwhichahigh-energySNeinalow-masshalototallyevacuatestheenrichedmaterial,erasingthenucleosyntheticsignatureofthethePopIIISNe.Increasingthehalomassmothisbehavior,asahigh-energySNeinahalothatistlymassivetoretaintheejectaisimmediatelyenrichedtosolarlevels.Finally,theythatalow-energySNewillexpellargeamountsofcarbontothesurroundingISM,whileironwillnotbefullyexpelledfromthestellarcore,andwillinsteadfallbackontotheremnant,resultingin[C/Fe]˛0andpotentiallygivingrisetocarbon-enhancedmetal-poorstars.2.3GalaxyClusters2.3.1ObservationsIntheabsenceofafeedbackmechanismtoheattheICMgas,radiativecoolingwouldre-sultinstrong\coolingws"ingalaxyclusters,transportinglargequantitiesofgastothecentralregions,andfuelingcorrespondinglylargeamountsofstarformation(Fabian,1994).Whenthestarformationassociatedwiththeseproposedcoolingwscouldnotbefound31observationally(McNamara&O'Connell,1989;Cardieletal.,1998),itwasdeducedthataprocessorprocessesmustbeactingtoheatthegasandcounteractingtheofradiativecooling.Peterson&Fabian(2006)reviewedthestateofX-rayobservationsinthecoresofgalaxyclusters,whichwerefoundtobetinemissionfromcoldgasrelativetowhatwouldbepredictedfromradiativecoolingmodels.ThislackofcoldgassuggeststhatsomeadditionalheatingsourcesmustbeactingontheICMgastoradiativecooling.Asampleof20galaxyclustersobservedwiththeChandraX-RayObservatorywasan-alyzedbySandersonetal.(2006),identifyingninecool-coreclusters11andnon-cool-coreclusters.Theyfoundthetemperaturesbeyondtheclustercoretobeveryconsistentacrossallclustersinthesample.Withinthecoreregions,cool-coreclustershadveryuniformtemperaturebutthistrendwasnotseeninthenon-cool-coreclusters.Thecoolingtimeofthecentralregionsofcool-coreclusterswasfoundtobeastrongfunctionofradius,withthebeingsimilaracrosstheclusters.AnanalysisofclustersfromtheHIFLUGCSsamplewasundertakenbyChenetal.(2007).Theyfoundanearlyevensplitbetweencool-coreandnon-cool-coreclusters,with49%oftheclustershostingcoolcores.Thecool-coreclustersintheirsamplehadsmallercoreradiithanthenon-cool-coreclusters.Theauthorspositthatthenon-cool-coreclustersmaybeinadynamicallyyoungerstatethantheircool-corecounterparts,andmayevolveovertimetodevelopcoolcores.Sandersonetal.(2009)measuredtheprojectedbetweentheBCGandtheX-raycentroidfor65clusters.Anbetweenthesetwolocationswastakentobeanindicationthattheclusterisinadynamicallydisturbedstate,andtheyfoundthatthisdisturbancecorrelateswithweakercool-cores.Themergerhistoryofclusterswasonceagaininvokedasapossibleoriginofthedivisionbetweencool-coreandnon-cool-coreclustersbyRossettietal.(2011),whosearchedforgiantradiohalosassociatedwithpastmergereventsaround32clusters,andfoundnonearoundcool-coreclusters,suggestingthatthesemayrepresentaclassofdynamicallyrelaxed,undisturbedgalaxyclusters.Eckertetal.(2012)observedthegasdensityintheoutskirtsof31clusters,andfoundthatnon-cool-coreclustershavethancool-coreclusters,anattributethattheyargueisindicativeofpastmajormergers.Sunetal.(2009)analyzed43clustersthathadbeenobservedwiththeChandraX-RayObservatory,thatthegastemperatureprbeyondaradiusof0:15r500aresimilar,inagreementwitha\universaltemperaturedespitealargervariationinclustervirialtemperature.TheconsistencyofthetemperatureoutsideoftheclustercoredemonstratesthatSNfeedbackaloneisinsuttoheattheICMgasinequalmeasuretothedegreeofcoolingprovidedbyradiativecooling.Leccardi&Molendi(2008)undertookastudyof50clustersobservedbyXMM-Newton,modelingthebackgroundratherthansimplysubtractingitoThisapproachyieldedaslightlyshallowertemperaturewhichwasingoodagreementwithsimulationsbeyond0:2r180.Pressureforasampleof33clusterswasanalyzedbyArnaudetal.(2010),andfoundthattheywereremarkablyconsistentandself-similarbeyond0:2r500.Atsmallerradiithedispersionaboutthemeanincreasedtly,withdeviationsowingtothemassofthecluster,aswellitsthermalanddynamicalstate.AmoredirectprobeofthepressureofclusterscanbeobtainedwiththeSunyaev-Zel'dovich(SZ),aswasusedbyBonamenteetal.(2013)todeterminethepressureof38clusters.2.3.2TheoryandSimulationAwidearrayofsimulationshavebeenundertakeninanattempttounderstandthephysicalprocesseswhichgoverntheformationandevolutionofgalaxyclusters,thepropertiesof33theICM,galaxyformationinaclusterenvironment,andthemechanismsgiverisetothecool-coreandnon-cool-coreclusterpopulations.AninvestigationbyLokenetal.(2002)simulatedacollectionofgalaxyclustersinacosmologyandfoundevidencefora\universaltemperaturebutonewhichonlyheldatradiir>0:2Rvir.Interiortothisradiusthedidnothold,norcouldtheirsimulationreproduceobservations,furtherindicatingthatphysicalprocessesbeyondradiativecoolingarenecessarytoexplainthestructureofclustercores.Borganietal.(2004)ranasimulationofgalaxyclustersandgroupswhichincludedradiativecoolingforzerometallicitygas,starformation,andfeedbackfromSNe.Theinclusionofstarformationpointedtowardstheneedformoresophisticatedmodelsofthisprocess,asthefractionofbaryonsinstarsinthesimulationwasapproximatelytwicetheobservedvalue.SimilartoLokenetal.(2002),theysuccessfullyreproducedtheICMtemperaturebeyond0:2Rvir,butwereunabletomatchobservationsinsidethisradius,suggestingthatmoretfeedbackthanthatprovidedbySNewasrequiredtosuppressthecentraldensityandregulatecoolingoftheICMinthecoresofsimulatedclusters.Nagaietal.(2007)investigatedtheroleofgalaxyformationintheevolutionoftheICMmorphologybyrunningsimulationsofidenticalclusters,oneinthenon-radiativeregimeandonewithstarformation,metalenrichment,andSNfeedback.ThegalaxyformationprocessesprovedcrucialtocreatingclusterswithICMpropertiesmatchingobservations,particularlytheentropyWhilethisworkimprovedagreementbetweensimulatedandobservedICMandscalingrelations,theobservedmorphologyoftheclustercoreswasnotwellreproducedbythesimulations,norwastheclusterbaryonfraction.AreviewbyBorganietal.(2008)drewattentiontotheyofformingrealisticBCGsingalaxyclustersimulationsthatincludeonlySNfeedbacktocounteractradiativecooling.Inparticular,the34stellarmassinsimulatedBCGswasafactorof2-3largerthanwhatwasobserved.Thisexcessofbaryonsinstarsgivesrisetoanotherproblemencounteredinsimulations:themetallicityoftheICMgasinclustercoresdrasticallyexceedsobservedlevels.TheofAGNfeedbackonBCGevolutionwasinvestigatedbyMartizzietal.(2012),whofoundthatthismanneroffeedbackiscrucialforreproducingtheBCGmorphology,stellarmassfraction,velocitydispersion,anddensityIncontrast,usingonlySNfeedbackfailstoaccuratelyreproduceanyoftheseobservablecharacteristics.TheroleofAGNindrivingwindswhichcanheatthesurroundinggaswasinvestigatedbyOmmaetal.(2004)inhydrodynamicsimulationsofidealizedclusters,showingthatthesejetscanleadtotheformationoflargecavities,butonlythemetallicitygradientofthegasinthemostcentralregions.Duboisetal.(2011)studiedtheroleofAGNinproducingcool-coreandnon-cool-coreclustersincosmologicalsimulationthatincludedsubgridmodelsforgascooling,starformation,SNfeedback,andAGNheating.TheyfoundthatAGNfeedbackplayeddtrolesatearlyandlatetimesinclusterevolution,preheatingthegasinthenascentprotoclusterandpreventinglargeamountsofmassfromcollectinginthecore,andlaterregulatingthewofmassintothecoreandpreventingexcessivestarformation.Intriguingly,suppressingtheroleofmetalsindeterminingthecoolingrateresultsinthecreationofcool-coreclusters,butincludingitsproducedonlynon-cool-coreclusters.Skoryetal.(2013)assessedthecapabilityofstellarheatingandSNfeedback,alongwithsophisticatedcoolingmodels,toproducecool-coreandnon-cool-coreclusterswithrealisticcentralcoolingtimes,entropies,andtemperatures.Whiletheproperuseofthesemodelscanimprovetheagreementbetweensimulatedandobservedclusters,theyareincapableofproducingrealisticclusterICMpropertiesintheabsenceofamoretfeedbackmechanism.35WorkingundertheassumptionthatAGNfeedbackisindeedtheheatingmechanismthatbalancesradiativecoolinginclustercores,Gasparietal.(2011)endeavoredtodeterminewhattriggerstheAGNresponse.Theytestedseveralscenariosinasuiteofsimulations,narrowingthecandidateprocessestotwo:theintermittentaccretionofcoldgaswhichtriggersexplosiveoutburstsoffeedback,andBondiaccretionontotheAGNwhichfuelstheAGNatamoreconstantrate.TriggeringofAGNfeedbackwasinvestigatedfurtherinLi&Bryan(2014a)andLi&Bryan(2014b),whofoundthatcondensationofcoldgasintheICMcouldfueltheAGN,inturndrivingstrongwsandhaltingcondensation.Deprivedoffuel,theAGNfeedbackwouldweaken,creatingaself-regulatingcyclecapableofmaintainingathermallybalancedcool-coregalaxycluster.Lietal.(2015)extendedthisinvestigationtoincludedstarformation,showingthatthisself-regulatingmannerofAGNfuelingalsoproducesrealisticstarformationrates.TheoreticalworkbyVoit&Donahue(2015)suggeststhatprecipitationofcoldcloudsinthegassurroundingBCGscanfuelAGNactivity.Inthismodel,thecriticalquantityistheratioofthecoolingtimetothefreefalltime.Whenthisratiofallsbelowavalueof10,precipitationsetsinandamultiphasemediumdevelops.FeedbackfromtheAGNincreasingthecoolingtime,suppressingprecipitation,reducingitssupplyoffuel,anddiminishingfeedback.2.4TheCircumgalacticMediumTheideaofamultiphasemediuminthegaseoushalosurroundingtheMilkyWaycantraceitsoriginstoSpitzer(1956),whoproposeditsexistencebasedontheoreticalgrounds.Observationssoonfollowed,andgrowthofourknowledgeofthestructureandcharacteristicsoftheCGMgrewrapidly,andcontinuestoexpandtoday.Hereispresentedabriefoverview36ofliteratureonthetopic,organizedintosectionsbasedonthecomponentoftheCGM,followedbyadiscussionofrecentobservations,andconcludingwithadiscussionofcurrenttheoreticaladvances.2.4.1NeutralHydrogenGasThedirectobservationsofhalogasintheMilkyWaywerebyMulleretal.(1963),whoobservedneutralHemissionatvelocitiesof175kms1relativetotheGalacticdisk.Termedhighvelocityclouds(HVCs),thesestructuresarethecoldest,densestcomponentoftheCGM,andaregenerallytohavevelocitiesrelativetothelocalstandardofrestinexcessof100kms1.HVCsarebelievedtooriginatefromstrippedsatellitegalaxieswhichhavebeenaccretedbytheMilkyWayandIGMwalongcosmicts.ModernobservationssuchastheLeiden/Argentine/Bonn(LAB)HIsurvey(Kalberlaetal.,2005)createdall-skymappingsofneutralHinGalactichaloandprovidednewinsightintotheprevalenceofHVCs.High-resolutionobservationsoflargeHVCcomplexesshowedthattheyareoftennotsinglestructures,butareinsteadcomposedofmanysmallerclouds.Putmanetal.(2002)followedupobservationsfromtheHIParkesAll-SkySurvey(HIPASS)andfoundnotonlyanincreasednumberofindividualclouds,butthattheyhaveatarymorphology.Stanimirovicetal.(2008),inobservingtheMagellanicStream(MS),foundthatthetipoftheMSiscomposedofalargepopulationofindividualHIclouds,andattributethisfragmentarystructuretothermalinstability.Kalberla&Haud(2006)usedLABdatatoinvestigateHVCstructure,reinforcingobservationsthatHVCsoftenhaveatwocomponent,envelope-corestructure.TheymeasuredHVCstopossessanarrowcomponentoftheirvelocitythatwouldcorrespondtoT<500Kgas,alongwithtypicallinewidthsof20kms1,inagreementwithdeHeijetal.(2002)andPutmanetal.(2002),37whomeasuredlinewidthsof2030kms1indicatingthepresenceofawarmneutralmediumat9000K(Hsuetal.,2011).TheionizationstateofcompactHVCsexposedtoanextragalacticUVbackgroundwasmodeledbyMaloney&Putman(2003),andthatthisexternalionizationoftheouterregionsofHVCsisastandardoutcome.2.4.2WarmIonizedandWarm-HotGasThewarmionizedandwarm-hotgascomponentoftheCGM,withtemperaturesrangingfrom104Kto106K,wasdetectedviaNIIandSIIabsorptioninHVCsbyseveralgroups,includingBland-Hawthornetal.(1998),Tufteetal.(1998),andPutmanetal.(2003a).Wakkeretal.(2008)constrainedthedistancestoseveralintermediatevelocityclouds(IVCs),tohavevelocitiesrelativetothelocalstandardofrestvLSRof50kms1<vLSR<100kms1,andHVCsusingabsorptionfromdistanthalostars.Hilletal.(2009)usedobservationsfromtheWisconsinHMapperwhichshowedthatthebrightestHemissionwascoincidentwiththebrightestHIemission,andfoundthattherearesimilarmassesofionizedandneutralhydrogeninHVCsintheSmithCloud.SimilarresultswerefoundbyShulletal.(2011)whenobservingHVCsinComplexCwiththeCosmicOriginsSpectrograph(COS).Collinsetal.(2009)observedSiIIIabsorption,tracinggaswithtemperaturesof104104:5K,andfoundacoveringfractionof91%.Additionally,theirobservationssuggestthatthegalacticreservoirofionizedgasmaycontainupto108Mofmaterial.ObservingOVIabsorption,Sembachetal.(2003)foundacoveringfractionofatleast60%,andpossiblyashighas85%.TheseobservationsledLehneretal.(2012)toconcludethationizedHcoversthemajorityofthesky.DistanceconstraintstoionizedHVCsbyLehner&Howk(2011)updatedthelocationandmassestimatesofionizedHVCsintheMW,placingthemwithin3815kpcofthediskandindicatingthattheycontainontheorderof108Mofionizedgas,makingitalargercontributiontotheCGMmassbudgetthanneutralH.2.4.3HotHaloGasInconsideringtheHandNIIabsorptionoftheSmithHVC,Bland-Hawthornetal.(1998)suggestedthathothalogashasitsorigininfeedbackfromthestellarpopulation,withradiationfromyoungstarsheatingandionizingthegas.Ontheobservationalside,Wang&McCray(1993)andKerpetal.(1999)observedhothalogasinX-rayemission,andmorerecentlyWangetal.(2005)andWilliamsetal.(2005)observedthesamemediuminabsorptionofOVIIandOVIIIInobservationsofemissionfromhothalogas,Fangetal.(2006)andYao&Wang(2007)suggestedthatthemajorityofthedirectlydetectedgasresideswithinafewkpcoftheMWdisk.SubsequentobservationsbyCollinsetal.(2005),Yaoetal.(2008),andAnderson&Bregman(2010)indicatedthathothalogasaccountsforlessthan1010Mwithin100kpc,andSembachetal.(2003)andFangetal.(2006)foundthatithasacoveringfractionofmorethan60%.2.4.4RecentObservationsAsampleofquasarsightlinesthrough159galaxieswasconstructedbyLiang&Chen(2014)whichshowedmuchmoreofthestructuretheCGM.Theyfoundhydrogengastoradiiof500kpc,wellbeyondtheDMhaloradius,Rhalo,ofthegalaxies,withacoveringfractionof60%.Inobservingheavierelements,nonewerefoundbeyondaradiusof0:7Rhalo.Betweenradiiof0:3Rhaloand0:7Rhalothereisaerentialcoveringfractionoflow-andhigh-ionizationgas,39withadecreasingfractionoflow-ionizationstateabsorbersrelativetohigh-ionizationstateabsorberswithincreasingradius,indicatingthattheCGMisprogressivelymoreionizedatlargerradii.TheCOS-HalossurveyundertakenbyWerketal.(2014)providedunprecedentedinsightintothenatureoftheCGM,withwide-ranginggs.Theyassembledasampleof44COSspectraofquasarsselectedtobewithin160kpcofanapproximatelyLgalaxy.Theyfoundastronganti-correlationbetweenthedegreeofionizationintheCGMgasandHIcolumndensity.Thedegreeofionizationwasobservedtoincreasewithprojecteddistancefromthegalaxycenter,antheauthorsattributedtodeclininggasvolumedensitywithincreasingradius,andinturn,areducedabilityofthegastoself-shieldfromionizingextragalacticUVbackgroundradiation.TheyprovidedimprovedlowerlimitsonthemassofthecoolandhotCGMgascomponents,ndingmorethan25%ofthebaryonbudgetofanLgalaxycanbeaccountedforbycool,photoionizedgasintheCGM,andthatbyincludingthecontributionfromhotter,morehighlyionizedgas,thegalaxybaryoncontentcancomeintoagreementwiththecosmologicalbaryonfraction,potentiallyresolvingthegalaxyhalomissingbaryonsproblem(Bregman&Lloyd-Davies,2007;McGaugh,2008;McGaughetal.,2010).ThebaryoncensusoftheCOS-HalossurveywasextendedbyPeeplesetal.(2014)toanaccountingofthemetalsresidinginthestellar,ISM,dust,andCGMcomponentsofthegalaxiesinthatsample.Theythatonly2025%ofthemetalsproducedinagalaxyareretainedinthestellar,dust,andISMcomponents,whileapproximately40%oftheproducedmetalmassisinthehighlyionizedCGMgas.Alesserbutnon-negligiblemassofmetalsalsoresidesinthelow-ionizationCGM.FollowingontheheelsofCOS-HaloswastheCOS-DwarfssurveyofBordoloietal.(2014)40whichassembledaspectraof43quasarsightlinesaroundsub-Lgalaxies.TheydetectedCIVtoapproximatelyhalfthehalovirialradius,withapowerlawdeclinewithinthatradiusandnotdetectionsofCIVbeyondit.AcorrelationofCIVabsorptionstrengthwithspstarformationrate(SFR)isreported,andstrongCIVabsorbersaregenerallyfoundintheCGMofactivelystar-forminggalaxies.ThemassofcarbondetectedintheCGMiscomparabletothecarbonmassintheISMofgalaxies,andexceedsthecarbonmassinthegalaxystellarpopulations.Incomparingtheirngswithhydrodynamicalsimulations,theauthorsconcludethattidaldebrisandrampressurestrippingofaccretedgalaxiesisttoproducetheobservedmassofmetals,andthatstrongwsarerequiredtoenrichtheCGMtoobservedlevels.Lehneretal.(2015)assembledasampleof18quasarsightlinesthroughtheCGMofM31,andfoundcharacteristicsinagreementwithobservationsoftheMilkyWayhaloandthehalosofthosegalaxiesobservedintheCOS-Halos(Werketal.,2014)andCOS-Dwarfs(Bordoloietal.,2014)surveys.TheCGMgasofM31ismultiphase,predominantlyionized,andthedegreeofionizationincreaseswithradius.Theirobservationssupporttheexistenceofahotcoronaextendingtothevirialradius,andpossiblyfurther.IndeterminingthemassoftheCGMgas,theythatitaccountsfor30%ofthebaryonicmassinM31,notincludingthemassingasattemperatures106K.2.4.5Precipitation-RegulatedFeedbackVoitetal.(2015b)presentedatheoreticalframeworkinwhichstarformationandfeedbackinthecentralgalaxyofgalaxyclustersisregulatedbyacombinationofthermalconductionandtheprecipitationofcoldcloudsinthehothalogassurroundinggalaxies.ThismodelwasextendedinVoitetal.(2015a)togalaxiesoutsideoftheclusterenvironment.Precip-41itationoccursasafunctionofthecoolingtime,tcool,andthefreefalltime,t,withcoldcloudsprecipitatingoutofthehotCGMgaswhentcool.10t.Thesecoolcloudsaccretechaoticallyontothecentralblackholeofthegalaxy,triggeringastrongfeedbackresponsewhichheatsandexpandstheCGM,increasingtcool,temporarilyhaltingprecipitationandfurtheraccretionontothecentralblackhole.Inadditiontotriggeringfeedback,precipitatedgasfuelsgalacticstarformation.Thismodelnaturallygivesrisetoawiderangeofobservedgalaxytrends.Bycouplingthismodeltoasimplechemicalenrichmentscheme,itreproducestheobservedanti-correlationbetweenchemicalenrichmentlevelandSFRingalaxies(Ellisonetal.,2008;Mannuccietal.,2010).Thegalaxymass-metallicityrelationarisesnaturallyfromthismodel,withthesaturationmetallicityscalingwiththestellarmassinthegalaxy,inagreementwithobservations(e.g.,Gravesetal.(2009);McConnachie(2012)).TheFaber-JacksonandTully-Fischerscalingrelations(Faber&Jackson,1976;Tully&Fisher,1977)connectinggalaxystellarluminositytothegravitationalpotentialmanifestsnaturallyfromthismodelaswell.Finally,theprecipitationregulatedfeedbackmodelpredictstheobservedrelationbetweenthemassofagalaxy'scentralblackholeandthevelocitydispersionofitsstars(Kormendy&Ho,2013).42Chapter3PopulationIIIStarFormationInLargeCosmologicalVolumes:HaloTemporalAndPhysicalEnvironment3.1Introduction1AccuratelymodelingPopulationIIIstarformationfacesamyriadofchallenges.Thein-abilitytodirectlyobservePopulationIIIstarsrequiresrecoursetotheoreticalinvestigations,andtheintricaciesofstellarformationandevolutionmakeadetailedanalyticapproachin-tractable.PopulationIIIstarsformindarkmatterhalosthatarenotlargerelativetothestarformingcloud,andpropertiesofthepre-stellarcloudarerelatedtothehaloformationhistory(O'Shea&Norman,2007).Giventheimportanceofhaloformationhistory,pri-mordialstarformationmustbestudiedinacosmologicalcontext.NumericalsimulationshavemadegreatprogressinourunderstandingofPopulationIIIstars,butitecomputa-tionalresourcesrequireabetweencosmologicalvolumeandsimulationresolution.ProperlymodelingPopulationIIIstarformationrequiresmultiphysicssimulationsthathavehighspatialandtemporalresolution,andbynecessitysimulateasmallnumberofhalosinsmallcosmologicalvolumestypicallyofafewhundredkpconaside(e.g.,Abeletal.1ThischapterwasoriginallypublishedintheAstrophysicalJournal(Crosbyetal.,2013).43(2002);Brommetal.(2002);O'Shea&Norman(2007);Turketal.(2009)).Studiesofhighredshiftgalaxyformationsimulatelargervolumes,butarelimitedtoresolvingonlyasinglehaloobject(e.g.,Ricottietal.(2002b);Wiseetal.(2012a,b))andareunabletoresolvetheintricaciesofstarformation.Theselimitations,studyingonlysmallvolumesandindividualobjects,provideveryweakstatisticsonthenatureofthePopulationIIIstellarpopulationasafunctionoftimeandenvironment,anunderstandingofwhichiscriticaltodetermin-ingtheroleofPopulationIIIstarsingalaxyformation.SmoothedparticlehydrodynamicssimulationshaveendeavoredtoconstrainthePopulationIIIIMF,bothwiththeuseofsinkparticles(e.g.,Stacy&Bromm(2013);Stacyetal.(2012);Clarketal.(2011a,b))andwith-out(Greifetal.,2012),thelatteremployingamoving-meshmethod.TheseworksindicatethatthePopulationIIIinitialmassfunctionmightbestronglydependentonthenatureofprotostellaraccretionanddiskfragmentation,processeswhichcouldpotentiallymitigateintheinitialconditionsofthepre-stellarcloud.ThestatisticalpowerofasimulationcanbeincreasedbysimulatingmanyPopulationIIIstarforminghalossimultaneouslyinlargercosmologicalvolumes,butthesestudieshavetypicallybeenlimitedtomethodssuchastheextendedPress-Schechterformalism(Wise&Abel,2005)inconjunctionwithaprescriptionforstarformation(Trenti&Stiavelli,2009).Whilethesemodelsarecapableofinvestigatingsomeofthestatisticsofthepopulation,theyareunabletodirectlyinvestigatethenatureofindividualPopulationIIIstars.AdvancedcodessuchasMUSIC(Hahn&Abel,2011)andGRAFIC(Bertschinger,2001)createinitialconditionsthatcanspanahugedynamicrange,allowingforsimulationsofcosmologicalvolumesthatarestillabletoresolve,ataresolutionappropriateformultiphysicssimulations,individualhalosthatwillhoststarprimordialformation.Itiscomputationallyprohibitivetosimulateanentirecosmologicalvolumeofthedesiredsizethatalsohastheappropriate44resolutiontostudystarformation,presentinganewproblem:whichhalosarelikelytoformprimordialstars?Whenahaloformsastar,latergenerationsofstarformationwillbegloballybythephotodissociatingandionizingradiationproducedbythestarduringitslifetime.Latergenerationsofstarformationwillbelocallybymetalsproducedbythestar,whichislikelytocauseanabruptchangeinthestar-formingpropertiesofthecloud(e.g.,Brommetal.(2001);Bromm&Loeb(2003);Smithetal.(2009)).TostudyPopulationIIIstarswiththedetailrequiredtoinvestigatethestellarinitialmassfunction(IMF)requiresmultiphysicssimulationsoverawiderangeofredshiftandenvironment.Halomergerhistoryiscrucialinthedevelopmentofstarformingclouds(Brommetal.,2002;O'Shea&Norman,2007),asistheofphotodissociatingradiation(O'Shea&Norman,2008;Machaceketal.,2001).Thesefactorsmustbetreatedinaself-consistentmannerinordertoproperlydeterminewhichhaloswillformPopulationIIIstars.Thispaperpresentstheresultsfromamodelthatseekstoexplorethebulkprop-ertiesofprimordialstar-forminghalosoveralargerangeofredshifts,andinmuchlargercosmologicalvolumesthanaretypicallyusedinsimulationsofPopulationIIIstarformation.Inthismodelweaccountforhalomergerhistory,metalenrichmentandthetransitiontonon-primordialstarformation,andthetofphotodissociatingradiationproducedbyallpopulationsofstars.PreviousstudieshavetypicallyensuredthatthehalosselectedtohostaPopulationIIIstararechemicallypristineandbyphotodissociatingradiationbychoosingthemostmassivehalointhesimulation(Abeletal.,2002;O'Shea&Nor-man,2007),thoughtheseobjectsareinherentlyrareandnotnecessarilyrepresentativeofallPopulationIIIstarforminghalos.ThePopulationIIIIMFispoorlyconstrainedtheo-retically,withestimatesrangingfromtensofsolarmasses(McKee&Tan,2008;Stacy&Bromm,2007)tohundredsofsolarmasses(Abeletal.,2002;O'Shea&Norman,2007;Tan45&McKee,2004).Observationalconstraintssuggestthatthemeanmassofprimordialstarsisontheorderoftensofsolarmasses(Tumlinson,2006),whichisinagreementwithsomecosmologicalsimulationsofPopulationIIIstarformation(e.g.,Turketal.(2009)).Theabsenceofanyobservedprimordialstarspresentscircumstantialevidencethatsub-solarmassPopulationIIIstarsareveryrare.Itisuncleartowhatextentthecurrenttheoreticalpredictionsarearesultofselectiontsfromcosmologicalsimulations,andamorerepre-sentativesampleofprimordialstar-forminghalosmayprovideuswithamorerealisticrangeofpredictions.Thisworkpresentsasemi-analyticalmodelofstructureformationthatcanbeappliedtoanN-bodysimulationtodeterminewhichhalosarelikelytobechemicallypristineandcapableofhostingaPopulationIIIstar,giventheprevioushistoryofthehaloandtheglobalradiationbackgroundprovidedbystarsformingelsewhereinthesimulationvolume.Giventhetoolsthatwereusedtogeneratetheinitialconditionsforthesesimulations,itwillbestraightforwardtothenresimulateindividualhalosofinterestathighresolutionandwithmorephysics,includinghydrodynamics,afullnon-equilibriumprimordialchemistrynetwork,radiativecooling,andtheofphotodissociatingbackgroundradiation.Inthispaper,theofaseries,wedescribeindetailthemodelweuseanditsbehavior,andvalidateitusingmultipleobservationalconstraints.Weusethismodeltoinvestigatethebulkbehaviorofprimordialandmetal-enrichedstellarpopulationsasafunctionofredshift,halomass,andenvironment.Theorganizationofthispaperisasfollows:thecosmologicalsimulationsusedarediscussedinSection3.2,oursemi-analyticmodelisdescribedinSection3.3,andresultsarepresentedinSection3.4anddiscussedincomparisontoobservationsandothercomputationalworkandfutureworkinSection3.5.WesummarizeourinSection3.6.463.2Simulations3.2.1EnzoThesimulationsusedasabasisforourmodelwerecarriedoutusingthepubliclyavailableEnzo2adaptivemeshent+N-bodycode(Bryanetal.,2014).Foursimulationswererun:twowithacomovingboxsizeof3:5h1Mpcandtwowithacomovingboxsizeof7:0h1Mpc.Weusedtwotsimulationvolumesandtworandomrealizationsperchosenvolumetogivesomeideaoftheimpactofcosmicvarianceaswellasmassandspatialresolutiononourresults.WeusetheWMAP7bcosmologicalmodel(Komatsuetal.,2011),with=0:7274,M=0:2726,B=0:0456,˙8=0:809,ns=0:963,andh=0:704inunitsof100kms1Mpc1,withthevariableshavingtheirusualAllsimulationsarecubicandhave1024gridcellsperedgeand10243darkmatterparticles,givingcelldimensionsof6:8h1comovingkpconaside,adarkmatterparticlemassof2:86104M,andameanbaryonicmasspercellof5:74103Mforthe7:0h1Mpcboxes.The3:5h1Mpcboxeshavecelldimensionsof3:4h1comovingkpconaside,adarkmatterparticlemassof3:57103M,andameanbaryonicmasspercellof718M.Thesimulationswereinitializedatz=99usingtheMUSICcosmologicalinitialcondi-tionsgenerator(Hahn&Abel,2011)withasecond-orderLagrangianperturbationtheorymethodandseparatetransferfunctionsfordarkmatterandbaryons.Asecond-orderLa-grangianperturbationmethodisnecessarytoobtainconvergedhalomassfunctionsatsuchearlytimesandhighredshiftsasthestartofPopulationIIIstarformation.Eachofthesetsofinitialconditionsweregeneratedusingatrandomseed.ThesimulationswererunwithEnzo'sunigrid(non-adaptivemesht)modeandwithadiabatichydrodynam-2http://enzo-project.org47icsfromz=99toz=10.Dataisoutputatintegerredshiftsuntilz=14,atwhichpointtheelapsedtimebetweenintegerredshiftswouldexceedthetimescaleforstarformation.Afterz=14,dataisoutputevery11Myr.Thesimulationisstoppedatz=10topreventmodesontheorderofthesizeofthesimulationvolumefromenteringthenon-linearregime.3.2.2HaloFindingandMergerTreeCreationHalosforalldataoutputsinthesimulationswereidenusingtheFriends-of-Friends(FOF)(Efstathiouetal.,1985)haloimplementedintheyt3analysistoolkit(Turketal.,2011c)withalinkinglengthof0:2timesthemeaninterparticlespacing.Oncethehaloswerefoundateachredshift,itwasnecessarytodeterminetheirmergerhistory.Halosareconsideredtohavemergedwhenparticlesfromtwoormoreseparately-idenhalosfromthepreviousdataoutputarepresentinasinglehaloatthecurrenttime.ytwasusedtocreateamergertreethattracedthehistoryofeachhalobasedonthehalosthathadpreviouslymergedtogethertoformit.Allofthehalosthatmergetogethertoformahalobetweentwoconsecutivedataoutputsareconsideredtobe\parent"halos,withtheresultinghaloatthecurrentdataoutputdenotedasthe\child"halo.Achildhalocanhaveanarbitrarynumberofparents,andthepossibilityofhalofragmentationatlatertimesisalsoconsidered,allowingaparenthalotobreakintomultiplechildhalos.Inadditiontofollowingthelineageofhalos,thepercentageofthemassofachildhalothatcomesfromeachparentisalsotracked,allowingforthecompleteaccountingofdarkmattermassinhalos.Figure3.1showsthecumulativehalodarkmattermassfunctionsofall4simulationsatz=15andz=10,plottedalongwiththeanalyticWarrenmassfunction(Warrenetal.,3http://yt-project.org482006).Thehalomassfunctioninthesimulationsbegantodeviatefromtheanalyticmassfunctionbelowadarkmattermassof2106M.TheimplementationofFOFthatwasusedonlytakesintoaccountthespatialdistributionofparticles,andwillcreateahalooutofanygroupof8moreparticlesthataretlyspatiallyclustered,withoutregardforwhetherornotthoseparticlesaregravitationallybound.TheexcessoflowmasshalosindicatesthatFOFisspuriousobjectsbasedonchanceclosegroupingsofparticles,andthatthesegroupscannotbetlyasgravitationallyboundhalos.StandardFOFhalosareknowntohavethisbehavior(Knebeetal.,2011).Wearepreventedfromusingamoresophisticatedhalobythenatureofoursimulations:particle-meshmethodssuppresshalopotentialduetheresolutionofthesimulation(Hockney&Eastwood,1988).TheminimumdarkmatterhalomasscapableofhostingaPopulationIIIprotostaris1:5105M(O'Shea&Norman,2007),whichisbelowtheminimumhalomassthatcanberesolvedinthe7:0h1Mpcboxes.Inantoincludeasmanyapplicablehalosaspossibleinthe7:0h1Mpcboxes,weuseallhalosidenbythehalothesmallestofwhicharecomposedof8particles,correspondingtoahalomassof2:29105M.Thereisapossibilitythatsomeofthesmallestgroupsidenbythehaloarechancearrangementsofparticlesthatarenotactuallygravitationallybound,butduetothepotentialimportanceoflowmasshalosaslocationsofPopulationIIIstarformationtheyareincludedinthehalocatalogs.Aminimumhalomassof1:0105M,correspondingto28particles,isappliedtothe3:5h1Mpcboxes.Thischoiceincreasesthedencethattheselectedhaloswereboundobjectsandconstrainedtheanalysistohalosthatwereinagreementwiththelow-massendoftheWarrenmassfunction(Warrenetal.,2006).Athighhalomasses,themassfunctionsforthesimulationsaresuppressedduetothesizeofthesimulationvolume.The7:0h1Mpcboxessomewhatunderproducelow-masshalos49atearlytimesduetothespatialresolutionofthegravitationalforce;the3:5h1Mpcboxesdothesame,butatlowredshiftduetotheirsmallvolume.Overall,wearecapturingthehalomassfunctionswithinafactorof2oftheanalyticresultsinthemassrangeandredshiftsofinterest,givingusthatthefoundationuponwhichoursemi-analyticmodelrestsissolidandthatourcosmologicalvolumesofchoicearereasonable.Figure3.1:Thecumulativehalodarkmattermassfunctionforallfoursimulationvolumesatz=15(dashedline)andz=10(solidline).PlottedinblackistheanalyticpredictionfromtheWarrenmassfunction(Warrenetal.,2006).Thereisgoodagreementbetweenthehalomassfunctionsinthesimulationsovertheredshiftsofinterestinthisproject.503.3ModelDescription3.3.1OverviewTheprimarygoalofourmodelistodeterminetheabilityofahalotoformprimordialstars.Toaccomplishthis,westartatthehighestredshiftinasimulationwheredarkmatterhalosarefound,andthenmoveforwardintime,traversingourmergertreestofollowthemetalenrichmenthistoryofeachhaloovertime,determiningwhichhalosarecapableofformingaPopulationIIIstarandwhenthatformationoughttooccur.IfahalocanformaPopulationIIIstar,weassumethatitdoes,andthatthegasinthathalowillinturnbeenrichedwithmetals.Movingforwardintime,halosaredeterminedtobeeitherchemicallypristineorchemicallyenriched.Ahaloisconsideredchemicallypristineifnoneofitspreviousgenerationshavehostedastar,whileahalowithoneormoreparentsthathavehostedastarisconsideredtobechemicallyenriched.Undertheassumptionofrapidmixing,anychemicallyenrichedhaloisbyonincapableofformingaPopulationIIIstar,butcanformchemicallyenrichedstars.Thedeterminationofchemicallypristineandchemicallyenrichedhalosoccursateverysimulationoutput,whilenumericalintegrationforwardintimebetweentwoconsecutivedataoutputsallowsformoretempmodelingofstarformation,feedback,andejectionofmaterialfromthehalos.Thehalocatalogsandmassesareusedtoestablishtheboundaryconditionsforthenumericalintegrationofchemicallyenrichedstarformation,asdetailedinSection4.2.3.Thisallowsformuchhighertemporalresolutionofthedevelopmentofthestellarpopulation,trackingofstellarages,chemicalenrichment,andgasejectionfromeachhalo.Asummaryoftheparametersofthemodelthatweretested,theirvalues,andtherangesinvestigatedisgiveninTable4.1.51Table3.1:Modelparameterswiththeirvalue,therangetested,andabriefdescrip-tion.ModelParametersParameterFiducialValueRangeDescription"0.040.008-0.2StarformationefLWesc10.01,0.1,1LWphotonescapefractionIMFSalpeterSalpeter,Kroupa,ChabrierChemicallyenrichedstellarIMF"SN0.00150.0003-0.0075SNeenergycoupling3.3.2PopulationIIIStarFormationPopulationIIIstarsaremetal-free,andhencetheirformationhingesonahalocoolingviaH2toatemperatureanddensityatwhichitscoreisgravitationallyunstableandcollapses(Abeletal.,2002;O'Shea&Norman,2007).ThemodelweadoptedforPopulationIIIstarformationisbasedonthemodelofTrenti&Stiavelli(2009),andasintheirworkwedeterminetheminimummassofahalocapableofformingaPopulationIIIstarbydeterminingthemassthatisrequiredinordertocooltoitsvirialtemperatureviaH2coolinginthelocalHubbletimeintheabsenceofH2photodissociatingradiation.FollowingTrenti&Stiavelli(2009),thecoolingtimeiscalculatedas˝cool=3kBTvirfH2;(3.1)wherekBisBoltzmann'sconstant,Tviristhehalovirialtemperature,istheH2coolingfunction,andfH2istheratioofmoleculartoatomichydrogen.WeadopttheH2coolingfunctionofGalli&Palla(1998)asadaptedbyTrenti&Stiavelli(2009)of'1031:6T100K3:4nH104cm3ergs1;(3.2)52wherenHisthehydrogennumberdensity.Sincethecoolingtimeislonginachemicallypris-tinehalo,thetimelagbetweengasreachingthevirialdensityandstarformationoccurringisveryhigh,typicallyontheorderofseveraltensofmillionyears(O'Shea&Norman,2007).Tomakethelaglesssevereweassumethatstarformationoccursatadensitythatishigherthanthevirialdensity.this,ourmodelassumesthatthehydrogennumberdensityinahaloatthetimeofcollapsewillbe10timesthevirialdensity,ratherthanthevirialdensityitself,asusedbyTrenti&Stiavelli(2009).Bytakingthetemperatureinequation3.2tobethevirialtemperature,estimatingnHas10timesthevirialdensity,substitutingthesequantitiesintoequation3.1andequatingthistothelocalHubbletime,theminimumH2fractionrequiredforthehalotocoolwithinthelocalHubbletimecanbecalculated.ThiscaninturnbeequatedtothemaximumH2fractionthatcanforminahalo,asfoundbyTegmarketal.(1997),fH2'3:5104T1000K1:52;(3.3)andupontakingthetemperatureinequation3.3tobethevirialtemperature,theminimumhalomasscapableofcoolingviaH2asafunctionofredshiftcanbedetermined.ThisprocessyieldsaminimumhalomassofMmin;Hubble=5:871041+z312:074M:(3.4)ThemotothehydrogennumberdensityinthehaloistheonlydeparturefromtheworkofTrenti&Stiavelli(2009),andresultsinareductionoftheminimumhalomassrequiredtocoolwithinaHubbletimebyafactorofapproximately2:6.Thisismorein53agreementwithrecentsimulations(e.g.,Wiseetal.(2012b,a))wherestarformationoccursatlowermassesthanonewouldestimateusingthevaluesofTrenti&Stiavelli(2009).Thepresenceofotherstarswillmodifythislimitwiththeintroductionofradiationcapa-bleofphotodissociatingH2.ThisradiationmustbeaccountedfortoaccuratelydeterminewhichhalosarecapableofformingaPopulationIIIstar.RadiationintheLyman-Werner(LW)band(11:1813:60eV)canphotodissociateH2,suppressingcoolinginahaloandrequiringalargerhalomassinordertocollapse(Machaceketal.,2001;O'Shea&Norman,2008).Lyman-WernerradiationcansimilarlydissociatetheHDmolecule(Wolcott-Green&Haiman,2011),butHDisthedominantcoolantonlybelowatemperatureofapproximately150K,andcoolingviaH2isrequiredtoapproachthisregime.ToenabletheformationofH2andecoolingofmetalfreegas,theH2formationtimescalemustbeatleastequaltheH2destructiontimescale,assetbytherateofphotodissociationduetoLWradiation.TheformationtimescalecanbewrittenasafunctionoftheH2fraction,andthedissociationtimescalecanbewrittenasafunctionoftheproperLWEquatingthesetimescales,solvingfortheH2fraction,andusingthistoevaluatethehalomassneededtocoolininthelocalHubbletimegivestheminimummassforahalotocooltlyviaH2inthepresenceofaphotodissociatingbackgroundasMmin;LW=1:91106J0:457211+z312:186M;(3.5)whereJ21istheproperLWEquation4.2isthecaseinwhichthereisnoH2self-shieldinginthehalo.Thislimitismodiforeachhalotoaccountforself-shielding,andisaddressedinSection3.3.4.J21isfromthecomovingLWphotonnumberdensity,54nLW,inMpc3,asJ21=1:61065nLW1+z313ergs1cm2Hz1sr1:(3.6)ThemethodforthedeterminationoftheLWisaddressedinSection3.3.4.TheminimumhalomassrequiredforcollapseandPopulationIIIstarformationatagivenredshiftandLWwillthenbethemaximumofequations4.1and4.2,Mmin=max8>>><>>>:5:871041+z312:074M1:91106J0:457211+z312:186M:(3.7)ThereaderisencouragedtoseeTrenti&Stiavelli(2009)fordetailsonthederivationoftheminimumhalomassrequirements.WhenachemicallypristinehalowithamasstlylargeforPopulationIIIstarformationisidenourmodelassumesthatastarforms.ThehaloisgivenamassofgasequaltoitsdarkmattermassmultipliedbyB=DM.Thishaloisthentaggedasbeingchemicallyenriched,anditschildhalosarenolongercapableofformingPopulationIIIstarsatlatertimes.PopulationIIIstarsareassumedtoendtheirlivesasTypeIIsupernovae(SNII).Thisexplosioncanexpelgasfromthehaloanddelaythestartofchemicallyenrichedstarfor-mation.Toaccountforthisdelay,afteraPopulationIIIstarforms,thehosthaloistaggedwithadelaytimeequaltothesumoftheassumedPopulationIIIstellarlifetimeandadelaytimeof30Myr.Duringthistimenochemicallyenrichedstarformationcanoccurinthishaloifthehaloeitherdoesnotgrowinmassorgrowsonlybymergingwithotherchemically55pristinehalos.Ifthehalomergeswithahalothatisalreadyhostingchemicallyenrichedstarformation,starformationinthecombinedhaloisnotstopped.3.3.3ChemicallyEnrichedStarFormationHaloscontainingparticlesthathavepreviouslybeeninahalothatformedstarsarecon-sideredtobechemicallyenriched,andtheirstarformationistreatedntlythanthechemicallypristinehalosthatformPopulationIIIstars.Chemicallyenrichedhalosinheritgasfromthehalosthatmergetoformthem,withthebetweenthesumofthemassofthemerginghalosandthecurrenttotalhalomasstreatedasaccretedpristinematerial,contributingamassofgasinthesamemannerasgasisaddedtoapristinehalo.Starformationinchemicallyenrichedhalosisassumedtobecontinuousandafunctionofthemassofgasavailableinthehalo.Therateofgrowthofstellarmassinahaloistakentobeafunctionofthemassofgasinthathalo(Ladaetal.,2010)andismodeledasdM?dt="˝Mgas(t);(3.8)where"isthedimensionlessstarformationand˝isthecharacteristicstarformationtime,takenheretobe108yr.Thequotient"=˝withthestarformationofthiswork,"=0:04,issimilartothegalacticgasdepletiontimeofafewGyr(Bigieletal.,2011).Equation4.7isintegratedforwardintimeacrosssimulationoutputsusingafourthorderRungeKuttamethod.Theintegrationtimestepisonepercentoftheelapsedtimebetweenthecurrentandsubsequentdataoutputs,soeachdataoutputistraversedin100integrationsteps,withresultsbeinginsensitivetotheprecisechoiceoftimestepsize.Ateveryintegrationtimestep,starsareformedandthegasreservoirinthehalois56decrementedbythesameamountasthemassofstarscreated.Trackingthestarformationinenrichedhalosisachievedbyfollowingthetotalstellarmassformedratherthanindividualstars,asthisremovesassumptionsabouttheinitialmassfunction(IMF)fromthestarformationprocess(thoughthechemicalfeedbackdependsonontheIMF;seeSection3.3.4and3.3.5).Thechemicalfeedbackfromthestellarpopulationinahalobacktothehalogasisafunctionoftheageofthestellarpopulation.Starsarecreatedateveryintegrationtimestep,soutilizingthisage-dependentfeedbackmodelrequiresthattheagedistributionofthestellarpopulationineachhaloistracked.Theentirestellarpopulationisfollowedacross100agebinsateachdataoutput,withthebinsequallyspacedfromthetimethatthestarinthesimulationformedtothetimeofthenextdataoutput.Thetimeofthenextoutputcorrespondstotheendboundaryconditionofthetimeintegrationofequation4.7inthecurrentdataoutput.Ateachintegrationtimestep,thestellarmassineachagebinreturnsmaterialtotheinterstellarmedium(ISM)equaltotheproductofthestellarmassinthatagebin,theintegrationtimestep,andthemassofgasandmetalsthatareejectedpersolarmassofstarsperyearfromthetabulatedvaluesthatcorrespondtothatstellarageandmetallicity.Asequation4.7isintegratedforwardintime,themassinthestellaragebinsareadvancedforwardtoaccuratelytheagedistributionatanygiventime.Whenthemodeladvancestoanewdataoutput,thechemical,gas,andstellarcontent,completewithagedistributionofeachparenthalo'sstellarpopulationisinheritedbythechildhaloinproportionwiththefractionoftheparenthalomassthatwaspassedtothechildhalo.Atthispointthestellaragebinsarereconstructedtothenew,longer,timespanimposedbytheendtimeofthenewdataset,andthestellarpopulationisremappedtothesenewagebins.Thisdecreasesthetimeresolutionofthepopulationages,butmaintainsthecharacterofthedistribution,andisdonetomitigatecomputationalmemoryusage.Inpractice,the57largestagebininthemodelspans3:72Myr,whichislargerthanonlythesmalleststellaragebininthetabulateddataofmaterialreturnedtotheISMbythestellarpopulation,resultinginthetemporalresolutionofthefeedbackmodelbeingprimarilylimitedtothetemporalresolutionoftheavailablestellarfeedbackdata.AfulldescriptionofthechemicalevolutionmodelandtheresultsfromitarepresentedinPaperII.3.3.4LymanWernerFluxDeterminationDeterminingthenumberdensityofLyman-Werner(LW)photonsproducedbythestarsinthesimulationrequiresdeterminingthestarformationrate(SFR)forbothPopulationIIIandchemicallyenrichedstars.ThePopulationIIISFRisdeterminedbymultiplyingthenumberofchemicallypristinehalosmassiveenoughtohostaPopulationIIIstarbyauser-determinedcharacteristicPopulationIIIstellarmassanddividingbythesimulationvolumeandoutputtimestep.ThisisfurthermultipliedbyafactorrepresentingthePopulationIIIstellarmultiplicityineachhalo,givingthetotalmassofPopulationIIIstarsformedperyearpercomovingMpc3duringthetimespannedbythissimulationoutput.ThecharacteristicPopulationIIImassistakeninthisworktohaveavalueof30M(Tumlinson,2006).Themultiplicityfactorisaparameterthatwassettoavalueof1:2,drawinginspirationfromthedingsofTurketal.(2009)whichobservefragmentationofthepre-stellarcloud,suggestingthepossibilityoftheformationofPopulationIIIbinarystarsystems.ArecentconstraintonthePopulationIIIbinaryfractionof36%isreportedbyStacy&Bromm(2013).Thisvaluewasnotusedinourmodel,butchangestothemultiplicityfactorwillmodifythePopulationIIISFRasadirectmultiplicativefactor,anddoesverylittletochangethetotalSFRaschemicallyenrichedstarformationgenerallydominatesthePopulationIIISFRbyseveralordersofmagnitude,asshowninSection3.4.58Similarly,theLWisdominatedbychemicallyenrichedstars,andtheminimumhalomassforPopulationIIIstarformationdoesnotchangetlywithchangestotheassumedPopulationIIImultiplicity.ThePopulationIIISFRisthenusedtodeterminethedensityofLWphotonsbymultiplyingbyanestimatedPopulationIIIstellarlifetimeof2:5Myr(Schaerer,2003)andtherateofLWphotonproductionpersolarmassperyearbyametalfreestarfromSchaerer(2003).DeterminingthenumberdensityofLWphotonsfromchemicallyenrichedstarsfollowsasimilarprocess.Thetotalstellarmassinallchemicallyenrichedhalosissummedandmulti-pliedbytherateofLWphotonproductionpersolarmassperyearbyachemicallyenriched,continuouslystarformingpopulationfromSchaerer(2003),whichassumesaSalpeterinitialmassfunction.Wedonotmodifythisvaluefortinitialmassfunctions.TheLWphotonproductionratesforbothPopulationIIIandchemicallyenrichedstarsismobymultiplyingbytheLWphotonescapefraction,fLWesc,toapproximatetheofabsorptionwithinthehaloinwhichtheyoriginate.Thisisaparameterwithavalueof1andotherexploredvaluesof0:01and0:1andisindependentofhalomass.ThesevalueswereadoptedfollowingKitayamaetal.(2004),whoinvestigatetheLWphotonescapefractionasafunctionofstellarmass,halomass,andredshift(amongotherthings)foranindividualstarinahalo,thattheLWescapefractiondecreaseswithincreasinghalomassanddecreasingstellarmass.Thisisobviouslynotequivalenttothescenarioofchemicallyenrichedstarformationinourmodel,butcanbeusedasaguidingapproximationbytakingthetotalmassofstarsinahalotobeakintotheindividualstellarmassofKitayamaetal.(2004).Theratioofstellarmasstohalomassinourmodelexceedsthecorrespondingratiorequiredforanescapefractionof0:01inKitayamaetal.(2004),forthemoststringentcaseofa500Mstar,inmorethan98percentofhalosatz=10.59Morethan97percentofhalosinourmodelmeetthecriteriaforaLWescapefractionof0:1,and88percentmeetthecriteriaforaLWescapefractionof1.WhileourcomparisontoKitayamaetal.(2004)makesnumeroussimplifyingassumptions,itsuggeststhattheeLWescapefractioninourmodelisalmostcertainlygreaterthan0:01,andisverylikelygreaterthan0:1.ThetotalLWphotondensityistakenasthesumoftheLWdensitiesfromPopulationIIIandchemicallyenrichedsourcesthathavenotbeenredshiftedoutoftheLWband.UsingthemiddleoftheLWbandasanaverage,photonsproducedatredshiftzpwillberedshiftedoutofthisbandataredshiftzexit=(zp+1)11:1812:391(3.9)andwillnolongerabletodissociateH2.Forexample,LWphotonsproducedatz=20willberedshiftedoutoftheLWbandatz=17:9.OncethecumulativeLWphotondensityhasbeendetermined,theLWJ21,canbecomputedasdescribedinSection4.2.2.Thisisdonebasedonthestellarcontentinthesimulationatagiventime,andisdoneasthemodelprogressesthroughthemergertree.Self-shieldingofH2toLWradiationcaninprinciplehaveantimpactontheabilityofthehalotocool(Wolcott-Greenetal.,2011).H2self-shieldingreducestheeLWinagivenhalo,whichinturnreducestheminimumhalomassnecessaryforPopulationIIIstarformationinthepresenceofaphotodissociatingbackground.AprescriptionforH2self-shieldingfollowingWolcott-Greenetal.(2011)isimplementedtodeterminetheshieldingfactorfshbywhichJ21isreduced.Theshielding60factoriscalculatedasfshNH2;b=0:956(1+x=b5)+0:035(1+x)0:5exph8:5104(1+x)0:5i;(3.10)wherexisthescaledH2columndensity,x=NH2=51014cm2,bisthescaledDopplerbroadeningparameter,b5=b=105cms1,andtheparametertakesavalueof1:1.TheeJ21,asJ21;=fshJ21,isusedinEquation4.2todeterminewhetherthathaloistlymassivetoformaPopulationIIIstar.3.3.5HaloGasEjectionThechemicalevolutionandfeedbackfrompristineandchemicallyenrichedhalosaretreatedseparately.PopulationIIIstarsaretakentoejectamassofmetalstotheinterstellarmedium(ISM)attheirdeath,setbyyieldsofTypeIIsupernova(SNII)calculations(Heger&Woosley,2002).Gasandmetalsarealsoejectedfromthehalototheintergalacticmedium(IGM)followingamethodsimilartoTumlinson(2010),whichcomparesthekineticenergyofthesupernovadrivenwindinthehalototheescapevelocityofthehaloatthevirialradius.Thegasmassejectedduetosupernova-drivenwindsiscalculatedasMlost=3:9108NSN"SNE51rvirGMvirM;(3.11)whereNSNisthenumberofsupernovaethatoccurredinthecurrentintegrationtimestep,"SNisthewithwhichsupernovaenergyisconvertedtothekineticenergyofthewind,E51isthesupernovaenergyinunitsof1051erg,rviristhevirialradiusinunitsofproperMpc,GisthegravitationalconstantinCGSunits,andMviristhevirialmassin61solarmasses.NSNisdeterminedasthemultiplicityfactormultipliedbythenumberofPopulationIIIstarsinahalo(alwaystakentobeoneinthiswork)forchemicallypristinehalos,andinchemicallyenrichedhalositisfoundfromtabulatedsupernovaratesgiventheageofastellarpopulationandtheadoptedstellarinitialmassfunction.E51and"SNareparametersthatcanbevaried."SNisgivenavalueof0:0015,followingTumlinson(2010),whichassumesthat5%ofthetotalsupernovaenergyiskinetic,andthatofthis3%istransferredtotheejectedmaterial.Changesto"SNhaveanegligibleimpactonthestarformationrate(SFR)density,astheamountofgasejectedfromahaloisverysmallcomparedtothereservoirofgasavailableforstarformationinthathalo.Thechangeinthetotalamountofgasinahalothatarisesfromvariationof"SNisinturnnegligiblysmall,thoughithasatimpactonthechemicalevolutionofthehalo,asdiscussedinPaperII.Yieldsasafunctionofstellaragewereconvolvedwithanintegratedinitialmassfunction(IMF)tocreateatableofthetotalejectedgasmass(Perutaetal.2013,submitted)inunitsofsolarmassesofmetalsperyearpersolarmassofstars.TablesinthisformwerecreatedforSalpeter,Chabrier,andKroupaIMFs,atvariousmetallicities,andseparatelyfortheTypeIasupernovae(SNIa)(Iwamotoetal.,1999;Kobayashi&Nomoto,2009)andthecombinedejectaofSNIIandasymptoticgiantbranch(AGB)stars(Karakas,2010;Nomotoetal.,2006).Twosetsofthesetableswerecreated,oneforstarsatandabovesolarmetallicity,andoneforstarsbelowsolarmetallicity.Thisprocesswasrepeatedforeachofthechemicalspeciesthatistracked.WhilechangestotheIMFprimarilyimpactthechemicalevolutionofthestellarpopulations,itesthebulkstarformationpropertiesbychangingtheamountofgasreturnedtotheISMthatisavailableforstarformation.ThethreeIMFshave62functionalformsdNdm=Salpeter=0:154m2:35(3.12)Kroupa=8>>>>><>>>>>:0:56m1:3m0:5M0:3m2:20:5M<m1M0:3m2:7m>1M(3.13)Chabrier=8><>:0:799e(logm=mc)2=2˙2m1M0:223m1:3m>1M(3.14)(3.15)whereintheChabrierIMFmcisthecharacteristicmassandtakesavalueof0:079Mandthedispersion˙=0:69(Salpeter,1955;Kroupa,2002;Chabrier,2003).TheIMFswereconsideredoverarangeofmassesfrom0:08Mto260M,andareshowninFigure4.1.Asequation4.7isintegratedforwardintimeforeachhalo,thestellarmassineachstellaragebinismultipliedbytheintegrationtimestepandthenormalizedyieldcorrespondingtothemetallicityandageofthestellarpopulationtodeterminethemassofmetalsejectedtotheISMviaSNIIandAGBstars.ThetotalmassejectedfromagivenstellaragebinisremovedfromthemassofstarsinthatbinandreturnedtotheISM.TablessimilarthosegivingthechemicalyieldsandgasmassejectedfromstarswerecreatedgivingtherateofSNIa,inunitsofnumberofSNIaperyearpersolarmassofstars,andareusedtocalculatethetotalnumberofSNIaexpectedtooccurinthestellarpopulationofagivenhaloinanintegrationtimestep.ThisisusedwiththemassofejectafromSNIaandequation4.10todeterminethemassofgasejectedtotheIGMfromthehaloasaresultofSNIaexplosions.TheinterestedreaderisdirectedtoPerutaetal.(2013;submitted)for63Figure3.2:ThethreeIMFsconsideredinthisworkareSalpeter(violet,solidline),Kroupa(blue,dashedline),andChabrier(red,dot-dashedline),overamassrangeof0:08Mto260M.Theintegratedareaundereachofthecurvesisthesame.TheSalpeterIMFemphasizeslowmassstars,theKroupaIMFemphasizesintermediatemassstars,andtheChabrierIMFisbythefarthemosttop-heavyofthethree,emphasizinghighmassstars.64moreinformation.Thegasejectionmodelofequation4.10wouldpotentiallyallowforallofthegastobeejectedfromahalofollowingthedeathofaPopulationIIIstar.Themodelhasthecapabilitytotreatthesehalosaschemicallypristine,astheydonothaveanymetalsintheISM,andtoallowthemtomergewithotherpristinehalosandformPopulationIIIstars.Inpracticethisalmostneverhappens,andanyhalothatformsstarsretainssomechemicallyenrichedmaterial,renderingitincapableofformingaPopulationIIIstar.3.4Results3.4.1OverviewThisprojectendeavorstodevelopasemi-analyticmodelthatcanbeusedinconjunctionwithacosmologicalsimulationtocreateacatalogofhaloscapableofformingPopulationIIIstars.Thehalosinthiscatalogextendbeyondthemostmassiveobjectinthesimulationtoencompasschemicallypristinehalosacrossawiderangeofredshiftsandenvironmentswhileself-consistentlyaccountingforthehalomergerhistoryandthephotodissociatingradiationproducedbythestarsinthesimulation.Inthispapertheinitialmassfunction(IMF)ofchemicallyenrichedstarswasvariedbetweenthreecommonlyusedIMFs:Salpeter,Kroupa,andChabrier.Anadditionalfreeparameterthatisvariedisthestarformation,",whichadoptsavalueof0:04,followingWise&Abel(2005).Thestarformationisvariedfromthisvaluebyafactorof5inbothdirections,investigatingvaluessimilartothoseexploredbyTrenti&Stiavelli(2009).Thisrangealsoencompassestheequivalentstarformationyof0:01adoptedastheducialvaluebyTumlinson(2010).TheLyman-Wernerphotonescapefraction,fLWesc,wasvariedfromitsvalue65of1to0:1and0:01.Figure3.3:Thestarformationrate(SFR)densitiesforallfoursimulationsforourchoiceofparameters.Thethick,solidlineshowsthetotalSFRdensity,thedashedlineisthechemicallyenrichedSFRdensity,andthethin,solidlineisthePopulationIIISFRdensity.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.Allfoursimulationsshowverygoodagreementdespitetestingtwotvolumesandallbeingcreatedfrominitialconditionsgeneratedwithtrandomseeds.Toassessthevalidityofthismodel,comparisonismadebetweenthepredictedstarformationrate(SFR)densityandobservationallimits.TheSFRdensityisprimarilysensitivetothestarformation,".Figure3.3showsthecomovingSFRdensitiesofallfourofthesimulationsinunitsofMyr1Mpc3.Allofthesimulationsshowverysimilar66total,PopulationIII,andchemicallyenrichedSFRdensities.Allsimulationsshowthesamequalitativebehavior,andthevariationsintheonsetofstarformationandthespreadinSFRdensitiesatz=10areallwithinarangethatwouldbeexpectedfromvariationsduetolargescalestructure(i.e.,cosmicvariance)intsimulations.Inparticular,atlatetimesallhalosconvergetoverysimilarvaluesasthetotalnumberofhalosincreasesandstochasticity,asaresult,decreases.Thisconvergencelendssupporttothenotionthatoursimulationvolumesareallelystatisticallyequivalenttoeachother.Asaresult,andforclarity,fortheremainderofthispaperalldiscussionandthecontentofallplotswillbelimitedtoone7:0h1Mpcbox(labeled7:0h1Mpcv1)unlessotherwisenoted,asinSection3.4.4.Usingthissimulation,themodelproducesacatalogofmorethan40,000halosthatarecapableofformingaPopulationIIIstar.Thesehalosspanaredshiftrangefromz=30toz=10,andrangeinmassfrom2:3105Mto1:21010M.3.4.2StarFormationRatesThestarformationrate(SFR)density,astheSFRpercomovingMpc3,wastrackedindividuallyforthePopulationIIIandchemicallyenrichedstellarpopulations.TheSFRdensitywassensitiveprimarilytothestarformationeformetal-enrichedstarsinequation4.7,withlargervaluesoftheincreasingthechemicallyenrichedSFRdensity,andinturndrivingupthetotalSFRdensity.TheSFRdensityforseveraltsetsofparametersisshowninFigure3.4.Whilechemicallyenrichedstarsdominatethestarformationatessentiallyallredshifts,PopulationIIIstarscontinuetoformthroughoutthedurationofthesimulation,atroughlyconstantbutvastlysubdominantlevels.Thetransi-tionfromthetotalSFRdensitybeingdominatedbyPopulationIIIstarstobeingdominatedbychemicallyenrichedstarshappensveryrapidly,inlessthan10millionyearsafterthe67starsinthesimulationform.Byz=10,thePopulationIIISFRdensityis3-5ordersofmag-nitudelowerthanthechemicallyenrichedSFRdensity.ThetotalSFRdensityatz=10rangesfrom6:4103Myr1Mpc3,usingastarformationof8103,to2:1101Myr1Mpc3usingastarformationeof0:2.ThesamestarformationyieldPopulationIIISFRdensitiesof5:2105and1:2106Myr1Mpc3,respectively.IncreasingthechemicallyenrichedstarformationsuppressesPop-ulationIIIstarformationbyincreasingtheLyman-WernerdrivinguptheminimumhalomassforPopulationIIIstarformation.IncludingfeedbackfromthestellarpopulationimpactsthechemicallyenrichedSFRdensityintwoways.Gasreturnedtotheinterstellarmedium(ISM)fromstarsincreasesthereservoirofgasavailableforstarformation,butgasejectedfromthehalototheintergalacticmediumbysupernovaereducestheavailablegas.ThenetchangeinthegascontentoftheISMasaresultofthesetwowilldeterminewhetherstellarfeedbackincreasesordecreasestheSFRdensityatanygivenintegrationtimestep.Theinitialmassfunction(IMF)hasnotimpactontheSFRdensityforPopulationIIIorchemicallyenrichedstars.TheLWphotonproductionisdeterminedbasedonthetotalmassofstarsthatareformed,andisagnosticofthedistributionofstellarmasses.TheslightvariationsthatbetweentheSFRdensitywithtIMFsarisefromtheinthemassofgasreturnedtothehalothatisavailableforstarformationandcesintheamountthatisejectedfromthehaloviasupernovae,bothofwhichareverysmallwhencomparedtothetotalreservoirofgasavailableforstarformationinagivenhalo.DecreasingtheLWphotonescapefractionincreasesthePopulationIIISFRdensityatlatetimesbysuppressingthephotodissociatingbackgroundradiation,decreasingthemassthresholdforPopulationIIIstarformationinahalo.ThePopulationIIIstarformationmassthresholddependsonontheproperLWasMthreshold˘J0:45721,sothe68magnitudeoftheincreaseinthePopulationIIISFRdensitycloselyfollowsthechangesintheLWaswouldbeexpectedfromacollectionofchemicallypristinehaloswithmassesbelowthePopulationIIIstarformationmassthreshold.ThereductioninthechemicallyenrichedSFRdensitythataccompaniestheincreasedLWphotonescapefractionoriginatesfromthedecreaseinnumberofhalosthatarecapableofformingPopulationIIIstars.Bynotformingstarsthesehalosarenotchemicallyenriched,andareunabletobecomesitesoffuturechemicallyenrichedstarformation.Figure3.4:Thestarformationrate(SFR)densityinMyr1Mpc3asafunctionofredshiftforvariationsinIMF,starformation,andLyman-Werner(LW)photonescapefraction.PanelAshowstheofvaryingtheIMF,PanelBshowstheofvaryingthestarformation,andPanelCshowstheectofvaryingtheLWphotonescapefraction.Inallpanels,thePopulationIIISFRdensityisplottedinthin,solidlines,thechemicallyenrichedSFRdensityisplottedindashedlines,andthetotalSFRdensityisplottedinthick,solidlines.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.InPanelA,thetotalandcomponentSFRdensitiesforthethreeIMFsarenearlyindistinguishable.PanelBshowstheSFRdensityusingaSalpeterIMFandvaryingthestarformation.IncreasingthestarformationincreasesthebetweenthePopulationIIIandchemicallyenrichedSFRdensities,drivingPopulationIIIstarformationdownandchemicallyenrichedstarformationup.InPanelC,changestotheLWphotonescapefractionhaveasmallonthechemicallyenrichedSFRdensity,anddecreasingtheescapefractionincreasesthePopulationIIISFRdensityatlatetimes.Inallcases,chemicallyenrichedstarformationrapidlydominatesPopulationIIIstarformationbyseveralordersofmagnitude,butPopulationIIIstarformationcontinuesatverylowlevelsfortheentiretyofthesimulation.PanelAofFigure3.5showstherangesspannedbythePopulationIIIandchemically69enrichedSFRdensitiesforallpossiblecombinationsofmodelparameters,alongwiththemeanvaluesand68percenteintervals.Thestarformationistheparam-eterwhichcreatesthemostvariationinthechemicallyenrichedSFRdensity.ThereisnocombinationofparametersthatcanchangethechemicallyenrichedSFRdensityasgreatlyasthestarformation,resultinginthreedistinctgroupingsintheSFRdensitycorrespondingtothethreevaluesofthestarformationciency.ThisisturndrivestheintervaltoencompassthemajorityoftherangespannedbythemaximumandminimumchemicallyenrichedSFRdensities.ThePopulationIIISFRdensityistlybyallparameterswiththeexceptionofthesupernova,resultinginacon-intervalthatismuchsmallerthanthemaximumandminimumSFRdensitiesatagivenredshift.PanelBofFigure3.5showstheratioofthechemicallyenrichedSFRdensitytothePopulationIIISFRdensityasafunctionofredshift.ThechemicallyenrichedSFRdensityrapidlysurpassesthePopulationIIISFRdensity.Byz=10thechemicallyenrichedSFRdensityisaminimumof1:9103timesgreaterthanthePopulationIIISFRdensity,andisanaverageof4:1105timesgreaterthanthePopulationIIISFRdensity.3.4.3PopulationIIIStarFormationHaloMassLimitTheimpactofthephotodissociatingradiationproducedbythestarsinthesimulationontheminimumhalomassrequiredforPopulationIIIstarsformationisshowninFigure3.6.PanelAofFigure3.6showstheproperLWandPanelBplotsequation4.1,givingtheminimumhalomassrequiredforPopulationIIIstarformationintheabsenceofphotodissociatingradiation,alongwithequation4.4,whichgivestheminimumhalomassforPopulationIIIstarformationwhenthephotodissociatingradiationproducedbythestarsinthesimulationisaccountedfor.Atroughlyz=25,thethresholdmassaccounting70Figure3.5:PanelAshowsthevariationinstarformationrate(SFR)densityinMyr1Mpc3asafunctionofredshiftforallcombinationsofparametersinourmodel.ThemeanPopulationIIISFRdensityisplottedasablacksolidline,andtheaveragechemicallyenrichedSFRdensityisplottedasablackdashedline.ThemaximumrangespannedbythePopulationIIIandchemicallyenrichedSFRdensitiesareshownbythelightredandlightblueshadedregions,respectively.Thedarkshadedregionsshowthe68percentintervalsaroundthemean.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.PanelBshowstheratioofthechemicallyenrichedSFRdensitytothePopulationIIISFRdensityasafunctionofredshiftforallparametercombinations,withtheblacklineshowingtheaveragevalueandtheshadedregionshavingthesamemeaningasinPanelA.Toaidininterpretation,dashedlinesareshownatlevelscorrespondingtochemicallyenrichedtoPopulationIIIstarformationrateratiosof1and1000.71forthephotodissociatingradiationdivergesfromthethresholddeterminedwhileneglectingthephotodissociatingradiation,aschemicallyenrichedstarformationbeginstodominatethetotalstarformationrate(SFR)density.Bytheendofthesimulation,atz=10,thethresholdhalomassforPopulationIIIstarformationhasincreasedbytwoordersofmagnitudeduetophotodissociatingradiationfromthestarsinthesimulation,drasticallychangingthemembershipandevolutionofthesetofhaloscapableofformingaPopulationIIIstarthroughoutthesimulation.Forreference,approximatingthethresholdmassesatthebeginningandendofthesimulationshowsthatatz=25,ahaloofmass105Mhasavirialtemperatureofapproximately260K,andatz=10ahaloofmass107:5Mwillhaveavirialtemperatureofapproximately5190K.Figure3.6:ThePanelAshowstheproperLyman-Werner(J21)andPanelBshowstheminimummassthresholdforPopulationIIIstarformationasafunctionofredshift,plottedforthethreeinitialmassfunctions(IMF)withastarformationof0:04aswellasforaSalpeterIMFwithstarformationof0:008and0:2.TheSalpeter,Kroupa,andChabrierIMFsareindistinguishableinthisplot.Forcomparison,inPanelBthemassthresholdwithoutaccountingforradiativefeedbackisshowninblack,andismuchlower,particularlyoncechemicallyenrichedstarformationbecomethedominantcomponentofthestellarmassinthesimulation.TheminimumhalomassforPopulationIIIstarformationisdependentonJ21,andasaresultPanelAcloselymirrorsthebehaviorofPanelB.Simultaneously,J21isdependentonthestellarmassinthesimulation,andwillrethetrendsofthetotalstarformationratedensityinFigure3.4.72Figures3.4and3.6illustratetherelationshipbetweentheSFRdensity,theminimumhalomassforPopulationIIIstarformation,andtheH2-photodissociatingLymanWerner(LW)TheLWdependsentirelyonthestellarmassinthesimulationvolumeandtheintegratedSFRdensity.TheminimumhalomassforPopulationIIIformationisafunctionofredshiftandtheLWandasmoreH2isphotodissociated,increasinglylargerhalosarerequiredinordertoformPopulationIIIstars.ThisinturndrivesdownthePopulationIIISFRdensitybutdoesnothinderchemicallyenrichedstarformationwhere,duetotheirmetalcontent,despitetheLWhaloscanstillcooltlyandformstarsasH2isnolongertheprimarycoolant.IncreasingthestarformationwillthereforeincreasethechemicallyenrichedSFRdensity,whichincreasestheLWdrivinguptheminimumhalomassforPopulationIIIformation,andinturndrivingthePopulationIIISFRdensitydown.IncreasingthestarformationcynotonlyincreasestheminimumhalomassforPopulationIIIstarformation,butalsochangestheenvironmentofthesehalosastimesgoesby,aswillbedescribedinSection3.4.5.ThiscycleisresponsibleforthedivergenceofthePopulationIIIandchemicallyenrichedSFRdensitiesasthestarformationisincreased.3.4.43:5h1MpcBoxStarFormationRatesThe3:5h1Mpcsimulationsprovideanopportunitytoinvestigatetheimpactoflowmasshalosonthestarformationrate(SFR)density.Thesesimulationshave8timesbettermassresolutionthanthe7:0h1Mpcsimulations,andthesmallesthaloobjectsidenbytheFriends-of-Friends(Efstathiouetal.,1985)halohaveaminimummassof2:86104M,signtlybelowtheminimumhalomassof1:5105M(O'Shea&Norman,2007)requiredtohostPopulationIIIstarformation.73Figure3.7:Thestarformationrate(SFR)densityinMyr1Mpc3asafunctionofred-shiftforvariationsinIMF,starformation,andLyman-Werner(LW)photonescapefraction.PanelAshowstheofvaryingtheIMF,PanelBshowstheofvaryingthestarformation,andPanelCshowstheectofvaryingtheLWphotonescapefraction.Inallpanels,thePopulationIIISFRdensityisplottedinthin,solidlines,thechemicallyenrichedSFRdensityisplottedindashedlines,andthetotalSFRdensityisplottedinthick,solidlines.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.Inallcases,chemicallyenrichedstarformationrapidlydomi-natesPopulationIIIstarformationbyseveralordersofmagnitude,butPopulationIIIstarformationcontinuesatlowlevelsfortheentiretyofthesimulation.Figure3.7showsvariationsfromthecanonicalmodel,withentIMFsinpanelA,tstarformationinpanelB,andtvaluesoffLWescinpanelC.TheresultsinFigure3.7areverysimilartothoseshownforthe7:0h1MpcsimulationinFigure3.4.InPanelA,thetotalandcomponentSFRdensitiesforthethreeIMFsarenearlyindistinguishable.PanelBshowstheSFRdensityusingaSalpeterIMFandvaryingthestarformation.IncreasingthestarformationincreasesthebetweenthePopulationIIIandchemicallyenrichedSFRdensities,drivingPopulationIIIstarformationdownandchemicallyenrichedstarformationup.PanelCshowsthemostpronouncedthedependenceonfLWescofthechemicallyenrichedSFRdensity,wherehighervaluesoffLWescleadtolowerchemicallyenrichedSFRdensities.IncreasingfLWescincreasesJ21,raisingminimumhalomassforPopulationIIIstarformation.WhenJ21istlyhighitwillpreventPopulationIIIstarformationinhalosthatwouldhavebeen74tlymassivetohoststarformationhadthephotodissociatingradiationbeenless,ascanbeseeninthedownturnsinthePopulationIIISFRdensitiesbetweenz=22andz=14.ThisdownturnoccursathigherredshiftwithgreaterfLWesc.Whenthishappens,fewerhalosformPopulationIIIstarsandbecomeenriched,inturnprovidingfewersitesforchemicallyenrichedstarformation.ThiscanbeseeninpanelCofFigure3.4inthedivergencesinthePopulationIIISFRdensitiesatz=22andz=18.Ineachcase,followingthedropinthePopulationIIISFRdensitythechemicallyenrichedSFRdensitydecreasesincomparisonthemodelswithlowervaluesoffLWescastherearenowfewerhaloscapableofhostingchemicallyenrichedstarformation.Figure3.8:SameasFigure3.5,thoughappliedtoa3:5h1Mpcbox.PanelAshowsthevariationinSFRdensityinMyr1Mpc3asafunctionofredshiftforallcombinationsofparametersinourmodel.ThemeanPopulationIIISFRdensityisplottedasablacksolidline,andtheaveragechemicallyenrichedSFRdensityisplottedasablackdashedline.ThemaximumrangespannedbythePopulationIIIandchemicallyenrichedSFRdensitiesareshownbythelightredandblueshadedregions,respectively.Thedarkshadedregionsshowthe68percentintervalsaroundthemean.AnextrapolatedobservationalupperlimitfromBouwensetal.(2011)isshowninorange.PanelBshowstheratioofthechemicallyenrichedSFRdensitytothePopulationIIISFRdensityasafunctionofredshiftforallparametercombinations,withtheblacklineshowingtheaveragevalueandtheshadedregionshavingthesamemeaningasinPanelA.Toeaseviewing,dashedlinesareshownat1and1000.75ComparingtheSFRdensitiesfoundinthe3:5h1Mpcboxtothosefoundinthe7:0h1Mpcboxshowsgoodagreement,withthePopulationIIISFRdensityusingourparametersatz=10byonly37%,andthechemicallyenrichedSFRden-sityby9:4%.ThemeanPopulationIIISFRdensityatz=10inthe3:5h1Mpcboxis2:9105Myr1Mpc3,andthemeanchemicallyenrichedSFRdensityis9:4102Myr1Mpc3.ThemostextremesetsofmodelparametersproduceaminimumPopu-lationIIISFRdensityof2:7106Myr1Mpc3,andamaximumof1:1104Myr1Mpc3.ThechemicallyenrichedSFRdensityspansfromaminimumof1:0102Myr1Mpc3toamaximumof0:36Myr1Mpc3.TheevolutionofthePopulationIIIandchemi-callyenrichedSFRdensitiesisalsosimilartothatinthelargersimulationvolume,withthechemicallyenrichedSFRdensityincreasingrapidlyoncestarformationinchemicallyenrichedhalosbegins.ThechemicallyenrichedSFRdensitysurpassesthePopulationIIISFRdensitybyz=27.Figure3.8isidenticalinformattoFigure3.5,butshowstheSFRdensitiesforthe3:5h1Mpcbox.ThethickblackanddashedlinesaretheaveragePopula-tionIIIandchemicallyenrichedSFRdensities,respectively,whilethedarkshadedregionsshowsthe68%intervalstheandthelightshadedshowtheextentofthemaxi-mumandminimumvaluesforallmodels.ThesimilaritiesinqualitativebehaviorandSFRdensitiesbetweenthe3:5h1Mpcboxand7:0h1Mpcboxsuggestthatthe7:0h1Mpcboxiscapturingthestarformationbehaviorwellandthattheashalosofob-jectsthataresigntlybelowtheminimumhalomassforPopulationIIIstarformationdoeslittletochangetheoverallcharacterofstarformationinthismodel.ThemergingofchemicallypristinelowmasshalostoformahalotlymassivetohostPopulationIIIstarformationisindistinguishablefromtheformationofthesamehalofromparticlesthatwerenotpreviouslyconsideredtobemembersofahalo.Themergingofalowmass,76chemicallypristinehalowithachemicallyenrichedhalothatisalreadyformingstarsisin-distinguishablefromthechemicallyenrichedhaloaccretingthatsameamountofunboundpristinematerial.TheoflowmassgroupsofpristinematerialasahalohasanegligibleimpactonthenatureofstarformationoncethemassthresholdforPopulationIIIstarformationhasexceededthehalomassresolution,whichhappensrelativelyrapidly.3.4.5HaloEnvironmentOneofthegoalsofthisstudyistodetermineiftherewasainthelocalenvironmentofchemicallyenrichedhalosandthosehalosthatarechemicallypristineandcientlymassivetoformaPopulationIIIstar.Thedistancetothenearesthaloisaproxyforthelocaloverdensityandthusenvironment.Whiletherearemanywaystoquantifylocaloverdensity,suchastheoverallmassoverdensityintegratedouttosomecomovingradius,ortosomemultipleofthevirialradius,thedistancetothenearestneighboringhaloisthemostclearlyandthustheclearestmetric.Figure3.9showsthedistancetothenearestneighboringhaloforourmodelforPopulationIIIandchemicallyenrichedhalosatz=18,14,and10.AtearliertimesthedistributionofdistancestothenearestneighborsisnearlyidenticalforthePopulationIIIandchemicallyenrichedhalos,suggestingthatthesehalosforminenvironmentsthatarecomparablydense.Astimeprogressesthechemicallyenrichedhalosbecomemuchmoreconcentrated(i.e.,chemicallyenrichedstarformationoccursinprogressivelydenserenvironments),withnearlynohalosmorethan10comovingh1kpcfromtheirnearestneighbor.Whilethechemicallyenricheddistributionbecomesmorepeaked,thePopulationIIIdistributionbecomesbroader,suggestingthatPopulationIIIstarsforminhalosthatareinprogressivelylessdenseenvironments.ThistheintuitiveexpectationthatareservoirofpristinegaslargeenoughtoformaPopulationIIIstar77ismorelikelytoassembleandexistinaregionthatisfurtherawayfromchemicallyenrichedhalos,asevenasinglemergerwithachemicallyenrichedhalowillrenderitincapableofformingaPopulationIIIstar.Thatbothdistributionshavelowermaximumdistancestothenearestneighboringhalothegeneralgrowthofcosmicstructureandthetendencyforobjectstobemoreclusteredatlowerredshifts.Figure3.9:Thedistancetothenearestneighboringhalo,originatingfromPopulationIII(red)andchemicallyenriched(blue)halos.PanelAshowsthedistributionofdistancesatz=18,PanelBshowsthedistributionatz=14,andPanelCshowsthedistributionatz=10.Atearlytimestheenvironmentsarealmostindistinguishable,butastimepassesthechemicallyenrichedhalosbecomemoreclusteredandPopulationIIIforminghalosbecomeincreasinglyspreadout.ThehistogramsarenormalizedtoallowforthecomparisonofthemuchmorenumeroussetofchemicallyenrichedhalostothesetofPopulationIIIhalos.ThechemicalenrichmentoftheenvironmentofPopulationIIIstarforminghaloscanbequanbycomparingthedistancesfromaPopulationIIIstarforminghalotothenearestchemicallypristinehaloofanymass(includingthosebelowthethresholdmassforPopulationIIIstarformation)andthedistancefromaPopulationIIIstarforminghalotothenearestchemicallyenrichedhalo.Figure3.10showsthathalosthatformPopulationIIIstarsaregenerallymuchclosertootherpristinehalosthantheyaretochemicallyenrichedhalos.ThisagreeswiththeindicationsfromFigure3.9thatPopulationIIIhaloswilltendtoforminlow-densityregionsthatarenotyetpollutedduetothelackofpreviousstarformationinthearea,asopposedtohigh-densityregionsthattypicallyhostchemically78enrichedstarformation.TheassemblyofahalomassiveenoughtoformaPopulationIIIstarinsuchanenvironmentistypicallymadepossiblebythepresenceandsubsequentrapidmergerofseveralsmaller,chemicallypristinehalosthatareseparatelybelowthethresholdforprimordialstarformation.Figure3.10:ThedistancefromhalosformingPopulationIIIstarstothenearestchemicallypristinehaloofanymass(red)andtothenearestchemicallyenrichedhaloofanymass(blue).ThechemicallypristinehalosdonotneedtobemassiveenoughtoformaPopulationIIIstar.PanelAshowsthedistributionofdistancesatz=18,PanelBshowsthedistributionatz=14,andPanelCshowsthedistributionatz=10.HaloshostingPopulationIIIstarformationaremuchclosertootherchemicallypristinehalosthantochemicallyenrichedhalos.TofurtherunderstandtheenvironmentinwhichPopulationIIIstarsform,Figure3.11showsthedistancefromhalosmassiveenoughtoformaPopulationIIItothenearestotherhalothatisalsomassiveenoughtohostPopulationIIIstarformation,andseparatelytothenearestchemicallyenrichedhaloofanymass.ThisshowsthatPopulationIIIstarstendtoforminhalosthatareisolatedfromoneanother,astheyarealmostalwaysmorelikelytobenearertoachemicallyenrichedhalothantheyaretoanotherPopulationIIIstarforminghalo.Figures3.10and3.11,takentogether,indicatethataPopulationIIIstarforminghaloismostlikelytoforminaregionofmanysmall,chemicallypristinehalosthatarebelowthemassthresholdforPopulationIIIstarformation.TheselowmasschemicallypristinehalosmergeuntilahalotlymassivetohostaPopulationIIIstarhasassembled.The79resultinghalothathassurpassedthemassthresholdforPopulationIIIstarformationwillbesurroundedbythechemicallypristinehalosthathavenotyetmergedwithitandwhichareincapableofstarformation,resultinginPopulationIIIstarsforminginenvironmentswherethenearestneighborsarechemicallypristine,smallerhalos.AfterthePopulationIIIstarhasformed,subsequentmergersofthelowmass,chemicallypristinehaloswiththispost-PopulationIIIhalowillfuelchemicallyenrichedstarformation.AsthePopulationIIIstarforminghalowasthemostmassivelocalobject,thiselyshutsPopulationIIIstarformationinthisregion.Figure3.11:ThedistancefromPopulationIIIstarforminghalostothenearestotherPop-ulationIIIstarforminghalo(red)andnearestchemicallyenrichedhaloofanymass(blue).PanelAshowsthedistributionofdistancesatz=18,PanelBshowsthedistributionatz=14,andPanelCshowsthedistributionatz=10.Theneareststarforminghalosarealmostentirelychemicallyenriched,andPopulationIIIstarforminghalostendtoforminisolationfromoneanother.TakenwithFigure3.10,thisplotindicatesthatPopulationIIIstarforminghalosaregenerallysurroundedbychemicallypristinehalosthatarenottlymassivetoformaPopulationIIIstar.WenextinvestigatethespatialdistributionofthePopulationIIIstarforminghalosandthechemicallyenrichedhalosusingtwo-pointstatistics.Thetwo-pointcorrelationfunction˘(r)quantheexcessprobability(w.r.t.random)totwohalosinvolumeelementsdV1anddV2separatedbydistancer,dP12(r)=n2[1+˘(r)]dV1dV2;(3.16)80wherenisthemeannumberdensityofhalos.Wecomputethe˘(r)usingtheestimatorintroducedbyHamilton(1993).Wecomplementthe(biased)halocorrelationfunctionswiththecorrelationfunctionsoftheunbiaseddarkmatterdensitywhichweestimatefrom100,000randomlydrawndarkmatterparticlesfromthesimulations.TheresultsofourclusteringanalysisaregivenforthreeredshiftsinFigure3.12,whereweshowthecorrelationfunctionsofPopulationIIIstarforminghalos(red),chemicallyenrichedhalos(blue),andthedarkmatterdensity(violet).Thedecreaseinthecorrelationfunctionsatscaleslargerthanapproximatelyhalftheboxsize(˘3:5h1Mpc)isduetothesizeofthesimulationvolume.Atalltimes,thechemicallyenrichedhalosareslightlymoreclusteredthanthePopulationIIIstarforminghalos.WeestimatethebiasofPopulationIIIstarforminghalostoevolvefromanextremevalueof˘10to˘5to˘3fromz=18to14to10.Thisevolutioniscomplementedbythegrowthofapronouncedexclusionregioninthetwo-pointcorrelationfunctionofPopulationIIIhalosthatbecomesclearlyvisiblebyz=10;noPopulationIIIstarformingpairsarefoundatseparationsbelow8:2comovingh1kpc,consistentwiththenearestneighboranalysisdiscussedaboveandshowninFigures3.9-3.11.ThenatureofPopulationIIIstarforminghaloassemblyatlatetimescanbebetterunderstoodbyexaminingthehalomergerhistorythatprecedesprimordialstarformationinatypicalhalo.Figure3.13showsacomparisonofseveralhalosthathostPopulationIIIstarstoseveralhalosthatformchemicallyenrichedstars.Thehalolineageisfollowedbackwardsthroughtime,andfollowsthemostmassiveprogenitor.Figure3.13worksbackwardsintimefromz=10:73,thoughsimilarbehaviorisseeninacrosslatetimesinourmodel.Themassofeachhalointhelineageisnormalizedtothemassofthehalo,andthetimeisnormalizedtothetimeelapsedinthesimulationsincethestarformed.Thereisaclearinthegrowthofthetwopopulationsofhalos.Halosthathostchemically81Figure3.12:ThehalocorrelationfunctionsforPopulationIIIhalos(red)andchemicallyenrichedhalos(blue),andtheunbiaseddarkmatterdensity(violet).PanelA,B,andCshowthecorrelationfunctionsatz=18,14,and10,respectively.Errorbarsareplottedforallpoints,butaregenerallynotvisible.AtalltimeschemicallyenrichedhalosaremoreclusteredthanPopulationIIIstarforminghalos.enrichedstarsgrowmorerapidlyatearlytimes,withslowergrowthlater.Thispatternofhalogrowthinoverdenseregions,inwhichrapidearlygrowthisfollowedbyslowergrowthatlatertimes,isinagreementwiththeofMcBrideetal.(2009),andsupportsourthatchemicallyenrichedstarformationoccursinhalosthatareinmoreoverdenseregions.Conversely,chemicallypristinehalosgrowslowlyatearlytimes,andexperiencerapidmergersatlatetimesthatpushtheirmassabovethethresholdrequiredforPopulationIIIstarformation.Therapid,lateassemblyofPopulationIIIhalosatlatertimesinourmodelsistheresultofmultiplemergersofsmall,chemicallypristinehalosoccurringinrapidsuccession.Thisrapidgrowth,takeninthecontextofFigures3.10and3.11,showsacoherentpictureofaregionofmanysmall,chemicallypristinehalos,allofwhichareindividuallytoosmalltoformaPopulationIIIstar,undergoingarapidseriesofmergersuntilthePopulationIIIstarformationmassthresholdissurpassed.WhenthePopulationIIIstarforms,itshosthaloisstillsurroundedbychemicallypristinehalos,butsubsequentmergerswiththisnowchemicallyenrichedhalofuelchemicallyenrichedstarformationratherthanPopulationIII82starformation.HalosinunderdenseregionsgrowasiftheyareinaloMuniverse,andarethusretardedcomparedtothemean(Mo&White,1996).Thisexplainstheslowgrowthandsystematicallytbehavior.TheslowgrowthofhalosintheseunderdenseregionsenablestheformationofchemicallypristinehaloslargeenoughtohostPopulationIIIstarformationatlatetimesaccordingtoourmodels.Figure3.13:Anexampleoftherateofgrowthofhalostotheirmassatz=10:73.Eachhaloisnormalizedtoitsmass,andeachlinerepresentsanindividualhalo.Timeisshownonthehorizontalaxis,withtbeingastheamountoftimesincethestarinthesimulationformed.Red,dashedlinesshowthe10mostmassivechemicallyenrichedhalosandblue,solidlinesshowthe10mostmassivechemicallypristinehalos.All10chemicallypristinehalosareplotted,thoughtheirverysimilargrowthatlatetimesmakesthemoverlapinthisChemicallyenrichedhalosexperiencefastergrowthatearlytimes,whilethechemicallypristinehalosthathostPopulationIIIstarsgrowslowlyatearlytimes,remainingbelowthemassrequiredforstarformation.Growthinchemicallypristinehalosoccursrapidlyatlatetimes,immediatelypriortostarformation.833.5Discussion3.5.1ComparisontoObservationToverifythatthismodelaccuratelycreatesasetofhaloscapableofformingPopulationIIIstars,severalmethodsofvalidationwereundertaken.Onemethodwastocomparethetotalstarformationrate(SFR)densitytoobservationalconstraintsfromBouwensetal.(2011).ThestellarmassdensityderivedSFRdensitytheyreportforz=10:3rangesfromapproximately2:5103to6:3103Myr1Mpc3,withaluminositydensityderivedSFRdensityplacinganupperlimitat2:5104Myr1Mpc3.ThisrangebracketstheSFRdensityfoundbyourmodelwithastarformationof0:008,andisinreasonableagreementwiththemodelswithhigherstarformations.ItshouldbenotedthattheSFRdensityreportedinBouwensetal.(2011)atz=10:3isanextrapolationfromdataextendingtoz˘8,andinthecaseoftheluminosityfunctionderivedSFRdensityisreportedasanupperlimit.3.5.2ComparisontoOtherWorkTheworkofTrenti&Stiavelli(2009)motivatedthePopulationIIIstarformationmethodusedinthismodel,andcomparisonwiththeirresultsshowsastrikingagreement.WhileTrenti&Stiavelli(2009)useananalyticdarkmatterhaloformationratederivedfromtheSheth&Tormen(1999)massfunction,asopposedtothecosmologicalsimulationsusedhere,thereisexcellentagreementbetweenthetwoworks.TheminimumhalomassforPopulationIIIstarformationatz=10isnearlyidentical:4:8107Mwithourmodelcomparedtoapproximately6:4107MbyTrenti&Stiavelli(2009).TheSFRdensityatz=10alsodemonstratesgoodagreement,withTrenti&Stiavelli(2009)84approximately4103Myr1Mpc3,comparedto1:3102Myr1Mpc3withourmodel.ThislevelofagreementisencouragingconsideringthatourmodelutilizesacosmologicalsimulationtodeterminehalopopulationsratherthantheanalyticSheth&Tormen(1999)massfunction,ourPopulationIIIstarformationmodelwasmoandthatourchemicallyenrichedstarformationmodelwasentirelyentthantherateofTrenti&Stiavelli(2009).Giventhatchemicallyenrichedstarformationdominatestheoverallstarformationatz=10inbothmodels,thisisparticularlyencouraging.ThisworkcompareswellwithworkbyRicottietal.(2002b),whoaSFRdensityofapproximately2102Myr1Mpc3atz=10despitevastinapproach.ThesimulationsofRicottietal.(2002b)self-consistentlysolvetheradiativetransferequation,utilizeH2chemistry,heating,andcoolingnetworks,aswellasaSchmidtlawstarformationprescription.Ricottietal.(2002b)usemuchsmallervolumesof0:5,1,and2comovingh1Mpconaside,givingconsiderablylessstatisticalpowertotheirresults.Theadvantagetotheirworkistheadditionofmuchmoreelaboratemultiphysicsprocessesgoverningstarformationandradiativefeedback.TheworkofWiseetal.(2012b)issimilarlymuchmorerobustinitsmultiphysicsca-pabilities,thoughisagainhamperedbyasmallsimulationvolumeof1h1Mpc3.ThesimulationsofWiseetal.(2012b)use12levelsofadaptivemesht,anine-speciesnon-equalibriumchemistrynetwork,prescriptionsforbothPopulationIIIandchemicallyenrichedstarformation,aswellaskineticandradiativestellarfeedback.Regardless,ourmodelverysimilarvaluesoftheSFRdensity,bothqualitativelyandquantitatively,forbothPopulationIIIandchemicallyenrichedstarformation(seetheirFigure3).OurmodelsutilizingfLWesc=0:01and0:1areinparticularlygoodagreementwiththeirFurthermore,inbothourresultsandthoseofothers,thechemicallyenrichedSFRdensity85risestodominatethePopulationIIISFRdensitybyseveralordersofmagnitudebyz=10.3.5.3ImplicationsforPopulationIIIModelingTreatingthephotodissociatingradiationself-consistentlyiscruciallyimportanttotheselec-tionofhalosthatarecapableofformingaPopulationIIIstar.Figure3.6indicatesthatthedestructionofH2dramaticallyimpactstheminimumhalomassthatiscapableofhostingPopulationIIIstarformation.AsPopulationIIIstarformationpersistswellbeyondtheformationofthestarinthesimulation,thevastmajorityofPopulationIIIstarswillforminthepresenceofanon-negligiblephotodissociatingbackground.Thesestars,termedPopulationIII.2(McKee&Tan,2008;O'Sheaetal.,2008),comprisethemajorityofstarsthatformfromchemicallypristinegas,butarefundamentallyimpactedbytheradiationpro-ducedbyotherstars.Thissuggeststhatthesimulationsthatusesmallsimulationvolumes(e.g.,Abeletal.(2002);Brommetal.(2002);Turketal.(2009))aretypicallyneglectingamajoraspectoftheenvironmentinwhichPopulationIIIstarsform.Evensomeofthosethatdoincludethis(e.g.,Machaceketal.(2001);O'Shea&Norman(2008);Yoshidaetal.(2003))fromtheofsmallsimulationvolumesandthethelackofmetal-enrichedstellarpopulations,andsimulationsthatincludeboth(e.g.,Ricottietal.(2002a);Wiseetal.(2012b))stillhavetoosmallofasimulationvolumetoadequatelysamplethestarformationbehavioroftheearlyuniverse.3.5.4LimitationsandFutureWorkThephotodissociatingbackgroundistreatedasbeinghomogeneousintheentiresimulationvolumeratherthanpreferentiallyimpactingthehalosnearesttostarforminghalos.Onthe86smallscale,oneexpectsthephotodissociatingbackgroundtovaryasr2,whereristhedistancefromnearestsmallnumberofhalos,andshouldvarysubstantially.Wecouldinprincipleaccountforthisvariationonsmallscales,thoughthelong-livedphotodissociatingbackgroundcanbemodeledasbeingthesumofahomogeneoustermandananisotropicterm.TheanisotropictermiscausedbystarformationinthelastapproximatelyLbox=c(1+z)years,whereLboxisthesizeofthesimulationvolumeandcisthespeedoflight.Onalargerscale,thephotodissociatingbackgroundisinhomogeneousonthemany-Mpcscalebasedonlarge-scalemodes(Ahnetal.,2009).Thisinhomogeneityisneglectedasitisneitheralargeincomparisontothehomogeneousphotodissociatingbackground,andbecauseitcannotbetreatedinamodelofthisnature.Theofionizingradiationproducedbythestellarpopulationsisneglected.Therecombinationratescalesasˆ2,whereˆisthedensity,whichinturnscalesas(1+z)3,sotherecombinationratewillscaleas(1+z)6.Attheredshiftsofinterest,haloswouldneedtobeveryclosetooneanotherfortheionizedhydrogenregionstobeimportant.Forexample,calculatingtheradiusoftheomgrensphereproducedbya3MchemicallyenrichedstarusingtheaverageionizingfromSchaerer(2003)andanaveragedensityapproximatingthehydrogenmassdensitycomponentofthevirialdensity,calculatedas178Bˆc(1+z)3)=(mH),whereˆcisthecriticaldensityoftheuniverse,andmHisthemassofahydrogenatom,givesanionizedregionaroundthestarextendingonly15pcatz=30,andonly122pcatz=10.Anygasthatisejectedfromahaloisconsideredtobepermanentlylost,andisneverincorporatedintofuturehalosorusedinstarformation.Asthemassofgasthatislostisdeterminedbytheenergeticsofthesupernovainthehaloandtheescapevelocityasdeterminedbythehalomass,theassumptionthatthematerialispermanentlylostfrom87itshalooforiginislikelyvalid.Kitayama&Yoshida(2005)showthatthefateofgasinahaloinwhichasupernovaoccurscannotbedeterminedsolelythroughthecomparisonoftheexplosionenergyandthebindingenergyofthehalo,butisstronglydependentongasdensityandthatinhalosofmass˘107Mandlarger,thehalowillnotbeevacuated,evenwhentheexplosionenergyexceedsthebindingenergyby2ordersofmagnitude.Chemicallyenrichedgascouldconceivablybeejectedfromonehaloandimpingeonanearbypristinehalo,renderingthathaloincapableofformingaPopulationIIIstardespiteneverhavinghostedstarformationinitsassemblyhistory.Whilechemicallyenrichedmaterialmaybeejectedfromahaloasaresultofasupernovaexplosion,itextendstoaradiusofonly˘1kpcwithin105107yrs(Brommetal.,2003;Whalenetal.,2008),andhasanegligibleimpactonstarformationinsatelliteminihalos(Whalenetal.,2010).Itisunlikelythatchemicallyenrichedmaterialejectedintotheintergalacticmediumwouldpollutesurroundingchemicallypristinehalos,asatz=10theminimumcomovingseparationbetweenaPopulationIIIandchemicallyenrichedhalois2:2h1kpc.Thesemotivationsareatthecoreoftheassumptionthatstarformation,evolution,anddeathinonehalodoesnotdirectlyimpactotherhalosthatarenearby,butonlycontributetotheglobalcharacteristicsofthesimulationvolume.Thismodeldoesnotincludeanyofreionization,butthisislikelynotanissueasthesimulationstowhichthemodelisappliedarestoppedatz=10,wellbeforetheepochofreionization.Theresultsofthismodelwillbeinvalidifappliedtotimesbeyondtheonsetoftheepochofreionization.Futureworkallowsseveralprimaryareasforimprovementinthismodel.Improvedmethodsforassociatingdarkmatterparticleswithasphalobasedonthegravitationalpotential,orbyutilizingasix-dimensionalFriendsofFriendsalgorithm(Diemandetal.,2006)thatincludesparticlevelocitydatainadditiontothespatialcriteriaforhaloidenti-88wouldprovideamorephysicallyrealistichalocatalogandmergertree.TheveryrapidgrowthofPopulationIIIhalosatlatetimes(seeFigure3.13)haspotentiallyimportantimplicationsfortheformationofPopulationIIIstars.O'Shea&Norman(2007)showedthatincreasingthehalomergerrate,andinturngrowthrate,increasedthetemperatureofthehalo,leadingtotheproductionofmoreH2,thoughtheresultsofO'Shea&Norman(2007)areformuchlargermasshalos,socareshouldbetakeninextendingtheirresultstothehalosinoursimulation.IncreasingtheH2contentofahalocouldleadtomoretcooling,andacolderhalocore.ThemethodfordeterminingifahaloiscapableofformingaPopulationIIIstarinthismodelisindependentofthehaloassemblyhistory,anduseshalomassasaproxyforthemaximumamountofH2thatcanresideinthehalo.AllowingthemodeltoincreasethemassofH2inahaloinresponsetorapidgrowthcouldpotentiallyenablehaloslessmassivethanthecurrentPopulationIIIstarformingmassthresholdtocooltlyandformstars.Treatmentandadditionofthistothemodelareleftforfuturework.ManyotherthatarenotincludedinthismodelmaybeimportanttothePopu-lationIIIstarformationandthedeterminationofthePopulationIIIinitialmassfunction(IMF).Forexample,molecularhydrogenrates(Turketal.,2011b),magnetic(Turketal.,2012),andsubgridturbulence(Latifetal.,2013)havebeenshowntobedynami-callyimportantinPopulationIIIstarformation.Turbulenceinprimordialcloudsenhancesfragmentation,evenwhensubsonic,andthisbehaviorisobservedinbothPopulationIII.1andPopulationIII.2starforminghalos(Clarketal.,2011a).RadiativefeedbackfromaPopulationIIIstarcanhaltaccretion,establishingitsmass,andH2photodissociatingradi-ationcouldreducethemassbetweenPopulationIII.1andPopulationIII.2starsbyinhibitingcoolingviaH2(Hosokawaetal.,2012).Investigationsusingsinkparticlesto89modeltheaccretingprotostarshaveindicatedthatlocalradiativefeedbackhaltsaccretionontotheprotostarsforminginafragmentedprimordialdisk,andthattheendofaccretioniswhatsetsthenalstellarmasses(Stacyetal.,2010,2012).TheimpactofadditionalenergyinputfromdarkmatterannihilationonthefragmentationpropertiesofaPopulationIIIstarformingcloudisinvestigatedbySmithetal.(2012),whothatfragmentationstilloccursdespitethisadditionalenergy.ItmaybethecasethatthePopulationIIIIMFissetprimarilybyonascalesmallerthanthehaloenvironment,andthatlargescaleinenvironmentareasub-dominantbutthisinvestigationmustbecarriedoutinordertoassesstheimportanceofhaloenvironmentonPopulationIIIstarformation.Theresultsofthismodelwillbeimprovedwithitsapplicationtolargersimulationvolumes,asincreasinglyrarehighmasshaloswillbemorelikelytoform.ThiswillallowforamorerepresentativeinvestigationofthehalosthathostbothPopulationIIIstarformationandthefeedbackthatensuesaschemicallyenrichedstarformationbegins.Theapplicationofthismodeltosimulationsrunwithfullphysicscapabilitieswillallowfordirectcomparisonbetweentheresultsofthetwomethods.Thiswillenabletheidenofphysicalprocessesthatarerelevanttostarformationandchemicalevolutionthatcannotbetreatedinthestatisticalmannerofthismodel.Idenandimprovementoftheseareaswillallowforthemodeltobecomemorerobustwhileretainingasmuchofthecurrentcomputationalaspossible.Thisisthepaperinaseries.PaperIIinvestigatesthenucleosyntheticevolutionofhighredshiftstructureincomparisontothelocaldwarfspheroidalpopulationandtheMilkyWayandAndromedastellarhalos.Furtherpaperswillincludefull-physicsadaptivemeshentsimulationsofselectedpristinehalosacrossarangeofredshiftsanddensityenvironments.903.6SummaryandConclusionsOurmodelidenthechemicallypristinehaloscapableofformingaPopulationIIIstarinanN-bodycosmologicalsimulation.Thesemi-analyticalmodelincludesPopulationIIIandchemicallyenrichedstarformation,halometalpollution,andtheH2photodissociatingradiationfromthestellarpopulation.Thisisasubstantialimprovementoverpreviousworkofthistype,andisalsoausefulcomplementtofull-physicssimulationsbecauseitallowsfortheinvestigationoflargercosmologicalvolumes,allowingforimprovedstatisticsandthecreationofamorerepresentativesampleofPopulationIIIstarforminghalos.PopulationIIIandchemicallyenrichedstarforminghaloshaveverysimilarpropertiesandenvironmentsathighredshifts,butthesepropertiesdivergesubstantiallyatlatertimes.AtlatetimesPop-ulationIIIstarsforminmassivehalosinunderdenseregionsthatgrowrapidly.PopulationIIIstarforminghalosassembleinisolationfrombothchemicallyenrichedandotherPopu-lationIIIstarforminghalos.ThisndingcarriesimplicationsforthesearchforPopulationIIIstarswiththeJamesWebbSpaceTelescopeandotherfutureobservationalmissions,asPopulationIIIstarsdonotforminorneargalaxies,andsearchesintheseenvironmentsareunlikelytoyieldresults.AccuratemodelingofPopulationIIIstarformationrequiresandconditionsthatarenotaccountedforincurrentsimulations.WorktomodelPopulationIIIstarformationintheredshiftrangeofz˘15toz˘10shouldbecarriedoutinlargersimulationvol-umesinordertoself-consistentlydeterminetheH2photodissociatingradiationproducedbyotherstars.ThedensityenvironmentthathostsaPopulationIIIstarforminghaloisgenerallymodeledimproperlyaswell,suggestingthatthePopulationIIIstarformationintheliteraturetodatemayonlyaportionofthecharacterofthatfoundinnature.91Thismodelhassucceededinproducingacatalogofmorethan40,000halosinasinglecosmologicalsimulationthatarecapableofformingPopulationIIIstars.Thesehalosrangeinmassfrom2:3105Mto1:21010Mandinredshiftfromz=30toz=10.SimulationsofthesehaloswillenableavastlymorerepresentativestudyofthecharacteristicsofPopulationIIIstars.3.7AcknowledgmentsThisworkusedtheExtremeScienceandEngineeringDiscoveryEnvironment(XSEDE),whichissupportedbyNationalScienceFoundationgrantnumberOCI-1053575.Allsimula-tionswerefundedbyXSEDEawardTG-AST090040.Inparticular,wewouldliketothankstheRDAVatNICSfortheirsupportandMSU'sInstituteforCyber-EnabledResearchforaccesstocomputingresources.ThisworkwasfundedbytheNASAATFPprogram(NNX09AD80GandNNX12AC98G),theNSFASTprogram(AST-0908819),theLANLInstituteforGeophysicsandPlanetaryPhysics,andMSU'sInstituteforCyber-EnabledRe-search.M.J.TwassupportedinthisworkbyNSFCITraCSfellowshipawardOCI-1048505.O.H.acknowledgessupportfromtheSwissNationalScienceFoundation(SNSF)throughtheAmbizionefellowship.B.W.O.wouldliketothankTomAbelandMichaelNormanforusefuldiscussions.WethankMicheleTrentiforhelpfuldiscussionofPopulationIIIstarformationmodeling,andStephenSkoryforhistechnicalassistanceinthecreationofthehalomergertrees.92Chapter4TracingTheEvolutionOfHigh-RedshiftGalaxiesUsingStellarAbundances4.1Introduction1Theprocessbywhichthechemicalcomplexityintheuniversewasbuiltup,fromthepri-mordialproductsofbigbangnucleosynthesistothecurrentproliferationofelements,isanenduringquestioninastrophysics.Thegeneralpictureiswellunderstood,withPopula-tionIIIstarsinitiatingchemicalenrichmentbyexpellingnucleosyntheticproductsintothesurroundinginterstellarmedium(ISM),whichisthensubsequentlyincorporatedintolater,metal-enrichedgenerationsofstars.Thiscycleofstarformation,chemicalenrichmentwithinstars,andreturnofenrichedgastotheISMformsthefoundationofgalacticchemicalevo-lutionmodels.Weinvestigatetheevolutionofhigh-redshiftgalaxiesbybuildinguponthisbasicmodelandconnectingthenucleosyntheticyieldsofstellarevolutionmodelsandstarformationinacosmologicalcontextwiththelarge-scalesetsofstellarabundancesobservedtoday.Thesuccessofcosmologyarguesforthescenarioofhierarchicalstructureforma-1ThischapterwasoriginallypublishedintheAstrophysicalJournal(Crosbyetal.,2016).93tion,withsmallgravitationallyboundhalosrepeatedlymergingtogethertocreateever-largerboundstructures.TheMilkyWayistheresultofthesmallerstructuresthathavemerged;itschemicalandkineticstructureencodesthehistoryofeverythingthatmergedtoformit(Feltzing&Chiba,2013).Ifthemostmetal-poorstarspreservearecordofthechemicalabundancesoftheirenvironmentatthetimeoftheirformation(Freeman&Bland-Hawthorn,2002;Beers&Christlieb,2005),studyoftheoldest,mostmetal-poorstarsintheMilkyWay,apracticetermed\GalacticArchaeology,"canprovideinsightintothenatureofthestarsandtheevolutionofhigh-redshiftgalaxies.Observationofmetal-poorstarsintheMilkyWayiscomplementarytothedirectstudyofhigh-redshiftgalaxyformation.Observationsofhigh-redshiftstructurehaveprogressedtothepointofobservingobjectsatz˘10,providingadirectviewoftheseearlygalaxies.Theseimpressiveobservationsareneverthelesslimitedbythesinherentinobservingaveryfaintstructureanddeducingitscharacteristics.Observationsofthemostmetal-poorstarsintheMilkyWaycarryatsetofadvantagesanddisadvantages.Spectroscopicobservationsofindividualstarsallowforprecisiondeterminationsofabundancesinamannerthathigh-redshiftobservationscannotaccomplish,givingcrucialinsightsintothestellarpopulationsthatprecededthatstar'sformation.Theseobservationsarelimitedbythefactthatmostdetailsofthegalaxyinwhichtheyformarelostduringthemergerprocess.AnalysisofthestellarhalooftheMilkyWayinkinematicphasespacehasmadestridesinstellarstreamsandpopulationsfromdisruptedandmergingstructures(Feltzing&Chiba,2013;Ivezicetal.,2012),butthelongandcomplicatedprocessofmergersthatbuilttheMilkyWayhasinevitablywipedawayalargeamountofthisinformation.Wehavecreatedamodelthatbridgesthesephysicalandtemporalscales,connectingstellarnucleosyntheticyieldsathighredshifttotheelemental-abundancepatternswecur-94rentlyobserveintheMilkyWay'soldeststellarpopulations.Toaccomplishthis,webeginbydevelopingasemianalyticmodelforstarformationincosmologicalsimulations.Weincludetheproductsofstellarnucleosynthesiswithinthismodelandusethisadditiontofollowthebuildupofvariouselementsasstarsform,evolve,anddie,ashalosmerge,andasdiversestellarpopulationsaremixed.Wemodeleachhaloasmultiplezonesofgasandstars,hostingstellarpopulationsofmultipleagesratherthanasingle\simplestellarpopulation"(SSP).ThestarsformedinourmodelaresimilartothosecurrentlyintheMilkyWayhaloanddwarfgalaxypopulations.Bycomparingtheabundancepatternsofourmodelwiththeseobservedstellarpopulations,wecangaininsightintotheformationenvironmentandhistoryofthesemetal-poorstars.Thismodelpresentsapowerfulnewframeworkforinterpretingobservations.Stellarevolutionandnucleosynthesismodelsareconstantlyimproving,leadingtoabetterunder-standingofthechemicalandkineticfeedbackfromstellarpopulations.Computingpowercontinuestogrow,enablingsimulationswithgreaterdynamicrangeinbothspatialandmassresolution,andenablingtheinvestigationoflargercosmologicalvolumeswhilepreservingorimprovingspatialandtemporalresolution.Currentandfutureobservationalsurveyspro-videawealthofstellarelemental-abundancedata.Theinterpretationofthesedatawillrequireamodelthatincorporatesasmanyrelevantphysicalprocessesaspossiblewhilestillmaintainingcomputational.WearecurrentlyabletocomparetoobservationaldatafromSEGUE(Yannyetal.,2009)andthehigh-resolutionstellarabundancemea-surementscollectedbyFrebel(Frebel,2010).Wemakequantitativecomparisonsbetweenourmodelandobservations,allowingforconstraintsonmodelparameterssuchasthena-tureofthestellarinitialmassfunction(IMF),thewithwhichgasformsstars,andtheaccuracyoftheoreticalstellaryields.Ongoingandfutureobservationalcampaigns95suchasLAMOST(Dengetal.,2012),APOGEE(AllendePrietoetal.,2008),Gaia-ESO(Gilmoreetal.,2012),GALAH2(Zuckeretal.,2012),andGaia(Pancino,2012)willprovidevastquantitiesofdataenablingarobuststatisticalcomparisonbetweenmodelparametersandobservations,bolsteringourunderstandingofhigh-redshiftstarformationandfeedbackalongwiththenatureofgalacticchemicalevolutionintheparadigmofhierarchicalstructureformation.Previousworkshaveendeavoredtoinvestigatetheformationofmetal-poorstars.ThesemianalyticmodelsofFontetal.(2006)constructmergerhistoriesforseveralgalaxiessimilartotheMilkyWayusingamethodbasedontheextendedPress-Schechterformalism(Lacey&Cole,1993)andfollowtheabundancesofalphagroupelementsinadditiontoirontotrackthechemicaldistributionofthegalactichalosattheirsatellites.Salvadorietal.(2010)combineN-bodysimulationswithsemianalyticmodelsforstarformationinasingle-phaseinterstellarmediumtotrackmetallicityviaironabundanceandmodelthespatialmetallicitydistributionofstarsintheMilkyWay.Tumlinson(2010)utilizessemianalyticchemodynamicmodelingofhigh-redshiftstarformationtoprobethedegreetowhichtheMilkyWayhalostarsthestarformationenvironmentpresentinhaloprogenitorgalaxiesbefore,during,andaftertheepochofreionization.Theabundanceandspatialdistributionofmetal-poorstarsinthegalaxyareusedtoprobethePopulationIIIIMFbyKomiya(2011),whoalsoconstructamergerhistoryusingtheextendedPress-Schechterformalismandexpandthenumberofelementalabundancesthattheytracktoseven,butfocusonyieldsfromsupernovae(SNe)ratherthantheentireensembleofmannersinwhichstarschemicallyanddynamicallyenrichthesurroundingmedium.Kobayashi&Nakasato(2011)couplesemianalyticmodelsofstarformationtoN-bodycosmologicalsimulationsof2http://www.mso.anu.edu.au/galah/home.html96aMilkyWay-likediskgalaxy,trackingtheabundancesof13elements,butowingtotheirhighparticlemassof(1:03:8)106Mandlateinitialredshiftof24,thesesimulationsdonotresolvetheformationofhigh-redshiftandlow-massprogenitorgalaxies.Thismodelovercomesmanyofthechallengesthathavelimitedpreviousworkonthissubjectbycombiningrobust,physicallymotivedsemianalyticmodelsofstarformationandstellarfeedbackwithwell-resolvedN-bodycosmologicalsimulationsandasuiteofyieldsfromstellarevolutionsimulations.Additionally,thismodelhasthecapabilitytomakestatisticallyt,quantitativecomparisonstocurrentandfutureobservationsratherthanthequalitativeanalysisthatpervadespreviousworks.Theseinitialmodelscanbereadilyextendedasmorecompleteandself-consistentstellaryieldsbecomeavailable,andthedatafromthismodelcanbenaturallypairedwithpowerfulstatisticaltoolssuchasGaussianMultiprocessemulationcoupledMarkovChainMonteCarlotoolsandANOVAdecompositionomezetal.,2012,2014),enablingtherapidexplorationandevaluationoftheparameterspaceofthesemodels.Thisisthesecondpaperinaseries.InCrosbyetal.(2013)(hereafterPaperI),wepresentedasemianalyticmodelforcalculatingthestarformationhistoryofallhalosinacosmologicalsimulationacrossthefulltemporalextentofthesimulation,thusallowingustoidentifyhaloswherePopulationIIIormetal-enrichedstarformationistakingplace.Thispaperinvestigatesthechemicalevolutionofapopulationofhigh-redshiftgalaxiesthroughtheuseofasemianalyticchemicalenrichmentmodelthatwasbuiltontopofthemodeldescribedinPaperI.Syntheticstellarpopulationsarecreatedforeveryhalointhesimulation,andastellarfeedbackmodelisimplementedtoconnecttheevolutionofthestellarpopulationtotheongoingstarformationineachhalo.Withthismodel,chemicalevolutionhistoriesforthestellarandgaseouscomponentsofallofthestar-forminghalosinthesimulationare97createdandcanthenbecompareddirectlytoobservationsofmetal-poorstars.Theoutlineofthispaperisasfollows:Abriefreviewofthesimulationsused,thestarformationmodel,andthechemicalevolutionmodelisgiveninSection4.2.OurresultsarepresentedinSection4.4andcomparedtoobservationaldataandothertheoreticalworkinSection4.5,wherewealsoincludeadiscussionofthelimitationsofthisstudy.Finally,wepresentasummaryofourconclusionsinSection4.6.4.2ModelDescription4.2.1OverviewThemodelemployedinthisworkisanextensionandmoofthestarformationmodelpresentedinPaperI(i.e.,Crosbyetal.,2013).Thismodeltracksthechemicalevolutionofhalosacrosstimebyfollowing10chemicalspecies:H,C,N,O,Mg,Ca,Ti,Fe,Co,andZn,inboththestellarandISMcomponentsofeveryhalo.AmoredetailedtreatmentoftheISMthanwasimplementedinPaperIisrequiredtoaccuratelymodelthestarformationandfeedbackprocesses.PaperItreatedthegasandmetalquantitiesinahaloasasinglezone,inwhichmaterialfromaccretionandstellarfeedbackwasmixedinstantaneouslythroughouttheentirehalo,whichdoesnotaccuratelythedispersalandrecyclingofmaterialbetweentheISMandthestellarpopulation.TheISMisnowtreatedasamultiphasegaswithacentralregionofdense,coldgasthatiscapableofformingstarsandahot,regionexteriortothestar-formingcentralregionthatisincapableofformingstars.Thistwo-phasemediumprovidesasimpleframeworkinwhichtoinvestigatethebulkpropertiesoftheISMinhalos(Cox,2005).Throughouttheremainderofthispaper,thisexteriorregionofwarm,gaswillbereferredtoasthe\reservoir"ofthehalo,andthecold,98dense,star-formingregionwillbereferredtoasthe\central"region.GasandchemicalspeciesaremovedbetweenthesetwoISMregionsandthestellarcomponentineachhalo.Materialaccretedfromtheintergalacticmedium(IGM)isdepositedinthereservoir,andgasinthereservoircancoolandtransitiontothecentralregion.Gasinthecentralregionisavailabletocondenseandformstars,andfeedbackfromthestellarpopulationreturnsenrichedmaterialtothisregion.KineticfeedbackfromSNewillmoveenrichedmaterialfromthestellarpopulationtothecentralregion,aswellastothereservoir.IfthefeedbackfromSNeistlypowerful,itwillejectmaterialtotheIGM,permanentlyremovingitfromthehalo.Theonsetofreionizationgenerallysuppressesstarformationinhalos,withagreaterattenuationoccurringinlow-masshalosandalesserimpactonhigher-masshalos.ThePopulationIIIstarformationmodelusedinthisworkispresentedinPaperI,andabriefsummaryisgivenhereinSection4.2.2.TheinterestedreaderisencouragedtoseeCrosbyetal.(2013)foradetaileddiscussion.ThetreatmentofthemultiphaseISMandchemicallyenrichedstarformationimplementedinthisworkisdiscussedinSection4.2.3.Asummaryoftheparametersofthemodelthatweretested,theirvalues,andtherangesinvestigatedisgiveninTable4.1.Table4.1:ModelParameterswithTheirFiducialValues,theRangeTested,andaBriefDescription.ModelParametersParameterFiducialValueRangeDescriptionE0.040.008-0.2StarformationefLWesc10.01,0.1,1LWphotonescapefractionIMFSalpeterSalpeter,Kroupa,ChabrierchemicallyenrichedstellarIMFzreion88,7,6.5,noneRedshiftofreionizationThesimulationsusedasabasisforourmodelwerecarriedoutusingthepubliclyavailable99Enzoadaptivemesht+N-bodycode3(Bryanetal.,2014)andarethesamesimulationsthatwereusedinPaperI.Foursimulationswererun{twowithacomovingboxsizeof3:5h1Mpcandtwowithacomovingboxsizeof7:0h1Mpc.Weusedtwotsimulationvolumesandtworandomrealizationsperchosenvolumetogivesomeideaoftheimpactofcosmicvarianceaswellasmassandspatialresolution,onourresults.WeusetheWMAP7bcosmologicalmodel(Komatsuetal.,2011),with=0:7274,M=0:2726,B=0:0456,˙8=0:809,ns=0:963,andh=0:704inunitsof100kms1Mpc1,withthevariableshavingtheirusualAllsimulationsarecubicandhave1024gridcellsperedgeand10243darkmatterparticles,givingcelldimensionsof6:8h1comovingkpconaside,adarkmatterparticlemassof2:86104M,ameanbaryonicmasspercellof5:74103M,andatotalmassof3:71013Mforthe7:0h1Mpcboxes.The3:5h1Mpcboxeshavecelldimensionsof3:4h1comovingkpconaside,adarkmatterparticlemassof3:57103M,ameanbaryonicmasspercellof718M,andatotalmassof4:61012M.ThesevolumescontainenoughmasstoformagalaxywithmasssimilartothatoftheMilkyWay.Inthecurrentepoch,approximatelyhalfofallgalaxiesresideingroups.Athighredshift,theprogenitorsoftheMilkyWayandotherLocalGroupgalaxiesaredecidedlyaverage,thoughpossiblysomewhatmorestronglyclusteredthangalaxiesattheequivalentredshift(Corliesetal.,2013).Thus,theMilkyWayprogenitorpopulationiscomparabletothestructuresinthesimulationsusedinthiswork,andavolumecontainingtheprogenitorsofaMilky-Way-likegalaxyisstatisticallycomparabletoarandomlychosencosmologicalvolumeofsimilarsize.Thesimulationswereinitializedatz=99usingtheMUSICcosmologicalinitialcondi-tionsgenerator(Hahn&Abel,2011),withasecond-orderLagrangianperturbationtheory3http://enzo-project.org100methodandseparatetransferfunctionsfordarkmatterandbaryons.Asecond-orderLa-grangianperturbationmethodisnecessarytoobtainconvergedhalomassfunctionsatsuchearlytimesandhighredshiftsasthestartofPopulationIIIstarformation(Crocceetal.,2006).Eachofthesetsofinitialconditionswasgeneratedusingatrandomseed.ThesimulationswererunwithEnzo'sunigrid(non-adaptivemesht)modewithadiabatichydrodynamics,fromz=99toz=6.Dataareoutputatintegerredshiftsuntilz=14,atwhichpointtheelapsedtimebetweenintegerredshiftswouldexceedthetimescaleforstarformation.Afterz=14,dataareoutputevery11Myr.Thesimulationisstoppedatz=6topreventmodesontheorderofthesizeofthesimulationvolumefromenteringthenonlinearregime.Wenotethatextensivephysics(e.g.,radiativecooling,starformation,andfeedback)isunnecessaryinthesesimulations,astheyaresimplybeingusedasthesourceofmergertreesforoursemianalyticmodels.Darkmatterhalosforalldataoutputsinthesimulationswereidenusingthefriends-of-friends(Efstathiouetal.,1985)haloimplementedintheytanalysistoolkit4(Turketal.,2011c),withalinkinglengthof0:2timesthemeaninterparticlespacing.Halomergertreeswerethencreatedtoshowtheassemblyhistoryofthesedarkmatterhalosbasedonparticlemembership.4.2.2PopulationIIIStarFormationPopulationIIIstarsforminchemicallypristinehalosthatcoolviaH2toatemperatureanddensityatwhichthecoreisunstabletogravitationalcollapse(Abeletal.,2002;O'Shea&Norman,2007).Inourmodel,ahaloisdeemedtobecapableofhostingPopulationIIIstarformationifthecoolingtimescaleislessthanthelocalHubbletime.IntheabsenceofanH24http://yt-project.org101phototdissociatingbackground,thiscanbecastasaminimummassthresholdthatdependsonlyontheredshift,z,Mmin;Hubble=5:871041+z312:074M:(4.1)Thismassthresholdwillbemointhepresenceofotherstars,asradiationintheLyman-Werner(LW)band(11:1813:6eV)iscapableofphotodissociatingH2,suppressingcooling.TheminimumhalomassthresholdforPopulationIIIstarformationinthepresenceofLWbackgroundradiationbecomesMmin;LW=1:91106J0:457211+z312:186M;(4.2)whereJ21istheproperLWJ21isdfromthecomovingLWphotonnumberdensity,nLW,inMpc3,asJ21=1:61065nLW1+z313ergs1cm2Hz1sr1:(4.3)TheeJ21seenbyeachpristinehaloismotoaccountforH2self-shieldingfollowingWolcott-Greenetal.(2011).TheminimumhalomassthresholdforPopulationIIIstarformationisthentakentothemoststringentofEquations4.1and4.2,Mmin=max8>>><>>>:5:871041+z312:074M1:91106J0:457211+z312:186M:(4.4)AnyhalothatischemicallypristineandmoremassivethanthemassthresholdforPopu-102lationIIIstarformationisassumedtoformastar.Thehaloistaggedaschemicallyenriched,anditandallofitsdescendantsarenolongercapableofformingaPopulationIIIstar.WhenaPopulationIIIstarisformed,adelaytimepriortothestartofchemicallyenrichedstarformationisdeterminedbasedontheassumedPopulationIIIstellarlifetime.ThedelaytimeisscaledinverselywiththehalomasstoaccountforgasblownoutofthehalobyaTypeIIsupernova(SNII),whichisassumedtobetheendofallPopulationIIIstarsinthismodel.AfulldescriptionofthePopulationIIIstarformationmodelispresentedinPaperI.4.2.3ChemicallyEnrichedStarFormationAnyhalothatcontainsparticlesthathadpreviouslybeeninahalothatformedstarsisdeemedincapableofformingaPopulationIIIstarowingtometalpollution,andstarfor-mationinthesechemicallyenrichedhalosistreatedtly.Chemicallyenrichedstarformationismodeledasacontinuousprocess,asopposedtoPopulationIIIstarformation,whichisdiscreteandafunctionofthemassofgasavailableinthehalo(Ladaetal.,2010).WenotethatchemicallyenrichedstarformationistreatedsomewhattlythaninPa-perI.Thebaryonsinagivenhaloaremodeledasthreeinteractingpopulations:areservoirofgasintheoutskirtsofthehalothatishotandandthusdoesnotformstars;amassofgasinthecenterofthehalothatiscold,dense,andstarforming;andamassofbaryonsthatarecurrentlylockedupinstars.Asetofthreetialequationsgovernsstarformationandgastransportbetweenthereservoirandcentralregionsofachemicallyenrichedhalo,dMresdt=Mres˝cool+rcMc1trhaloMhalo1t;(4.5)103dMcdt=Mres˝coolrcMc1tE˝Mc+Mejectt;(4.6)dM?dt=E˝Mc:(4.7)Equation4.5governstherateofchangeofthemassofgasinthereservoir,Equation4.6governstherateofchangeofthemassofgasinthecentralregion,andEquation4.7governsthestarformationrate(SFR).InEquation4.5,thetermrepresentsgasthatcoolsfromthereservoirandcondensesintothecentralregion,and˝coolisthecoolingtimeofthegas,whichiscalculatedusingtheGracklechemistryandcoolinglibrary5(Bryanetal.,2014;Kimetal.,2014).ThesecondtermrepresentsgasejectedfromtheSNeinthecentralregionthatentersthereservoir,wheretistheintegrationtimestepandisafactorencapsulatinginformationabouttheSNethatoccurredduringthisintegrationtimestep(seeEquation4.11inSection4.2.4).Thethirdtermissimilartothesecond,butrepresentsgasejectedcompletelyfromthehaloviaSNe.InEquation4.6,thetwotermsarethesameasthetwotermsinEquation4.5butwiththeoppositesigns,togascoolingintothecentralregionandgasejectedfromitviaSNe,respectively.Thethirdtermmodelstheconversionofgasinthecentralregionintostars,whereEisthedimensionlessstarformation(SFE)and˝isthecharacteristicstarformationtime,takentohaveaconstantvalueof˝=108yr.Thefourthtermrepresentsgasexpelledbythestarstotheinterstellarmedium(ISM).Equation4.7isequivalenttothethirdterminEquation4.6,andcreatesamassofstarsfromtheavailablegasinthecentralregion.Equation4.7formsamassofstarsratherthanindividualstars,allowingfortstellarinitialmassfunctions(IMFs)5https://grackle.readthedocs.org/104tobeapplied.Thetimeintervalbetweeneachsimulationdataoutputistraversedin100integrationtimesteps,advancingEquations4.5-4.7forwardintime.Theagedistributionofthestellarcomponentofeachhaloistrackedin100linearlyspacedagebins,spanningthetimethatthestarformedinthesimulationtotheendofthecurrentsimulationdataoutput.Astimepasses,thestellarcontentisadvancedthroughtheagebins,enablingeachstellaragebinineveryhalotobeevolvedasanSSP.EverystellaragebinreturnsgasandenrichedmaterialtothehaloISMateachintegrationtimestep.Additionally,theexpectednumberofSNeisdeterminedandmaterialisejectedfromthehalototheIGM.ThehaloejectionmodelispresentedinSection4.2.4.NewstarsthatforminahaloareformedwithafractionofmetalsequaltothatoftheISMatthetimeofformation.Acompletedescriptionofthechemical-evolutionmodelisgiveninSection4.2.5.Theonsetofreionizationattenuatesstarformationinhalosandhasamorepronouncedonsmallerhalosthanonlargerones.WemodelreionizationbydrawinginspirationfromTumlinson(2010).Aftertheonsetofreionization,starformationinhaloswithacircularvelocitylessthan30kms1iscompletelysuppressed.Haloswithacircularvelocityinexcessof50kms1experiencenosuppression,andthosewithcircularvelocitiesfallingwithinthisrangeexperiencesuppressioninSFEthatvarieslinearlywithcircularvelocity.Ashalosmergebetweensimulationdataoutputs,allattributesofparenthalosareinher-itedbythechildhaloinproportiontothefractionoftheparenthalomassthatisinheritedbythechildhalo.Childhalosgenerallyinheriteitherallorthemajorityofthebaryoniccontentoftheparenthalosthatmergetoformit.Thisincludesinheritingthemassofgasavailabletoformstarsinthehalo,themassofallchemicalspeciesintheISM,themassofallchemicalspeciesinthestellarcomponents,andthestellarpopulationalongwithitsagedistribution.Theagedistributionisremappedateachsubsequentsimulationdataout-105put.Thisremappingdecreasesthetimeresolutionasthepopulationages,anditisdonetopreventexcessivecomputationalmemoryusage.Thisremappingproducesamaximumstellaragebinsizeof3:72Myr,whichislargerthanonlythesmalleststellaragebininthetabulateddataofmaterialreturnedtotheISMbyasymptoticgiantbranch(AGB)stars,resultinginatemporalresolutionofthechemicalandkineticfeedbackmodelbeinglimitedprimarilybythetimeresolutionoftheavailablestellarfeedbackdata.4.2.4GasandMetalEjectionTheprescriptionforejectionofmaterialviaSNefromahalototheIGMisbasedonseveralquantities{thenumberofSNethatoccurred;themassofgasejectedtotheISMbySNe,MISMgas;themassofspeciesZejectedtotheISMbySNe,MISMZ;andthevirialparametersofthehalo,spthemass(Mvir)andradius(rvir).ThestepofthisprocessistodeterminethemassofgasejectedfromthehalototheIGMasaresultofSNe,Mlost.ThisisaccomplishedfollowingTumlinson(2010),bycomparingtheenergyimpartedtothehalogasbyalloftheSNethatexplodedduringthecurrenttimestepwiththekineticenergyofgasmovingatthehaloescapevelocity,vesc.ESNe=Ewind=12Mlostv2esc(4.8)SolvingEquation4.8forMlostandusingtheoftheescapevelocityapproximatingthehaloasspherical,withmassMvirandradiusrvirallowsforthecalculationofMlostintermsoftheSNenergeticsandthehalophysicalproperties,Mlost=ESNervirGMvir:(4.9)106TheenergyimpartedtothewindbySNecanbeparameterizedasESNe=NSNeSNeE51,whereNSNeisthenumberofSNethatoccurredduringthecurrenttimestep,SNeisthewithwhichtheSNenergyisconvertedtothekineticenergyofthegas,andE51istheenergyofasingleSNinunitsof1051ergs.AvalueofSNe=0:0015isadoptedfollowingTumlinson(2010),whichmakestheassumptionsthat5%ofthetotalSNenergyiskineticandthatofthis,3%istransferredtotheejectedmaterial.InbothPaperIandKomiya(2011),theevolutionofthesimulationandmetallicitydistributionfunctionsarelargelyindependentoftheprecisevalueoftheSNe.Assuch,SNewillnotbevariedinthiswork.UsingthisparameterizationalongwithEquation4.9allowsforthecalculationofMlostasMlost=7:792108NSNeSNeE51rvirGMvirM;(4.10)whereMviristhehalovirialmassinunitsofM,rviristhehalovirialradiusinproperMpc,andGisthegravitationalconstantininCGSunits.Wealsothequantity=7:792108NSNeSNeE51G;(4.11)foruseinEquations4.5-4.7tocalculatethemassofgasthatisejectedviaSNefromthecentralregiontothereservoirregion,aswellasoutofthehaloentirely.4.2.5ChemicalEvolutionThismodeltrackstheabundancesof10elementsinboththecentralandreservoirregionsoftheISM,aswellastheelementalmassesinthestellarcomponentofeveryhalo,inadditiontothetotalmassofgasavailableforstarformationandinthereservoir.TheelementsH,107C,N,O,Mg,Ca,Ti,Fe,Co,andZnarefollowed.TabulatedyieldsfromstellarevolutionandnucleosynthesissimulationsareusedtodeterminethemassesofeachoftheseelementsthatareejectedfromstarstotheISM,aswellasthetotalejectedmassofgas.ChemicalenrichmentinaPopulationIIIstar-forminghaloistreatedtlythanthatinachemicallyenrichedhaloowingtothetmannersinwhichstarformationismodeledinthesetenvironments.AllPopulationIIIstarsareassumedtoendtheirlivesasTypeIISNe,atwhichpointtheyreturnenrichedmaterialtothehaloISM,usingyieldsfromHeger&Woosley(2002).TheinitialmassofeachPopulationIIIstarisrandomlyselectedwithequalprobabilityfromallmassesforwhichyieldsareavailable,rangingfrom30to100M.AfactorrepresentingthePopulationIIIstellarmultiplicityineachhaloisadoptedandhasavalueof1:2,motivatedbytheofTurketal.(2009)whichshowfragmentationintheprestellarcloud,suggestingthepossibilityoftheformationofPopulationIIIbinarystarsystems.GasandenrichedmaterialarereturnedtothehaloinaquantityequaltothetabulatedyieldsmultipliedbythePopulationIIImultiplicityfactor,treatingthepossibilityofPopulationIIIbinarystarsystemsinastatisticalmanner.Themovementofchemicalspeciesbetweenthecentral,reservoir,andstellarcomponentsofahaloisgovernedbyasetoftialequationssimilartoEquations4.5-4.7,dMZresdt=MZtorestMZlosttMZres˝cool;(4.12)dMZcdt=MZres˝coolMZc˝+MZejecttMZtorest;(4.13)108dMZ?dt=MZc˝;(4.14)whereEquation4.12describesthetimeevolutionofthemassofspeciesZinthereservoirgasthatisnotformingstars,Equation4.13describesthesameforthecentralregion,andEquation4.14describestheevolutionofthemassofspeciesZinthestellarcomponent.ThesuperscriptZdenotesthatthequantityisthemassofachemicalspecies,andisusedtotiatefromtheequationgoverningtheevolutionofthegasinEquations4.5-4.7.MZtoresisthemassofspeciesZthatmovesfromthecentralregiontothereservoirregioninagivenintegrationtimestep,andMZlostisthemassejectedfromthehalototheIGM.ThesetwotermsaredeterminedbythenumberofSNethatoccurandthemassofgasandeachchemicalspeciesejectedbySNeinthehaloduringagivenintegrationtimestep.GasandmetalsareinstantaneouslymixedwithineachISMcomponent.ThekineticenergyimpartedtoSNproductsshouldgiverisetopreferentialejectionofthismaterialfromthehalo(Tumlinson,2010).ThemassofgasejectedfromthehalototheIGMbySNeisdeterminedbyEquation4.10.ThisquantityisusedinconjunctionwiththemassofgasejectedtotheISMbySNetodeterminethemassofeachelementejectedbothfromthecentralregiontothereservoirregionandfromthehaloentirely.LookingatMZtores,amassofelementZproducedinSNewillreachthereservoirinproportiontotheratioofthemassofgasejectedtothereservoirtothetotalmassofgasejectedbySNe,MZtores=MZejectMtoresMeject=MZejectrc=McMeject:(4.15)Thismethodissimilarlyusedtodeterminethemassofeachspeciesejectedfromthereservoir109totheIGM,MZlost=MZejectrvir=MvirMeject:(4.16)ChemicalfeedbackfromstarsinchemicallyenrichedhalosismodeledtlythaninPopulationIIIstar-forminghalosowingtothedinstarformationmethods.EachstellaragebininahaloistreatedasanSSPofuniformmetallicityandidenticalstarformationtimethatwillejectgasandchemicallyenrichedmaterialasitages.Time-dependentyieldtableswerecreatedbyconvolvingtheyieldsfromstellarevolutionmodelswithweightingsfromanadoptedstellarIMF.tversionsofthesetableswerecreatedforSalpeter(Salpeter,1955),Chabrier(Chabrier,2003),andKroupa(Kroupa,2002)IMFsatvariousmetallicities.ThethreeIMFshavefunctionalformsdNdm=Salpeter=0:154m2:35(4.17)Kroupa=8>>>>><>>>>>:0:56m1:3m0:5M0:3m2:20:5M<m1M0:3m2:7m>1M(4.18)Chabrier=8><>:0:799me(logm=mc)2=2˙2m1M0:223m2:3m>1M(4.19)(4.20)IntheChabrierIMFmcisthecharacteristicmassandtakesavalueof0:079Mandthedispersion˙=0:69(Salpeter,1955;Kroupa,2002;Chabrier,2003).TheIMFsareallconsideredtobeapplicableinamassrangeof0:08Mto260MandareshowninFigure4.1.TableswerecreatedfollowingtheyieldsfromTypeIasupernovae(SNeIa),SNe110II,andAGBstars.AdditionaltableswerecreatedtogivetheratesofSNeIaandSNeIIasafunctionoftimesincetheformationoftheSSP.ThesetableswerecreatedforallthreeIMFsandforfourtmetallicities.Themetallicityofthegasinthecentralstar-formingregionofeachhaloisexaminedateachintegrationtimestep,andtheappropriateyieldsareused.DetailsofthecreationoftheyieldtablesarepresentedinSection4.3.Figure4.1:ThethreeIMFsconsideredinthisworkareSalpeter(violetsolidline),Kroupa(bluedashedline),andChabrier(reddot-dashedline),overamassrangeof0:08260M.Theintegratedareaundereachofthecurvesisthesame.TheSalpeterIMFemphasizeslow-massstars,theKroupaIMFemphasizesintermediate-massstars,andtheChabrierIMFisbythefarthemosttop-heavyofthethree,emphasizinghigh-massstars.Ateveryintegrationtimestep,thestellarmetallicityineachhaloisusedtodetermine111whichyieldsetwillbeusedforthestellarfeedback.AllofthestellaragebinsusethesetablestoejectgasandchemicallyenrichedmaterialintotheISM.ThenumberofSNepredictedtooccurinthehaloisdetermined,andthemassofgasthusejectedtotheIGMiscalculatedusingEquation4.10.ThisiscomparedtothemassofgasejectedbySNetotheISM,andeitherEquation4.15orEquation4.16isusedtoupdatethemassofallchemicalspeciesintheISM,settingthecompositionofthenextstarstoforminthishalo.4.3StellarYieldsCreationofthefeedbacktableswasaccomplishedbyconvolvingtheyieldsofagridofstellarevolutionmodelswithastellarIMFtocreatechemicalandkineticfeedbacktablesforanintegratedstellarpopulation.ThesetablesencapsulateinformationregardingfeedbackasafunctionofthetimesinceformationofthestellarpopulationandassumethatallstarsareformedinaccordancewiththeadoptedIMFandthemetallicity-dependentstellarlifetime.ThesetablescanbeappliedtoasingleSSPofagivenage,andinthecaseofahalothathasexperiencedstarformationinitspast,thetablescanbeusedtodeterminethetotalamountofchemicalandkineticfeedbackbyapplyingthemseparatelytoeachstellaragebininthehalo.SeparatetableswerecreatedforAGBandsuper-AGBstars,aswellasforSNeIaandII.Thesetableswerecreatedusingseveralmetallicities.Themodularnatureoftheyieldtablesallowsfortheinvestigationoftheimpactofindividualsourcesandthesuccessorfailureofyieldsforentstellarmetallicities.Additionally,newyieldscaneasilybeintegratedintothemodelandtestedindependentlyofthefunctionalityoftherestofthecode.1124.3.1YieldsofAGBStarsIntermediate-massstarsarepresumedtobethemainproducersofheavys-processnuclidesandalsocontributesubstantiallytotheyieldsofseveralothernuclides,mostnotablycarbonandnitrogen,duringtheirAGBphase(Siess,2007).Karakas&Lattanzio(2007)andKarakas(2010)calculateddetailedstellarmodelsandpost-processednucleosyntheticdatatoproduceAGByields.Theirmodelscoverarangeinmassfrom1.0to6MandcompositionsZ=0.02,0.008,0.004,andZ=0.0001,whereZisthemetalmassfraction.Allmodelswereevolvedfromthezero-agemainsequencetonearthetipofthethermallypulsingAGBphase.Karakas(2010)usedanupdatedsetofproton-and-captureratesandassumedscaled-solarabundancesforlow-metallicitymodels,ratherthanadoptingtheinitialabundancesoftheSmallandLargeMagellanicCloudsaswasdoneinKarakas&Lattanzio(2007).Super-AGBstarsarebyaspmassrangebetweentheminimummassforcarbonignitionandthemasslimitabovewhichthestarignitesneonatitscenterandevolvesthroughallnuclearburningstagesuptoaniron-corecollapseSNe(Siess,2007).Themassrangeofsuper-AGBstarsvarieswithmetallicity,withalowerlimitbetween7.5and9Mandanupperlimitofapproximately11M(Siess,2007,2010).InSiess(2010),yieldsarecomputedinapost-processingstep,withinitialmassrangesfocusedoncoveringthecomputationallydemandingthermalpulses.TheSiess(2010)modelcomputestheevolutionofconvective-zoneabundances,withinstantaneousmixingofchemicalspecies,andallowsfortnuclearreactionratesanduncertaintieswithinvariousspatialandtemporalregionsofthestar.Owingtotheseconsiderations,weusetheyieldsofKarakas(2010)forAGBstars,inconjunctionwithyieldsfromSiess(2010)forsuper-AGBstars.1134.3.2YieldsofSNeIIStarswithazero-agemain-sequencemassof8-40MareexpectedtoendtheirlivesasSNeII(Hegeretal.,2003).TheSNIIrateisinturndeterminedbycalculatingthemain-sequencelifetimeofstarsinthismassrangeusingthemass-agerelationofRaiterietal.(1996).Theselifetimes,usedinconjunctionwithanIMF,enableustocalculatetheSNIIrateasafunctionoftimeforastellarpopulationofagivenmass.Kobayashietal.(2006)calculatedyieldsforstarsofmetallicityZ=0,0.001,0.004,and0.02andmassesintherangeof13-40M.Finalyieldsaretunedtoproduce0.07Mofejectediron.Portinarietal.(1998)calculatedasetofyieldsrangingforstarsfrom6-120MwithmetallicitiesfromZ=0:00040:05undergoingexplosivenucleosynthesis.InPortinarietal.(1998),SNearetriggeredbyelectroncapturesonheavynuclei,photodissociationofironinto-particles,andrapidneutralizationofcollapsingmaterial.OurmodelutilizesacombinationofyieldsfromKobayashietal.(2006)forstellarmasses13-40MPortinarietal.(1998)formasses40-120M,andratesderivedfromRaiterietal.(1996).4.3.3YieldsofSNeIaThermonuclearSNeareimportantcontributorstothechemicalenrichmentoftheISM,primarilywithiron-peaknucleiandsomeintermediate-massnuclei.SNeIaareusuallymodeledasexplosionsofwhitedwarfsthathaveapproachedtheChandrasekharlimit(Mch˘1:39M)throughaccretionfromacompanioninabinarysystem(Nomoto,1982).Progenitormodelsareaseithersingledegenerate,inwhichawhitedwarfgrowsinmassowingtoaccretionfromanevolvingbinarycompanion,ordoubledegenerate,inwhichtwoC-Owhitedwarfsmerge.OurmodelusesyieldsfromIwamotoetal.(1999),whicharebased114ontheprogenitormodelofNomotoetal.(1997),andemploysasingle-degeneratescenario.TheSNIaratesarefromKobayashi&Nomoto(2009),whichagainusesasingle-degeneratescenarioformodelingtheSNIaprogenitor.4.4ResultsThismodeltracksthechemicalevolutionof10elementsinallofthehalosinasimulation:H,C,N,O,Mg,Ca,Ti,Fe,Co,andZn.Comparisonofthesynthesizedstellarmetallicitydistributionstoobservationaldataallowsfortheevaluationofourmodelandallowsustoplaceconstraintsontheparameterswehavechosentoinvestigate.Wecompareourresultstothelimitedsetofelemental-abundanceratios([Mg/Fe],[C/Fe])determinedforthelargesampleoflow-resolutionstellarspectrafromtheSEGUEdatabase(Yannyetal.,2009)andtothemuchsmallersampleofmetal-poorstarswithavailablehigh-resolutionspectroscopicelemental-abundanceratiosassembledbyFrebel(2010).AllelementstrackedinthismodelarerepresentedintheFrebeldataset.Thechemicalevolutionofthestellarpopulationsofallhalosin[C/Fe]-[Fe/H]6spaceisshowninFigure4.2,andin[Mg/Fe]-[Fe/H]spaceinFigure4.3,withobservationaldatafromSEGUE(Yannyetal.,2009)andFrebel(2010)overplottedinredandyellow,respectively.Datafromthesesourceshavebeenbinnedin0:25dexincrementsin[Fe/H],withthestellarnumberweightedmeanplottedasacontinuousline,the68%intervalshownasthicklines,andtheminimumandmaximumextentsshownasthinlines.Theseshowtheabundancedistributionsofthestellarmassproducedbyourmodelatz=6.Thecentralpaneloftheseshowsthemass-weightedabundancedistributionofstellarmaterial6Weadoptthestandardconvention[X/Y]=log10(NX=NY)log10(NX=NY).115asashadedblueregion(withdarkblueindicatingareaswithalargerfractionofthetotalstellarmass,andlightbluerepresentingareaswithaverysmallfractionofthetotalstellarmass),whilethetopandrightpanelsarehistogramsoftheabundancedistributionofstellarmassforasinglequantityofinterest.Itshouldbenotedthatthepeaksofthehistogramsshowingthedistributioninindividualabundancesarenotnecessarilyatthesamevaluesasthepeakinthecentralpanel,asthepeakofthecentralpanelcorrespondstothemostcommonpairofabundances.Forexample,themostcommoncombinationof[Fe/H]and[Mg/Fe]mighthavean[Fe/H]valuethatisnotthesameasthemostcommonvaluewhenthedistributionofstellarmassinonly[Fe/H]isconsidered.4.4.1ComparisontoObservationsQuantitativecomparisonismadetotheobservationaldatabycalculatingtheimplausibilityvalue,I=Pbins(h[X=Y]iobsh[X=Y]isim)2Pbins˙2obs+˙2sim;(4.21)andajointprobabilitymetric,J=XallbinsPi;simPi;obs"noverlapXoverlapPj;sim+XoverlapPj;obsnlone;simXlonePk;sim+nlone;obsXlonePl;obs#1ndists(4.22)wherethesimulatedandobserveddatahavebeenbinnedintosquare,half-dexincrementsin[X/Fe]-[Fe/H]space.InEquation4.21,h[X=Y]iobsandh[X=Y]isimaretheobservedandsimulatedweightedmeansineachbin,and˙obsand˙simaretheassociatedstandarddevi-ationineachbinforeachdataset.InEquation4.22,ndistsisthenumberofdistributions116beingcompared,Pi;simandPi;obsarethesimulatedandobservedprobabilitydensitiesinbini,noverlapisthenumberofbinsinwhichthesimulatedandobservedelemental-abundancedistributionsoverlap,andnlone;simandnlone;obsarethenumberofnon-overlappingbinsinthesimulatedandobserveddistributions,respectively.Thereisatemptationtorandomlydrawanumberofpointsfromoursimulatedelemental-abundancedistributionsequaltothenumberofstarsintheobservationaldatasets,butunfortunatelythiswouldbeaninvalidcomparison.TheunderlyingselectionfunctionsoftheSEGUEandFrebeldatasetsarefun-damentallytfromoneanother,andmoreimportantly,theyarenotwellunderstood.AswecannotdrawasampleofstarsfromthemodelthatwouldrealisticallythosethatwouldbeobservedbyasurveysuchasSEGUE,wechoosetopresenttheentiretyofourmodeledstellarelemental-abundancedistributions.Ratherthandrawingasamplefromourmodeleddata,wewillusetheimplausibilityandjointprobabilitymetricstoevaluatetheobservationaldataaspotentiallyincompletesubsetsofoursimulatedelemental-abundancedistributions.Equations4.21and4.22wereusedtoevaluatethe[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]dis-tributionsfromtheSEGUEdataset,andthe[X/Fe]-[Fe/H]distributionsforallabundancesintheFrebeldataset.Theimplausibilityisametricbywhichtoassesstheagreementofthesimulatedandobservedelemental-abundancedistributionswhileaccountingfortheiras-sociateduncertainties.Thejointprobabilityisamannerbywhichtoquantifythesimilaritybetweenthesimulatedandobserveddistributions.Thismetricwasconstructedtoenablenonparametriccomparisonofthemultidimensionaldistributionswithunknownincomplete-ness,whileaccountingfortheregionsinmetallicityspacethatareonlypopulatedbyasingledistribution.Thetermmultipliestheprobabilitiesofpairwisebetweendistributionsforeachbininmetallicityspace,quantifyingthedegreetowhichtheoverlappingregionsofthe117distributionsareinagreement.Theterminbracketsweightstheamountofoverlapinmetallicityspacebythetotalprobabilitiesintheoverlappingregionofthetwodistributions,whilethesecondterminbracketsreducesthevalueofthemetricbyweightingthenon-overlappingregionsbythetotalprobabilityintheseregions.Thetermnormalizesthejointprobabilityvaluebythenumberofdistributionsbeingcompared.Thenumericalvalueofthismetrichasnointrinsicmeaning,butitprovidesaconvenientmannerofcomparisonbetweendistributions.Twoperfectlymatchingdistributionswillproduceajointprobabilityvalueof1,whileincreasingdisagreementwillproducelowervalues,includingnegativevalues.Thecloserthejointprobabilityto1,thebettertheagreementbetweenthetwodistributions.Theresultsoftheimplausibilityandjointprobabilityvaluesallowfortheevaluationofmodelparametersinseveralways.Oneapproachistoseewhetherthereisaparticularsetofmodelparametersthatbestreproducethemetallicitydistributionofaparticularelementacrossbothoftheavailableobservationaldatasets.Similarly,itcanbeseenwhetherthereisaconsistentsetofparametersthatbestmatchesseveralabundancesfromanindividualobservationaldataset.Takingthesetwomethodsinunisonenablestwoothermethodsofcomparison{theistodeterminewhethercertainparametervaluescanberuledout,andthesecondistodeterminetheparametervaluesthatbestreproducetheobservedmetallicitydistributions.Theparameterspaceofthisworkislargeenoughtoprohibitinvestigatingallpossiblecombinationsofparameters.Tomakethisinvestigationcomputationallyfeasible,agridofmodelswasruntoz=10.Thesemodelswereanalyzedbycomparingthesimulatedelemental-abundancedistributionfunctionstoobservationsfromtheSEGUEandFrebeldatasets.Fromthis,severalregionsofparameterspacewereruledout,andfurtherinvestigationfocusedonmodelswithparametersthatproducedparticularlypromisingresults.Thisinitial118Table4.2:ImplausibilityandJointProbabilityValuesWhenFittingtheObservedIndividual[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]DistributionsFromtheSEGUEDataSetatz=6.CMgIMFEzreionImpJointImpJointSalpeter0.0460.66543-34.8010.47764-92.0746.50.66611-33.8770.49025-90.52070.66306-36.7890.48998-89.35780.66876-34.3370.47427-87.7720.260.58070-20.4590.35518-89.1726.50.59219-20.7110.36893-87.35170.56984-22.4620.37321-85.92480.63827-23.0980.38780-85.309Kroupa0.0460.62102-37.0260.45699-93.5446.50.62239-35.6400.46969-92.33370.63048-37.6980.46897-90.93480.72212-33.2910.45183-86.4560.260.63011-22.9760.35383-89.9276.50.63580-23.0830.37221-88.63270.63253-24.9760.37471-87.46180.63457-24.9970.38655-87.241Chabrier0.0460.54636-25.7970.39780-87.9886.50.54778-25.6680.39778-85.55870.62486-28.0340.39657-83.94880.61776-26.7980.37787-83.5750.260.54602-13.0670.34978-84.2646.50.54788-13.3870.35004-81.82870.54888-14.5680.34961-80.05980.63050-15.0540.34959-81.403119Table4.3:ImplausibilityandJointProbabilityValuesWhenFittingtheObservedIndividual[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]DistributionsFromtheFrebelDataSetatz=6.CMgIMFEzreionImpJointImpJointSalpeter0.0460.40936-30.7860.40781-65.5446.50.41302-30.0890.42094-63.31570.41895-32.7160.37755-65.22180.46519-30.0560.57862-62.6680.260.38601-18.3610.42158-41.2916.50.38247-19.3200.43138-42.20470.38771-21.0430.43797-45.97480.38983-21.5430.44947-46.483Kroupa0.0460.47112-31.3330.48583-66.3376.50.46241-30.6980.48671-65.60970.43870-33.3130.44070-67.08880.41796-28.9870.47829-61.7260.260.35720-22.0720.35616-50.5136.50.34716-22.5960.36389-50.91170.34359-24.4970.36088-54.99280.35588-24.0720.36856-53.810Chabrier0.0460.34632-23.7560.44308-53.4826.50.35343-23.5910.43774-52.72470.43434-25.8240.43712-57.51080.41066-24.7590.45616-55.5420.260.29121-14.8740.33708-30.9456.50.29481-15.7650.34166-31.92770.28832-17.2120.33926-34.80880.40477-17.3240.39578-35.978120gridofsimulationsconstrainedthechemicallyenrichedSFEtotheintermediateandhighvalues,0:04and0:2,andruledoutattenuatedvaluesoftheLWphotonescapefraction,stronglyfavoringanescapefractionof1.Thissubsetofmodelswasfurtherinvestigatedbyadvancingthesimulationstoz=6whileadditionallytestingtheoftheredshiftofreionization.Reionizationwasallowedtocommenceatredshiftsof8,7,6:5,ornotatall(whichiselyaredshiftofreionizationofz6,asthatistheredshiftwherethesimulationterminates).Theimplausibilityandjointprobabilityvaluesofvariousmodelsandthe[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]abundancedistributionsfortheSEGUEdataareshowninTable4.2,andthevaluesfortheFrebeldataareshowninTable4.3.Fittingtheindividual[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]distributionsshowsaverystrongpreferenceforaChabrierIMFandanSFEof0:2.Inallcases,forboththeSEGUEandFrebeldatasets,thispairofparametersminimizestheimplausibilityandmaximizesthejointprobability.Withinthispairofparameters,thearesplitbetweenthosefavoringmodelswitharedshiftofreion-izationof7andthosewithreionizationoccurringatz6.ThevariationinthestatisticalmetricsduetochangingtheredshiftofreionizationwhileholdingtheIMFandSFEismuchsmallerthanthevariationwhenholdingtheredshiftofreionizationandchangingeithertheIMForSFE.Withthesemetricswecannotadvocateaparticularredshiftofreionization,butstrongconstraintscanbeputontheIMFandSFE.VaryingtheSFEwhileholdingtheIMFandredshiftofreionizationconstantshowsthataSFEof0:2isalmostalwayspreferredoverancyof0:04inboththeimplausibilityandjointprobabilitymetrics.IncomparingparametersetsinwhichtheIMFistheonlyparameterthatvaries,thejointprobabilityshowsaslightpreferenceforaSalpeterIMFoveraKroupaIMF,theimplausibilityshowsnosubstantialdistinctionbetweenthetwo,butbothmetricsclearly121Figure4.2:The[C/Fe]-[Fe/H]distributionatz=6asmodeledwithaChabrierIMF,achemicallyenrichedSFEof0:2,anLWphotonescapefractionof1,andaredshiftofreionizationofzreion=7.Theshadedregioninthecenterpanelshowsthedistributionofstellarmassinoursimulationin[C/Fe]-[Fe/H]spacewiththeshadethefractionofstellarmassatthatpairofabundances.Darkblueregionshavethelargestfractionofthestellarmass,whilelightblueregionshavelessstellarmass.SEGUEdataareplottedinred,andtheFrebeldatasetisplottedinyellow.Observationaldataarebinnedin0:25dexincrements,withthebinmeanshownasacontinuousline,the68%denceintervalshownasathickline,andthemaximumandminimumextentofthedatasetshownasthinlines.Thetopandrighthistogramsshowthedistributionsofstellarmassineither[Fe/H](top)or[C/Fe](right).Simulateddataareshowninblue,SEGUEdatainred,anddatafromFrebelinyellow.Thissetofparametersmaximizesthejointprobabilityforthecombinedof[Mg/Fe]and[C/Fe]intheSEGUEdataandminimizestheimplausibilityforthesameabundancesintheFrebeldata.122Figure4.3:The[Mg/Fe]-[Fe/H]distributionatz=6forthesamemodelparametersasshowninFigure4.2,withallcoloringandweightingthesameasinthatThissetofparametersmaximizesthejointprobabilityforthecombinedof[Mg/Fe]and[C/Fe]intheSEGUEdataandminimizestheimplausibilityintheFrebeldata.123favoraChabrierIMFovereitheroftheothers.Evaluatingthesuccessofvariousmodelparameterswithimplausibilityandjointproba-bilityhasseveralcaveatsthatbearconsideration.AscanbeseeninthetoppanelofFigures4.2and4.3,theselectionfunctionsoftheSEGUEandFrebeldatasetsareveryt,withtheFrebeldatasetbeinggenerallycomposedofmoremetal-poorstarsthantheSEGUEdataset.Thediscrepancybetweenthetwoobserved[Fe/H]distributions(which,wenote,ispurelyduetoobservationalselectionandnotanyinherentinconsistencybetweenthedatasets)makesadirectandsimultaneouscomparisontobothdatasetsaprospect.Additionally,notallmodelparametersetsproducestellarpopulationsthatextendoverthesamerangesin[X/Fe]-[Fe/H]space.Somemodelswillhavefewerbinswithwhichtocomparetoobservations.Wearerestrictedinourimplausibilityanalysistousingonlybinsthathavenonzerostandarddeviationsforbothmodelandobservationaldata,andwemitigatethisbynormalizingtheimplausibilityvaluesbythenumberofbinsforthatparameterset.4.4.2FittingSeveralAbundancesSimultaneouslyTheFrebeldatasetcontainsabundancesforsixelementsthataretrackedinourmodelbutthatarenotpresentintheSEGUEdata:N,O,Ca,Ti,Co,andZn.Thissetofabundancesallhaveanelemental-abundancedistributionwithfeaturesthatarequalitativelytfromtheobserveddistributions.Thesimulatedelemental-abundancedistributionshavearegionat[Fe/H]<2:5thatextendstoverylow[X/Fe],farbelowwhatisobserved.Anexamplecanbeseeninthe[Zn/Fe]-[Fe/H]distributioninFigure4.4.ThisfeatureinthedistributionoriginatesfromtheinitialenrichmentofahalobyaPopulationIIIstarwheretheyieldsdrasticallyoverproduceFeinrelationtotheotherelements.Theestablishesthe124abundancesinthishaloatthestartofchemicallyenrichedstarformationatlevelsfarlessthanisobserved.Figure4.4:[Zn/Fe]-[Fe/H]distributionatz=6asproducedbyamodelusingaChabrierIMF,achemicallyenrichedSFEof0:2,andaredshiftofreionizationof7.ObservationaldatafromFrebelareshowninyellow,binnedin0:25dexincrements.Themeanineachbinisplottedalongwiththe68%intervals(thickverticallines)andmaximumandminimumextentofobservedabundancedataineachbin.ThismodelproducesthelowestimplausibilityvaluewhenallFrebelabundancessimultaneously.TheparametersetshowninFigure4.4isaChabrierIMFwithahighchemicallyenrichedSFEof0:2,anLWphotonescapefractionof1,andaredshiftofreionizationof7.Thetracksrisingfrom[Zn/Fe]<0:25and[Fe/H]<2:8totheprimarylocusin[Zn/Fe]-[Fe/H]spacearenotseenintheobservationaldata(thoughwenotethatthisformsanegligiblefractionofthetotalstellarmass{seethehistogramontherightsideoftheThesetracks125originatefromthematerialreturnedbyPopulationIIIstars.Thisenrichmentsetstheinitialabundancespresentinthehaloatthestartofchemicallyenrichedstarformation.Subsequentgenerationsofstarformationandfeedbackforcetheabundancesinthehalotoconvergetowardthevaluessetbytheyieldsofenrichedstellarpopulations,butthestarscreatedintheearlyphasesofchemicallyenrichedstarformationleaveanimprintonthepopulationthatisnotobserved.Thispatternisseenin[N/Fe],[O/Fe],[Ca/Fe],[Ti/Fe],[Co/Fe],and[Zn/Fe].Inallcases,theinitialenrichmentofthehalofromPopulationIIIstarsleadstotheformationofstarswithabundancesthatarenotobserved,buttheabundancesinthesehalosrapidlyconvergetovaluesthatareinbetteragreementwithobservations.Multipleabundanceswithineachobservationaldatasetcanbesimultaneouslytode-terminethesetofparametersthatbestreproducesawiderangeoftheobservationaldata.Theimplausibilityandjointprobabilityvaluesforvariousparametersetsresultingfromthesimultaneousoftheobserved[C/Fe]and[Mg/Fe]distributionsfromSEGUE,the[C/Fe]and[Mg/Fe]distributionsfromFrebel,andallabundancesfromFrebelareshowninTable4.4.ThesecombinationsarebestwithaChabrierIMFandanelevatedchem-icallyenrichedSFEof0:2,inagreementwiththeparametersthatprovidethebesttotheobservedindividual[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]abundancedistributions.Theim-plausibilityandjointprobabilitymetricsshowadistinctpreferenceforachemicallyenrichedSFEof0:2,withthisvaluebeingfavoredregardlessofIMF.Conversely,varyingtheIMFwhileholdingtheSFEclearlyfavorsaChabrierIMFandsuggestsaslightpreferenceforaSalpeterIMFoveraKroupaIMF.Similartotheofindividualabundances,param-etersetswitheitheraredshiftofreionizationof7orlatereionizationatz6comparethemostfavorablywiththeobservedabundancedistributions.Ifreionizationpriortoz=6istakentobemandatory,everyinwhichlatereionizationwasfavoredissupplantedbya126Table4.4:ImplausibilityandJointProbabilityValuesWhenSimultaneouslyFittingMultipleElemental-AbundanceDistributionsatz=6.SEGUECandMgFrebelCandMgFrebelallIMFEzreionImpJointImpJointImpJointSalpeter0.0460.63812-126.870.40861-96.3300.45705-83.2986.50.64081-124.400.41683-93.4040.46248-83.21570.63805-126.150.39871-97.9370.45171-88.46980.64041-122.110.51994-92.7240.48180-84.7890.260.54419-109.630.40252-59.6520.47584-54.3596.50.55675-108.060.40511-61.5240.48119-56.49970.53884-108.390.41098-67.0180.47837-60.88380.59824-108.410.41745-68.0250.46229-61.408Kroupa0.0460.59569-130.570.47837-97.6700.47518-88.3196.50.59902-127.970.47438-96.3070.47820-87.95970.60580-128.630.43969-100.400.44923-92.04580.68063-119.750.44751-90.7140.44359-87.5940.260.58491-112.900.35671-72.5850.44919-62.9756.50.59372-111.720.35505-73.5070.45297-65.24070.59168-112.440.35177-79.4890.44888-69.68980.59483-112.240.36189-77.8820.43028-69.560Chabrier0.0460.52509-113.790.39312-77.2380.46890-68.9096.50.52641-111.230.39428-76.3150.46747-70.37470.59185-111.980.43570-83.3330.47859-76.04280.58419-110.370.43262-80.3010.45190-73.0870.260.51766-97.3320.31258-45.8190.44074-40.2866.50.51934-95.2150.31664-47.6920.43810-42.90970.52004-94.6270.31205-52.0200.43457-46.34580.58762-96.4570.40051-53.3020.47000-47.250Thelowestimplausibilityandleastnegativejointprobabilityvaluesatz=6areshowninbold.Thesimulatedelemental-abundancedistributionsarecomparedtothecombined[C/Fe]-[Fe/H]and[Mg/Fe]-[Fe/H]distributionsforboththeSEGUEandFrebeldatasets,aswellastothecombineddistributionsofallelementspresentinboththesimulationandtheFrebeldatasets.127onefavoringaredshiftofreionizationof6:5.Extendingthemodeltoredshiftsbelowtheredshiftofreionizationhasonlyasmallontheobservedelemental-abundancedistributionfunction.Thiscanbeseenintheverysmallvariationsintheimplausibilityandjointprobabilityvaluesastheredshiftofreionizationisvaried.Reionizationquenchesstarformationinallbutthelargesthalos,attenuatingtheformationofnewstarsandslowingglobalchemicalenrichment.ThisisdemonstratedintheSFRdensitiesatz=6,wherethemodelsthatincludereionizationpriortotheendofthesimulationhaveSFRdensitiesthatareapproximatelyhalfthatofmodelswithoutreionization.4.5Discussion4.5.1TheModelThismodelsintwaysfromotherchemical-evolutionmodels.Everycosmo-logicalhaloistrackedindependentlyandevolvesasanensembleofSSPs.ThefeedbackfromtheseSSPsisafunctionoftheageofeachpopulation,aswellasitsmetallicity,andtakesseveralforms.PhotodissociatingLWradiationisproducedbythestellarcomponentofeachhalo.StarsandSNereturnenrichedmaterialandaquantityofgasavailableforstarformationtotheISMofthehalo.SNeprovidemechanicalfeedbackthattransportsgasandenrichedmaterialbetweenthecentral,star-formingregionofthehaloandthehot,reservoirintheouterregions,aswellasallowingformaterialtobeejectedfromthehaloentirelyandlosttotheIGM.chemicallyenrichedstarformationisafunctionofthemassofcold,densegasavailableinthehalo,andthereturnedenrichedmaterialdeterminesthemetallicityofthenewstarsthatformoutofthegas.128Manyoftheprocessesinthismodelarecoupled,resultinginfeedbackloopsthatactbothonthehalolocallyandontheglobalhalopopulation.ThestellarcomponentofallhaloscontributestothephotodissociatingLWbackground,whichdetermineswhichhalosarecapableofformingaPopulationIIIstaratanygiventime.ThisiscoupledtothelocalstateofthechemicallypristinehalosthroughtheabilityofH2toself-shieldinthepresenceofLWradiation,andthepristinehalocoolingandcollapsecriteriaarefunctionsofthemassofthehaloandthecurrentredshift.Withineachhalo,themetallicityanddensityofthegasinthereservoirregiondeterminethecoolingtimeand,alongwithitsmassofgas,setstherateatwhichgasisexchangedwiththecentralstar-formingregion.Themassofgasinthecentralregiondeterminestherateatwhichnewstarsareformed.Themetallicityofnewstarsisdeterminedbythechemicalcompositionofthegasfromwhichtheywereformed.TheageandmetallicityofastellarpopulationdeterminethemassofgasandenrichedmaterialthatwillbereturnedtotheISMofthecentralregionofthehaloaswellasthenumberofSNethatoccurduringthattimestep.Thesequantitiesdeterminethemovementofgasandenrichedmaterialwithinthehalo,aswellastheamountofgasandmetalsthatareejectedfromthehalototheIGM.Themultitudeofcoupledfeedbackmechanismsmakethismodelsubstantiallymorephysicallyrepresentativeoftheprocessesoccurringingalacticchemicalevolutionthansimpler,one-zonemodelsthattreathalosinisolation,orthestellarcomponentofahaloassingleSSP.ThismodelcanbeappliedtoanyN-bodysimulationforwhichahalomergertreecanbeconstructed.Executingthismodelismuchlesscomputationallyexpensivethatrunningtheoriginalsimulationwiththemultiphysicscapabilitiesthatwouldberequiredtodosimilaranalysisofthechemicalevolution.Thismodelbfromtheabilitytopost-processasimulation{itdoesnotneedtobeimplementedatsimulationruntime,greatlyenhancing129itsyinregardtothecomputationalfacilitiesthatcanbeusedtoprobechemicalevolution.Runningthismodeliscomputationallyinexpensive(takingafewhoursonamoderndesktopcomputer),enablingtheinvestigationofawideregionofparameterspacewhileusingminimalresources.Themodularnatureofthecodemakesitsimpletoincludetsetsofstellaryieldsandupdatethemasnewyieldsbecomeavailable.Furthermore,thetreatmentofthestellarcomponentofeachhaloasanensembleofSSPsallowsfortheIMFtobevariedindependentlyoftheyields,andonecanintroducenewvariationssuchastime-ormetallicity-dependentIMFs.Theabilitytomakestatisticallytquantitativecomparisonsbetweentheresultsofthismodelandobservationaldatafurtherbolstersitscapabilities,extendingitsreachbeyondwhathasbeenachievedinotherchemicalevolutionstudies.Othergroupshaveimplementedcertainsimilarfeaturesintheirmodels.Grazianietal.(2015)coupledasemianalyticmodelofgalacticchemicalevolutiontoaradiationtransfercode,enablingtheself-consistentcalculationofionizationradiationfromstellarsourcesinthesimulationanditsinteractionwiththegasinstar-formingregions.Theionizationstateandtemperatureofaparcelofgascanthenbeusedascriteriaforlocalstarformation,creatinganSSPthatevolvesviatheinstantaneousrecyclingapproximation(Tinsley,1980).DeLuciaetal.(2014)relaxtheinstantaneousrecyclingapproximationbytreatingthestellarcomponentoftheirsimulationasacollectionofSSPstoallowforfeedbackfromstarstooccuroverarangeoftimesfollowingstarformation,aswellastoinvestigatetheimpactoftheSNIadelaytimedistributiononthechemicalevolutionofaMilky-Way-likegalaxy.Ourmodelgoesbeyondtheirscheme,trackingmanymoreelementsandcalculatingtime-dependentyieldsforeachSSPinthesimulation,returningtamountsofmaterialattstagesintheevolutionofthestellarpopulation.DeLuciaetal.(2014),onthe130otherhand,returnauniform,time-averagedfractionofthetotalejectaoftheSSPoverthecourseofitslife.4.5.2ComparisontoObservationsComparisontoobservationaldataisstraightforwardwiththismodel.Datasetsincludingsubstantialnumbersoflow-metallicitystars,suchastheSEGUEspectroscopicdataset(Yannyetal.,2009)andthecollectionofstarswithhigh-resolutionspectroscopycompiledbyFrebel,providecollectionsofstellarabundancesintherangesofinteresttothiswork.Thiscomparisondoescomewithatcaveat:thismodelstopsatz=6,andtheavailableobservationaldatasetsareallforlow-redshiftstarsindwarfgalaxiesandthegalacticstellarhalo.ThelowmetallicitiesofthesepopulationsmakethemprimecandidatesforuseinGalacticArcheologyandsuggestthattheircomparisontothehigh-redshiftchemicalevolutionisvalid.Bolsteringthiscomparisonistheobservationthatapproximatelyhalfofallgalaxiescurrentlyresideingroups,andtheMilkyWayfallsintothiscategoryasamemberoftheLocalGroup.Athighredshift,theprogenitorsoftheLocalGrouparestatisticallyaveragestructures,reasonablycomparabletothestructuresinthismodel.Inaddition,previoustheoreticalworksuggeststhatstarsatmetallicitiesbelow[Fe/H]'1:5almostexclusivelycomefromz>6(Tumlinson,2010).WenotethattheestimatedSFRdensityprovidesanadditionalmethodforcomparingthemodelpredictionstoobservations,andthatthismethodiscomplementarytocomparisonsofz=0stellarabundances.High-redshiftobservations(e.g.,Bouwensetal.2011,Oeschetal.2014)areprovidingconstraintsontheSFRdensityatz10.UsingobservationsoftheSFRdensityathighredshiftprovidesanindependentman-nerofevaluatingtheabilityofagivensetofmodelparameterstoreproduceobserva-131tions.Oeschetal.(2014)reportanSFRdensityof1:58102Myr1Mpc3atz˘6.ThesetofparametersfavoredbyabundanceaChabrierIMF,achemicallyen-richedSFEof0:2,andaredshiftofreionizationof7,hasanSFRdensityatz=6of1:23101Myr1Mpc3,higherthantheobservedSFRdensity.AlowerchemicallyenrichedSFEof0:04providesbetteragreementwithobservations.Forexample,aChabrierIMF,witharedshiftofreionizationof6:5,andthislowerproducesaSFRdensityatz=6of2:55102Myr1Mpc3.ThetensionbetweenourSFRdensitiesandthevaluereportedbyOeschetal.(2014)couldariseasaresultofinthemannersinwhichtheSFRdensityisestimated{thisdiscrepancycouldariseifOeschetal.(2014)areintegratingdowntoaluminositylimitmuchbelowours,orfurtherdowntheluminosityfunctionbutusingashallowerslope.ComparisonofoursimulatedabundancedistributionswiththeSEGUEandFrebeldatafavorsaChabrierIMFandachemicallyenrichedSFEof0:2,butdoesnotprovidestrongconstraintsontheredshiftofreionization.Themostcommonlyfavoredreionizationpa-rameterswereeitheraredshiftofreionizationof7orlatereionizationoccurringatz6.RecentworkbyRobertsonetal.(2015)showsthathigh-redshiftstarformationisttoproduceenoughionizingphotonstodominatethereionizationoftheuniverse.Theinabil-ityofourmodeltomakeastrongpredictiononafavoredredshiftofreionizationsuggeststhatourmodelisnotparticularlysensitivetothisparameter.Inspectionofthestatisticalmetricssupportsthisinterpretation.VariationsintheimplausibilityandjointprobabilityduetotvaluesoftheredshiftofreionizationaremuchsmallerthanvariationsduetochangesintheIMForchemicallyenrichedSFE.Thepreferenceforparametersetswitharedshiftofreionizationofz6forseveralobservationalabundancecombinationsandstatisticalmetricssuggeststhatourmodelmaybelackingsomephysicalprocessesthatare132necessarytoaccuratelycapturethisFigure4.5:[Ca/Fe]-[Fe/H]distributionatz=6asproducedbyamodelusingaChabrierIMF,ahighchemicallyenrichedSFEof0:2,andaredshiftofreionizationof7.Themajorityofobservedstarsmatchthesimulatedmetallicitydistributionfunction,butthequalitativebehavioratlowvaluesof[Fe/H]strongly.EnrichmentfromPopulationIIIstarsdrasticallyunderproducesCainrelationtoFe,establishinginitialabundancesforchemicallyenrichedstarformationfarbelowthosethatareobserved.Reproducingtheobservedfractionofcarbon-enhancedstarsasafunctionof[Fe/H],aswellasthe[C/Fe]-[Fe/H]abundancedistribution,isasubstantialproblemforourmodel.Inparticular,ourmodelpredictsthatthemajorityofstarswillbecarbonenhancedhereasstarswith[Ce/Fe]>0:7),inwithobservations.Thequalitativetrendofadecreasingcarbon-enhancedfractionwithincreasing[Fe/H]isseen,butourmodelpredictsacarbon-enhancedfractionthatismuchtoolarge.Thereareseveralpossibleexplanations133forthisbehavior.deBennassutietal.(2014)evaluatedseveralphysicalconditionsthatcouldmediatethetransitionbetweenPopulationIIIandchemicallyenrichedmodesofstarformationandfoundthatatlyhighratioofdusttogasinthegalacticmediumproducedthebestagreementwiththeobservedMilkyWaymetallicitydistributionfunction.Acriticaldust-to-gasratiowasdistinguishedfromtheothertransitioncriteriainvestigatedinthatworkbybeingtheonlycriterionthatreproducedboththecarbon-enhancedandcarbon-normalmetal-poorstellardistributionsobservedintheMilkyWayanditssatellites.Ourmodeldoesnotincludedust,insteadtransitioningfromPopulationIIItochemicallyenrichedstarformationbasedonthemetallicitycontentofthehalo:anyhalowithametal-licitybeyondtheprimordialcompositionformschemicallyenrichedstars.Theomissionofdustfromourmodellikelysuppressestheformationofcarbon-normalmetal-poorstars,contributingtothediscrepancybetweenobservationsandoursimulatedcarbon-enhancedmetal-poor(CEMP)stellarabundancedistributionsat[Fe/H]>4.Athigher[Fe/H],otherphysicalprocessesabsentinourmodelgiverisetodisagreementwithobservations,asothercosmologicalmodelswithoutdusthavereproducedtheobserveddistributions(e.g.,Cooke&Madau,2014;Salvadorietal.,2015).4.5.3PopulationIIIStellarYieldsYieldsfromPopulationIIIstarsdeterminetheinitialabundancesinahaloatthestartofchemicallyenrichedstarformation.ThecurrentpaucityofavailablePopulationIIIstellaryieldscreatesadiscretesetofabundancesthatahaloisenrichedtobyaPopulationIIIstar.Thesevaluesgiverisetothetracksseenin[X/Fe]-[Fe/H]spacethatconvergetothevaluessetbytheyieldsfromchemicallyenrichedstars.Inthecasesof[N/Fe],[O/Fe],[Ca/Fe],[Ti/Fe],[Co/Fe],and[Zn/Fe],certainPopulationIIIyieldssettheinitialabundancesof134thehaloatlevelsfarbelowthosethatareobserved.Thismanifestsasasetoftracksrisingin[X/Fe]-[Fe/H]spacetowardtheabundancevaluesthatthechemicallyenrichedyieldsconvergeto,asshowninFigure4.4forthe[Zn/Fe]-[Fe/H]distribution.Subsequentgenerationsofchemicallyenrichedstarformationproducedistincttracksinmetallicityspaceastheabundancesinthehaloconvergetowardthechemicallyenrichedyields,butthesetracksarenotobservedintheGalacticstellarhalo,indicatingthatthesePopulationIIIyieldsarelikelynotaccurate(or,attheveryleast,additionalstellaryieldsmaybenecessarytoproducemorerealisticchemicalevolutionoutcomes).Wenote,however,thatthemassfractionofstarsinoursimulationsthatarecontainedwithinthesetracksisextremelysmall,andthusitisentirelypossiblethatwesimplyhavenotobservedsuchstarsyet.AnotherexampleofthisbehaviorcanbeseeninFigure4.5,whichshowsthe[Ca/Fe]-[Fe/H]distributionatz=6.Whileourbestsetofparametersproducesagoodagreementwiththeobserved[Ca/Fe]distributionfortheoverwhelmingmajorityofthestellarmass,theregionwith[Fe/H]<2:7and[Ca/Fe]<0:2isincleardisagreement.Nostarsareobservedwiththesecombinationsof[Ca/Fe]and[Fe/H],butthePopulationIIIstellaryieldsaresuchthatasubstantialfractionofchemicallyenrichedstarformationbeginsattheseabundances.ThecleardisagreementbetweentheobservedandsimulatedyieldsstronglysuggeststhatthesimulatedPopulationIIIstellaryieldsdonotrealityinsomeimportantway.TheinterplayofPopulationIIIstars(particularlywithregardtotheSNethatareas-sumedtobetheirfates)andthehalosthathosttheseobjectsiscruciallyimportantinestablishingthecompositionofthematerialthatwilleventuallyformchemicallyenrichedstars.Cooke&Madau(2014)proposethatthecombinationofPopulationIIISNexplo-sionstrengthandthemassofthehosthaloiscienttoaccountfortherangeofCEMPfractionsasafunctionof[Fe/H].TheauthorsarguethataweakSNwillexpelthelighter135elements,includingcarbon,fromtheSNprogenitorintothemediumofthehosthalo,butthattheheavyelementssuchasiron,whichareonlyweaklymixedandresideprimarilyinthestellarcore,willnotbeexpelled,insteadremaininglockedinthecompactremnant,resultinginejectawithlow[Fe/H]andhigh[C/Fe],andimprintingthiscompositiononthegenerationofchemicallyenrichedstarstoforminthishalo.IftheSNearepowerfulenoughtoejectironfromtheprogenitorcoreandthehaloisnotmassiveenoughtoretaintheejecta,itwillbeevacuatedcompletelyandneverformsubsequentgenerationsofstars.Ifthehaloismassiveenoughtocontaintheejectaofapowerful,iron-expellingSN,therelativeamountsofejectedcarbonandironwillenrichthegasinthehalosuchthatthefollowinggenerationofstarswillbemetal-poorbutcarbon-normal.deBennassutietal.(2014)atscheme,inwhichtheyplacerestrictionsonthePopulationIIIIMFbyarguingthattheironcontributionfrompairinstabilitySNewouldbetoogreattoproduceverymetal-poorstars,placinganupperlimitonPopulationIIIstellarmassat140M.Addi-tionally,theyareonlyabletoreproducetheobservedMilkyWaymetallicitydistributionfunctionbystipulatingthatPopulationIIIstarswithmassesm<140MendtheirlivesasfaintSNe,andthattheejectafromthosewithmassesm>40Mallfallbackontothecompactremnantanddonotenrichtheirsurroundings.ThisleavesonlyPopulationIIIstarswithmassesm40Mavailabletoenrichthegalacticmedium.WeplacenoneoftheserestrictionsontheyieldsfromPopulationIIIstarsinourmodel,andwhilewedoallowforthepossibilityofPopulationIIISNeevacuatingtheirhosthaloscompletely,theexplosionstrengthoftheSNeisnotaparameterinourmodel.ThesetofPopulationIIIyieldsweutilizeisbothsmallanddiscreteandspansalargerangeofstellarmasses.Thisincompletemasscoverage,pairedwithlimitedassumptionsontheexplosionenergiesofPopulationIIISNe,likelynegativelyimpactsourresults.Thisdiscrepancyismostvisibleinthe[C/Fe]-136[Fe/H]elemental-abundancedistribution,butadvisescautionwithourotherresultsaswell:issuesthatcauseyinreproducingtheobservedtrendsof[C/Fe]couldimpactotherlightelementsaswell.4.5.4PossibleConstraintsfromHydrodynamicalSimulationsThisworkhighlightsseveralareaswheremodelparameterscanbeconstrainedwithresultsfromhigh-resolutionhydrodynamicalsimulations.Suchsimulationscanhelptoelucidatethegasdistributionindarkmatterhalos{forexample,thefractionofgasthatiscoldanddense,andtheradiusinwhichthisdensegasiscontainedareaspectsofthismodelthatcanbewiththehelpofhydrodynamicsimulations.SimulationsofSNfeedbackinsimulatedhigh-redshiftgalaxies(e.g.,Wiseetal.,2012b)canalsoguidethetofthemodelsofmetalandgastransportinthehalos,ascansimulationsinvestigatingthenatureofaccretionandhalomergers.High-resolutionsimulationsusingmoresophisticatedstarformationalgorithmscanaidintheconstraintofthechemicallyenrichedSFE,oneoftheprimaryfreeparametersinthemodelofchemicallyenrichedstarformationusedinthiswork.Furthermore,inourmodelsweimplicitlyignoreanyinteractionsbetweenhalosotherthantheH2-photodissociatingLWbackgroundandhalomergers,whichincludessuchashalocross-pollutionandionizingregionsaroundgalaxies.Whileanalyticestimatessuggestthatitisreasonabletoignorethesephysics-richcosmologicalsimulationscantestthevalidityoftheseassumptions.1374.5.5LimitationsandFutureWorkAcompletediscussionofthelimitationsofthestarformationmodelispresentedinPaperI,butabriefrecapofseveralsalientpointsisgivenhere.Ionizingradiationistreatedasauniformmetagalacticbackgroundratherthanbeingmodeledasalocalinteractionbetweenhalos.Localinteractionsmaybeparticularlyimportantforquenchingstarformationinsmallhalos,thoughaswasshowninPaperI,thesehaloshostverylittlestarformationandcontributeanegligibleamounttothetotalSFRandchemicalenrichment.Additionally,materialthatisejectedfromahalodoesnotinteractwithanysurroundinghalos.Thismaterialcouldconceivablybeaccretedbyanearbyhalo,butthisisveryunlikely,aschemi-callyenrichedmaterialejectedbyaSNwillonlyextendtoaradiusof˘1kpcin105107yr(Brommetal.,2003;Whalenetal.,2008)andwillhaveanegligibleonnearbysatelliteminihalos(Whalenetal.,2010).TheroleofionizingradiationandSNejectawillbeinvestigatedinfuturework,butcanbeneglectedhereastheimpactwouldnotbeglobalandwouldhaveaminimalontheoverallabundanceratiodistributions.Oursimulationsstopatz=6,whichpresentsapotentialcaveatforcomparisonwithobservationaldatagatheredatz=0.Thisisreasonable,as[Fe/H]<1:5starsalmostallformatz>6(Tumlinson,2010),enablingustocompareoursimulationstothelow-metallicitystellarhalo.Whilethisenablescomparisonbetweenobservationsandourwork,itisimperfect.Inlookingattherelationshipbetweenstellarageandmetallicityatz=0,Komiyaetal.(2010)andSalvadorietal.(2010)thatasubstantialfractionofstarswith[Fe/H]>1:5haveagesoflessthan12:5Gyr,makingtheirformationredshiftlowerthantheredshiftatwhichoursimulationsend.Wecanmoretlycomparetheresultsofourmodelatz=6toobservationsatz=0byrestrictingouranalysistostarswith138[Fe/H]<2:5,thevastmajorityofwhichwouldhaveformedduringtheredshiftssimulatedinourwork(Fontetal.,2006;Salvadorietal.,2007;Tumlinson,2010).Largersimulationvolumescapableofrunningtoz=0andtheadditionofmorecomplete,self-consistentstellaryielddatawillhelpaddresstheseissues.Futureworkwillextendourmodelstoz=0usinghigh-resolutioncosmologicalN-bodysimulations.Extendingoursimulationstoz=0willenablecomparisonswithmoreandlargerobservationaldatasets,boththosethatarecurrentlyavailable(e.g.,SEGUE)andthosethatwillbecomeavailableinthenearfuturesuchasLAMOST(Ivezicetal.,2012),APOGEE(AllendePrietoetal.,2008),Gaia-ESO(Gilmoreetal.,2012),GALAH(Zuckeretal.,2012),andRAVE(Steinmetz,2003).Wehaveincompletecoverageofstellarmassesandmetallicitiesintheavailableyields,andwhatcoveragewedohaveisnotself-consistent.tmodels(i.e.,simulationcodes)withtfundamentalassumptionsgointoseparatelyproducingAGB,SNII,andSNIayieldssinceweemployabundancesfromtauthorswhohavetcodes,andwhooftenonlydonear-solarandprimordialcompositions.Thelackofreliablelow-metallicityyields(belowapproximately0.1Z)isunderstandable{stellarevolutionmodelsarecali-bratedusinglocalstarsthataretypicallyclosetoSolarmetallicity{butpresentschallengestothosewhowishtoself-consistentlymodelgalacticchemicalevolution.Weareworkingwithcollaboratorsthatareexpertsinstellarevolution,andareintheprocessofgeneratingaself-consistentgridofyieldsusingtheMESAcode(Paxtonetal.,2011,2013)thatwillspanthenecessaryrangeofmassesandmetallicities,andwhichwillbeusedinfuturework.AdditionalPopulationIIISNmodelswillbeaddedtoenablefurtherinvestigationofvaryingthePopulationIIIIMFandthestrengthoftheSNexplosions.Finally,futureworkwillincludebettermethodsofcomparingdatatoobservationsandofanalyzingtherelationshipbetweenmodelinputsandobservations.Wearecurrentlyusing139simplemetrics,suchasjointprobabilityandagenericmeasureofimplausibility,andsmallgridsofmodels.However,moresophisticatedtechniques,suchasGaussianMultiprocessemulationcoupledwithMarkovChainMonteCarlotoolsandANOVAdecompositionofourmodels,havebeendevelopedbyourgroupforotherpurposesomezetal.,2012,2014)andwillsoonbeappliedtochemicalevolution.4.6SummaryandConclusionsThisworkpresentsanewsemianalyticalmodelofchemicalevolutionthatcanbeappliedtocosmologicalN-bodysimulationsoflargepopulationsofhigh-redshiftgalaxiesandwhichcanbecompareddirectlytoabundancemeasurementsoftheMilkyWaystellarhalo.OurmodelassumesthatstarformationoccurringoverashortperiodoftimeresultsinSSPshavinguniformmetallicityandidenticalstarformationtime,anditusespubliclyavailableabundancetablesfromsimulationsofAGBandSNIaandIItocalculatethefeedbackofmetal-enrichedgasandenergyintothehalo'sISM.AsinglehalocanbecomposedofmanyoftheseSSPswitharangeofages,anditsoveralloutputatanypointintimeisthesumoftheSSPoutputsatthattime.Weconsiderarangeofmodelinputs,includingahalo'schemicallyenrichedSFE,theescapefractionofH2-photodissociatingLWphotons,thechoiceofIMFfunction,andthechoiceofnucleosyntheticabundancesthatareputintotheSSPs.Wecompareourmodeloutputstotwoobservationaldatasets:theSEGUEstellarsample(Yannyetal.,2009)andalsoasampleofseveralhundredmetal-poorstarswithdetailedabundancescompiledbyFrebel(2010).Ourprimaryresultsareasfollows:1.ThemodelparametersthatbestreproducetheobservedabundanceratiodistributionsareaChabrierIMF,achemicallyenrichedSFEof0:2(similartoagalacticgasdepletion140timeofapproximatelyhalfagigayear(Bigieletal.,2011))andaLWphotonescapefractionof1.2.TheredshiftofreionizationismuchmoreweaklyconstrainedthantheIMFandchem-icallyenrichedSFE.Thisislikelybecausebyaredshiftof8{theearliestthatweallowfortheonsetofreionization{themajorityofstarformationisoccurringinhalosthatarelargeenoughtonotbestronglybyreionization.3.OtherfeaturesinthesimulatedabundanceratiodistributionssuggestinaccuraciesinthePopulationIIIstellaryields.AbundancesinhalosatthestartofchemicallyenrichedstarformationaresetbytheyieldsofPopulationIIIstarsand,inthecasesofN,O,Ca,Ti,Co,andZn,aredrasticallylessthantheobservedabundances,indicatingthattheseelementsarebeingunderproducedinrelationtoFeintheyieldcalculations.Morebroadly,wehaveintroducedanewmodelforthechemicalevolutionofgalaxypop-ulationsthatcanbecoupledtolargeN-bodysimulationsandthushasthecapabilitytoself-consistentlyprovidebothspatialandtemporalinformationaboutstarformation,chem-icalevolution,andotherquantitiesrelatingtoMilkyWayprogenitors.Thismodelcanbebothqualitativelyandquantitativelycomparedtotheobservedabundancedistributionsinlargestellarsurveys,andwehavedesignedourmodeloutputssothatitwillbestraightfor-wardtocouplethemodeltosophisticatedstatisticaltools(e.g.,omezetal.,2012,2013).Thesetoolswillenabledetailed,quantitativecomparisonofmodelstobothcurrentandfu-tureobservationsofMilkyWaystellarpopulationsandareparticularlyusefulwhendealingwithmultiplelargedatasets(suchascombinationsofmanytobservables).1414.7AcknowledgmentsB.D.C.andB.W.O.weresupportedbytheNationalScienceFoundationunderGrantNo.PHY-1430152(JINACenterfortheEvolutionoftheElements).B.W.O.wassupportedbytheNationalAeronauticsandSpaceAdministrationthroughgrantNNX12AC98GandHubbleTheoryGrantHST-AR-13261.01-A.HewasalsosupportedinpartbythesabbaticalvisitorprogramattheMichiganInstituteforResearchinAstrophysics(MIRA)attheUni-versityofMichiganinAnnArbor,andhegratefullyacknowledgestheirhospitality.T.C.B.acknowledgespartialsupportforthisworkfromgrantsPHY08-22648,PhysicsFrontierCen-ter/JointInstituteorNuclearAstrophysics(JINA),andPHY14-30152,PhysicsFrontierCenter/JINACenterfortheEvolutionoftheElements(JINA-CEE),awardedbytheU.S.NationalScienceFoundation.ThesimulationspresentedherewereperformedandanalyzedontheNICSKrakenandNautilussupercomputingresourcesunderXSEDEallocationsTG-AST090040,andthesemianalyticalmodelswereperformedusingMSU'sHighPerformanceComputingCenter.WethankBrittonSmithandFacundoGomezforhelpfuldiscussionsduringthecourseofpreparingthismanuscript,CarolynPerutaforsharingcodeandforusefuldiscussions,andananonymousrefereeforcommentsthatsubstantiallyimprovedthequalityofthemanuscript.Enzoandytaredevelopedbyalargenumberofindependentresearchersfromnumerousinstitutionsaroundtheworld.Theircommitmenttoopensciencehashelpedmakethisworkpossible.142Chapter5TowardsRealisticSimulationsofGalaxyClusters:GalaxyParticles5.1MotivationsCreatingrealisticgalaxyclustersincosmologicalsimulationsisalong-standingchallengeincomputationalastrophysics.Asthemostmassivevirializedobjectsintheuniverse,capturingtheirformationfromcosmologicalinitialconditionsrequiressimulatingcosmologicalvolumesofhundredsofMpconaside.Atthesametime,theprocessesdrivingstarformationintheclustergalaxiesareoccurringonscalesofhundredsofparsecsorless.Resolvingtheseprocessesatthemostrudimentarylevelswouldrequiresimulationsspanningupwardsofsixordersofmagnitude,exceedingthecomputationalcapabilitiesofeventhelargestsupercomputingfacilities.Thephysicalprocessesofstarformation,supernova(SN)feedback,andactivegalacticnuclei(AGN)triggeringandfeedbackoccuronscalesmuchsmallerthenthesizeofindividualresolutionelements.Recentsimulationshavemadeprogressinreproducingcertainbulkquantitiesofgalaxyclusters.Theintraclustermedium(ICM)temperature,density,andentropyofsim-ulatedclustershavebeenfoundtobeingoodagreementwithobservations,particularlybe-yondtheclustercore.Advancesinthemodelingofnon-thermalprocessessuchasmagneticintheICMhasproducedsimulatedclustersthatmatchotherlarge-scaleproperties143andobservationalsignaturesofgalaxyclusters(Borgani&Kravtsov,2011).Observationsshowthatroughlyhalfofclustersare\cool-core"clusters,withcentralgastemperaturesthatareaboutathirdofthevirialtemperature(Ikebeetal.,1997;Lewisetal.,2002;Petersonetal.,2003),demonstratingtheimpactofnon-gravitationalphysicsongalaxyclusterevolution.Theexistenceofcoolcoresinasubsetofgalaxyclusterssuggeststhatanapproximatethermalbalanceisbeingmaintainedbyacombinationofphysicalprocessesthatheatandcoolthegasnearlyequally(Voit&Donahue,2015).Simulationsutilizingonlyradiativecoolingdonotreproducethisbehavior,insteadyieldingclustercoresthataretoodense,cold,andlowinentropy(e.g.,Lokenetal.(2002)).StellarandSNfeedbackalonearettooradiativecoolingandproducerealisticpopulationsofcool-coreandnon-coolcoreclusters(Nagaietal.,2007;Borganietal.,2008;Skoryetal.,2013),andthisinspiredtheadditionofAGNfeedbacktogalaxyclustersimulations.TheinclusionofAGNfeedbackhasimprovedagreementbetweensimulationsandobservationsinthecentralregionsofclusters(Duboisetal.,2011),andthereareindicationsthattheresultingthermodynamicstateoftheclustercorecanproducemorerealisticbrightestclustergalaxies(BCGs,Martizzietal.(2012)).WhiletheinclusionofAGNfeedbackhasdrasticallyimprovedtheagreementbetweenobservationsandsimulationsoftheICM,thegalaxypopulationinsimulatedclustersfailstomatchobservations.Thegalaxiesingalaxyclustersimulationsgenerallyrelyon\starparticle"methods(Cen&Ostriker,1992;Springel&Hernquist,2003)whichwereintendedtorepresentstarformingcloudsingalaxy-scalesimulations.Thestarparticleformationandfeedbackalgorithmsaredesignedtoencapsulateprocesseswhichoccuronmuchsmallerscalesthanareresolvedinacosmologicalgalaxyclustersimulation,andassuchlosemostoftheirphysicalbasisinthisapplication.Theseprescriptionsdeposittoomuchenergyinaverysmall144regionofthesimulationvolume,pushingasmallparcelofgasintoaregionofphasespacewhereitcoolsextremelyrapidly.Thiscoolingmorethannegatestheintendedheatingfromthestellarpopulation,givingrisetothewell-knownovercoolingproblem(Borganietal.,2008;Borgani&Kravtsov,2011).Bydepositingthermalandmetalfeedbackonscalescomparabletothesizeofasingleresolutionelement,starparticlealgorithmsarehighlydependentonthenumericaldetailsofthesimulation,particularlymassandspatialresolution.Thesemethodsarecurrentlyunconvergedwithrespecttosimulationresolution,anditunlikelythatfurtherincreasesinresolutionalonewillproduceclustersinagreementwithobservation.TheinabilitytoproducerealisticgalaxypopulationsindicatesthatthecurrenttreatmentoftheinteractionbetweengalaxiesandtheICMisincomplete,inconsistent,orboth.5.2Methods5.2.1IntroducingGalaxyParticlesGalaxyparticlesareimplementedinEnzo,usingtheactiveparticleframeworkintroducedinEnzo3:0(Goldbaumetal.2016,submitted).Activeparticlesprovideageneralizedframeworkfordevelopingspecializedparticleswithsophisticatedformation,feedback,andtroutines.Thisfunctionalityisanaturalforgalaxyparticles,asattheircoretheyareanensembleofsub-gridsemi-analyticmodels.Withgalaxyparticles,internalgalaxyprocessesaretreatedasinherentlysub-resolutionphenomena.Starformation,theevolutionofthestellarpopulations,chemicalenrichmentoftheISM,andSNefeedbackareallsimulatedwithsub-gridsemi-analyticmodels.Galaxyparticlespossessanextendedphysicalextent,allowingtheirinteractionwiththeCGMtobeself-consistentlymodeled.SNefeedbackejectsgasandmetalstotheCGMacrossadistributedspatialextent,avoiding145theovercoolingproblem(Borganietal.,2008;Borgani&Kravtsov,2011)andproducingamorerealisticdistributionofmetalsintheCGM.RampressurestrippingremovesgasfromtheoutskirtsofthegalaxyasitmovesthroughtheCGM(Gunn&Gott,1972).Galaxyparticlesarecapableofbothsecularevolutionandinteractingwithoneanother.Particlescangrow,gaininggasandDMmassastheirhosthalogrows.Particlescanalsomergewithoneanother,combiningtheirattributesifthehalosthatarehostingthemmerge.Galaxyparticlesdrawinspirationfromthe\galaxyconstruct,"or\galcon"particlesimplementedbyArielietal.(2010).GalconsshowedpromiseinimprovingthestateoftheCGMandcharacteristicsofthegalaxypopulationincosmologicalsimulations,butwerelimitedinseveralcrucialways.Directuserinterventionwasrequiredforthecreationofgalcons.Thesimulationwasstoppedatahighredshift(z'6),andhalondingwasdonetoidentifylocationsforgalconcreation.Aparticlewascreatedineachhalo,thesimulationwasrestarted,andthegalconswereallowedtoevolvesecularly.Galconswerecollisionlessparticles,andcouldnotinteractwitheachother.Theywereinsertedonlyonceduringthecourseofthesimulation,makingtheevolutionoftheclustersensitivetotheredshiftatwhichparticleformationoccurred.Galaxyparticlesaredesignedtosurmounttheseproblems,withformationandmergingprescriptionsthatoccurwithoutuserintervention,makingthemodelmoreself-consistentandfastertorun.5.2.2ParticleCreation5.2.2.1HaloFindingGalaxyparticlesarecreatedinhalosidenbytheRockstarhalo(Behroozietal.,2013).TheRockstaralgorithmidenhaloandsub-halosbyusingaFriends-of-146Friends(FOF)methodtoidentifyspatiallyco-locatedDMparticlesinthesimulation,thenfurtherthehalosidenbyFOFbyevaluatingwhethertheparticlesinagivenhaloaregravitationallybound.Particlekinematicphase-spaceinformationisusedtoidentifysub-haloswhileexcludingparticlesthatarespatiallyco-locatedwithahalobutarenotgravitationallybound.Halooccursduringsimulationruntime.Thesimulationperiodicallypausesandpassesitscurrentstatetotheytanalysisandvisualizationcode(Turketal.,2011c),whichinturncallsRockstarandreturnsahalocatalogtoEnzo.Whenanewhaloisidenthatexceedstheminimummassthresholdforparticlecreation,Enzocreatesagalaxyparticleatthehalocenterofmass(COM),withavelocityequaltotheCOMvelocityofthehalo,tobethemass-weightedmeanvelocityofalltheDMparticlesinthehalo.Whengalaxyparticlesarealreadypresentinthesimulation,amoresophisticatedmethodisusedtoassociatehaloswithgalaxyparticlesthatalreadyexist,andthisisaddressedinSection5.2.4.5.2.2.2MassAssignmentWhenahaloisreturnedtoEnzoanddeemedtobethesiteofcreationofanewgalaxyparti-cle,severalfundamentalquantitiesaresetdirectlyfromvaluesreturnedinthehalocatalog.Theposition,velocity,andhalovirialradiusaresetimmediately,butothercharacteristics,suchasthegalaxygasmassareestablishedbasedonthestateoftheICMinthesurroundingregion.Thegalaxymassisestablishedasafunctionofthegasdensityinthecellswithinthegalaxyradius,Rgal.Thegalaxyradiusisafractionofthehalovirialradius,andisauser-parameterwithadefaultvalueof0:25.Asetfractionofthegasdensityineachcell147withinthegalaxyradiusisremovedfromthegridandgiventotheparticle.Thisfractionisalsoaparameter,andhasadefaultvalueof0:1.Themassgiventotheparticleisusedtosettwodistinctquantities:thetotalparticlemassandthegalaxyparticleinternalgasmass.Theformerisusedforsimulationdynamicsandthegravitationalinteractionbetweenthegalaxyparticleandtherestofthesimulation.Thelatterisusedasaninputforinternalgalaxyparticlemodels.Itplaysaroleintheamountofstarformationthatoccurswithintheparticle,aswellasprovidingthereservoirofgasavailableforrampressurestripping.5.2.2.3OtherParticleAttributesWhenagalaxyparticleiscreated,severalotherparticleattributesmustalsobeset.Thecentraldensityisneededasaparameterofthebeta(Cavaliere&Fusco-Femiano,1978)whichisusedtodescribetheradialdistributionofgaswithinthegalaxyparticle.Thecentraldensityissetatparticlecreationtimeandmaintainedforthedurationofthesimulation.Thisisdonetosetthevalueofthecentraldensityforthebetapriortotheremovalofgasfromthegridduringparticlemassassignment,asthatprocessreducesthemagnitudeofthecentraloverdensitywheretheparticleislocated.Themetallicityofthegalaxyparticlegasisestablishedbytakingthemassweightedaveragemetaldensityofthegaswithinthegalaxyradius.5.2.3FeedbackandEvolutionAttheirheart,galaxyparticlesareobjectsthatencapsulatethestellarprocessesingalaxiesandprovideaframeworkfortheinteractionofthegalaxywiththeICM.Starformation,feed-back,andinteractionwithICMareallprocesseswhichcanbemathematicallycharacterizedinmultipletways.Assuch,galaxyparticlesaredesignedinamodularfashionsuch148thatthemodelgoverningoneprocesscanbechangedindependentlyofthemodelswhicharebeingusedtocharacterizetheotherprocesses.Thismodularityallowsthesevariousmodelsandtheparameterswhichcontroltheirbehaviortobeself-consistentlytestedandcomparedtooneanother.Forexample,themodelusedtocharacterizerampressurestrippingoftheouterregionsofagalaxycanbevariedwithoutchangingthemodelusedtosimulatestarformationinthegalaxy,allowingfortheofthischangetobeisolatedandinvestigated.5.2.3.1StarFormationTheSFRasafunctionoftimeisoneofthefundamentalobservationalcharacteristicsoftheclustergalaxypopulationthatmustbereproducedinsimulationstodemonstrateagreementwithobservation.Starformationingalaxyparticlesisprimarilyafunctionofthemassofgaswithininthegalaxy,Mgas.FollowingArielietal.(2010),aglobalcosmicSFRdensity_ˆcosmicismobythehalomassdensityˆhalotoyieldavalueswhichencodesthecharacteristicandtimescaleofstarformation,s=_ˆcosmic=ˆhalo:(5.1)Thestarformationciencyisadimensionlessquantity,givingsunitsofinversetime.Withthisvalue,theSFRineachgalaxy,_M?,canbecalculatedas_M?=Mgass;(5.2)andthestellarmassM?formedinagiventimesteptissimplyM?=_M?t:(5.3)149Ateachtimestep,themassofgasconvertedtostarsisremovedfromthegalaxyparticlegasreservoir.Starformationingalaxyparticlesistakentobeacontinuousprocessinwhichapopula-tionofstarsisformedateachtimestep,ratherthandiscreteformationinwhichindividualstarsarecreated.Inordertotracktheevolutionofthestellarpopulationinthegalaxy,thestellaragesandformationmetallicityarebothtracked.Eachgalaxyparticlecarriestwoarraysfortrackingtheformationtimeandmetallicityofitsstellarpopulation.Asstarformationcreatesnewmassesofstars,thesemassesareenteredintothearrayatthecorre-spondinglocalgasmetallicityandcurrentsimulationtime.Twoarraysaremaintainedwithidenticalmetallicitybinningbutttimebinning:aspacedarrayfortrackingyoungstellarpopulations,withatimeresolutionof10Myrandspanningarangeof100Myr,andcoarsearraywithadaptivebinningthatspansthefulldurationofthesimulationin150linearly-spacedincrements.Thismethodisadoptedtocapturetherapidevolutionofmassiveyoungstarsinthearray,whilealsotrackingtheslowerevolutionoflong-livedlowmassstars.Whileitwouldbepreferabletohavehightimeresolutionfortheentiredurationofthesimulation,thisisnotcomputationallyfeasibleduetothesubstan-tialmemoryoverheadthatwouldbeimposedbycarryingthatmuchdataoneachparticle.Thismethodstrikesabalancebetweencomputationalmemoryusageandtimeresolutionbyallocatinglimitedmemoryresourcestothemostrapidperiodofevolutionofthestellarpopulation.5.2.3.2StellarFeedbackTheprimarydriveroffeedbackofenrichedmaterialfromthegalaxyISMtothesurroundingICMisaSNe-drivengalacticwind.Ofthese,TypeIIsupernovae(SNeII)arethemainsource150ofenergy.SNeIIoriginatefromhighmassstarswhichhaveaveryshortmainsequencelifetime.Assuch,therateofSNeIIcloselytheunderlyingSFRinagalaxy,atrendwhichisinobservation(Heckman,2003).SNefeedbackwithgalaxyparticlestakestwoforms:massejectionandenergyejection.Theseareparameterizedas_Mwind=wind_M?;(5.4)and_Ewind=ewind_M?c2;(5.5)respectively,wherewindandewindarethemassandenergyejectionandcisthespeedoflight.Thesecienciesarenotderivedfromprinciples,butcanbeconstrainedobservationally.Forgalaxyparticlesimulationstheyaregivenvaluesofwind=0:25andewind=106(Leithereretal.,1992;Cen&Ostriker,1993).Ateverytimestep,theamountofmassandenergydepositedintheICMiscalculatedasMwind=_MwindtandEwind=_Ewindt.ThefeedbackisdepositedinashellaroundthegalaxyparticlewithaninnerradiusoftheRgalandouterradiussettobethefeedbackradius,Rfb,heretobe0:5Rvir.Massisdepositedequallyinallcellsofthesimulationwhichfallwithinthisshell.Energyisdepositedinproportiontothegasdensityineachcell,suchthattheincreaseinenergydensityisequalinallcellswithintheshell.Toensuremassisconservedinthesimulation,themassofgasdepositedintheICMisremovedfromthegalaxyparticlemass.Intrackingtheinternalstellarandgasmasses,themassthatisejectedistakentocomewhollyfromthestellarcomponent,whichisdecrementedaccordingly.MaterialwhichhasbeenenrichedviastellarwindsandSNeisalsoexpelledintotheICM.SNeejectarapidlymixeswiththesurroundingISM,andtheenergeticfeedbackissuchthat151galacticmaterialisentrainedbytheseexplosionsandcarriedtotheICM.OwingtoitsorigininSNe,thisejectahasahigherfractionofenrichedmaterialthantheISM,andtocapturethisthemetaldensityofgalaxyparticleejectaistakentobeafactorofthreegreaterthantheISMmetaldensity.Thecorrespondingmassofmetalsisdepositedevenlyamongstthecellsinthefeedbackshell.5.2.3.3RamPressureStrippingAsgalaxyparticlesmovethroughtheICM,rampressurestrippingremovesgasfromtheirouterregions.FollowingArielietal.(2010),galaxyparticlesuseageneralizedformulationofthemassofgasremovedbyrampressurestripping.Theoriginalmethod(Domainkoetal.,2006;Kapfereretal.,2007)determinedthemassremovedfromadiskgalaxymovingthroughamediumwithavelocityorientednormaltothediskbydeterminingtheradiusatwhichthepressureexertedbythesurroundingmediumwasequaltothegravitationalattractionofthegalaxywithinthatradius.Gasbeyondthatradiusisassumedtoberemovedfromthegalaxyinadynamicaltime.Arielietal.(2010)generalizethismodelforgalaxiesinwhichthegravitationalpotential,particularlyintheouterregions,isdominatedbyDM.ThemassofgasremovedbeyondastrippingradiusRsisMs=ˆICMV2gR4sGMtot;(5.6)whereˆICMisthedensityoftheICMatRs,VgisthevelocityofthegalaxyrelativetothetheICM,MtotisthegalaxymasswithinRs,andGisthegravitationalconstant.WhenmaterialisstrippedfromagalaxyparticleitsmassisremovedfromtheparticleanddepositedisotropicallyintheshellofcellsatRs.StrippedgashasthesamemetaldensityastheISM152gasoftheparticle,andthesimplifyingassumptionismadethatthemetallicityoftheISMandgaseoushaloofthgalaxyisuniform.BoththeinternalgalaxyparticlegasreservoirandtheinternalmassofmetalsaredecrementedinlockstepwiththemassofgasandmetalsdepositedintheICM.5.2.4Particle-HaloAssociationWhenanewhalocatalogisreturnedbyRockstaritmustbeparsedbyEnzotodeterminewhichhalosalreadyhostgalaxyparticles,whichneedtohavenewgalaxyparticlescreatedinthem,andwhichhostmultiplegalaxyparticlesthatneedtobemerged.Thisprocessismadesubstantiallymorechallengingasthehalosthatarereturneddonotcontainanyinformationregardingtheirprovenance.Eachhalointhehalocatalogcontainsinformationaboutthehaloposition,bulkvelocity,mass,andradius.Withoutinformationconcerningwhetheragivenhalohasrecentlyformed,hasbeengrowingsecularly,oristheresultthemergerofmultiplehalos,othermeansmustbeusedtoassociatehaloswithpreexistinggalaxyparticles.Thistaskismademorebythepresenceofspatially-nestedsub-halos.Rockstariscapableofidentifyinghalosthatarespatiallycoincidentbutdistinctinkinematicphasespace;inessence,structureswhicharepassingthroughoneanother,eachofwhichcouldbehostingoneormoregalaxyparticles,orneedtohaveagalaxyparticlecreatedinit.Thereareseveralscenariosinthegalaxyparticle-haloassociationprocesswhichmustbecorrectlydistinguishedinordertoproperlytreatgalaxyparticlecreation,updating,andmerging.Thecaseistheeasiest,inwhichahalocontainsneithersub-halosnorgalaxyparticles.Inthiscase,anewgalaxyparticlewillbecreatedinthehalo,andthegalaxyparticleandhalowillbeassociatedwithoneanother.Thesecondcaseiswhenahalocontainsnosub-halosandasinglegalaxyparticle,andisnotasub-haloitself,inwhichcase153thehaloandgalaxyparticleareassociated,andthegalaxyparticlewillbeupdatedtothenewquantitiesofitshosthalo.Athirdscenarioiswhenahalocontainsnosub-halosbutmultiplegalaxyparticles.Inthiscase,thegalaxyparticlesmustbemerged,andthecombinedgalaxyparticleassociatedwiththehalo.Ifahalocontainsoneormoresub-halos,butnogalaxyparticles,thenthelargesthaloandallsub-halosabovethemassthresholdforgalaxyparticleformationmusthavegalaxyparticlescreatedinandassociatedwiththem.Theremainingscenariosaresubstantiallymorecomplicatedtodisentangle.Thesearecharacterizedbyahalohostingbothsub-halosandgalaxyparticles.Thiscanmanifestasahierarchically-nestedarrangementofhalosandsub-halosinwhicheverysub-haloiscontainedbyallotherhalosmoremassivethanitself,oranyarrangementinvolvingmoregalaxyparticlesthansub-halos,moresub-halosthangalaxyparticles,orbalancednumberdistributionsofsub-halosandgalaxyparticles,butwithaspatialdistributionthatleavessomesub-haloswithnogalaxyparticlesandotherwithmultiplegalaxyparticles.Unravelingthisscenariorequiresrecoursetokinematicdataofthegalaxyparticlesandhalos.WhenassigninggalaxyparticlestoDMhalosorsub-halos,itisconvenienttothestandardmethodofthinkingaboutahaloandthesub-haloswithinit,andinsteadtoconsiderahaloandthesetofsuper-haloswhichcontainit.Additionally,itisimportanttonotethatwhileahalocanbedeemedtohostmultiplegalaxyparticles,eachgalaxyparticlecanonlybeassociatedwithasinglehalo.Thegalaxyparticle-haloassociationalgorithmoperatesbyworkingupthesizehierarchyofhalos,fromsmallesttolargest.AllgalaxyparticlesthatfallwithinagivenhaloandhavenotalreadybeenassignedtoanotherhaloareidenForeachgalaxyparticleinthisset,allsuper-halosthatcontainthisgalaxyparticlearealsofound.Acomparisonismadebetweenthemagnitudeofthegalaxyparticle'svelocityandthemagnitudeoftheCOMvelocityofallhaloswhichcontainit.Thegalaxyparticleisthen154associatedwiththehalothatmostcloselymatchesitsvelocitymagnitude.Thevelocitymagnitudeisusedratherthevelocitywithdirectioninformationbecausethegalaxyparticleisresidinginthegravitationalpotentialofthehalo,andbetweenthegalaxyparticlepositionandhaloCOMcanleadtooscillationsofthegalaxyparticlewithinthispotentialwell,occasionallyresultinginthegalaxyparticleandhalomovinginoppositedirectionsofoneanotherdespitebeinggravitationallycoupled.Onceallgalaxiesparticleshavebeenassociatedwithhalos,galaxyparticlecreation,updating,andmergingoccurs.5.2.5GalaxyParticleGrowthandMergingFollowinggalaxyparticle-haloassociation,galaxyparticleupdatingandmergingoccurs.Galaxyparticlesthatarethesoleparticleinahaloareupdatedwiththequantitiesofthenewhalo.Thehalovirialradiusisupdated,whichinturnupdatesthegalaxyandfeedbackradii.Iftheparticlehasdeviatedfromthehalocenterofmass,itisshiftedtothatposition.Theparticlevelocityisalsoupdatedtomatchthebulkvelocityofitshosthalo.Additionally,theparticlegasandtotalmassesareupdated.Galaxyparticlemassupdatingissimilartomassassignmentduringparticlecreation.Theincreaseingalaxygasmassissetbydeterminingtheexcessgasdensitywithinaspherewitharadiusthatissomefractionofthehalovirialradius.Inpracticethisradiusistakentobe0:25Rvir.Theaveragedensityisevaluatedatthisradius,andanyexcessgasdensitywithintheenclosedsphereisaddedtothegalaxyparticle.Thegasmassgiventotheparticleisremovedfromthegrid.Byoperatinginthisway,massinthesimulationisconservedanddiscontinuousjumpsinthegasdensityinthesimulationareminimized,mitigatinghydrodynamicartifactsthatcouldotherwisearisewithparticleupdatingand155subsequentmanipulationofthegas.Mergingofgalaxyparticlesisverysimilartoparticleupdating,withanadditionalsteptocombineattributesofthemergedparticles.Thegasandstellarmassesarecombined,asarethearraysholdingtheageandmetallicitydistributionofeachparticle.Themassofmetalsiscombined,allowingthemetallicityofthemergedparticletobedetermined.Afterthesequantitiesarecombined,themergedparticleisupdatedinthesamemannerparticleswhicharethesoleinhabitantsofahalo.ItisrelocatedtotheCOMofthehalo,itsvelocityisupdated,asisitsmass.Inanyhalothatdoesnotcontainoneormoregalaxyparticles,anewoneiscreatedinit,followingthestandardparticlecreationprocedure.5.3SimulationSetupAsuiteof5cosmologicalsimulationswasrunwithgalaxyparticlesusingtheEnzo1adaptivemesht+N-bodycode(Bryanetal.,2014)withtheZEUShydrodynamicsscheme(Stone&Norman,1992).Allsimulationshaveacubicvolumeof(360Mpc=h)3initializedatz=99withinitialconditionsgeneratedusingtheMUSICcosmologicalinitialconditionsgenerator(Hahn&Abel,2011).cosmologyisusedwithparametersm=0:272,=0:728,b=0:0456,h=0:704,˙8=0:809,ns=0:963,andtheCDMtransferfunctionofEisenstein&Hu(1999).Thesimulationshavearootgridofcomposedof2563cellsandallowforanadditional8levelsoft,givingamaximumspatialresolutionof5:5kpc=handaminimumdarkmatterparticlemassof6:06107M.tisallowedinthecentralregionofeachsimulationwheneitherthebaryonicordarkmatter1http://enzo-project.org156densityreaches8:0timesthemeandensityonthatlevel.Atz=0themeangasmassinahighest-resolutiongridcellis1:4105M.Thepresenceofagalaxyparticleonaparticulargridalsotriggerst,ensuringthatallgalaxyparticlesoperateonthemostlevel.Clustermassesatz=0rangefrom7:741014Mto1:441015M.TheGrackle2chemistryandcoolinglibrary(Bryanetal.,2014;Kimetal.,2014)isusedtocomputethecoolingrates.ThesimulationchemistrynetworktrackstotalmetaldensityofthegasaswellastheionizationstatesofHandHe,whichareusedtocalculatetheradiativecoolingratesfollowingGlover&Jappsen(2007).Metal-dependentcoolinginGrackle(Smithetal.,2008)usestabulatedratesfromCloudy(Ferlandetal.,2013),andauniformUVbackgroundispresent,withaformfollowingHaardt&Madau(2012).DarkmatterhalosareidentiwiththeRockstarhalo(Behroozietal.,2013)duringsimulationruntimeusingtheinlineinterfacebetweenEnzoandtheyt3analysisandvisualizationpackage(Turketal.,2011c).Haloswithamassgreaterthan9:71010MarereturnedtoEnzoforgalaxyparticlecreationandassociation.5.4PreliminaryResultsGalaxyparticledevelopmentandusageisongoing,andthepreliminaryresultspresentedbelowderivefromasamplesimulationevolvedfromz=99toz=0:6.Inthislight,theseresultsshouldbeconsideredindicationsofwhatcanbedonewithgalaxyparticles.Theyhighlightbothareaswherethegalaxyparticlemethodshowspromisingresults,andareaswheredisagreementbetweensimulationandobservationsindicateaspectsofthemethodthatrequirefurtherdevelopment.Adiscussionoffutureavenuesofresearchanddevelopmentwith2https://grackle.readthedocs.org/3http://yt-project.org157galaxyparticlesisgiveninSection7.2.3.5.4.1GalaxyPopulationThegalaxyparticleinthesimulationformedatz=3:2.ThenumberofgalaxyparticlesasafunctionoftimeisshowninFigure5.1.Byz=0:6thenumberofgalaxyparticleshasincreasedto814.Thedeclinesinthenumberofgalaxyparticlesatz=1:501:42,z=1:341:27,andz=1:000:92showmergerevents.Atthesepointsthegrowthofcosmologicalstructureviahierarchicalmergingcombinedacollectionofsmallerhaloswhichhadallpreviouslyhostedtheirowngalaxyparticlesintolargerstructures,eachcontainingasingle,mergedgalaxyparticle.Figure5.1:Thenumberofgalaxyparticlesasafunctionofredshift.Theparticleformsatz=3:2.Majormergereventsoccuratz=1:501:42,z=1:341:27,andz=1:000:92.158Figure5.1demonstratesseveraluniquecapabilitiesofgalaxyparticles.Thenatural,self-consistentgrowthofthegalaxypopulationisasubstantialimprovementuponthe\Galcon"method(Arielietal.,2010),inwhichthesimulationwasstoppedandallthegalconswhichwouldexistforthedurationofthesimulationwereinsertedbyhand,atonetime.Thismergingprocessisalsouniquetothegalaxyparticlemethod,andpresentsasubstantialim-provementoverothermethods.Galconswerecollisionlessparticles,andcouldinteractwithoneanotheronlyviagravity.Themergingprocessisafundamentalaspectofhierarchicalstructureformation,andmustbecapturedinsimulationsthataimtocreatepopulationsofclustergalaxiesthatagreewithobservations.Figure5.2isaslicethroughthecenteroftheclusteratz=0:6showingthegastemper-ature.Overplottedinblackarethepositionsofasubsetofgalaxyparticles.Whiletherearemanymorepresentintheclusterthanarevisibleinthisimage,itillustratesseveralimpor-tantresultsofthegalaxyparticlemethod.Firstandforemost,andspatialdistributionofgalaxyparticleswithintheclusterisanimprovementoverprevioussimulations.Simulationsusinggroupingsofstarparticlestorepresentgalaxiesinclustersimulationsproduceagalaxypopulationthatismuchtoocentrallyconcentrated.Thisbehaviordoesnotmanifestwithgalaxyparticles.Galaxyparticlesarecapableofforminginanytlymassivehalointhesimulation.Asaresult,galaxyparticlescananddoforminsubstructuresbeyondtheclustercenter.Insomecasesthisincludesstructureswhichoriginatedbeyondtheclustervirialradius,givingrisetogalaxieswhichformintheclusteroutskirts.TheimportanceofsophisticatedhaloidenisdemonstratedinFigure5.2.TheRockstarhalo(Behroozietal.,2013)idenDMparticlesthatareassociatedwithaparticularhalothroughacombinationofspatialproximityandtheusevelocity-phasespaceinformationtodetermineiftheparticlesaregravitationallyself-bound.Thisenables159Figure5.2:Aslicethroughthecentralregionofthesimulationdomainatz=0:6showingthegastemperaturewiththelocationsofgalaxyparticlesoverplottedinblack.Galaxyparticlesdonotdisplaytheexcessivecentralclusteringseeninpreviouscosmologicalsimulationsofgalaxyclusters.160Rockstartoidentifykinematicallydistinctsub-halosthatwouldbesubsumedintotheirenclosinghalosbyamethodthatusesonlyspatialinformation.Galaxyparticlescapitalizeonthissub-structureinformationbyassociatingparticleswithhalosbasedonacomparisonofthekinematicstateofagalaxyparticleandallthehalosthatcontainit.Thisenablessimulationswithgalaxyparticlestoindependentlyrepresentgalaxiesthatresideindistincthalosbuthaveasmallspatialseparation.Occurrencesofthisbehaviorcanbeseeninseveralclosely-spacedgroupsofgalaxyparticlesinFigure5.2.Whilenearlyspatiallyco-located,theseparticlesandthehalosinwhichtheyresidearekinematicallydistinctandnotgravitationallyboundtooneanother.Figure5.3:Themassofstarsingalaxyparticlesasafunctionofredshift.161Figure5.3showsthestellarmassingalaxyparticlesasafunctionofredshift.Anapprox-imatecomparisoncanbemadebetweenthesimulatedstellarmassandthestellarmassthatwouldbeexpectedinagalaxyclusterofthissizebasedonobservedtrends.ThesimulatedclusterhasaDMmassMDM=1:731014M.TakingthecosmicbaryonfractiontobeapproximatelyequaltothebaryonfractionintheclustergivesaclusterbaryonmassofMb=MDMbmb=3:481013M;(5.7)whereb=0:0456andm=0:272arethecosmologicalbaryonandmatterdensityparam-eters,respectively,asdrawnfromtheWMAP7bcosmologicalmodel(Komatsuetal.,2011).Theratioofstellarmasstogasmassinagalaxyclusterofthismassisroughly0:15(Gonzalezetal.,2013),givinganestimatedstellarmassof4:541012M.Thesimulatedstellarmassismorethanafactorof3larger,at1:731013M.Thisdiscrepancysuggeststhatthegalaxyparticlestarformationmodelneedsimprovementthougheithercalibrationofparameterscontrollingthestarformationormonofthealgorithmbywhichstarsareformed.Thesourceofexcessivestellarmassinthegalaxyparticlepopulationcanbeseeninstellarmassfunction,showninFigure5.4.Thenumberofgalaxyparticlescontainingatleastagivenmassofstarsisplottedasafunctionofgalaxyparticlestellarmass.Figure5.4showsthatthegalaxyparticlepopulationhasacharacteristicstellarmassofafew108M.Thelongtailofthedistributionextendingtostellarmassesgreaterthan1010Missparselypopulated,comprisinglessthan7%ofthegalaxyparticlepopulation,butcontainsthebulkofthetotalstellarmass.Thehandfulofgalaxyparticlescontainingmorethan1012Mofstarsdominatesthestellarmassofthesystem,andindicatesthatamoresophisticated162Figure5.4:Thestellarmassfunctionforgalaxyparticlesatz=0:6.Themajorityofthestellarmassiscontainedinonlyafewgalaxyparticles,contributingtotheexcessivestellarmassseeninFigure5.3.163starformationalgorithmisneeded,asthesemassivegalaxiesareformingstarswithanunrealisticallyhigh.Furtherdevelopmentofthestarformationmodelwilllikelytruncatethehigh-masstailofthestellarmassfunctionandsimultaneouslyreducetheoverallstellarcontent,bringingitintobetteragreementwithobservations.5.4.2ICMPropertiesAccuratelycapturingtheinteractionandco-evolutionofclustergalaxiesandtheICMisasubstantialchallengeincosmologicalsimulationsofgalaxyclusters.Theobservedmetallicitydistributioningalaxyclustershasproventobeparticularlytoreplicate,withmostsimulationsproducingadistributionthatistoohighlypeakedinthecentralregionsoftheclusteranddropstoorapidlyatlargerradii.Figure5.5showsthegasmetaldensityinprojectionthroughthesimulationvolume.Allthemetalsintheclusteroriginateasfeedbackfromthestellarpopulationwithingalaxyparticles.ThisfeedbackcanbeclearlyseenintheelevatedenrichmentoftheICMintheregionssurroundinggalaxyparticleswhicharehostingvigorousstarformation.Examplesofthiscanbeseenmostdistinctlyat+5Mpcalongthey-axisand5Mpcalongthez-axis.Anotherenrichedregioncanbeseenat+3Mpcalongthey-axisand+4Mpcalongthez-axis.Figure5.6isaslicethroughtheclustershowinggasmetallicity.Themetallicityvaluesinthegasareingoodagreementwithobservations,whichshowcentralmetallicityofroughly0:3Z.Themetallicitydoesnotdisplayasharpdropinmagnitudewithradius,unlikemanyothergalaxyclustersimulations,andinbetteragreementwithobservations.AlargedegreeofsubstructurecanbeseeninFigure5.6.ThedistributionofenrichedmaterialintheICMistlyinhomogeneous(Simionescuetal.,2010),atrendthatisreproducedinthissimulation.164Figure5.5:Aprojectionthroughthecentralregionofthesimulationdomainatz=0:6showingthemetaldensityweightedbythegasdensitywiththelocationsofgalaxyparticlesoverplottedinblue.Aburstofstarformationandtheassociatedchemicalenrichmentcanbeat+5Mpcalongthey-axisand5Mpcalongthez-axis.Theremnantofanotherburstcanbeseenat+3Mpcalongthey-axisand+4Mpcalongthez-axis.165Figure5.6:Aslicethroughthecentralregionofthesimulationdomainatz=0:6showingthegasmetallicity.Thelocationsofgalaxyparticlesareoverplottedinred.Similartowhatisseeninobservations,theenrichmentoftheICMisveryuneven,andtheoveralllevelofICMenrichmentisingoodagreementwithobservations.166TheradialofgasmetallicityisshowninFigure5.7.Thishighlightsbothsuccessesandshortcomingsofthegalaxyparticlemethod.Incontrasttomanyprevioussimulationsofgalaxyclusters,themetallicitydistributionisnotexcessivelypeaked.Starparticle-basedmethodsofsimulatinggalaxiesinaclusterenvironmentproducecentralmetal-licityvaluesthataretoohighanddistributionsthatdeclinetoorapidlyasafunctionofradius.Themetallicityproducedbygalaxyparticlesdisplaysamuchmoregradualdecline,inbetteragreementwithobservations,butitstilldeclinestoorapidly.Despitethissuccess,thecentralmetallicityistoohigh,exceedingobservedvaluesbyafactorof23.Thisbehaviorisconsistentwiththeexcessivelyhighstellarmassproducedinthissimulation.Asallthemetalsintheclusteroriginateinthestellarpopulationsofgalaxyparticles,anexcessofstarswillproduceanexcessofmetals,resultingislevelsofchemicalenrichmentthataretoohigh.TheinclusionofAGNfeedback,andtheresultantmixingoftheICMwilllikelyservetothisasenrichedmaterialisdriventolargerradii,bothreducingthecentralenrichmentandincreasingthelevelofenrichmentinthegasintheclusteroutskirts.Whileafullassessmentoftheabilityofthegalaxyparticlemethodtoproducerealisticstellarpopulationsincosmologicalsimulationsofgalaxyclusterscannotbemadeatthispoint,preliminaryresultsareencouraging.Galaxyparticlesareproducingapopulationofgalaxieswithreasonablepopulationnumbers,spatialdistribution,andmergingbehavior.TheinteractionbetweenstellarfeedbackandtheICMisresultinginmetallicitylevelsanddistributionsthatareinbroadagreementwithobservations.Elevatedstellarmassandcentralmetallicityvaluesunderscoretheneedforfurthertofthismethod,butearlyexperimentssuggestthatgalaxyparticlesareapromisingstepforwardincreatingrealisticsimulationsofgalaxyclusters.167Figure5.7:Thespherically-averagedradialofgasmetallicityinthegalaxyclusteratz=0:6.Thedistributionislesscentrallyconcentratedtheothersimulationtechniques,inbetteragreementwithobservations,butthecentralvalueisafactorof23largerthanobservedvalues.168Chapter6ThermalInstabilitiesandPrecipitationintheCircumgalacticMedium6.1Motivations6.1.1ObservationsThecircumgalacticmedium(CGM)isacriticalcomponentingalaxyformationandevolu-tion.Bridgingthedividebetweentheintergalacticmedium(IGM)andthedense,star-forminginterstellarmedium(ISM)ofgalacticdisks,theCGMservesasaconduitbe-tweentheseregions.GasfromtheIGMisdepositedintheCGM,whereitservesasareservoirtofuelstarformationinthedisk.Simultaneously,stellarfeedbackdrivesenrichedmaterialoutofthethedisk,intotheCGM,andpotentiallybeyondthegalaxy'svirialradiustoenrichtheIGM.RecentobservationalcampaignshaveindicatedthattheCGMisahighlycomplex,mul-tiphaseregionthatcancontainlargefractionsofthegalacticbaryonbudgetandthemetalsproducedinstars.ColdgasintheCGMaccountsforatleast25%ofthebaryonbudgetofanLgalaxy,andincludingthecontributionfromhot,highlyionizedgascanbringthebaryon169contentofgalaxiesintoagreementwiththecosmicbaryonfraction,potentiallyresolvingthegalaxyhalomissingbaryonsproblem(Werketal.,2014;Bregman&Lloyd-Davies,2007;McGaugh,2008;McGaughetal.,2010).TheCGMisalsoamajorrepositoryforenrichedstellarejecta,withthehot,highlyionizedgascontainingapproximately40%ofthemetalsproducedinagalaxy,whileonly2025%areretainedinthestellar,dust,andISMcompo-nents(Peeplesetal.,2014).Alesserbutnon-negligiblemassofadditionalmetalsresideinthelow-ionizationCGM.ThemultiphasestructureoftheCGMishighlycomplexandpresentsamyriadofques-tions.TheCGMappearstobegenerallyincreasinginbothtemperatureanddegreeofioniza-tionwithincreasingradius.Hot,approximatelyvirialtemperaturegasisfoundthroughouttheentiretyoftheCGM(Liang&Chen,2014).Ensconcedwithinthishotgasandresidingnearthecenterofthehaloarediscretecloudsoflow-temperaturegas(Liang&Chen,2014;Werketal.,2014).Itisunclearwhichphysicalprocessesmediatethistransitionfromamultiphasemediumwithcloudsofcold,low-ionizationstategastothehot,highly-ionizedouterregionsoftheCGM.ArelationshiphasbeenobservedbetweenthedegreeofionizationofCGMgasandtherateofstarformationinthatgalaxy,withlargeramountsofabsorptionfromOVIandCIVcorrelatingwithagreaterSFR(Werketal.,2014;Bordoloietal.,2014).Thenatureofthisrelationshipisunclear,astransportprocessesofmaterialbothintoandoutofthediskfromtheCGMarenotfullyunderstood.Theoreticalworkhasrecentlyproposedthatprecipitationisresponsibleforthedevel-opmentofamultiphasemediumintheCGM(Voitetal.,2015a).Inthismodel,asimplerelationbetweentwobasictimescales,thecoolingtime,tcool,andthefree-falltime,t,de-termineswhetherornotprecipitationwilloccur.Simulationsofbrightestclustergalaxiesinclusterenvironmentssuggestthatiftheratiotcool=tdropsbelow10insomeportion170oftheCGM,itbecomeslikelythatamultiphasemediumwilldevelopandprecipitationwillbegintooccurwhenthecold,densephaseofthemediumbecomesnegativelybouyant.Onceformed,theprecipitatingcloudsofcoldgasfallontothediskofthegalaxy,fuelingstarformationandtriggeringfeedbackfromeitheracentralengine(suchasanAGN)orSNe,increasingtcoolandhaltingprecipitation.ThecessationofheatingfromfeedbackallowsthegasintheCGMtocool,tcool=tcanonceagainfallbelow10,andprecipitationcanresume,completingthisself-regulatingcycle.Ifthissametcool=tcriterioncanbeappliedtolower-massgalaxies,predictionscanbemadeaboutmanyfacetsofgalaxyformationandevolution,includingthedeclineinSFRwithincreasinggalacticchemicalenrichment(Ellisonetal.,2008;Mannuccietal.,2010),theabundancelevelatwhichchemicalenrichmentwillsaturate,starformationhistoryasafunctionofgalaxymass,thegalaxymass-metallicityrelationship(Gravesetal.,2009;McConnachie,2012),theFaber-JacksonandTully-Fisherrelations(Faber&Jackson,1976;Tully&Fisher,1977)betweengalaxystellarluminosityandgravitationalpotential,andthepresenceoflow-ionizationcloudsonlywithinr500(Liang&Chen,2014).Whileitspredictionsarewide-ranging,thismodelisappealinglysimple,androbustmultiphysicssimulationareneededtotestwhethertheprocesseswhichcharacterizeitarecapableofreproducingthethestateoftheCGMandtheevolutionofgalaxies.6.2MethodsThesimulationsetupusedforthisinvestigationisanidealizedisolatedgalaxyinanon-cosmologicalvolume.Thegalaxyconsistsofgaseousdiskandhalocomponents,withadiskgravitationalpotential.DetailsofthegalaxysetupareprovidedinSection6.3.1.StellarpopulationsaremodeledusingstarparticlesbasedonamoCenandOstrikerformalism,171implementedintheEnzo1activeparticleframework.6.2.1StarParticlesThestarparticlesusedinthisworkareamoversionofCenandOstrikerstarparticles.Bydesigntheyrepresententirestellarpopulationsratherthanindividualstars,withforma-tioncriteriabasedonthelocalstateofthegasandevaluatedwithinindividualsimulationgridcells.Overtimethestellarpopulationrepresentedbytheparticleevolves,returninggas,energy,andmetalstothesurroundingregions.6.2.2FormationFormationofastarparticlefollowingthestandardCenandOstrikermethodiscontingentonthentofseverallocalgasquantities:1.Thedensityistlyhigh.2.Thegasisconvergingtothelocationatwhichstarformationisbeingevaluated.3.Thecoolingtimeisshorterthanthelocaldynamicaltime.4.ThebaryonmassintheformationregionexceedstheJeansmass.5.Theparticletobeformedexceedsaprescribedminimummass.Inpractice,withagrid-basedhydrodynamicscodesuchasEnzo,thesecriteriaareeval-uatedonacell-by-cellbasis.Assuch,theirbehaviorishighlyresolution-dependentandsubstantialparametertuningisrequiredtoproducerealisticstellarpopulations.Tomitigate1https://bitbucket.org/enzo/enzo-3.0172someoftheresolution-dependenttuning,arequirementthatthegasinthecellbegravi-tationallyself-boundwasadded,followingthemethodpresentedinHopkinsetal.(2013).Thiscriterionisbasedontheevaluationofthevirialparameter,,inaregionofsizer,as˙2rGM(<r);(6.1)where˙isthevelocitydispersionincludingcontributionsfromrotationalandrandommotions,isaconstantthatdependsontheinternalstructureoftheregionr,Gisthegravitationalconstant,andM(<r)isthegasmasscontainedwithinaradiusr.ConsideringEquation6.1inthelimitwhererissmall,allowsthetionsM(<r)=(4ˇ=3)r3,whereˆistheaveragedensityintheregionr,and˙!vrr.Writing˙2intermsofthegasdivergenceandcurlthenyields˙2=vjrvj2+jrvj2vrr:(6.2)InEquation6.2,rvencapsulatesthelocalradialvelocitydispersion,accountingforgaswandw,whilervdescribesthelocalrotationalstateofthegasanditstangentialdispersion.Thecriterionforevaluatingwhetherthegasinacellisgravitationallyself-boundisfoundbycombiningEquations6.1and6.2,0jrvj2+jrvj2Gˆ<1;(6.3)where0ˇ1=2isacombinationoftheorder-unityandvterms.Inadditiontothegravitationallyself-boundcriterion,anyoftheformationcriteriafromtheoriginalCen&Ostriker(1992)methodcanbeused.Anycombinationofthefollowing173criteriacanbeutilizedtoidentifycellswhicharecapableofformingastarparticle:1.Baryonoverdensity:thebaryonoverdensityˆb=ˆb,mustexceedsomethresholdvalue,,whereˆbisthegasdensityinthecell.2.Converginggasvelocity:rv<0.3.Thecoolingtimemustbelessthanthelocaldynamicaltime:tcool<tdynq3ˇ32Gˆ.Tothiscriterion,weaddedanothercheck,whetherthegastemperaturewaslessthan100K.Ifeitheroftheseconditionsaremet,thecellisdeterminedtohaveedthethermalcriteriaforcollapse.4.Gravitationallyunstable:thebaryonmassinthecell,mb,mustexceedtheJeansmass,mJeans,asmJeansG3=2ˆ1=2bC3s1+ˆdm=ˆdmˆb=ˆbˆdmˆb3=2;(6.4)whereCsisthelocalsoundspeed,andthesubscriptsbanddmdenotethebaryonicanddarkmattercomponents,respectively.5.Molecularhydrogenfraction:starformationisrestrictedtothemassofmoleculargasavailableinacell.IfH2isbeingtrackedinthechemistrynetworkofthesimulation,themassoftheparticletobeformedcannotexceedtheavailablemassofH2inthecell.Whenacellisidenthatallthespformationcriteria,aparticleiscreatedatthecenterofthecell,givenavelocityequaltothelocalgasvelocity,andametallicityequaltothatofgasinthehostcell.Theparticlemassissetinoneoftwoways:174aparticlecanbeused,inwhichcaseeveryparticleisformedwithanidentical,user-spmass,ordynamicparticlemassescanbeusedinwhichcasetheparticlemassisdeterminedtobempart="?mb;(6.5)wherembisthebaryonicgasmassinthecelland"?isathewithwhichgasisconvertedintostars.IftheH2fractionisbeingusedasaformationcriterion,"?isscaledbytheH2massfractioninthecell,fH2,andEquation6.5becomesmpart="?fH2mb:(6.6)Amassofgasisremovedfromthegridequaltothemassofgasthatwasassignedtotheparticle.Theparticlecreationtime,t0,andthedynamicaltimeoftheparticleatcreation,tdynareusedtodeterminetheevolutionofthestellarpopulationencapsulatedbytheparticle,andarealsosetwhentheparticleisformed.6.2.3FeedbackandEvolutionParticleevolutiondirectlyfollowsthemethodlaidoutinCen&Ostriker(1992).Ascollapseandstarformationdonotoccurinstantaneously,themassofstarsintheparticle,m?,attimetismodeledasm?(t)=mgasZtt0(tt0)tdynexp(tt0)tdyndt;(6.7)175wheremgasisthecurrentmassofstarparticle.Duringtimestept,thenewstellarmassthatisformed,m?,ism?=mgast=tdyn(tt0)=tdynexp(tt0)=tdyn:(6.8)Asstellarmassisformed,thegasintheparticleisdepleted.Gasisbothsequesteredinstarsandejectedtothesurroundingmedium.Feedbackfromthestellarpopulationreturnssomegastotheparticleforfuturestarformation,butasmalleramountthanthecombinedmasswhichisejectedfromtheparticleorlockedupinstars.Starformationandfeedbackoperatesfor12dynamicaltimes,atwhichpointitceasestooccur.FeedbackfromSNeandmassiveyoungstarsismodeledasafunctionoftheSFRwithinaparticle.Energy,gas,andmetalsaredepositedintheISMsurroundingtheparticle.TheenergyreturnedduringatimesteptisE="em?c2;(6.9)wherecisthespeedoflightand"eisanfactorwithacanonicalvalueof105.Massejectioniscalculatedsimilarly,M=fmm?;(6.10)wherefmisthemassejectionfractionwhichhasastandardvalueof0:25.ThemassreturnedtotheISMissubtractedfromtheparticlemass.Gasrecyclingwithinthestellarpopulationisaccountedfor,withinternalchemicalenrichmentoccurringinadditiontoejectionofenriched176materialtothesurroundinggas.ThemassofmetalsejectedfromtheparticleisMmetals=m?"metals(1Zp)+fmZp;(6.11)where"metalsisthemetalyieldmassfraction,takentohaveavalueof0:02inagreementwiththesolarmetalmassfraction,andZpistheparticlemetallicity.Feedbackcanbeappliedeithersolelyinthecellinwhichtheparticleresides,orwithinaspheresurroundingtheparticle.Theradiusofthisfeedbackregioncanbespaseitheraphysicalradiusorinunitsofthesimulationcellsize.6.3SimulationSetupThesimulationsinthisworkwereaseriesofidealizedisolateddiskgalaxiesruninanon-cosmologicalvolumeandfollowedthesetupofTasker&Bryan(2006)andSalem&Bryan(2014).Thegalaxyiscomposedofgaseousdiskandhalocomponents.Inadditiontothegravitationalandhydrodynamicalinteractionsofthegasandstarparticles,adgravi-tationalpotentialdesignedtomimictheoftheunderlyingdarkmatterandolderstellardistributionsisused.Theinclusionofastaticpotentialfromanolderstellarpopula-tion,whilesimulatingongoingstarformationwithoutaback-reactiononthestellarpotentialisslightlyinconsistent.Thischoiceisinthatthisworkisconcernedwithgalaxyregulationonbillionyeartimescalesratherthanthecosmologicalevolutionofthegalaxy.Additionally,simulatingallofthestarsformedinthegalaxyattheresolutionnecessaryforthisinvestigationovertheageoftheuniversewouldbecomputationallyprohibitive.Thediskgravitymodeliscomposedofstellardiskandbulgecomponentsaswellasadarkmat-177terhalo.TheseparametersweresetinamannerintendedtoapproximateaMilkyWay-likegalaxy,andarediscussedinSection6.3.1.Twosimulationswererunattresolutions,thebeingalowerresolution(LR)runusedfortestingandexplorationofparameterspace,andalargervolume,higherresolu-tion(HR)runtocapturetheinteractionofthestructureoftheCGMwithgreatery.ThedomainoftheHRsimulationis1638:4kpconaside,withaminimumresolutionof12:8kpc,amaximumresolutionof400pc,and5levelsoft.TheLRsimulationvolumeis600kpconaside,withaminimumresolutionof18:75kpc,amaximumresolutionof586pc,and5levelsoft.Cellsarefortbasedonthegas(baryon)mass,gasmetallicity,andthepresenceofstarparticles.Ifacellcontainsastarparticle,hasametallicityabove104Z,orhasanoverdensitygreaterthan12:5timesthemeandensityinthesimulationonthetopgridlevel,thecellistothemaximumlevel.Thesimulationusesperiodicgasboundaryconditionstoensuremassconservationandavoidbulkworw.Thesimulationvolumeismuchlargerthenthegalaxytominimizenumericalartifactsatthedomainedgeswhilepreventinggalacticmaterialfromreachingtheedgesofthevolume.Thegravityboundaryconditionsarenon-periodictopreventspuriousBothsimulationsutilizeidenticalgalaxycharacteristics,chemistry,andcoolingnetworks.Thetwoonlyinspatialresolutionandasubsetofthestarparticleparameters,whicharedetailedinSection6.3.2.1786.3.1GalaxyCharacteristicsTheunderlyingdensitydistributionusedtodeterminethedarkmatterpotentialfollowsthesphericalmodelofBurkert(1995),ˆDM(r)=ˆ0r30(r+r0)r2+r20;(6.12)withacharacteristicradiusr0=3kpcanddensityˆ0=3:41024gcm3.Thestaticstellarpotential,?,utilizesaPlummer-Kuzmindiskpotential(Miyamoto&Nagai,1975),?(r;z)=GM?"r2+a?+qz2+b2?2#1=2;(6.13)whereGisthegravitationalconstant,stellarmassM?=109M,radialscalelengtha?=3:5kpc,andverticalscaleheightz?=325pc.Thegaseousdiskisinitializedasisothermalat104Kwithdensityˆdisk(r;z)=ˆ0exp(r=r0)sech2z2z0;(6.14)usingaverticalscaleheightz0=325pc,andaradialscalelengthr0=3:5kpc.Atruncationradiusof31:2kpcandatotaldiskgasmassof1011Mareadopted,producingaroughlyMilkyWay-likegalacticdisk(Klypinetal.,2002)withˆ0=6:81023gcm3.ThegaseoushaloisinitializedwithatemperaturethatassumesthatthevelocityofthehalogasisvirializedandfollowsthedarkmatterdensitygiveninEquation6.12.Ahydrostaticdensityisthencalculatedfollowingthistemperaturewithascaleradiusof31:2kpcandacentraldensityof1:671027gcm3.Thediskisgivenandinitialmetallicityof103Z,andthehalohasaninitialmetallicityof105Z.1796.3.2StarParticleParametersInordertoformastarparticle,thefollowingcriteriamustbemet:1.Baryonoverdensitymustexceed100intheLRsimulation,and1000intheHRsimu-lation.2.Thegasinthecellmustbeconverging.3.Thegasmustbegravitationallyself-bound(seeSection6.2.2).4.Eitherthegastemperaturemustbelessthan100K,orthecoolingtimemustbeshorterthanthedynamicaltimeandthetemperatureislessthan1:1104K.Aparticleiscreatedwhenallofthesecriteriaareed,andtheparticleisformedwithamassof107M.IntheHRrun,feedbackisappliedtoonlythecellinwhichtheparticleresides,whileintheLRrunitisdistributedwithinaphysicalradiusof500pc.6.3.3ChemistryandCoolingBoththeHRandLRsimulationstracktotalmetallicityandtheionizationstatesofHandHe,includingneutralH2,ionizedH2,H+,andtheelectrondensity(Abeletal.,1997).H2formationthroughtheHandH+2channelsisfollowed,asareH2rotationaltransitionsandchemicalheating.H2formationondustgrainsandgas-grainheattransferiscalculated(Omukai,2000).CoolingisfollowedusingtheGrackle2chemistryandcoolinglibrary(Bryanetal.,2014;Kimetal.,2014)tocomputethecoolingratesfromradiativeandmetalcooling.RadiativecoolingiscomputeddirectlyfromtheH,H2,andHespeciesabundances,whilemetalcoolingiscomputedwithCloudytables(Ferlandetal.,2013)andfollowsGlover&2https://grackle.readthedocs.org/180Jappsen(2007),accountingforlineemissionfromC,O,andSi,aswellasad-ditionalmetalcoolingratesfromSutherland&Dopita(1993).AnisotropicUVbackgroundwithheatingandcoolingratesfromHaardt&Madau(2012)isused.6.4PreliminaryResultsSimulationsofthedevelopmentofmultiphasegasintheCGMusingthestarparticletech-niqueandisolatedgalaxysetupdescribedinthischapterarestillactivelyunderway.Thefollowingpresentspreliminaryresultsfromtwosimulations:theLRsimulationdescribedinSection6.3andasecondsimulationwithanidenticalsetupbutasmallertregion.Thisrapidexploratory(RE)simulationwasusedtoinvestigatethelate-timeevolutionofthedisk,stellarpopulation,andregionsofthegaseoushaloextendingapproximately100kpcabovethedisk.TheLRsimulationhasprogressed320Myr,andtheREsimulationhasprogressed1:14Gyr.Neithersimulationhasevolvedforalongenoughtimetoallowconclusionstobedrawn,butearlyresultsareencouraging.TheREsimulationisusedasthebasisofdiscussioninSection6.4.1andresultsfromtheLRsimulationarediscussedinSection6.4.26.4.1CGMThermalandKineticPropertiesTheinitialconditionsofthesesimulationsareconstructedsuchthatstarformationbeginsimmediately.Theensuingstellarfeedbackrapidlybeginsdrivingwsofhot,chemicallyenrichedgasoutofthedensediskofthegalaxyandintothemorehalo.ObservationsoftheCGM(e.g.,Bordoloietal.(2014);Liang&Chen(2014);Werketal.(2014);Lehneretal.(2015))cold,densecloudsinterspersedintheotherwisehotter,moreCGM181gas.IndicationsthatthismorphologyisdevelopingintheREsimulationcanbeseeninFigure6.1,whichshowsthecentral120kpcofthesimulationvolumeandviewsthegalaxydiskedge-on,815Myrafterthestartofthesimulation.Thisisaprojectionofgastemperatureweightedbythegasmetaldensity.Filamentsandcloudsofcold,chemicallyenrichedgasextendaboveandbelowthegalacticdisk,inagreementwithobservations,andsuggestingthateveninanexploratorysimulationwithlowresolutionourmethodissuccessfullyproducingmultiphasegasintheCGM.ThecoldcloudsintheCGMinFigure6.1arenotstatic.Afterstellarfeedbackdrivesgasoutofthedisk,dense,chemicallyenrichedregionsbegintocool.Theincreaseddensityandmetalcontentconspiretoincreasethecoolingrate,furtheringcondensationofthecloud.Thesecloudsbecomenegativelybuoyantwithregardtothesurroundinggasandbegintofallbacktowardsthedisk.Figure6.2illustratesthisbehavior.SimilartoFigure6.1,itshowsthecentral120kpc,viewingthegalaxydiskedge-on,815Myrafterthestartofthesimulation.Thecomponentofthegasvelocitynormaltotheplaneofthediskisshowninprojection,weightedbymetaldensity.Figure6.2indicatesthatthegasinthecentralregionsoftheplumesarefallingbacktowardsthedisk.ComparisonofFigures6.1and6.2showsthatthegasthatisfallingfastesttowardsthediskisalsothecoldestandmostchemicallyenriched.Laterevolutionofthissimulationshowsthatwhenthisgasreachesthediskitfuelsaburstofstarformation.Thefeedbackfromthisincreaseinstarformationincreasesthetemperatureanddecreasesthedensityofthehalogas,temporarilyhaltingthedevelopmentofthesecoldclouds.TheconnectionbetweengastemperatureandmotiontowardsthediskisshowninFigure6.3.Thegasinaregion240kpcacross,starting30kpcabovethemidplaneofthegalaxyandextendingupwards100kpcisshownintemperature-velocityspace,usingonlythevelocity182Figure6.1:Aprojectionofgastemperatureweightedbygasmetaldensity815MyrafterthestartoftheREsimulation.Thecentral120kpcofthesimulationareshown,andthegalaxydiskisbeingviewededge-on.Filamentsandcloudsofcold,enrichedgascanbeseenbothaboveandbelowthedisk.Thesecloudsarefallingbacktowardsthedisk.183Figure6.2:Aprojectionofthecomponentofgasvelocitynormaltotheplaneofthedisk,weightedbygasmetaldensity,815MyrafterthestartoftheREsimulation.Thecentral120kpcofthesimulationareshown,andthegalaxydiskisbeingviewededge-on.Theenriched,coldgasinthecentralregionsoftheplumesoriginallydrivenoutwardsbystellarfeedbackarefallingbackontothedisk.184componentnormaltothedisk.Whilemostofthegasmassisclusteredaroundadisk-normalvelocityof0,themajorityofgaswithatemperatureT>105Kiswing.Thisisinstarkcontrastwiththegascolderthan105K,allofwhichismovingtowardsthedisk.Gasofalltemperatures,hotandcoldismovingtowardsthedisk,butonlyhotgasismovingawayfromthedisktogreaterradialdistances.Coldgas,alternately,isonlywingtowardsthedisk;nomaterialwithatemperaturelessthan105Kismovingoutwards.ThisagreeswiththequalitativeresultvisibleinFigures6.1and6.2.ThecoldcloudsintheplumesaboveandbelowthediskinFigure6.1arefallingtowardsthedisk,ascanbeseeninthevelocitystructureofFigure6.2.6.4.2CGMChemicalPropertiesOneofthemostdistinctfeaturesoftheCGMthathasbeenrevealedinrecentobservationsisthentialcoveringfractionoflowandhighionsasafunctionofradius(Liang&Chen,2014).TheCGMbecomesprogressivelymoreionizedatlargerradii.TheCOS-Halossurvey(Werketal.,2014)foundanOVIcoveringfractionof80%outtoaradiusof150kpc,andLiang&Chen(2014)foundasharpdropintheOVIcoveringfractionat70%oftheDMhaloradius.ThecoveringfractionofCIVindwarfgalaxiesdeclinesfromnearunitywithin0:2Rvirto60%at0:4Rvirto0beyond0:5Rvir(Bordoloietal.,2014).ThisbehaviorisdevelopingintheLRsimulation,ascanbeseeninFigures6.4and6.5.TheseshowtheprojectednumberdensitiesofOVIandCIV,respectively,asgeneratedwiththeTrident3syntheticspectrumgenerator(Hummels,C.B.,Smith,B.D.,Silvia,D.inprep.).Theseshowthesameregionofthesimulationvolume,bothat320Myrafterthestartofthesimulation.Whilethecentralregionsofthewingplumesofenrichedmaterialdisplay3http://trident-project.org/185Figure6.3:Thedistributionofgasmassintemperature-velocityspaceintheREsimulation.Toshowgasmotiontowardsandawayfromthegalaxy,onlythecomponentofvelocitynormaltotheplaneofthediskisused.Thedatashownisforaregionofgas240kpcwideand100kpctallextendingupwardsabovethegalaxy,withthebottomedge30kpcabovethegalaxymidplane.186nearlyidenticalmorphologiesandnumberdensities,theOVIdistributionsextendstolargerradiithanCIV.Astheradiusincreasethenumberdensitiesofbothspeciesdecrease,andtheinhomogeneousstructureofthedistributionwouldmanifestinobservationsasareducedcoveringfraction.Figure6.4:AprojectionoftheOVInumberdensityinthecentral360kpcoftheLRsimulationafter320Myr.Thediskisviewededge-on.Figure6.6showstheprojectednumberdensityofMgIIintheplumesextendingaboveandbelowthediskofthegalaxy.ThesimulationtimeandregionshownisthesameasinFigures6.4and6.5.MgIItrackscoldgas,andthisisinFigure6.6,withthenumber187Figure6.5:SameasFigure6.4,butshowingtheprojectedCIVnumberdensity.Theplumesarestillpropagatingoutwards,buttheCIVdistributiondoesnotextendtoaslargeofradiiastheOVIdistribution.188densitybeingtlymorecentrallyconcentratedthaneitherCIVorOVI,withhighdensitiesinthediskanditsimmediatesurroundingsaswellasinthecentralregionsofthecoldcloudsintheplumes.Takentogether,Figures6.4,6.5,and6.6illustratetheobservedbehavioroftherelativefractionsoflowandhighionsasafunctionofradius.Thehigh-ionizationstategasextendsfurtherfromthecenterofthegalaxythanlower-ionizationstategas,andthecoveringfractionofallthreespeciesdecreaseswithradius.Figure6.6:SameasFigure6.4,butshowingtheprojectedMgIInumberdensity.MgIIisbeingdrivenintothehalogas,butitisnotreachingasgreatofaradialextentasOVIorCIV.189ThedevelopmentoftheOVIradialdistributionasafunctionoftimeisshowninFigure6.7.Thisureshowsthespherically-averagedradialpoftheOVInumberdistributionaroundthecenterofthegalaxy.Thevariouslinesshowthetimeevolutionofthein5Myrincrements,withthetheyellow,leftmostlinesshowingtheearliesttimesinthesimu-lation,andtherightmost,darkestvioletlineshowingtheafter320Myrofevolution.AstimeprogressesanincreasingamountofOVIisexpelledfromthediskintothehalogas,reachingprogressivelylargerradii.Figure6.7:RadialoftheOVInumberdensitythroughouttimeintheLRsimulation.Eachlinerepresentsattime,rangingfromthestartofthesimulation(yellow,leftmostline)to320Myr(darkestviolet,rightmostline)in5Myrincrements.AtrendsimilartrendintothatofOVIisseenwithCIV.Figure6.8showstheevolution190ofthespherically-averagedradialoftheCIVnumberacrossthedurationofthesimulation.AsinFigure6.7,eachlineshowstheatagiventime,with5Myrintervalsbetweenlines.Theearliesttimeisshownbytheyellow,leftmostline,andthedarkestviolet,rightmostlineshowsthestateofthesimulationafter320Myrofevolution.ComparingFigures6.7and6.8illustratestheintheextentofthedistributionsofthetwospecies.TheCIVnumberdensitydropssharplyataradiusofapproximately160kpc,whileasimilaredgeisnotseenintheOVITheOVIdeclinesatthisradius,butmuchmoregradually,extendingfarfurtherintothehalothanCIV.Theinextentisincreasingwithtime,suggestingthatthisseparationwillbecomemorepronouncedwithtime.Thespherically-averagedradialdistributionofMgIIisshowninFigure6.9.IncontrasttotheofOVIandCIV,thedistributionofMgIIhasamuchsmallerradialextent.Inadditiontobeingmorecentrallyconcentrated,thedensityofMgIIinthecentral60kpcismuchhigherthaneitherOVIorCIV.Thisbehaviorisagaininagreementwithobservationsofthediminishedradialextentoflow-ionizationspecies,whilehigherionscontinuetoexistarelargerradii.Thesepreliminaryresultsshowgreatpromisefortheabilityofourmethodtorepro-ducetheobservedcharacteristicsoftheCGMandaidintheunderstandingofthephysicalprocessesthatproduceitsmorphology,chemistry,andkinematicstate.Theywillalsopro-videapowerfulcomputationaltoolforinvestigatingthemodelofprecipitationregulatedfeedbackingalaxiesandattemptingtoreproduceitspredictedbehaviorinhigh-resolutionmultiphysicssimulations.191Figure6.8:RadialoftheCIVnumberdensitythroughouttimeintheLRsimulation.Eachlinerepresentsattime,rangingfromthestartofthesimulation(yellow,leftmostline)to320Myr(darkestviolet,rightmostline)in5Myrincrements.192Figure6.9:RadialpoftheMgIInumberdensitythroughouttimeintheLRsimulation.Eachlinerepresentsattime,rangingfromthestartofthesimulation(yellow,leftmostline)to320Myr(darkestviolet,rightmostline)in5Myrincrements.193Chapter7ConclusionsandFutureWork7.1ConclusionsThisdissertationhasexploredtheuseofsemi-analytictechniquesinmodellingstellarpop-ulationsandtheirinteractionswiththeirsurroundingsacrossarangeofastrophysicalenvi-ronments.Chapter3studiedtheenvironmentofPopulationIII(PopIII)starformationanddevelopedamodeltoidentifyPopIIIstar-forminghalosinanN-bodycosmologicalsimula-tion.ThismodeldemonstratedthatPopIIIstarformationpersistsforamuchlongerperiodthanpreviouslythought,andthatatlatetimesPopIIIstarsforminmassivehalosthatgrowrapidlyinunderdenseregions.Chapter4builtonthisworkbydevelopingandintegratingasophisticatedmodelforstarformation,feedback,andgalacticchemicalevolution.Byuti-lizingstellarevolutionandnucleosynthesisdataitisabletomodelthechemicalevolutionofhighredshiftproto-galaxiesastheybothmergeandevolvesecularly.AChabrierIMFandanelevatedstarformationwerebestabletoreproducetheobservationaldata,anddiscrepanciesbetweensimulatedandobservedabundancedistributionsidenseveralelementsthatarebeingtreatedincorrectlyinstellarnucleosynthesissimulations.Chapter5introducedthe\galaxyparticle"methodforsimulatinggalaxiesincosmologicalsimula-tionsofgalaxyclusters.Galaxyparticlestreatinternalgalaxyprocessesassub-resolutionphenomena,possessanextendedspatialextentwhichallowsthemtointeractwiththeirsurroundings,andevolvebothsecularlyandthroughinteractionsbetweenparticles.Pre-194liminaryresultsfromsimulationswithgalaxyparticlesindicatethatthismethodproducesrealisticpopulationsofgalaxies,withaspatialdistributionandmergingbehaviorthatisagreementwithobservations.Stellarfeedbackenrichestheintraclustermedium(ICM)torealisticlevelsandproducesamorphologyandradialmetallicitysimilartowhatisobserved.Discprepanciesbetweentheobservedandsimulatedstellarmassandcentralmetallicityarelikelylinkedandindicatethatthestarformationmodelneedsment.InChapter6mo\starparticles"areusedtomodelstellarpopulationsindiskgalax-ies,studytheformationandevolutionofthecircumgalacticmedium(CGM),andexplorewhetherprecipitationofcloudsofcoldgasintheCGMcanproduceaself-regulatingsystemwithstarformationandAGNfeedback.PreliminaryresultsshowthatthemultiphasegasisdevelopingintheCGM,andthatthemorphology,ionizationstate,andkinematicsoftheCGMareinagreementwithobservations.BelowIpresentseveraldirectionstoextendandimproveupontheinvestigationsexploredinthisdissertation.7.2FutureWork7.2.1PopulationIIIStarFormationChapter3introducedanewmethodformodelingPopIIIstarformationincosmologicalN-bodysimulationsandpresentedresultsontheevolutionoftheenvironmentsinwhichPopIIIstarsform.Afulldiscussionofpossibleavenuesforfuturework,includingimprovementstomitigatelimitationsofthemodelsarediscussedinSection3.5.4,butareviewofseveralparticularlysalientpossiblitiesisgivenhere.Amoresophisticatedmannerofassociatingdarkmatter(DM)particleswithspec195halos,suchastheRockstarhalo(Behroozietal.,2013)wouldprovideamorephys-icallyrealistichalocatalogandmergertree,moreaccuratelymodelingthestarformationenvironments.Thehaloassemblyhistoryisnotcurrentlyconsideredinthismodel.Rapidhalogrowthincreasesthetemperatureofahalo,whichcanspurH2production,leadingtomoretcoolingandcolderhalocores(O'Shea&Norman,2007).Thiscouldpoten-tiallyenablehaloslessmassivethanthecurrentPopIIIstarformingmassthresholdtocooltlyandformstars.Theimpactofthiswouldbemostpronouncedatlatetimes,whenPopIIIstarformationoccursprimarilyinhalosthataregrowingrapidly.Radiativefeedbackistreatedasbeinghomogeneousthroughouttheentiresimulationvolume.Thisisalikelyareasonableassumption,buttheinclusionofanisotropicradiativefeedback,aswellasionizingradiationfromstellarpopulations,wouldbemorerealistic.Interactionsbetweenhalosarecurrentlynotconsidered,andwhilePopIIIstarsarefoundtoforminisolatedregionswellawayfromhaloswhicharehostingchemicallyenrichedstarformation,thepollutionofnearby,pristinehalosbyenrichedmaterialexpelledfromahaloinwhichstarformationisoccurringispossible.Smithetal.(2015)demonstratedthatenrichedmaterialdrivenfromahaloinwhichaPopIIIsupernova(SN)hasoccurredcanimpingeonnearbychemically-pristinehalos,inducingturbulenceandfragmentationwhichtlymixestheSNejectaintothepristinegas.Thismodelwasdesignedwiththeconcurrentgoalsofstudyingtheformationenviron-mentsofPopIIIstarsbeyondtheformationofthestar,andtodevelopatoolfortheidenofPopIIIstarforminghalosforhigh-resolutionresimulation.Theresultsofthisstudyidenmorethan40;000halosinasinglecosmologicalsimulationthatarecapableofformingPopIIIstars.Byutilizingacatalogofthissort,simulationsofPopIIIstarformationcancreateamuchmorecompletepictureofthenatureofPopIIIstars.The196ofhaloassemblyhistory,environment,andthepresenceofionizingandphotodisso-ciatingradiationcanbeexplored.PopIIIformationbehaviorandstellarpropertiescanbestudiedintheeraofconcurrentprimordialandchemicallyenrichedstarformation,helpingtoformamorecompletepictureofthesebygoneobjectsandtheroletheyplayedinthedevelopmentoftheuniverseasitistoday.7.2.2GalacticChemicalEvolutionSuggestionsforfutureworkandadiscussionofthelimitationsofthechemicalevolutionmodelsexploredinChapter4aredetailedinSection4.5.5andsummarizedhere.Thisworkwouldbesubstantiallyimprovedbytheadditionsofamorecomplete,self-consistentsetofstellarnucleosyntheticyields,particularlybelow0:1Z.Therearesub-stantialgapsinthemassandmetallicityrangesforwhichstellaryielddataisavailable,andthedatathatisavailableareprovidedbyawidevarietyofgroupsusingttechniques,fundamentalassumptions,andsimulationcodes.TheyieldsfromPopIIIstarsarepartic-ularlyunreliable,astheabsenceofobservationaldataexacerbatesthealreadysubstantialuncertaintiesinthestellarnucleosynthesissimulations,andtheweakconstraintsonthePopIIIinitialmassfunction(IMF)requiresalargenumberofsimulationstoprovidefullcoverageofpotentialPopIIImasses.ThefateofPopIIIstarsandthenatureofthesupernovae(SNe)whicharethoughttohavebeentheirfatespresentsanotheruncertainty,astheenergeticsoftheseexplosionscanplayacrucialroleintheevolutionofthehalosinwhichtheyoccurandthetransitiontoachemically-enrichedmodeofstarformation(Cooke&Madau,2014).Extendingthesesimulationsbeyondz=6wouldallowforamoredirectandcompletecomparisonbetweenthepredictionsofourmodelandobservationaldatagatheredatz=0.Reachinglowerredshiftswillenablecomparisonwithmoreandlargerobservationaldatasets.197CarryingthesesimulationstoredshiftslowenoughthatMilkyWay-likegalaxiesformwouldallowforanassessmentofthefateofthehighredshiftproto-galaxiesthataremodeledinthiswork,whileenablingcomparisonbetweentheseingsandthegrowingbodyofobservationsofMilkyWaydwarfgalaxies.Improvedmethodsofcomparingthesimulatedstellarabundancedistributionstoob-servationaldatawillimprovethequalityoftheseresults.SophisticatedtechniquessuchasGaussianMultiprocessemulationcoupledwithMarkovChainMonteCarlotoolsandANOVAdecompositionwillallowforrapid,quaninvestigationofthelargeparam-eterspacecoveredbythismodelomezetal.,2012,2014).Theinclusionofadditionalphysicalprocesses,suchasadust-mediatedtransitiontochemicallyenrichedstarformation,willbothbolsterthecapabilitiesofthismodelwhileincreasingtheneedforthesetypesofsophisticatedstatisticaltools.7.2.3GalaxyClusterSimulationsWithGalaxyParticlesTwooftheprevailingchallengesinsimulationsofgalaxyclustersarereproducingtheob-servedcharacteristicsofthegalaxypopulationsandreproducingthestructureofthecentralregionsofclusters,includingproducingrealisticpopulationsofcool-coreandnon-cool-corecluster(e.g.,Sandersonetal.(2006);Chenetal.(2007)).The\galaxyparticle"methodde-velopedinChapter5primarilyworkstoaddresstheformerofthesechallenges,butthesetwoarenotindependent.Thereisclearevidenceoftheco-evolutionoftheintraclustermedium(ICM)andstellarpopulationsingalaxyclusters.ThiscanbeseeninthemetallicitygradientoftheICM,thedeclineinstellarmassfractionwithincreasingclustermass(Gonzalezetal.,2013),andthemanyconnectionsbetweenthebrightestclustergalaxy(BCG)andtheoverallmorphologyofthecluster.Manyrecentsimulationshaveshownthatfeedbackfromactive198galacticnuclei(AGN)isnecessarytoproducegalaxyclusterswithrealisticcentralregionsandcool-corefractionsthatareinagreementwithobservations(e.g.,Borganietal.(2008);Duboisetal.(2011);Martizzietal.(2012);Skoryetal.(2013)).GiventhesethenaturalextensionofthegalaxyparticlemethodistocoupleitsfunctionalitytomodelsofAGNfeedback.Lietal.(2015)hasinvestigatedtherelationshipbetweenstarformationandAGNfeedbackinidealizedclustercoresandfoundthatprecipitation-regulatedAGNfeedbackcanproducerealisticstarformationrates.SimulatingrealisticgalaxyclustersfromcosmologicalinitialconditionsandreproducingboththeobservedgalaxypopulationsandthestructureofclustercoreswilllikelyrequirebothAGNfeedbackandasophisticatedmethodofmodelinggalaxyformationandevolutionsuchasgalaxyparticles.Galaxyparticlesaredesignedinamodularfashion,andadditionalmodelsforinternalgalacticprocessessuchasstarformation,SNfeedback,andrampressurestrippingcanbereadilyaddedandtested.Amoresophisticatedmannerofmodelingstellarchemicalfeedback(akintothatpresentedinChapter4)couldbeintegratedtostudytheprocessofchemicalenrichmentinclustergalaxiesandtheattendantenrichmentoftheICM.Itisknownthatnon-thermalprocessesplayanimportantroleingalaxyclusterevolution.Simulationsthatincludetheectsofnon-idealmagnetohydrodynamicsandcosmicraytransportcanpotentiallyproducegalaxyclustersinbetteragreementwithobservationsthanthosethatneglecttheseIntegrationoftheseprocesseswithgalaxyparticle-basedsimulationspresentanenticingavenueofstudyingalaxyclusterformationandevolution.1997.2.4ThermalInstabilitiesandPrecipitationintheCircumgalac-ticMediumThesimulationframeworkandstarparticlealgorithmdevelopedinChapter6presentapowerfultoolforunderstandingthenatureoftheCGMandinterpretingthegrowingbodyofobservationsofthismedium.Thismethodisparticularlywell-suitedforuseinstudyingtheprecipitation-regulatedfeedbackmodel(Voitetal.,2015a)andthepredictionsthatitmakesaboutgalaxyevolution.ThethermalanddynamicalstateoftheCGMcanbedeterminedinamannerthatenablescomparisonofthegascoolingtime,tcool,andthefreefalltime,t,enablinganassessmentofwhetheraparcelofgaswitharatiooftcool=t<10ispredisposedtocoolandprecipitate.Ifso,doesthisgasfuelstarformationinthedisk,triggeringafeedbackresponsethatincreasesthecoolingtimetlytohaltprecipitationuntilstarformationceasesandthecoolingtimecandropagain?Otherpredictionsofthismodelcanbetestedwiththeframeworkdevelopedhere.Themassofthegalaxycanbevariedinasystematicway,makingitpossibletoassesswhetherthegalaxymass-metallicityrelationisrecovered.Similarly,therelationshipbetweenanincreaseinthegalaxymetallicityandacorrespondingdecreaseinthestarformationratecanbeexplored.Thesimulationscurrentlybeingusedarehighlyidealized.Relaxingsomeofthesecon-straintswouldfacilitatethesimulationsofmorerealisticgalaxiesandtheinclusionofmorephysicalandcosmologicalprocesses.Itisknownthatmaterialfromtheintergalacticmedium(IGM)istransportedintotheCGM,andthisprocessisnotcapturedinthecurrentsimu-lationsetup.Theuseofinwboundaryconditionsinthesimulationwouldallowforthisprocesstobeincludedinamanner.Goingbeyondthat,thecurrentidealizedinitialconditionscouldbereplacedwithcosmologicallygeneratedinitialconditions.This200wouldallowfortheofcosmologicalstructureformationtobemodeled,replacingtheregular,predictablesupplyofmaterialfromwboundaryconditionswithahighlyirregular,inconsistentsupplyofexternalmaterial.Higherresolution,large-scalesimulationswillbeneededtoaccomplishthesenextsteps,alongwithanexpandedsuiteofphysicalprocesses.WithfurtherdevelopmentofthetoolsandmethodspresentedinthisworkamorecompleteunderstandingoftheCGManditsroleingalaxyformationiswithinreach.201BIBLIOGRAPHY202BIBLIOGRAPHYAbel,T.,Anninos,P.,Zhang,Y.,&Norman,M.L.1997,NewAstronomy,2,181Abel,T.,Bryan,G.L.,&Norman,M.L.2000,ApJ,540,39|.2002,Science,295,93Ahn,K.,Shapiro,P.R.,Iliev,I.T.,Mellema,G.,&Pen,U.-L.2009,ApJ,695,1430AllendePrieto,C.,etal.2008,AstronomischeNachrichten,329,1018Anderson,M.E.,&Bregman,J.N.2010,ApJ,714,320Arieli,Y.,Rephaeli,Y.,&Norman,M.L.2010,ApJ,716,918Arnaud,M.,Pratt,G.W.,R.,ohringer,H.,Croston,J.H.,&Pointecouteau,E.2010,A&A,517,A92Beers,T.C.,&Christlieb,N.2005,ARA&A,43,531Behroozi,P.S.,Wechsler,R.H.,&Wu,H.-Y.2013,ApJ,762,109Belokurov,V.2013,NewAstronomyReviews,57,100Bertschinger,E.2001,ApJS,137,1Bigiel,F.,etal.2011,ApJ,730,L13Bland-Hawthorn,J.,Veilleux,S.,Cecil,G.N.,Putman,M.E.,Gibson,B.K.,&Maloney,P.R.1998,MNRAS,299,611Bonamente,M.,etal.2013,inIAUSymposium,Vol.289,AdvancingthePhysicsofCosmicDistances,ed.R.deGrijs,339{343Bordoloi,R.,etal.2014,ApJ,796,136Borgani,S.,Fabjan,D.,Tornatore,L.,Schindler,S.,Dolag,K.,&Diaferio,A.2008,SpaceSci.Rev.,134,379Borgani,S.,&Kravtsov,A.2011,AdvancedScienceLetters,4,204Borgani,S.,etal.2004,MNRAS,348,1078Bouwens,R.J.,etal.2011,ApJ,737,90Bovill,M.S.,&Ricotti,M.2009,ApJ,693,1859Bregman,J.N.1980,ApJ,236,577203Bregman,J.N.,&Lloyd-Davies,E.J.2007,ApJ,669,990Bromm,V.,Coppi,P.S.,&Larson,R.B.1999,ApJ,527,L5|.2002,ApJ,564,23Bromm,V.,Ferrara,A.,Coppi,P.S.,&Larson,R.B.2001,MNRAS,328,969Bromm,V.,&Loeb,A.2003,Nature,425,812Bromm,V.,&Yoshida,N.2011,ARA&A,49,373Bromm,V.,Yoshida,N.,&Hernquist,L.2003,ApJ,596,L135Brooks,A.M.,Governato,F.,Quinn,T.,Brook,C.B.,&Wadsley,J.2009,ApJ,694,396Bryan,G.L.,etal.2014,ApJS,211,19Burkert,A.1995,ApJ,447,L25Cardiel,N.,Gorgas,J.,&Aragon-Salamanca,A.1998,MNRAS,298,977Cavagnolo,K.W.,Donahue,M.,Voit,G.M.,&Sun,M.2008,ApJ,683,L107Cavaliere,A.,&Fusco-Femiano,R.1978,A&A,70,677Cen,R.,&Ostriker,J.P.1992,ApJ,399,L113|.1993,ApJ,417,404Chabrier,G.2003,PASP,115,763Chen,P.,Wise,J.H.,Norman,M.L.,Xu,H.,&O'Shea,B.W.2014,ApJ,795,144Chen,Y.,Reiprich,T.H.,ohringer,H.,Ikebe,Y.,&Zhang,Y.-Y.2007,A&A,466,805Clark,P.C.,Glover,S.C.O.,Klessen,R.S.,&Bromm,V.2011a,ApJ,727,110Clark,P.C.,Glover,S.C.O.,Smith,R.J.,Greif,T.H.,Klessen,R.S.,&Bromm,V.2011b,Science,331,1040Collins,J.A.,Shull,J.M.,&Giroux,M.L.2005,ApJ,623,196|.2009,ApJ,705,962Cooke,R.J.,&Madau,P.2014,ApJ,791,116Corlies,L.,Johnston,K.V.,Tumlinson,J.,&Bryan,G.2013,ApJ,773,105Couchman,H.M.P.,&Rees,M.J.1986,MNRAS,221,53Cox,D.P.2005,ARA&A,43,337204Crocce,M.,Pueblas,S.,&Scoccimarro,R.2006,MNRAS,373,369Crosby,B.D.,O'Shea,B.W.,Beers,T.C.,&Tumlinson,J.2016,ApJ,820,71Crosby,B.D.,O'Shea,B.W.,Smith,B.D.,Turk,M.J.,&Hahn,O.2013,ApJ,773,108deAvillez,M.A.2000,MNRAS,315,479deAvillez,M.A.,&Breitschwerdt,D.2005,A&A,436,585deBennassuti,M.,Schneider,R.,Valiante,R.,&Salvadori,S.2014,MNRAS,445,3039deHeij,V.,Braun,R.,&Burton,W.B.2002,A&A,391,159DeLucia,G.,Tornatore,L.,Frenk,C.S.,Helmi,A.,Navarro,J.F.,&White,S.D.M.2014,MNRAS,445,970Deng,L.-C.,etal.2012,ResearchinAstronomyandAstrophysics,12,735Diemand,J.,Kuhlen,M.,&Madau,P.2006,ApJ,649,1Domainko,W.,etal.2006,A&A,452,795Dopcke,G.,Glover,S.C.O.,Clark,P.C.,&Klessen,R.S.2013,ApJ,766,103Dubois,Y.,Devriendt,J.,Teyssier,R.,&Slyz,A.2011,MNRAS,417,1853Eckert,D.,etal.2012,A&A,541,A57Efstathiou,G.,Davis,M.,White,S.D.M.,&Frenk,C.S.1985,ApJS,57,241Eisenstein,D.J.,&Hu,W.1999,ApJ,511,5Ellison,S.L.,Patton,D.R.,Simard,L.,&McConnachie,A.W.2008,ApJ,672,L107Erb,D.K.2008,ApJ,674,151Faber,S.M.,&Jackson,R.E.1976,ApJ,204,668Fabian,A.C.1994,ARA&A,32,277Fang,T.,Mckee,C.F.,Canizares,C.R.,&WM.2006,ApJ,644,174Feltzing,S.,&Chiba,M.2013,NewAstronomyReviews,57,80Ferland,G.J.,etal.2013,Rev.MexicanaAstron.49,137Font,A.S.,Johnston,K.V.,Bullock,J.S.,&Robertson,B.E.2006,ApJ,638,585Frebel,A.2010,AstronomischeNachrichten,331,474Frebel,A.,&Bromm,V.2012,ApJ,759,115205Frebel,A.,Kirby,E.N.,&Simon,J.D.2010a,Nature,464,72Frebel,A.,&Norris,J.E.2015,ARA&A,53,631Frebel,A.,Simon,J.D.,Geha,M.,&Willman,B.2010b,ApJ,708,560Frebel,A.,Simon,J.D.,&Kirby,E.N.2014,ApJ,786,74Freeman,K.,&Bland-Hawthorn,J.2002,ARA&A,40,487Fuller,T.M.,&Couchman,H.M.P.2000,ApJ,544,6Galli,D.,&Palla,F.1998,A&A,335,403Gaspari,M.,Brighenti,F.,&Temi,P.2015,A&A,579,A62Gaspari,M.,Melioli,C.,Brighenti,F.,&D'Ercole,A.2011,MNRAS,411,349Gaspari,M.,Ruszkowski,M.,&Oh,S.P.2013,MNRAS,432,3401Gaspari,M.,Ruszkowski,M.,&Sharma,P.2012,ApJ,746,94Gilmore,G.,Norris,J.E.,Monaco,L.,Yong,D.,Wyse,R.F.G.,&Geisler,D.2013,ApJ,763,61Gilmore,G.,etal.2012,TheMessenger,147,25Glover,S.C.O.,&Jappsen,A.-K.2007,ApJ,666,1omez,F.A.,Coleman-Smith,C.E.,O'Shea,B.W.,Tumlinson,J.,&Wolpert,R.L.2012,ApJ,760,112|.2014,ApJ,787,20omez,F.A.,Helmi,A.,Cooper,A.P.,Frenk,C.S.,Navarro,J.F.,&White,S.D.M.2013,MNRAS,436,3602Gonzalez,A.H.,Sivanandam,S.,A.I.,&Zaritsky,D.2013,ApJ,778,14Graves,G.J.,Faber,S.M.,&Schiavon,R.P.2009,ApJ,693,486Graziani,L.,Salvadori,S.,Schneider,R.,Kawata,D.,deBennassuti,M.,&Maselli,A.2015,MNRAS,449,3137Grcevich,J.,&Putman,M.E.2009,ApJ,696,385Greif,T.H.,Bromm,V.,Clark,P.C.,Glover,S.C.O.,Smith,R.J.,Klessen,R.S.,Yoshida,N.,&Springel,V.2012,MNRAS,424,399Greif,T.H.,Springel,V.,White,S.D.M.,Glover,S.C.O.,Clark,P.C.,Smith,R.J.,Klessen,R.S.,&Bromm,V.2011,ApJ,737,75206Gunn,J.E.,&Gott,III,J.R.1972,ApJ,176,1Haardt,F.,&Madau,P.2012,ApJ,746,125Hahn,O.,&Abel,T.2011,MNRAS,415,2101Hamilton,A.J.S.1993,ApJ,417,19Heckman,T.M.2003,inRevistaMexicanadeAstronomiayConferenceSeries,Vol.17,RevistaMexicanadeAstronomiayConferenceSeries,ed.V.Avila-Reese,C.Firmani,C.S.Frenk,&C.Allen,47{55Heger,A.,Fryer,C.L.,Woosley,S.E.,Langer,N.,&Hartmann,D.H.2003,ApJ,591,288Heger,A.,&Woosley,S.E.2002,ApJ,567,532Hill,A.S.,L.M.,&Reynolds,R.J.2009,ApJ,703,1832Hockney,R.W.,&Eastwood,J.W.1988,ComputersimulationusingparticlesA.S.,Donahue,M.,Hicks,A.,&Barthelemy,R.S.2012,ApJS,199,23Hopkins,P.F.,Narayanan,D.,&Murray,N.2013,MNRAS,432,2647Hosokawa,T.,Omukai,K.,Yoshida,N.,&Yorke,H.W.2011,Science,334,1250Hosokawa,T.,Yoshida,N.,Omukai,K.,&Yorke,H.W.2012,ApJ,760,L37Hsu,W.-H.,Putman,M.E.,Heitsch,F.,Stanimirovic,S.,Peek,J.E.G.,&Clark,S.E.2011,AJ,141,57Ikebe,Y.,etal.1997,ApJ,481,660Ishigaki,M.N.,Aoki,W.,Arimoto,N.,&Okamoto,S.2014,A&A,562,A146Ivezic,Z.,Beers,T.C.,&Juric,M.2012,ARA&A,50,251Iwamoto,K.,Brachwitz,F.,Nomoto,K.,Kishimoto,N.,Umeda,H.,Hix,W.R.,&Thiele-mann,F.-K.1999,ApJS,125,439Ji,A.P.,Frebel,A.,&Bromm,V.2014,ApJ,782,95Ji,A.P.,Frebel,A.,Chiti,A.,&Simon,J.D.2016,Nature,531,610Johnson,R.,Ponman,T.J.,&Finoguenov,A.2009,MNRAS,395,1287Kalberla,P.M.W.,Burton,W.B.,Hartmann,D.,Arnal,E.M.,Bajaja,E.,Morras,R.,&oppel,W.G.L.2005,A&A,440,775Kalberla,P.M.W.,&Haud,U.2006,A&A,455,481Kapferer,W.,Kronberger,T.,Weratschnig,J.,&Schindler,S.2007,A&A,472,757207Karakas,A.,&Lattanzio,J.C.2007,PASA,24,103Karakas,A.I.2010,MNRAS,403,1413Karlsson,T.,Bromm,V.,&Bland-Hawthorn,J.2013,ReviewsofModernPhysics,85,809Keres,D.,Katz,N.,Weinberg,D.H.,&Dave,R.2005,MNRAS,363,2Kerp,J.,Burton,W.B.,Egger,R.,Freyberg,M.J.,Hartmann,D.,Kalberla,P.M.W.,Mebold,U.,&Pietz,J.1999,A&A,342,213Kim,J.-h.,etal.2014,ApJS,210,14Kirby,E.N.,Simon,J.D.,Geha,M.,Guhathakurta,P.,&Frebel,A.2008,ApJ,685,L43Kitayama,T.,&Yoshida,N.2005,ApJ,630,675Kitayama,T.,Yoshida,N.,Susa,H.,&Umemura,M.2004,ApJ,613,631Klypin,A.,Zhao,H.,&Somerville,R.S.2002,ApJ,573,597Knebe,A.,etal.2011,MNRAS,415,2293Kobayashi,C.,&Nakasato,N.2011,ApJ,729,16Kobayashi,C.,&Nomoto,K.2009,ApJ,707,1466Kobayashi,C.,Umeda,H.,Nomoto,K.,Tominaga,N.,&Ohkubo,T.2006,ApJ,653,1145Komatsu,E.,etal.2011,ApJS,192,18Komiya,Y.2011,ApJ,736,73Komiya,Y.,Habe,A.,Suda,T.,&Fujimoto,M.Y.2010,ApJ,717,542Kormendy,J.,&Ho,L.C.2013,ARA&A,51,511Kravtsov,A.V.,&Borgani,S.2012,ARA&A,50,353Kroupa,P.2002,Science,295,82Lacey,C.,&Cole,S.1993,MNRAS,262,627Lada,C.J.,Lombardi,M.,&Alves,J.F.2010,ApJ,724,687Latif,M.A.,Schleicher,D.R.G.,Schmidt,W.,&Niemeyer,J.2013,MNRAS,432,668Leccardi,A.,&Molendi,S.2008,A&A,486,359Lehner,N.,&Howk,J.C.2011,Science,334,955Lehner,N.,Howk,J.C.,Thom,C.,Fox,A.J.,Tumlinson,J.,Tripp,T.M.,&Meiring,J.D.2012,MNRAS,424,2896208Lehner,N.,Howk,J.C.,&Wakker,B.P.2015,ApJ,804,79Leitherer,C.,Robert,C.,&Drissen,L.1992,ApJ,401,596Lewis,A.D.,Stocke,J.T.,&Buote,D.A.2002,ApJ,573,L13Li,Y.,&Bryan,G.L.2014a,ApJ,789,54|.2014b,ApJ,789,153Li,Y.,Bryan,G.L.,Ruszkowski,M.,Voit,G.M.,O'Shea,B.W.,&Donahue,M.2015,ApJ,811,73Liang,C.J.,&Chen,H.-W.2014,MNRAS,445,2061Liu,L.,Gerke,B.F.,Wechsler,R.H.,Behroozi,P.S.,&Busha,M.T.2011,ApJ,733,62Loken,C.,Norman,M.L.,Nelson,E.,Burns,J.,Bryan,G.L.,&Motl,P.2002,ApJ,579,571Machacek,M.E.,Bryan,G.L.,&Abel,T.2001,ApJ,548,509Machida,M.N.,Omukai,K.,Matsumoto,T.,&Inutsuka,S.-i.2008,ApJ,677,813Maloney,P.R.,&Putman,M.E.2003,ApJ,589,270Mannucci,F.,Cresci,G.,Maiolino,R.,Marconi,A.,&Gnerucci,A.2010,MNRAS,408,2115Marinacci,F.,Fraternali,F.,Nipoti,C.,Binney,J.,Ciotti,L.,&Londrillo,P.2011,MNRAS,415,1534Martizzi,D.,Teyssier,R.,&Moore,B.2012,MNRAS,420,2859Mateo,M.L.1998,ARA&A,36,435Matsushita,K.2011,A&A,527,A134McBride,J.,Fakhouri,O.,&Ma,C.-P.2009,MNRAS,398,1858McConnachie,A.W.2012,AJ,144,4McConnachie,A.W.,etal.2009,Nature,461,66McGaugh,S.S.2008,inIAUSymposium,Vol.244,DarkGalaxiesandLostBaryons,ed.J.I.Davies&M.J.Disney,136{145McGaugh,S.S.,Schombert,J.M.,deBlok,W.J.G.,&Zagursky,M.J.2010,ApJ,708,L14McKee,C.F.,&Tan,J.C.2008,ApJ,681,771209McNamara,B.R.,&Nulsen,P.E.J.2007,ARA&A,45,117|.2012,NewJournalofPhysics,14,055023McNamara,B.R.,&O'Connell,R.W.1989,AJ,98,2018Meece,G.R.,Smith,B.D.,&O'Shea,B.W.2014,ApJ,783,75Miyamoto,M.,&Nagai,R.1975,PASJ,27,533Mo,H.J.,&White,S.D.M.1996,MNRAS,282,347Muller,C.A.,Oort,J.H.,&Raimond,E.1963,AcademiedesSciencesParisComptesRendus,257,1661Nagai,D.,Kravtsov,A.V.,&Vikhlinin,A.2007,ApJ,668,1Nomoto,K.1982,ApJ,253,798Nomoto,K.,Iwamoto,K.,Nakasato,N.,Thielemann,F.-K.,Brachwitz,F.,Tsujimoto,T.,Kubo,Y.,&Kishimoto,N.1997,NuclearPhysicsA,621,467Nomoto,K.,Tominaga,N.,Umeda,H.,Kobayashi,C.,&Maeda,K.2006,NuclearPhysicsA,777,424Norris,J.E.,Gilmore,G.,Wyse,R.F.G.,Wilkinson,M.I.,Belokurov,V.,Evans,N.W.,&Zucker,D.B.2008,ApJ,689,L113Oesch,P.A.,etal.2014,ApJ,786,108|.2016,ApJ,819,129Omma,H.,Binney,J.,Bryan,G.,&Slyz,A.2004,MNRAS,348,1105Omukai,K.2000,ApJ,534,809O'Shea,B.W.,McKee,C.F.,Heger,A.,&Abel,T.2008,inAmericanInstituteofPhysicsConferenceSeries,Vol.990,FirstStarsIII,ed.B.W.O'Shea&A.Heger,D13O'Shea,B.W.,&Norman,M.L.2007,ApJ,654,66|.2008,ApJ,673,14O'Shea,B.W.,Wise,J.H.,Xu,H.,&Norman,M.L.2015,ApJ,807,L12Pancino,E.2012,MemoriedellaSocietaAstronomicaItalianaSupplementi,19,354Paxton,B.,Bildsten,L.,Dotter,A.,Herwig,F.,e,P.,&Timmes,F.2011,ApJS,192,3Paxton,B.,etal.2013,ApJS,208,4210Peeples,M.S.,Werk,J.K.,Tumlinson,J.,Oppenheimer,B.D.,Prochaska,J.X.,Katz,N.,&Weinberg,D.H.2014,ApJ,786,54Peterson,J.R.,&Fabian,A.C.2006,Phys.Rep.,427,1Peterson,J.R.,Kahn,S.M.,Paerels,F.B.S.,Kaastra,J.S.,Tamura,T.,Bleeker,J.A.M.,Ferrigno,C.,&Jernigan,J.G.2003,ApJ,590,207Pila-DB.,Kuijken,K.,deJong,J.T.A.,Hoekstra,H.,&vanderBurg,R.F.J.2014,A&A,564,A18Placco,V.M.,Frebel,A.,Beers,T.C.,&StancliR.J.2014,ApJ,797,21Portinari,L.,Chiosi,C.,&Bressan,A.1998,A&A,334,505Putman,M.E.,Bland-Hawthorn,J.,Veilleux,S.,Gibson,B.K.,Freeman,K.C.,&Maloney,P.R.2003a,ApJ,597,948Putman,M.E.,Peek,J.E.G.,&Heitsch,F.2009,ArXive-printsPutman,M.E.,Peek,J.E.G.,&Joung,M.R.2012,ARA&A,50,491Putman,M.E.,Staveley-Smith,L.,Freeman,K.C.,Gibson,B.K.,&Barnes,D.G.2003b,ApJ,586,170Putman,M.E.,etal.2002,AJ,123,873y,D.A.,McNamara,B.R.,&Nulsen,P.E.J.2008,ApJ,687,899Raiteri,C.M.,Villata,M.,&Navarro,J.F.1996,A&A,315,105Rees,M.J.,&Ostriker,J.P.1977,MNRAS,179,541Ricotti,M.,Gnedin,N.Y.,&Shull,J.M.2002a,ApJ,575,33|.2002b,ApJ,575,49Robertson,B.E.,Ellis,R.S.,Furlanetto,S.R.,&Dunlop,J.S.2015,ApJ,802,L19Rossetti,M.,Eckert,D.,Cavalleri,B.M.,Molendi,S.,Gastaldello,F.,&Ghizzardi,S.2011,A&A,532,A123Safranek-Shrader,C.,Bromm,V.,&Milosavljevic,M.2010,ApJ,723,1568Salem,M.,&Bryan,G.L.2014,MNRAS,437,3312Salpeter,E.E.1955,ApJ,121,161Salvadori,S.,Ferrara,A.,Schneider,R.,Scannapieco,E.,&Kawata,D.2010,MNRAS,401,L5Salvadori,S.,Schneider,R.,&Ferrara,A.2007,MNRAS,381,647211Salvadori,S.,Skottir,A.,&Tolstoy,E.2015,MNRAS,454,1320Sanderson,A.J.R.,Edge,A.C.,&Smith,G.P.2009,MNRAS,398,1698Sanderson,A.J.R.,Ponman,T.J.,&O'Sullivan,E.2006,MNRAS,372,1496Sarazin,C.L.1988,X-rayemissionfromclustersofgalaxiesSaslaw,W.C.,&Zipoy,D.1967,Nature,216,976Schaerer,D.2003,A&A,397,527Schneider,R.,&Omukai,K.2010,MNRAS,402,429Schneider,R.,Omukai,K.,Inoue,A.K.,&Ferrara,A.2006,MNRAS,369,1437Sembach,K.R.,etal.2003,ApJS,146,165Shapiro,P.R.,&Field,G.B.1976,ApJ,205,762Shapley,A.E.2011,ARA&A,49,525Sheth,R.K.,&Tormen,G.1999,MNRAS,308,119Shull,J.M.,Stevans,M.,Danforth,C.,Penton,S.V.,Lockman,F.J.,&Arav,N.2011,ApJ,739,105Siess,L.2007,A&A,476,893|.2010,A&A,512,A10Silk,J.1977,ApJ,211,638Simionescu,A.,Werner,N.,Forman,W.R.,Miller,E.D.,Takei,Y.,ohringer,H.,Chura-zov,E.,&Nulsen,P.E.J.2010,MNRAS,405,91Simionescu,A.,etal.2011,Science,331,1576Skory,S.,Hallman,E.,Burns,J.O.,Skillman,S.W.,O'Shea,B.W.,&Smith,B.D.2013,ApJ,763,38Smith,B.,Sigurdsson,S.,&Abel,T.2008,MNRAS,385,1443Smith,B.D.,Turk,M.J.,Sigurdsson,S.,O'Shea,B.W.,&Norman,M.L.2009,ApJ,691,441Smith,B.D.,Wise,J.H.,O'Shea,B.W.,Norman,M.L.,&Khochfar,S.2015,MNRAS,452,2822Smith,R.J.,Iocco,F.,Glover,S.C.O.,Schleicher,D.R.G.,Klessen,R.S.,Hirano,S.,&Yoshida,N.2012,ApJ,761,154212Spitzer,Jr.,L.1956,ApJ,124,20Springel,V.,&Hernquist,L.2003,MNRAS,339,289Stacy,A.,&Bromm,V.2007,MNRAS,382,229|.2013,MNRAS,433,1094Stacy,A.,Greif,T.H.,&Bromm,V.2010,MNRAS,403,45|.2012,MNRAS,422,290Stanimirovic,S.,S.,Heiles,C.,Douglas,K.A.,Putman,M.,&Peek,J.E.G.2008,ApJ,680,276Starkenburg,E.,etal.2010,A&A,513,A34Steidel,C.C.,Erb,D.K.,Shapley,A.E.,Pettini,M.,Reddy,N.,Bogosavljevic,M.,Rudie,G.C.,&Rakic,O.2010,ApJ,717,289Steinmetz,M.2003,inAstronomicalSocietyofthePConferenceSeries,Vol.298,GAIASpectroscopy:ScienceandTechnology,ed.U.Munari,381Stone,J.M.,&Norman,M.L.1992,ApJS,80,753Sun,M.,Voit,G.M.,Donahue,M.,Jones,C.,Forman,W.,&Vikhlinin,A.2009,ApJ,693,1142Sutherland,R.S.,&Dopita,M.A.1993,ApJS,88,253Tafelmeyer,M.,etal.2010,A&A,524,A58Tan,J.C.,&McKee,C.F.2004,ApJ,603,383Tasker,E.J.,&Bryan,G.L.2006,ApJ,641,878Tegmark,M.,Silk,J.,Rees,M.J.,Blanchard,A.,Abel,T.,&Palla,F.1997,ApJ,474,1Tinsley,B.M.1980,Fund.CosmicPhys.,5,287Tollerud,E.J.,Boylan-Kolchin,M.,Barton,E.J.,Bullock,J.S.,&Trinh,C.Q.2011,ApJ,738,102Tolstoy,E.,Hill,V.,&Tosi,M.2009,ARA&A,47,371Trenti,M.,&Stiavelli,M.2009,ApJ,694,879Tufte,S.L.,Reynolds,R.J.,&L.M.1998,ApJ,504,773Tully,R.B.,&Fisher,J.R.1977,A&A,54,661Tumlinson,J.2006,ApJ,641,1213|.2010,ApJ,708,1398Tumlinson,J.,etal.2013,ApJ,777,59Turk,M.J.,Abel,T.,&O'Shea,B.2009,Science,325,601Turk,M.J.,Clark,P.,Glover,S.C.O.,Greif,T.H.,Abel,T.,Klessen,R.,&Bromm,V.2011a,ApJ,726,55|.2011b,ApJ,726,55Turk,M.J.,Oishi,J.S.,Abel,T.,&Bryan,G.L.2012,ApJ,745,154Turk,M.J.,Smith,B.D.,Oishi,J.S.,Skory,S.,Skillman,S.W.,Abel,T.,&Norman,M.L.2011c,ApJS,192,9Voit,G.M.2005,ReviewsofModernPhysics,77,207Voit,G.M.,Bryan,G.L.,O'Shea,B.W.,&Donahue,M.2015a,ApJ,808,L30Voit,G.M.,&Donahue,M.2015,ApJ,799,L1Voit,G.M.,Donahue,M.,Bryan,G.L.,&McDonald,M.2015b,Nature,519,203Wachter,A.,Scoder,K.-P.,Winters,J.M.,Arndt,T.U.,&Sedlmayr,E.2002,A&A,384,452Wakker,B.P.,York,D.G.,Wilhelm,R.,Barentine,J.C.,Richter,P.,Beers,T.C.,Ivezic,Z.,&Howk,J.C.2008,ApJ,672,298Wang,Q.D.,&McCray,R.1993,ApJ,409,L37Wang,Q.D.,etal.2005,ApJ,635,386Warren,M.S.,Abazajian,K.,Holz,D.E.,&Teodoro,L.2006,ApJ,646,881Werk,J.K.,etal.2014,ApJ,792,8Whalen,D.,Hueckstaedt,R.M.,&McConkie,T.O.2010,ApJ,712,101Whalen,D.,vanVeelen,B.,O'Shea,B.W.,&Norman,M.L.2008,ApJ,682,49White,S.D.M.,&Frenk,C.S.1991,ApJ,379,52White,S.D.M.,&Rees,M.J.1978,MNRAS,183,341Williams,R.J.,etal.2005,ApJ,631,856Wise,J.H.,&Abel,T.2005,ApJ,629,615Wise,J.H.,Abel,T.,Turk,M.J.,Norman,M.L.,&Smith,B.D.2012a,MNRAS,427,311Wise,J.H.,Turk,M.J.,Norman,M.L.,&Abel,T.2012b,ApJ,745,50214Wolcott-Green,J.,&Haiman,Z.2011,MNRAS,412,2603Wolcott-Green,J.,Haiman,Z.,&Bryan,G.L.2011,MNRAS,418,838Xu,H.,Norman,M.L.,O'Shea,B.W.,&Wise,J.H.2016,ApJ,823,140Xu,H.,O'Shea,B.W.,Collins,D.C.,Norman,M.L.,Li,H.,&Li,S.2008,ApJ,688,L57Yanny,B.,etal.2009,AJ,137,4377Yao,Y.,Nowak,M.A.,Wang,Q.D.,Schulz,N.S.,&Canizares,C.R.2008,ApJ,672,L21Yao,Y.,&Wang,Q.D.2007,ApJ,658,1088Yong,D.,etal.2013,ApJ,762,27Yoshida,N.,Abel,T.,Hernquist,L.,&Sugiyama,N.2003,ApJ,592,645Zucker,D.B.,deSilva,G.,Freeman,K.,Bland-Hawthorn,J.,&HermesTeam.2012,inAstronomicalSocietyofthePConferenceSeries,Vol.458,GalacticArchaeology:Near-FieldCosmologyandtheFormationoftheMilkyWay,ed.W.Aoki,M.Ishigaki,T.Suda,T.Tsujimoto,&N.Arimoto,421215