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Giant Molecular Cloud Collisions as Triggers of Star Cluster Formation

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Title:
Giant Molecular Cloud Collisions as Triggers of Star Cluster Formation Numerical Simulations and Observational Predictions
Creator:
Wu, Benjamin
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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english
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1 online resource (161 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
TAN,JONATHAN CHARLES
Committee Co-Chair:
FRY,JAMES N
Committee Members:
WHITING,BERNARD F
LADA,ELIZABETH ANNE
GONZALEZ,ANTHONY HERNAN
Graduation Date:
8/6/2016

Subjects

Subjects / Keywords:
Average linear density ( jstor )
Cooling ( jstor )
Density ( jstor )
Heating ( jstor )
Magnetic fields ( jstor )
Magnetism ( jstor )
Magnets ( jstor )
Simulations ( jstor )
Star formation ( jstor )
Velocity ( jstor )
Physics -- Dissertations, Academic -- UF
astronomy -- astrophysics -- numerical -- physics -- simulations -- star
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Physics thesis, Ph.D.

Notes

Abstract:
Stars primarily form in clusters from within giant molecular clouds (GMCs), but the dominant mechanisms triggering fragmentation and collapse are poorly understood. We investigate collisions between GMCs and their ability to induce gravitational instability and star cluster formation. This process may be a major driver of star formation activity in disk galaxies. Using magnetohydrodynamics (MHD) simulations with adaptive mesh refinement (AMR), we focus both on understanding the prevailing physical processes as well as predicting key observational signatures. We first develop and implement new photodissociation region (PDR) based heating and cooling functions that span the atomic to molecular transition, mirroring a chemically diverse, multiphase ISM and allowing modeling of non-equilibrium temperature structures. Then we develop an idealized 2D model of magnetized GMCs, systematically exploring the parameter space and investigating magnetic criticality in the context of cloud collisions. Expanding to 3D and adding supersonic turbulence, we model physically realistic GMCs, comparing and contrasting colliding vs. non-colliding cases. We characterize the morphologies of dense gas and magnetic field structure, signatures of cloud kinematics, and cloud dynamics, comparing results to Galactic clouds. Finally, we implement stochastic star formation sub-grid models exploring various levels of density and magnetic regulation. We explore the star formation rate over time, the spatial clustering of the formed stars, and the kinematics of the star particles in comparison to their natal gas cloud. We find key observational diagnostics of cloud collisions, especially: relative orientations between magnetic fields and density structures, like filaments; and 13CO(J=2-1), 13CO(J=3-2), 12CO(J=8-7) integrated intensity maps, line ratios, and spectra; cloud virial parameters; and properties of the resulting star clusters formed through GMC collision simulations. In comparison to observations of dense GMCs, a number of indicators suggest similarities toward the colliding scenario though it is difficult to draw definitive conclusions from current data. However, we have outlined a variety of potentially new observational signatures that can be the basis for future tests. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
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Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2016.
Local:
Adviser: TAN,JONATHAN CHARLES.
Local:
Co-adviser: FRY,JAMES N.
Statement of Responsibility:
by Benjamin Wu.

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UFRGP
Rights Management:
Copyright Wu, Benjamin. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Classification:
LD1780 2016 ( lcc )

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GIANTMOLECULARCLOUDCOLLISIONSASTRIGGERSOFSTARCLUSTERFORMATION:NUMERICALSIMULATIONSANDOBSERVATIONALPREDICTIONSByBENJAMINWUADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2016

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c2016BenjaminWu

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Tomylovingandsupportivemother,father,andsister,andtomychildhoodself,whosedreamsliveontothisday

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ACKNOWLEDGMENTSIwouldliketothankmyadvisor,JonathanC.Tanforhisguidance,patience,knowledge,andespeciallyunrelentingdetermination.IamthankfulforFumitakaNakamuraandthemembersoftheNationalAstronomicalObservatoryofJapanfortheirtutelageandhospitality,andtoDavidCollinsforhisenthusiasmandnumericalexpertise.Ithankthemembersofmysupervisorycommitteeaswellasthefacultyandpost-docsattheUniversityofFloridaforsharingtheirknowledgethroughoutallstagesofmygraduateeducation,especiallySvenVanLoo,DuncanChristie,andKeiTanaka,aswellastheothermembersoftheUFTheoreticalAstrophysicsgroupfortheirinsightfulconversationsandcamaraderie.IamimmenselygratefulformyUFPhysicscohort:ManishAmin,GordonTam,ChrisAoyama,JonathanThompson,andhonorarymemberMelissaGoo;formyUFAstrooce:ShuoKong,WenliMo,NolanGrieves,andEmilyMoravic{\it'sgreattobein309!";andformyUFcolleagues,friends,caeine-maintainers,andlife-savers:ChutipongSuwannajak,RachelWagner-Kaiser,KendallAckley,WanggiLim,XiaoHu,MengyaoLiu,DenoStelter,TahliaDeMaio,andmanyothers.Ithankthe\GainesvilleBoulderingMaa"forkeepingmesaneandactive:KellyGanzen,StephanieCruz,StephenIreland,andespeciallycoeemasterJamieCaulder;Prof.SamWongthewise,forhelpingmeembracethepain;myDukebuddies,whoareasinspirationalastheyaresupportive:JasonWang,BowaLee,YiXiang,JeHu,andMuyanJin,amongothers;andoldfriendswhohaveaccompaniedmeatvariousstagesofthisadventure:AdnanJaved,KevinWang,UsmanBashir,PatrickLavigne,AdamYeh,CarolineLe,ChiZhang,andAngieLi.Ofcourse,Iwouldnotbeherewithouttheunwaveringsupportofmyfamilyduringtheseyearsandthroughoutmylife.Iameternallythankfulformyparents,Shin-TsonWuandChoyanHsieh,andmysister,JanetW.Song.Lastly,Iwouldliketoacknowledgetheorganizationsthatmadethisresearchpossiblebyprovidingcomputationalresources,technicalassistance,andnancialsupport:theUniversityofFloridaResearchComputing(https://www.rc.u.edu),developersoftheEnzocode(http://enzo-project.org),developersoftheytanalysispackage(http://yt-project.org), 4

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theNASAAstrophysicsTheoryandFundamentalPhysicsgrant,theNASAFloridaSpaceGrantConsortiumDissertationandThesisImprovementFellowship,theNationalScienceFoundationEastAsiaandPacicSummerInstitutes,theJapanSocietyforthePromotionofScienceSummerProgram,theStratosphericObservatoryforInfraredAstronomytravelgrant,theNationalAstronomicalObservatoryofJapanvisitingscholargrant,andtheGraduateStudentFellowshipfromtheUniversityofFlorida. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................... 4 LISTOFTABLES ...................................... 9 LISTOFFIGURES ..................................... 10 ABSTRACT ......................................... 13 CHAPTER 1INTRODUCTION ................................... 15 1.1Background:StarFormation ........................... 15 1.2PhysicalMechanisms ............................... 18 1.2.1GravitationalInstability .......................... 18 1.2.2SupersonicTurbulence .......................... 20 1.2.3MagneticFields .............................. 21 1.3Motivation:Cloudcollisions ........................... 24 1.4Outline ...................................... 26 2NUMERICALFRAMEWORKANDPARAMETERSPACEEXPLORATIONWITH2DSIMULATIONS .................................. 28 2.1Introduction ................................... 28 2.2NumericalModel ................................. 31 2.2.1InitialConditions ............................. 31 2.2.2NumericalCode ............................. 36 2.3HeatingandCoolingFunctions ......................... 37 2.3.1ImplementationofThermalProcesses .................. 37 2.3.2Density-ExtinctionRelation ....................... 38 2.3.3NonequilibriumPDRHeatingandCoolingRates ............ 38 2.3.4HeatingandCoolingComponents .................... 43 2.3.5ObservationalDiagnostics ........................ 46 2.4Results ...................................... 47 2.4.1Out-of-planemagneticelds ....................... 47 2.4.1.1Isolatedcloud ......................... 48 2.4.1.2Isolatedcloudwithembeddedclump ............. 50 2.4.1.3Collidingclouds:head-oncollisions .............. 53 2.4.1.4Collidingclouds:o-axiscollisions .............. 56 2.4.2In-planemagneticelds ......................... 58 2.4.2.1Isolatedcloudwithembeddedclump ............. 59 2.4.2.2Collidingclouds ........................ 59 2.4.3MixedFieldGeometries ......................... 60 2.4.3.1Isolatedcloudwithembeddedclump ............. 60 6

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2.4.3.2Collidingclouds:head-oncollisions .............. 60 2.4.3.3Collidingclouds:o-axiscollisions .............. 65 2.5ObservationalDiagnostics ............................ 70 2.5.1IntegratedIntensityMaps ........................ 70 2.5.2Spectra .................................. 72 2.6DiscussionandConclusions ........................... 75 33DTURBULENT,MAGNETIZEDSIMULATIONS .................. 79 3.1Introduction ................................... 79 3.2NumericalModel ................................. 83 3.2.1InitialConditions ............................. 83 3.2.2NumericalCode ............................. 87 3.2.3ThermalProcesses ............................ 88 3.2.4ObservationalDiagnostics ........................ 90 3.3Results ...................................... 90 3.3.1MassSurfaceDensityandTemperatureMorphology .......... 91 3.3.1.1Fiducialmodels ........................ 91 3.3.1.2Parametermodels ....................... 95 3.3.2MagneticFields .............................. 97 3.3.2.1Relativeorientations:Bvs.iso-NH .............. 98 3.3.2.2Magneticeldstrengths:jBjvs.nH ............. 105 3.3.3MassSurfaceDensityProbabilityDistributionFunctions ........ 106 3.3.4IntegratedIntensityMaps ........................ 110 3.3.5Kinematics ................................ 114 3.3.5.1Spectra ............................. 114 3.3.5.2Velocitygradients ....................... 116 3.3.6Dynamics ................................. 118 3.4DiscussionandConclusions ........................... 123 4DENSITYANDMAGNETICALLYREGULATEDSTARFORMATION ........ 126 4.1Introduction ................................... 126 4.2NumericalModel ................................. 128 4.2.1InitialConditions ............................. 128 4.2.2NumericalCode ............................. 129 4.2.3ThermalProcesses ............................ 131 4.2.4StarFormation .............................. 133 4.2.4.1Fixedstarformationeciencyperfree-falltimewiththresholddensity ............................. 133 4.2.4.2Magneticallyregulatedstarformation ............. 134 4.2.4.3Starparticledynamics ..................... 135 4.3Results ...................................... 135 4.3.1ClusterMorphology ............................ 136 4.3.2StarFormationRatesandEciencies .................. 139 4.3.3SpatialClustering ............................. 141 7

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4.3.3.1Minimumspanningtree .................... 141 4.3.4Kinematics ................................ 144 4.4DiscussionandConclusions ........................... 146 5CONCLUSIONSANDFUTUREAPPLICATIONS .................. 148 5.1SummaryandConclusions ............................ 148 5.2FutureApplications ............................... 149 5.2.1AmbipolarDiusion ........................... 149 5.2.2[CII]MappingofIRDCs ......................... 150 5.2.3ApplicationtoSerpensSouth ...................... 150 5.2.4ApplicationtoIN-SYNC ......................... 153 REFERENCES ........................................ 155 BIOGRAPHICALSKETCH ................................. 161 8

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LISTOFTABLES Table page 2-1GMCandclumpproperties .............................. 33 2-2Summaryofsimulationrunparameters ........................ 35 3-1Initialsimulationproperties .............................. 85 3-2Summaryofsimulationsandexploredparameterspace ................ 85 3-3Propertiesof-PDFs ................................. 111 3-4Velocitygradients ................................... 118 4-1Initialsimulationproperties .............................. 129 4-2Starformationmodels ................................. 132 4-3Parametersofobservedclusters ............................ 143 4-4Gasandstarkinematics ................................ 145 9

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LISTOFFIGURES Figure page 1-1Crutcherrelation .................................... 22 1-2PlanckTauruspolarizationmap ............................ 23 1-3Kennicutt-Schmidtrelation .............................. 25 2-1Idealized2Dcloudcollisionsetup ........................... 33 2-2Density-extinctionrelation ............................... 39 2-3Chemicalabundances ................................. 42 2-4Heatingandcoolingfunctions ............................. 44 2-5Heatingandcoolingcomponents ........................... 45 2-6Averageclumpdensity(Bzuniformisolated) ..................... 49 2-7Averageclumpdensityandtemperature(Bzclumpisolated) ............. 51 2-8Averageclumpdensityandtemperature(Bzcloudisolated) ............. 52 2-9EvolutionofBzcollidingdead-on ........................... 54 2-10Averageclumpdensityandtemperature(Bzcollidinghead-on) ........... 55 2-11EvolutionofBzcollidingimpactparameter ...................... 56 2-12Averageclumpdensityandtemperature(Bzcollidingimpactparameter) ...... 57 2-13EvolutionofBxcollidingdead-on ........................... 61 2-14EvolutionofBycollidinghead-on ........................... 62 2-15Averageclumpdensityandtemperature(Bxcollidinghead-on) ........... 63 2-16Averageclumpdensityandtemperature(Bycollidinghead-on) ........... 64 2-17Resolutionstudy2D .................................. 66 2-18Evolutionofmoleculartracers ............................. 68 2-19Zoom-inofmoleculartracers ............................. 69 2-20Ratiomapofnon-equilibriumtemperature ...................... 70 2-21Averageclumplineratio(Bmixcollidingimpactparameter) ............. 73 2-22SyntheticCOspectra2D ............................... 74 10

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2-23Velocitygradients2D ................................. 76 3-13Dinitialconditions .................................. 86 3-2Evolutionofandtemperature(ducialcollidingandnon-colliding) ........ 89 3-3Evolutionof(parametermodels) .......................... 92 3-4Evolutionoftemperature(parametermodels) ..................... 93 3-5LICpolarizationvisualization(ducialcollidingandnon-colliding) .......... 97 3-6Stokesparameters:angledenitions .......................... 98 3-7HROs(Fiducialcollidingandnon-colliding) ...................... 99 3-8HROshapeparameter ................................. 103 3-9Bvs.nHrelation .................................... 105 3-10Evolutionof-PDFs(ducialcollidingandnon-colliding) .............. 108 3-11-PDFs(parametermodels) ............................. 109 3-12Evolutionofmolecularlinetracers(ducialcolliding) ................. 112 3-13Evolutionofmolecularlinetracers(ducialnon-colliding) .............. 113 3-14Syntheticspectra3D ................................. 115 3-15P-P-Vkinematics ................................... 117 3-16Virialradii(ducialcolliding) ............................. 119 3-17Virialparameters .................................... 120 4-1Evolutionof(ducialno-SF) ............................ 130 4-2SummaryofSF-colmodels .............................. 136 4-3SummaryofSF-nocolmodels ............................. 137 4-4Starformationrates .................................. 140 4-5Minimumspanningtrees ................................ 141 4-6Qparametervs.time ................................. 142 4-7P-P-Vkinematics:starformation ........................... 144 5-1SOFIAIRDCs ..................................... 151 5-2SerpensSouthPolarization .............................. 152 11

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5-3IN-SYNCOrion .................................... 154 12

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyGIANTMOLECULARCLOUDCOLLISIONSASTRIGGERSOFSTARCLUSTERFORMATION:NUMERICALSIMULATIONSANDOBSERVATIONALPREDICTIONSByBenjaminWuAugust2016Chair:JonathanC.TanMajor:PhysicsStarsprimarilyforminclustersfromwithingiantmolecularclouds(GMCs),butthedominantmechanismstriggeringfragmentationandcollapsearepoorlyunderstood.WeinvestigatecollisionsbetweenGMCsandtheirabilitytoinducegravitationalinstabilityandstarclusterformation.Thisprocessmaybeamajordriverofstarformationactivityindiskgalaxies.Usingmagnetohydrodynamics(MHD)simulationswithadaptivemeshrenement(AMR),wefocusbothonunderstandingtheprevailingphysicalprocessesaswellaspredictingkeyobservationalsignatures.Werstdevelopandimplementnewphotodissociationregion(PDR)basedheatingandcoolingfunctionsthatspantheatomictomoleculartransition,mirroringachemicallydiverse,multiphaseISMandallowingmodelingofnon-equilibriumtemperaturestructures.Thenwedevelopanidealized2DmodelofmagnetizedGMCs,systematicallyexploringtheparameterspaceandinvestigatingmagneticcriticalityinthecontextofcloudcollisions.Expandingto3Dandaddingsupersonicturbulence,wemodelphysicallyrealisticGMCs,comparingandcontrastingcollidingvs.non-collidingcases.Wecharacterizethemorphologiesofdensegasandmagneticeldstructure,signaturesofcloudkinematics,andclouddynamics,comparingresultstoGalacticclouds.Finally,weimplementstochasticstarformationsub-gridmodelsexploringvariouslevelsofdensityandmagneticregulation.Weexplorethestarformationrateovertime,thespatialclusteringoftheformedstars,andthekinematicsofthestarparticlesincomparisontotheirnatalgascloud. 13

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Wendkeyobservationaldiagnosticsofcloudcollisions,especially:relativeorientationsbetweenmagneticeldsanddensitystructures,likelaments;13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)integratedintensitymaps,lineratios,andspectra;cloudvirialparameters;andpropertiesoftheresultingstarclustersformedthroughGMCcollisionsimulations.IncomparisontoobservationsofdenseGMCs,anumberofindicatorssuggestsimilaritiestowardthecollidingscenariothoughitisdiculttodrawdenitiveconclusionsfromcurrentdata.However,wehaveoutlinedavarietyofpotentiallynewobservationalsignaturesthatcanbethebasisforfuturetests. 14

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CHAPTER1INTRODUCTIONFromthedaysofantiquity,mankindhasgazeduponthestarsinwonder.Overtime,misconceptiongavewaytounderstandingandspeculationtosophisticatedobservationalandtheoreticalframeworks.However,theproblemofhowstarsformremainsoneofthekeyopenquestionsinastrophysics.Understandingthegoverningprocessesinitiatingstarformationisfundamentallysignicant,astheydeterminetheevolutionofgalaxies,thestructureoftheinterstellarmedium(ISM),andthecreationofplanetarysystems.Wereviewthebackgroundofourcurrentunderstandingofstarformation,thenfocusonthethreephysicalmechanismswhichlikelydominatethestarformationprocess:gravitationalinstability,supersonicturbulenceandmagneticelds.Finally,wemotivatetheparticularglobalstarformationtheory{triggeringviaGMCcollisions{onwhichthisdissertationfocuses. 1.1Background:StarFormationSpiralgalaxiessuchasourMilkyWayareconglomeratesofstars,stellarremnants(e.g.,whitedwarfs,neutronstars,blackholes),andthediusegasanddustoftheISM.Whilemostofthemassexistsasdarkmatter,itisthebaryonsthatdominatetheenergyemissionandvisualstateofagalaxy.ThegasintheISMexistsinanumberofcharacteristic\phases"determinedbyitsionizationandchemicalstateofHydrogen,rangingfromdensitiesof10)]TJ /F4 7.97 Tf 6.59 0 Td[(4to106particlespercm3withrespectivetemperaturesof107to10K.Itiswithinthecold,densemoleculargas{existingasgravitationallyboundmolecularclouds(MCs){thatstarsareborn.Inellipticalgalaxies,ontheotherhand,thecoldcomponentoftheirISMislostwithinonebillionyears,thusquenchingstarformation.However,mergerswithothergalaxiesmaytriggerstarburstsviatidalforcesandcompressionofgas.Thus,thekeytounderstandingstarformationinthepresentuniverseistostudyMCsinspiralgalaxies.Moststarsforminclusterswithingiantmolecularclouds(GMCs),whichhavetypicalhydrogennumberdensitiesofnH=100cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,diametersoftensofparsecs(1014km),massesofupto106M,andaveragetemperaturesof10)]TJ /F5 11.955 Tf 12.5 0 Td[(30K.Approximatelyhalfof 15

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thetotalmassoftheGalacticISMisfoundinGMCs,withtheinnerMilkyWay(r<2kpc)containinganestimated6,000GMCswithM>105M( Sandersetal. , 1985 ).ThegaswithinGMCsisprimarilymolecularhydrogen(H2),withapproximately10%atomichelium(He)innumberdensityandtraceamountsofotherelements.BecausetherstrotationallevelofH2isaccessibleonlythroughaquadrupolartransitionandismorethan500Kabovethefundamental,thebulkofGMCgasiseectivelyinvisible.ThepresenceofH2mustthenbeinferredthroughthenextmostabundantmolecule,carbonmonoxide(CO),whichhasasmalldipolemoment(0.1Debye)andisthuseasilyexcitedandcanactasatracerforH2.Forexample,12CO(J=1-0)at2.6mm(rstlevelat5.52K)canbedetectedthroughouttheGalaxy,ascanothertracerssuchasNH3,HCO+,N2H+,andCS,whichprobevariousgaseousstates.Morerecently,thethermalcontinuumemissionofinterstellardust(e.g.,70)]TJ /F5 11.955 Tf 11.95 0 Td[(500mforHerschel)havebeenusedasprobesoftotalcolumndensity.Theactivelydevelopingunderstandingofstarformationbeginswiththefragmentationofamolecularcloud( Shuetal. , 1987 ).Someregionseventuallycondenseintogravitationallyboundstarlesscores,whichfurthercollapsegravitationallytoformprotostellardisksystems.Diskmaterialaccretesontotheprotostar,formingbipolaroutowsandjets.Hydrogenfusionignites,accretionishalted,andtheresultingstarbeginsitslifeonthemainsequence.Individuallowmassstars(<8M)aregenerallywell-understoodboththeoretically(e.g., Shuetal. , 1991 )andobservationally.Somesitesoflow-massstarformationhavebeenidentiedasBokglobules( Bok&Reilly , 1947 ),whicharerelativelyisolatedpatchesofopticalextinction(AV=1)]TJ /F5 11.955 Tf 13.04 0 Td[(25mag)withsmallcharacteristicsizesof0.1)]TJ /F5 11.955 Tf 13.04 0 Td[(2pc,massesof1)]TJ /F5 11.955 Tf 12.23 0 Td[(100M,andsimplemorphologies.Thesubsequentevolutionarystages{fromglobuletoprotostellarcoretopre-mainsequenceobject{haveallbeenobserved(e.g., Lada , 1999 ).Ontheotherhand,theearlystagesofmassivestars(>8M),whichgenerallyformalongwithclustersofhundredstothousandsofpredominantlylow-massstars,arepoorlyunderstood.Thesehigh-massstarsarethemainsourcesofenergyinjectionintheGalaxy,astheydominatetheinterstellarradiationeld(ISRF)withUVphotonsduringtheirrelatively 16

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short(tensofMyr)lifetimesandviolentlyexplodeassupernovaeintheirdeaths,recyclingandenrichingthemetallicityofinterstellarmatter.However,thereexistmanydicultieswithdirectlyobservingtheearlieststagesofmassivestarformation.Duetotheirrapidevolutionandshortlifetimes,theyarecomparativelymuchfewerinnumberintheGalaxy.Additionally,oncemassivestarformationbegins,theUVphotonsquicklyionizeandheattheirnatalmolecularclouds,disruptingthegasanderasingsignsofinitialconditions.Directobservationsofmassivestarformationinclude\hotcores",whichhavetemperaturesof50)]TJ /F5 11.955 Tf 12.33 0 Td[(250K,sizesof<0.1pc,massesof100)]TJ /F5 11.955 Tf 12.07 0 Td[(300M,anddensitiesof105)]TJ /F5 11.955 Tf 12.06 0 Td[(108cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,whichareassociatedwithultra-compactHIIregionsandmolecularoutows( Garay&Lizano , 1999 ; Kurtzetal. , 2000 ; Churchwell , 2002 ).However,theseobservedstagesoccuraftertheprotostarhasalreadyformed,andthusearlierprestellarphasesareundetermined.TheinitialconditionsofmassivestarsmaythenbeanaloguestoBokglobules,withapresumablysimilarevolutionarytrackfromcloudtoprotostar.However,thetheoreticalcomplexityofreconcilingcontinuedaccretionwithever-increasingamountsofradiationpressurealongwiththepoorlyunderstoodeectsofturbulenceandmagneticeldscoupledwiththeobservationaldicultyofdetectinghighmassandhighsurfacedensity()gashaspreventedtheconvergenceofanacceptedtheoryofmassivestarformation.InfraredDarkClouds(IRDCs)arerecentlydiscoveredregionsofhighextinctioninthemid-IRofGalacticbackgroundlight( Peraultetal. , 1996 ; Eganetal. , 1998 ; Hennebelleetal. , 2001 ).IRDCs,locatedwithinGMCs,havesuchhighmasssurfacedensities(&0.1gcm)]TJ /F4 7.97 Tf 6.59 0 Td[(2)thattheyaredarkatmid-IR(10m)andevenfar-IR(70m).Theirlowtemperatures(10)]TJ /F5 11.955 Tf 12.39 0 Td[(20K;derivedviaNH3inversiontransitions(e.g., Pillaietal. , 2006 ; Wangetal. , 2008 ; Sakaietal. , 2008 ; Chiraetal. , 2013 ),highvolumedensities(nH>105cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3),sizes(fewpc),andmasses(102)]TJ /F5 11.955 Tf 12.15 0 Td[(104M)indicatethattheymaybethehigh-massanaloguetoBokglobulesandthelikelyprecursorsofmassivestar-formingclumpsandstarclusters( Rathborneetal. , 2006 ; Tanetal. , 2014 ).Further,theyhavebeenobservedthroughouttheGalaxy( Simonetal. , 2006a ),withstudiesofkinematicdistancesoflargesamplesindicatingthat 17

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thepopulationofIRDCsisenhancednearthe\GalacticRing",themostmassivestarformingstructureintheMilkyWay( Simonetal. , 2006b ).UnderstandingtheformationofIRDCs,then,iscriticaltounderstandingtheinitiationofstarclusterformation,whichinturncontrolstheglobalgalacticstarformationrates(SFRs).Currently,thedominantprocessesthatinducethecollapseandfragmentationofGMCsintoIRDCsarepoorlyunderstood.Varioustheoreticalmodelsincludeinstabilitiesfromtheglobalgalacticdisk(e.g., Elmegreen , 1994 ; Lietal. , 2006 ),triggeringfrombyspiralarmpassage(e.g., Wyse&Silk , 1989 ; Tamburroetal. , 2008 ),triggeringviaGMC-GMCcollisions(e.g., Scovilleetal. , 1986 ; Tan , 2000 ; Wuetal. , 2015 , 2016 ),triggeringbystellarfeedback(e.g.,supernova; Inutsukaetal. , 2015 ),triggeringbyconvergingatomicows(e.g., Heitschetal. , 2009 ),regulationbyturbulence(e.g., Krumholz&McKee , 2005 ),andregulationbymagneticelds(e.g., VanLooetal. , 2015 ).Onlythroughunderstandingthephysicalmechanismsinvolvedwitheachtheoreticalmodel,aswellasthepredictionofdistinctobservationaldiagnostics,canwedeterminethedominantmodeofstarformation. 1.2PhysicalMechanisms 1.2.1GravitationalInstabilitySelf-gravityisthedominantdriverofcontractionandcollapsewithintheISM.Agascloudwillremaininhydrostaticequilibriumifthekineticenergyofthegaspressureisinbalancewiththepotentialenergyfrominternalgravitationalforces.Thisisexpressedusingthevirialtheorem,whichstatesthatthegravitationalpotentialenergymustequaltwicetheinternalthermalenergyinordertomaintainequilibrium.Thisrelationcanbeconvenientlydescribedbythevirialparameter vir52R GM=2aEK jEGj,(1{1)whereMisthemassofthecloudandRistheradius,isthe1Dmass-averagedvelocitydispersion,ajEGj=(3GM2=[5R])istheratioofgravitationalenergy,EG(assumingnegligibleexternaltides),tothatofauniformsphere,andEKisthekineticenergy( Bertoldi&McKee , 18

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1992 ).Thus,vir<2denotesgravitationallyboundcloudsandvir=1denotesvirializedclouds.Ifthemassofacloudexceedsthatwhichthegaspressurecansupport,thecloudwillundergogravitationalcollapse.Thisthresholdmass,abovewhichacloudwillundergosuchcollapse,iscalledtheJeansmass.TakingasphericalgaseousregionwithradiusRandmassMasdenedabove,thegaseoussoundspeedisgivenas cs=p p=,(1{2)where=Cp=Cvistheratioofspecicheatsofagasatconstantpressuretoagasatconstantvolume,pisthegaspressure,andisthegasdensity.TheJeansinstabilityoccursforlength >J2 kJ=c2s G(1{3)wherekJ(4G)=c2sandGisthegravitationalconstant.TheJeansmassisthen MJ4 3J 23=1 8kT G1 1=2'0.32MT 10K3=2mH 3=2106cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3 nH1=2.(1{4)Whentypicalvaluesofdensitiesandtemperatureswithindensecoresaresubstituted,werecoverthemassoftypicallow-massstars.Intermsoftimescales,apressurelesssphereofgasatuniformdensityandnoinitialvelocitywillundergoglobalcollapseinanitefree-falltime( Spitzer , 1978 ), =s 3 32G=4.4104yr p nH=106cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.(1{5)However,theseequations,whileusefulapproximations,describeisolatedcloudswithpurelythermalpressuresupport.Inreality,theISMismuchmoredynamic.Forexample,otherwisestableandquiescentcloudsmaybecompressedviaatriggeringmechanismsuchascollisionsbetweenMCs,orshocktriggeringfromnearbyasupernova.Galaxymergerscouldalsoprovide 19

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aninuxofgaspressureandtidaldisruption.Ineachcase,suchcompressionsmayinitiategravitationalcollapse. 1.2.2SupersonicTurbulence Larson ( 1981 )summarizedkeydynamicalfeaturesofobservedGMCs,referredtoas\Larson'slaws".Oneresultisthelinewidth-sizerelation:GMCsaresupersonicallyturbulentwithvelocitydispersionsincreasingasapowerofthesize. Solomonetal. ( 1987 )foundthat v=(0.720.07)R0.50.05pckms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,(1{6)wherevisthethree-dimensionalvelocitydispersionandRpcR=(1pc).Thisobservedpower-lawrelation(wherethepowerlawindex0.5)hassimilaritiestothe\Kolmogorovpowerspectrum"(v/L1=3)foraturbulentcascadeinanincompressibleuid.ForlengthscalesofRpc>0.1,vexceedstheisothermalsoundspeedofcoldgas,givenby(kT=)1=20.23(T=15K)1=2kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Thustheturbulenceissupersonic.BelowRpc<0.1,thelinewidthsappeartostayconstantat0.2kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1,indicatingthatthegasisapproximatelythermal(e.g., Goodmanetal. , 1998 ).Usingthevirialtheorem, h2vi=6GM 5L,(1{7)wecanestimateacharacteristicclumpmass M52vL 6G230L2+1M,(1{8)anddensity nH1.3104L2)]TJ /F4 7.97 Tf 6.59 0 Td[(2cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3.(1{9)Observationally,thescalingrelationforvdoesapproximatelydescribenearbymolecularregions,indicatingthatGMCshaveapproximatelyvirialsupersonicturbulentvelocitydispersions(e.g., Solomonetal. , 1987 ; Roman-Duvaletal. , 2010 ; Hernandez&Tan , 2015 ). 20

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1.2.3MagneticFieldsSomeregionsoftheISMarefullyionizedandevengasintheatomicandmolecularphasesisslightlyionized,thusmagneticeldspermeatetheISM( Draine , 2011 ).Thoughstilldebatedandoftennotincludedinnumericalsimulations,thereismountingevidencethatmagneticeldsaredynamicallyimportantinmolecularclouds.Observationally,theline-of-sightcomponentofthemagneticeld(Bk)canbemeasuredviatheZeemaneect.InthediuseHIgas,thisisdoneonthe21-cmline.Indensermoleculargas,theOH-doublinglines(1.665,1.667,1.720GHz)andtheCN(1-0)rotationaltransition(113GHz)isused.Zeemanmeasurementsofinterstellarmagneticeldsaredicultinpractice,withsmallsignal-to-noiseratios. Crutcheretal. ( 2010 )collectedandcompiledZeemanmeasurementsfrom66HIand72molecularcloudsandconcludedthat,throughBayesiananalysis,ajBmaxjvs.nHrelationexistedintheformof: Bmax=8>><>>:B0)]TJ /F10 7.97 Tf 20.77 -4.58 Td[(nH 300cm)]TJ /F4 5.978 Tf 5.75 0 Td[(32=3,fornH>300cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3,B0,otherwise,(1{10)whereB0=10G.Thisisreferredtoasthe\Crutcherrelation"(seeFig. 1-1 ).Inasomewhatcomplementarymethod,theplane-of-skymagneticelddirectioncanbeinferredfrompolarizationmeasurementsofdustgrains.Asymmetriesinthedustgrainswillcausetheirlongaxistoalignperpendiculartomagneticelds.Thus,thepreferentiallypolarizeddustabsorptionofbackgroundstarlightaswellasthepolarizedemissionofdustinthefar-IRorsub-mmcanbothbemeasuredobservationally.Recently,thePlanckspaceobservatoryperformedall-skydustemissionpolarizationmappingat353GHz(850microns),providingawealthofobservationaldataonGalacticMCs.OnesuchexamplemapoftheTaurusMCisshowninFig. 1-2 .TheChandrasekha-Fermi(CF)methodcanalsobeusedtoinfermagneticeldinformation,givenanassumedgeometry.TheCFmethodusesthedispersioninthepolarizationdirectiontoestimatethestrengthofthemagneticeld.Smalldispersionsin 21

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Figure1-1. (from Crutcher 2012 )ThesetofdiusecloudandmolecularcloudZeemanmeasurementsofthemagnitudeoftheline-of-sightcomponentBLOSofthemagneticvectorBandtheir1uncertainties,plottedagainstnH=n(HI)or2n(H2)forHIandmolecularclouds,respectively( Crutcheretal. , 2010 ).AlthoughZeemanmeasurementsgivethedirectionoftheline-of-sightcomponentaswellasthemagnitude,onlythemagnitudesareplotted.ThesolidbluelineshowsthemostprobablemaximumvaluesforBTOT(nH)determinedfromtheplottedvaluesofBLOSbytheBayesiananalysisof Crutcheretal. ( 2010 ).Alsoshown(plottedaslightblueshading)aretherangesgivenbyacceptablealternativemodelparameterstoindicatetheuncertaintyinthemodel. thepolarizationdirectionsuggeststrongermagneticelds,astheyarestrongenoughtoresistdistortionduetoturbulence.Theoretically,nowtakingmagneticeldsintoaccount,themagneticpressureB2=(8)canpreventaclumpfromcollapsingif M> Mcrit=3r 2aG 5b=1.5410)]TJ /F4 7.97 Tf 6.58 0 Td[(3r a bgausscm2g)]TJ /F4 7.97 Tf 6.59 0 Td[(1(1{11)wherethedimensionlesstermsa(typically1.67)andb(typically1.25)arebasedoncloudgeometry( Mouschovias&Spitzer , 1976 ).Inthisscenario,theclumpissaidtobe\magneticallysubcritical". 22

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Figure1-2. (From PlanckCollaborationetal. 2016 )MagneticeldandcolumndensitymeasuredbyPlancktowardstheTaurusMC.Thecolorsrepresentcolumndensity.Thedraperypattern,producedusingthelineintegralconvolutionmethod(LIC,Cabral&Leedom1993),indicatestheorientationofmagneticeldlines,orthogonaltotheorientationofthesubmillimeterpolarization. Toundergogravitationalcollapse,theux-to-massratio=Mmustbelessthanthecriticalux-to-massratio: M< Mcrit=1.810)]TJ /F4 7.97 Tf 6.58 0 Td[(3gausscm2g)]TJ /F4 7.97 Tf 6.58 0 Td[(1(1{12)fora1.67andb1.25.Inthiscase,theclumpissaidtobe\magneticallysupercritical"andthemagneticeldalonecannotpreventgravitationalcollapse. 23

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1.3Motivation:CloudcollisionsCollisionsbetweenGMCshavebeenproposedasamechanismforcreatingIRDCsandtriggeringstarformation,potentiallyevensettingtheglobalstarformationratesofdiskgalaxies.Inthisscenario,GMCsaresupportedagainstgravitationalcollapsethroughturbulentandmagneticpressure.Drivenbygalacticshear,GMCsoccasionallyundergosupersoniccollisionsinwhichtheyarecompressed,creatingdenselamentsandclumpsthatarepronetogravitationalinstabilitythusbecomethebirthsitesofstarclusters.Thisisanattractivemechanismbecauseitconnectssmall,pc-scalestarformationwithlarge-scalegalacticdynamicsincludinggalacticshear( Tan , 2000 ; Tasker&Tan , 2009 ; Suwannajaketal. , 2014 )andspiralarms( Dobbs , 2008 ).TheconnectionbetweenstarformationrateandorbitalshearnaturallyexplainsthedynamicalKennicutt-Schmidtrelation( Kennicutt , 1998 ; Leroyetal. , 2008 ), SFR/ gas,(1{13)whereSFRandgasarethesurfacedensitiesofthestarformationrateandtotalgas,respectively,andisthegalacticorbitalangularfrequency,thusplacingthecloudcollisionmodelinagreementwithobservedrelations.(SeeFig. 1-3 .)Further,simulationsofglobalgalaxiestrackingGMCshaveshownthatforadiskgalaxywithaatrotationcurve,GMCscollideatarelativelyfrequenttimescaleoftcoll'0.2torbit( Tasker&Tan , 2009 ; Dobbsetal. , 2015 ).ThisdissertationseekstoanswerthequestionofwhetherGMC-GMCcollisionsresultindensegasstructuresandstarformationactivitythatcanexplaintypicalobservedstar-formingregionsandyoungstars.Theapproachistwo-pronged:(1)understandthephysicsofGMCcollisionsthroughnumericalsimulations,and(2)determinepotentialobservationalsignaturesbywhichthismechanismcanbedetected.Thus,wehavecarriedoutaseriesofnumericalstudiesutilizingmagnetohydrodynamics(MHD)simulationswithadaptivemeshrenement(AMR)tocreateincreasinglymoredetailedmodelsofGMCcollisions.Further,wehave 24

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Figure1-3. (from Kennicutt 1998 ),DynamicalKennicutt-SchmidtRelation, SFR/ gas.Dataaredisk-averagedquantitiesfornormalgalacticdisks(lledcircles)andcircumnuclearstarburstdisks(lledsquares).Thelineisamedianttothenormalgalacticdisksample,withtheslopexedatunity.Systematicuncertaintiesbetweenthenormalizationofthenormalandstarburstsamplesareoftheorderofafactorof2. developedrealisticheatingandcoolingfunctionsbasedonphotodissociationregion(PDR)micro-physicsmodelsspecicallyforthisstudyinordertoaccuratelytrackthethermalbehaviorofthegas,aswellasabundancesofCII,CIandCO. 25

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1.4OutlineChapter21( Wuetal. , 2015 ,hereafterPaperI)laysoutthenumericalframeworkforourGMCcollisionmodels.Weintroduceheatingandcoolingfunctionsderivedfromphotodissociationregion(PDR)models,whichtrackthechemicalstateofthegasandprovidepotentialobservationaldiagnosticsintheformofCO.Additionally,wesetupmagnetohydrodynamics(MHD)modelsofcloudcollisionswhichbeginwithsimple,idealisticconditionsandsubsequentlyaddsnewparametersinasystematicfashiontounderstandphysicalprocessesinawideparameterspace.Magneticcriticalityinparticularisexaminedinthecontextofcloudcollisions.Themodelsareinitiallyperformedin2DtoisolateindividualphysicalmechanismsandtheireectsonGMCevolution.InChapter3( Wuetal. , 2016 ,hereafterPaperII),weextendthestudyto3D,addingsupersonicturbulenceinordertorepresentrealisticGMCs.WemodelGMCsinitializedwithtypicalobservedpropertiesandcomparecollidingvs.non-collidingscenariosoverasmallerparameterspace.Thispaperfocusesontwoprimaryaspects:(1)understandingthephysicalmechanismsinvolvedincollisionsbetweenrealisticGMCsand(2)investigatingpotentialobservationaldiagnosticsandcomparingmeasuredparameterswithGalacticGMCsandIRDCs.Specically,wecomparethedensityandtemperaturemorphology,magneticeldvs.lamentarystructureorientation,magneticeldstrengthvs.densityrelation,thestatisticalprobabilitydistributionfunctions(PDFs)ofmasssurfacedensity,integratedintensitymaps,gaskinematics,syntheticvelocityspectra,andvirialanalysisofgasdynamics.Chapter4(Wuetal.,inprep.,hereafterPaperIII)addsstarformationtothemodelsestablishedinPaperII.Weimplementtwosub-gridstarformationroutinesintotheMHDcode:(1)\Density-Regulated,"i.e.,xedeciencyperfree-falltimeaboveasetdensity 1Themainchaptersinthisdissertationrepresentrelativelyself-containedjournalarticles.Chapter2hasbeenpublishedintheAstrophysicalJournal,whileChapter3hasbeensubmittedtotheAstrophysicalJournal.Chapter4,inprep.,willbesubmittedtotheAstrophysicalJournal. 26

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threshold;(2)\Magnetically-Regulated,"i.e.,xedeciencyperfree-falltimeinregionsthataremagneticallysupercritical.Foreachofthese,andassociatedmodelparameters,weexplorethestarformationrateovertime,thespatialclusteringofthestarsviaaminimumspanningtree(MST)method,andtheresultingkinematicsofthestarparticlesincomparisontotheirnatalgas.AsummaryofconclusionsalongwithcurrentandfutureapplicationsoftheGMCcollisionmodelsisdiscussedinChapter5.Applicationsinclude:extendingthephysicstonon-idealMHDviaambipolardiusion,usingtheStratosphericObservatoryforInfraredAstronomy(SOFIA)tomap[CII]emissionofIRDCs(aprojectcurrentlyunderway),targetedmodelingandcomparisonwiththeSerpensSouthIRDC,comparisonofstellarkinematicswiththeINfraredSpectroscopyofYoungNebulousClusters(IN-SYNC)survey. 27

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CHAPTER2NUMERICALFRAMEWORKANDPARAMETERSPACEEXPLORATIONWITH2DSIMULATIONSWeutilizemagnetohydrodynamic(MHD)simulationstodevelopanumericalmodelforGMC-GMCcollisionsbetweennearlymagneticallycriticalclouds.Thegoalistodetermineif,andunderwhatcircumstances,cloudcollisionscancausepre-existingmagneticallysubcriticalclumpstobecomesupercriticalandundergogravitationalcollapse.Werstdevelopandimplementnewphotodissociationregion(PDR)basedheatingandcoolingfunctionsthatspantheatomictomoleculartransition,creatingamultiphaseISMandallowingmodelingofnon-equilibriumtemperaturestructures.Thenin2DandwithidealMHD,weexploreawideparameterspaceofmagneticeldstrength,magneticeldgeometry,collisionvelocity,andimpactparameter,andcompareisolatedversuscollidingclouds.Wendfactorsof2)]TJ /F5 11.955 Tf 12.59 0 Td[(3increaseinmeanclumpdensityfromtypicalcollisions,withstrongdependenceoncollisionvelocityandmagneticeldstrength,butultimatelylimitedbyux-freezingin2Dgeometries.Forgeometriesenablingowalongmagneticeldlines,greaterdegreesofcollapseareseen.Wediscussobservationaldiagnosticsofcloudcollisions,focussingon13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)integratedintensitymapsandspectra,whichwesynthesizefromoursimulationoutputs.WendtheratioofJ=8-7tolower-JemissionisapowerfuldiagnosticprobeofGMCcollisions. 2.1IntroductionUnderstandingstarformationisakeyastrophysicalproblem,withmanyfundamentalquestionsstillunresolved.Inparticular,whatmechanismsdriveorinhibitthestarformationprocess?Studyingtheevolutionofgiantmolecularclouds(GMCs)withinthediuseinterstellarmediumandtheformationofprestellarclumpsandcoreswithinGMCsiscomplicatedbecauseofthelargerangeofdensities(nH1cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3to106cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3),lengthscales(kpcto0.1pc), ReprintedwithpermissionfromWu,B.,VanLoo,S.,Tan,J.C.,&Bruderer,S.2015,ApJ,811,56 28

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andtimescales(108yrforgalacticorbitsto105yrforcoredynamicaltimescales)involved,aswellasthenonlineareectsofself-gravity,thermal,magnetic,andturbulentpressures,large-scalemotionssuchasgalacticshearorcollisionalconvergingows,radiation,chemistry,andfeedback.Additionally,theinitialconditionsareuncertainandboundaryconditionsarepoorlyconstrained.Thenalconditions,gleanedthroughobservations,suggestthatstarformationishighlyclusteredandlocalized,withrelativelyhighlocaleciencywithinclusters(e.g., Lada&Lada , 2003 ; Gutermuthetal. , 2009 ).However,overallstarformationisslowandinecient,withonlyafewpercentoftotalgasformingstarsoverlocaldynamicaltimescales(e.g., Zuckerman&Evans , 1974 ; Krumholz&Tan , 2007 ; DaRioetal. , 2014 ).Withregardtotheimportanceofmagneticelds(see,e.g., Crutcher , 2012 ; Lietal. , 2014 ),therehavebeentwomainviews.Strong-eldmodelsproposerelativelylongGMClifetimesinwhichmagneticeldsplayimportantrolesincontrollingformationandevolutionoftheclouds.Inthesemodels,non-star-formingcloudsareinitiallysubcritical,i.e.,theirmagneticeldsarestrongenoughtopreventgravitationalcollapse.Weak-eldmodelshaveGMCsasintermittentphenomenawithshortlifetimes(106yr)andturbulentowscontrollingtheformationofclouds,clumpsandcores.Thesemodelspositmagneticallysupercriticalmasses,i.e.,themagneticpressurealoneistooweaktosupportagainstgravity.Zeemanmeasurementsshowthatmass-to-magneticuxratios(M=)areapproximatelycriticaltoslightlysupercriticalinmolecularclouds( Crutcher , 1999 ; Troland&Crutcher , 2008 ; Crutcher , 2012 ; Lietal. , 2014 ).IfGMCsarepartiallystabilizedbymagneticelds,thenthismayincreasetheirlifetimesto&20Myrtimescales,whicharethencomparabletoGMC-GMCcollisiontimes,especiallyforcloudsinsidethesolarcircle( Gammieetal. , 1991 ; Tan , 2000 ; Tasker&Tan , 2009 ; Dobbsetal. , 2015 ).IndirectobservationalevidenceforfrequentGMCcollisionscomesfromthenearrandomorientationsofprojectedangularmomentumvectorsofGMCs( Rosolowskyetal. , 2003 ; Kodaetal. , 2006 ; Imara&Blitz , 2011 ; Imaraetal. , 2011 ).FrequentGMCcollisionscouldbeanimportantmechanismforinjectingturbulentenergyintoGMCs( Tan , 2000 ; Tanetal. , 2013 ),withtheenergybeingextractedfromgalacticorbital 29

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motion.Othermechanismsforinjectingturbulenceinvolvestarformationfeedback( Matzner , 2007 ; Goldbaumetal. , 2011 ).Withoutsuchreplenishment,turbulenceisexpectedtodecaywithinaboutacrossingtime( MacLowetal. , 1998 ; Ostrikeretal. , 1999 ).Byproducingdensegas,compressedinshocks,GMC-GMCcollisionsmaybeanimportanttriggerofstarclusterformation( Scovilleetal. , 1986 ).Ifthemajorityofstarformationisinitiatedbythisprocess,thenamodelofshear-mediatedcloudcollisionscannaturallyexplaintheobserveddynamicalKennicutt-Schmidtrelation( Kennicutt , 1998 )inwhicharoughlyconstantfractionofgas,orb'0.04isconvertedintostarseverylocalorbitaltime( Tan , 2000 , 2010 ; Suwannajaketal. , 2014 ).Notethatthismechanismofcreatingstar-formingmolecularclumpsfromlocalizedcompressedregionsofpre-existingGMCs,isdierentfromthatproposedforcreatingmolecularcloudsfromshocksinconvergingowsofatomicgas(e.g., Heitschetal. , 2006 ; vanLooetal. , 2007 ; Heitschetal. , 2009 ; vanLooetal. , 2010 ).Cloud-cloudcollisionshavebeeninvestigatedbyanumberofpreviousstudies. Habe&Ohta ( 1992 )performed2DaxisymmetricSPHsimulationsofhead-oncollisionsofnon-identicalclouds.Thesecollisionsproducedabowshockwhichdisruptedthelargercloudwhilecompressingthesmallercloud.ThiscompressioncouldleadtogravitationalinstabilityforthesmallercloudevenifitsinitialmasswasbelowtheJeansmass. Klein&Woods ( 1998 )presented2DAMRhydrodynamicssimulationsofhomogeneouscloudcollisions.Thecollisionsresultedinbendingmodeinstabilitiescreatinglargeaspectratiolaments.Withsurfaceperturbations,themergedcloudsystembecamehighlyasymmetricalandhighlyinhomogeneouswithislandsofhighdensitysurroundedbylowdensityregions. Anathpindika ( 2009 )performedaseriesof3DSPHsimulationswhichinvestigatedthegravitationalstabilityofpost-shockcompressedslabsresultingfrommolecularcloudcollisions.Additionally,shearedcollisionsresultinnonlinearthinshellinstabilitiesandKelvin-Helmholtzinstabilities.Morerecently, Takahiraetal. ( 2014 )performed3DhydrodynamicsimulationswithAMRshowingcoreformationoccurringfromaGMCcollisioninterface.Theyfoundthatfaster 30

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collisionvelocitiesformedagreaternumberofcores,butcoregrowthwaspredominantlyviaaccretionintheshockfront,withslowershocksbeingfavoredformakinglargercores.IntermsofMHDcollisionstudies, Kortgen&Banerjee ( 2015 )investigatedmolecularcloudformationandthetransitionfrommagneticallysub-tosupercriticalHIcloudsviaconvergingmagnetizedows.Evenwithmagneticdiusioneects,theyfoundthatcylindricalowscreatednomagneticallysupercriticalregionsandstarformationisstronglysuppressedforevenrelativelylowinitialmagneticeldstrengths.Thispaper,therstofaseries,explorestheprocessofmagnetizedcloud-cloudcollisionsanditseectonindividualGMCandclumpscales.Herewerestrictanalysistoaparameterspaceexplorationwith2Dsimulationsofsimpliedcloudgeometries,includinganembeddedclump:formallycollidinginnitecylinders,whichcanapproximatecollisionsofspheroidalclouds.x 4.2 explainstheducialset-upandvarioussimulationandanalyticmethodsemployed.x 2.3 describesnewheatingandcoolingfunctionsthatwehavedevelopedforthisproject.x 4.3 describesthesetupandsubsequentresultsofexploringthefollowingparameters:magneticeldstrength,magneticeldorientation,collisionvelocity,andimpactparameter.x 2.5 discussespredictionsofobservationaldiagnosticsofshocks.Discussionandconclusionsfollowinx 4.4 . 2.2NumericalModel 2.2.1InitialConditionsForourdefaultinitialconditionsweusetypicalobservedvaluesofGalacticGMCandISMproperties.GMCsareconventionallydenedashavingmasses104M.Theyhavemeanmasssurfacedensities100Mpc)]TJ /F4 7.97 Tf 6.58 0 Td[(2(e.g., McKee&Ostriker , 2007 ; Tanetal. , 2013 ).TypicalmeanvolumedensitiesarenH'100cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,althoughclumpsandcoreswithinthecloudshavedensitiesthatcanbeordersofmagnitudelarger.GMCshaveinternalvelocitydispersionsthataresimilartovirialvelocities,typicallyseveralkm/s,whichismuchlargerthanthe0.2km/ssoundspeedsof10Kgas.Supersonic 31

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turbulenceandself-gravityarethoughttobetwoimportantprocessesthathelpgiverisetothehierarchicaldensitystructuresseeninGMCs.However,thesestructuresmayalsoberegulatedbymagneticelds.ThemagneticeldofthelocaldiuseISMbackgroundis62G( Beck , 2001 ).Ifarandom,uniformdistributionofeldstrengthsisassumeduptoamaximumvalue,Bmax,Zeemanmeasurementsrevealthatthismaximummagneticeldvaluemeasuredwithinmolecularclouds,clumpsandcoreswithnH>300cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3scalesasBmax=B0(nH=300cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)0.65,whereB0=10G( Crutcheretal. , 2010 ).Atlowerdensities,Bmax=B0=10G,independentofdensity.Wewillhenceforthrefertothisasthe\Crutcherrelation".Thus,fornH=103cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,Bmax'22G.ObservedrandomvelocitiesofGalacticGMCsareapproximately5-7kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1(e.g., Lisztetal. , 1984 ; Stark , 1984 ).However,interactionvelocitiesbetweencollidingGMCsarelikelytobesetbytheshearvelocityat1to2tidalradiioftheclouds( Gammieetal. , 1991 ; Tan , 2000 ),whichcanbeseveraltimeslarger.Giventhe2Dnatureofthesimulationsofthispaper,themodeledstructurescanbeconsideredaslamentsextendingperpendiculartothesimulationdomain.Wefollow\clouds",i.e.,\GMCs,"withauniformdensityofnH,GMC=100cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3.Althoughthecloudsare,inprinciple,cylindersofinniteextent,weassumethatthecloudshaveanitemass,i.e.,MGMC=105M.Amasssurfacedensityof=100Mpc)]TJ /F4 7.97 Tf 6.59 0 Td[(2integratedalongthecloudaxis,then,givesatypicalcloudradiusRGMC=17.8pc.Wesettheradiusoftherstcloud,i.e.,Cloud1,toR1=23.8pcandofthesecondone,i.e.,Cloud2,toR2=0.5R1=11.9pc.GMCsarestructured,containingdenseclumps.Whenacollisionoccurs,theeectofthiscollisiononpre-existingclumpsmaybethemostimportantfortriggeringstarformation.Wethereforeintroduceanidealizedembedded,overdenseclumpintoCloud1.TheclumphasauniformdensityofnH,cl=1000cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,i.e.,10overdensecomparedtotheGMC,andaradiusof5.6pc.Wepositiontheclumpocenterat(x,y)=(0.5R1,0)(seeFig. 3-1 ).ThepropertiesofourcloudsandclumparelistedinTable 2-1 . 32

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Table2-1. GMCandclumpproperties MtotanHRBcritb(105M)(cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3)(pc)(G) Ambient-10-10GMC1c1.7810023.842.0GMC20.5610011.913.9Clump0.1010005.6466.0 aMassesareforanequivalentsphericalcloud. bCriticalB-eldstrengthsarelistedfortheGMCsandtheclump,alongwiththeducialambienteldstrength. cGMC1includesaclump,butpropertieslistedherearefornon-clumpmaterialwithinthecloud. Figure2-1. Basiccloudcollisionsetup.GMC1(leftcloud)hasradiusR1.ItincludesanembeddedclumpwithradiusRcllocatedatadistanceofonehalf-radiustotheedge.GMC1collideswithGMC2,auniformcloudwitharadiusR2=R1/2.Thecloudsareinitiallyseparatedbyadistancethatischangeddependingonrelativevelocitysothatcollisionsoccuratthesametime. 33

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Fortypicalmolecularcloudtemperatures,10)]TJ /F5 11.955 Tf 12.31 0 Td[(20K,suchGMCsandclumpsarenotthermallysupportedagainstgravitationalcollapse.Forexample,ifthecloudsareconsideredaslonglamentsinthedirectionperpendiculartothesimulationplane,thenthemassperunitlengthforGMC1,ml=6150Mpc)]TJ /F4 7.97 Tf 6.59 0 Td[(1,farexceedsthecriticallinemassforacylindricalcloud,givenbyml,crit=2c2s=G,whichis20Mpc)]TJ /F4 7.97 Tf 6.59 0 Td[(1foracold10Kcloud( Ostriker , 1964 ).Theinclusionofmagneticeldshelpstostabilizetheclouds.Wevarythedirection,i.e.,parallel,perpendicularandobliquetothecylindricalaxisofthecloud,andthemagnitudeoftheeld.Theeldstrengthsaredetailedintheresultssection,butareoftheorderof10)]TJ /F5 11.955 Tf 11.95 0 Td[(100G,givenobservedeldstrengths( Crutcher , 2012 ).InternalcloudturbulenceisanothermechanismthatmayhelpsupportGMCs.Toseparateouttheeectsofmagneticeldsfromturbulence,inthispaperwedonotinitializethecloudswithanyturbulence,deferringthistoPaperII,whichalsoextendsthedimensionalityto3D.However,turbulentmotionsaregeneratedbytheGMC-GMCcollision,whichmaythenprovideadditionalsupporttotheclouds.Theambientmediuminwhichthecloudsareembedded,representativeoftheatomiccoldneutralmedium,issettohavenH,0=10cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,withamagneticeldofB0=10G.Thedefaultrelativecollisionvelocityofthecloudsissettobevrel=10kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,withvariationsfrom5to40kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Thedefaultimpactparameter,b,ofthecollisionissettozero,i.e.,anon-axiscollision,butsomecaseswithb=0.5,1,1.5R1arealsoexplored.Thesurroundingmedium,whichweconsidertobeaco-movingatomicenvelopearoundtheGMC,isalsocolliding.Thusintermsofthesimulationdomain,halftheboxismovingwith+vrel=2andtheotherhalfhas)]TJ /F3 11.955 Tf 9.3 0 Td[(vrel=2.However,atfastervelocities&20kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1wesometimesnoticemodesteectsofnumericalviscosityonclumppropertiesandsoalsorunsimulationsinthevelocityframeofCloud1.AsummaryofkeyparametersinallrunsperformedinthispaperislistedinTable 3-2 .Velocitiesdenotedwitha\*"indicatemodelsrunintheframeofCloud1. 34

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Table2-2. Summaryofsimulationrunparameters RunnH,0nH,1nH,clnH,2B0B1BclB2vrelb(cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)(cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3)(cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)(cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)(G)(G)(G)(G)(km/s)(R1) 0.Out-of-planeelds(0,0,Bz)0.Isolatedcloud0.A.010100--(0,0,10)(0,0,27.9)----0.A.110100--(0,0,0)(0,0,0)----0.A.210100--(0,0,10)(0,0,10)----0.A.310100--(0,0,10)(0,0,20)----0.A.410100--(0,0,10)(0,0,40)----1.Out-of-planeelds(0,0,Bz)1.B.Isolatedcloudwithclump1.B.0101001000-(0,0,10)(0,0,40)(0,0,65)---1.B.1.1101001000-(0,0,10)(0,0,10)(0,0,65)---1.B.1.2101001000-(0,0,10)(0,0,20)(0,0,65)---1.B.1.3101001000-(0,0,10)(0,0,65)(0,0,65)---1.B.2.1101001000-(0,0,10)(0,0,40)(0,0,40)---1.B.2.2101001000-(0,0,10)(0,0,40)(0,0,55)---1.B.2.3101001000-(0,0,10)(0,0,40)(0,0,75)---1.C.Cloudcollision1.C.0101001000100(0,0,10)(0,0,40)(0,0,65)(0,0,13.2)1001.C.1.1101001000100(0,0,10)(0,0,40)(0,0,65)(0,0,13.2)501.C.1.2101001000100(0,0,10)(0,0,40)(0,0,65)(0,0,13.2)20*01.C.1.3101001000100(0,0,10)(0,0,40)(0,0,65)(0,0,13.2)40*01.C.2.2101001000100(0,0,10)(0,0,40)(0,0,65)(0,0,13.2)100.51.C.2.4101001000100(0,0,10)(0,0,40)(0,0,65)(0,0,13.2)1011.C.2.5101001000100(0,0,10)(0,0,40)(0,0,65)(0,0,13.2)101.52.In-planeelds(Bx,0,0)and(0,By,0)2.B.Isolatedcloudwithclump2.B.1.0101001000-(40,0,0)(40,0,0)(40,0,0)---2.B.1.1101001000-(10,0,0)(10,0,0)(10,0,0)---2.B.1.2101001000-(65,0,0)(65,0,0)(65,0,0)---2.B.2.0101001000-(0,40,0)(0,40,0)(0,40,0)---2.B.2.1101001000-(0,10,0)(0,10,0)(0,10,0)---2.B.2.2101001000-(0,65,0)(0,65,0)(0,65,0)---2.C.Cloudcollision2.C.1.0101001000100(40,0,0)(40,0,0)(40,0,0)(40,0,0)1002.C.1.1101001000100(10,0,0)(10,0,0)(10,0,0)(10,0,0)1002.C.1.2101001000100(65,0,0)(65,0,0)(65,0,0)(65,0,0)1002.C.2.0101001000100(0,40,0)(0,40,0)(0,40,0)(0,40,0)1002.C.2.1101001000100(0,10,0)(0,10,0)(0,10,0)(0,10,0)1002.C.2.2101001000100(0,35,0)(0,65,0)(0,65,0)(0,65,0)1003.Mixedelds(Bx,By,Bz)3.B.Isolatedcloudwithclump3.B.1101001000-(10,0,0)(10,0,38.7)(10,0,64.2)---3.B.2101001000-(0,10,0)(0,10,38.7)(0,10,64.2)---3.C.Cloudcollision3.C.1.0101001000100(10,0,0)(10,0,38.7)(10,0,64.2)(10,0,12.9)1003.C.1.1101001000100(10,0,0)(10,0,38.7)(10,0,64.2)(10,0,12.9)503.C.1.2101001000100(10,0,0)(10,0,38.7)(10,0,64.2)(10,0,12.9)20*03.C.1.3101001000100(10,0,0)(10,0,38.7)(10,0,64.2)(10,0,12.9)40*03.C.2.0101001000100(0,10,0)(0,10,38.7)(0,10,64.2)(0,10,12.9)1003.C.2.1101001000100(0,10,0)(0,10,38.7)(0,10,64.2)(0,10,12.9)503.C.2.2101001000100(0,10,0)(0,10,38.7)(0,10,64.2)(0,10,12.9)20*03.C.2.3101001000100(0,10,0)(0,10,38.7)(0,10,64.2)(0,10,12.9)40*03.D.Cloudcollisionwithimpactparameter3.D.0101001000100(10,0,0)(10,0,38.7)(10,0,64.2)(10,0,12.9)100.5 35

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2.2.2NumericalCodeThenumericalcodeisamodiedversionoftheAdaptiveMeshRenement(AMR)codeEnzo2.0( Bryan&Norman , 1997 ; Bryan , 1999 ; O'Sheaetal. , 2004 ).Tosolvethemagnetohydrodynamicalequations,weusea2nd-orderRunge-KuttatemporalupdateoftheconservedvariableswiththeLocalLax-Friedrichs(LLF)Riemannsolverandapiecewiselinearreconstructionmethod.Toensurethesolenoidalconstraintonthemagneticeld,thedivergencecleaningalgorithmof Dedneretal. ( 2002 )isadopted( Wang&Abel , 2008 ).Weimplementedheatingandcoolingfunctionsinthecodethatdescribebothatomicandmolecularheatingandcoolingprocesses(seex 2.3 fordetails).Thesefunctionstakeintoaccountadensityversuscolumndensityextinctionrelationsimilartothatof VanLooetal. ( 2013 ,henceforth,VLBT2013).Asthetemperatureofthegasneedstobecalculatedaccurately,weusea\dualenergyformalism"bysolvingtheinternalenergyequationaswellasthetotalenergyequation.Thetemperatureisthendeterminedfromtheinternalpressurewhenmagneticandkineticenergytogetherexceed0.999thetotalenergy,andfromthetotalenergyotherwise.Totracktheevolutionofpropertiesoftheclump,weuseascalarvaluetodierentiatebetweengasoutsideandinsidetheclump.WesetthescalarSto1insidetheclumpand0outside.WeaddedaconservationequationinEnzo2.0toadvectthescalar,i.e., @(S) @t+r.(Sv)=0,(2{1)withthecelldensityandvthevelocity.Wemodelanumericaldomainof2562pc2whichiscoveredbyauniformgridof10242,givingagridcellsizeof0.25pc.Fortheducialmodel,twoadditionalAMRgridlevelsareincluded,thusincreasingtheeectiveresolutionto40962withagridcellsizeof0.0625pconthenestlevel.Thisresolutionissucienttostudythetransitionfromsubcriticaltosupercriticalcloudsandclumps. 36

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Weuseseveralcriteriatodeterminerenement:acellisrenedwhenthereisastronglocalgradientofvariables(i.e.,whentherelativeslopejq(i+1))]TJ /F3 11.955 Tf 9.95 0 Td[(q(i)]TJ /F5 11.955 Tf 9.95 0 Td[(1))=q(i)jacrossvariableqatindexiexceeds0.4),whenitispartofashockfront(denedbyarelativepressurejumpof>0.33),andwhenthelocalJeanslengthisnotcoveredbyatleast4cells(neededtoavoidarticialfragmentation Trueloveetal. , 1997 ). 2.3HeatingandCoolingFunctionsWemodelthethermalpropertiesoftheISMusingaPhoto-DissociationRegion(PDR)-basedmethodthatfollowsandexpandsuponVLBT2013andisdetailedinthefollowingsubsections. 2.3.1ImplementationofThermalProcessesImplementationintotheEnzocodeinvolvescalculatingthenetheatingrateforagivencell: H=nH[)]TJ /F2 11.955 Tf 12.95 0 Td[()]TJ /F3 11.955 Tf 11.95 0 Td[(nH]ergcm)]TJ /F4 7.97 Tf 6.59 0 Td[(3s)]TJ /F4 7.97 Tf 6.59 0 Td[(1,(2{2)where)]TJ /F1 11.955 Tf 10.67 0 Td[(istheheatingrateandisthecoolingrate.Thenetcoolingrateintroducesacoolingtimescale:tcoolEint=jHj.TheinternalenergyofthegasisdenedbyEint=p=()]TJ /F5 11.955 Tf 11.96 0 Td[(1).Weadoptameanparticlemassof=2.33mH(validformoleculargaswith1Heper10Handignoringcontributionsfromotherspecies).Forsimplicity,thisvalueofisadoptedthroughthesimulationdomain,i.e.,evenintheambient,\atomic"medium.Thedynamicsofthesimulation(andtheobjectsofmaininterest)aredominatedbygasatdensitiesofnH&102cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,whichcorrespondtoequilibriumtemperaturesof10K(detailsdescribedbelow).Thus,weadoptthevalueof=5=3fortheentiresimulationdomain.WhilethisdoesnotaccountfortheexcitationofrotationalandvibrationalmodesofH2thatwouldoccurinshocks,weconsiderthatthisisthemostappropriatesingle-valuedchoiceofforoursimulationset-up,givenourfocusonthedynamicsofthedensemoleculargas.Thechosenvaluesofandsetsoundspeedsofcs=p kT=mp0.24p T=10Kkms)]TJ /F4 7.97 Tf 6.58 0 Td[(1.Sincetcoolisoftenshorterthanthehydrodynamicaltime,thetemperatureandinternalenergyaresub-cycledandupdated,assumingconstantdensity,untilthehydrodynamical 37

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timestepisreached.Thisismorecomputationallyecientasamethodforpreventingexcessiveheatingorcooling,thanevolvingallvariablesontimestepsequaltothecoolingorheatingtimes. 2.3.2Density-ExtinctionRelationSimulatingakpc3regionofagalacticdisk,VLBT2013foundamonotonicallyincreasingrelationbetweendensityandaverage(sixorthogonalray)columnextinction,whichdenedaneectivevisualextinction( Glover&MacLow , 2007 ).Thisrelationwasresolution-limitedathighdensitiesduetotheeectivevisualextinctionbeingdominatedbyabsorptionwithinasingle0.5pccell.Forthesimulationsperformedinthispaper,weuseamodiedextinctioncurvenormalizedtoestimatedvaluesoftheWarmNeutralMedium(WNM):AV'0.01magfornH=0.03cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3( Wolreetal. , 2003 ),GMCs:AV'1magfornH=100cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,andstarlesscores:AV'30magfornH=106cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3.TottheseconstraintsaswellasretainthephysicalrelationshipsrepresentedintheVLBT2013curve,weignoretheeectsofindividualcellextinctionathighdensitiesandinsteadperformalogarithmicextrapolationfromnH=103cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.Thisintermediatecurveisttedtothenormalizationpointsviaasmoothscalingfunction,producingthenaldensity-extinctionrelation(seeFig. 2-2 ). 2.3.3NonequilibriumPDRHeatingandCoolingRatesWenextutilizebothPyPDR1(describedbelow)andCloudy(version13.02,lastdescribedin Ferlandetal. ( 2013 )),photoionizationsimulationcodes,togeneratetablesofnon-equilibriumheatingandcoolingratesasfunctionsofdensity,temperatureandradiationeldintensity.OurdefaultvalueofFUVradiationeldintensityisG0=4,followingconditionsdevelopedforthe4kpcmolecularringregionoftheinnerMilkyWay(VLBT13).Then,giventheAVvs.nHrelationdescribedinthelastsubsection,eachvalueofdensityhasauniquevalueofreceivedFUVintensity,allowinga2D(nH,T)gridofheatingandcoolingrates 1 http://www.mpe.mpg.de/simonbr/research pypdr/index.html 38

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Figure2-2. Averagevisualextinctionasafunctionofdensity.TheredsolidlinerepresentstheadoptedAVversusnHrelation,basedonthreeobservationalconstraints(seetext).Forcomparison,thebluedashedlinerepresentstherelationusedbyVLBT2013,withthedottedlineshowingtheresolutionlimitduetoextinctionwithinthecellitself. tobesucient.However,tocalculatethis2Dgridself-consistentlydoesrequirecalculationofarbitraryPDRmodelswithinputdensity,temperatureandradiationeld,inordertocalculatespeciesabundancescorrectly,especiallyofmoleculeslikeH2andCOthathaveabundancessetbyFUVphotonswhosepropagationisaectedbyself-shielding.TocarryoutthesePDRmodelsweprimarilyutilizePyPDR,whichisaminimalPython-basedPDRcodethatself-consistentlycalculateschemical,thermal,andmolecularpropertieswithinaslabofgasirradiatedwithFUVphotons.PyPDRimplementsthesamechemicalnetworkasin Rolligetal. ( 2007 ),whichincludesreactionsforH2formation,cosmicrayinducedreactions,photodissociation(includingself/mutual-shieldingofH2,COandC)andgas-phasereactions. 39

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Thefollowingheatingandcoolingratesareimplemented:H2pumpingandlinecooling( Rolligetal. , 2006 ),H2formation( Sternberg&Dalgarno , 1989 ),H2dissociation( Jonkheidetal. , 2004 ),gas-grainheating/cooling( Tielens , 2005 ),photoelectricheatingandrecombinationcooling( Bakes&Tielens , 1994 ),Ly-cooling( Sternberg&Dalgarno , 1989 ),opticalOxygen-6300Acooling( Sternberg&Dalgarno , 1989 ),heatingbyC-ionization( Black&vanDishoeck , 1987 ; Jonkheidetal. , 2004 ),cosmicrayheating( Jonkheidetal. , 2004 ),linecoolingbyOI,CII,CI(nestructure),COand13CO(rotational)calculatedfromthenon-LTEexcitationofOI,CII,CI,CO,and13COusinganescapeprobabilityapproach.DatafromtheLAMDAdatabase( Schoeieretal. , 2005 )isused.WhilethePyPDRchemicalnetworkincludesonly30atomsandmolecules,itstillperformswellinbenchmarktests,producingresultssimilartolargerPDRcodes( Rolligetal. , 2007 ).However,asPyPDRwasdevelopedfortemperaturesonlyupto104K,wedonotuseitforhighertemperatureconditions.Cloudy,ontheotherhand,followsamuchlargernumberofspeciesthanPyPDRandcantreatT>104Kgas.Thus,weutilizeitinthisregime.However,forourpurposesofdeningnon-equilibriumheatingandcoolingfunctionsthatutilizeatwostepprocesswherehighspectralresolutionlineself-shieldingoutputisneededasageneralinputforthenextPDRcalculation,thepublicversionofCloudydoesnotautomaticallyprovidesuchoutputinformation.ThuswehaveadaptedthePyPDRcodeofBrudererforthispurpose.Wesetupthedensity-temperatureparameterspaceforthearraysasfollows.ThedensityrangeisnH=10)]TJ /F4 7.97 Tf 6.58 0 Td[(3to106cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,instepsof0.1dex(91values)whilethetemperaturespansfrom2.7Kto105Kinstepsof0.046dex(100values).PyPDRwasusedtocalculatethebulkoftherates,fromT=2.7to104K,whileCloudywasusedforT=104to105K.TheprocedureforbothPDRcodesgenerallyfollowsthatofVLBT2013,whichusedCloudyversion8.02andwasbasedoof Smithetal. ( 2008 ).Anycode-specicdierenceswillbementionedintherelevantsections. 40

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First,theunextinguishedlocalinterstellarradiationeld(ISRF)withG0=4isincidentonanabsorbingslabofgaswithabundances,metallicities,anddustresemblingthatofthelocalISM.Weincludethecosmicmicrowavebackgroundradiationaswellasabackgroundofcosmicrayswithprimaryionizationrateof=1.010)]TJ /F4 7.97 Tf 6.59 0 Td[(16s)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Thecolumndensityofthegasslabisdeterminedbythepreviouslydescribeddensity-extinctionrelationandthelinearrelationbetweencolumndensityandvisualextinction(AV=5.3510)]TJ /F4 7.97 Tf 6.58 0 Td[(22NHmag).Foragivendensity,aPDRmodeliscalculatedthroughaslabwithcolumncorrespondingtotheparticulardensity.Inourcase,thedensityoftheslabalsofollowsthisgivendensity,astheextinctionshouldbedominatedbythelocaldensityforGMCregions.Note,inVLBT13,thedensityoftheslabwasxedatnH=1cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3.Atthedepthofthespeciedcolumn(i.e.,thenalcellofthePDRmodel)thetemperatureofaparcelofgasisthenvaried,withheatingandcoolingratescalculatedforthespecictemperature.Thecalculationsarerepeatedfortheentiretemperaturerange,yieldingthetemperatureanddensitydependentheatingandcoolingfunctions.InPyPDR,thecodeallowsself-consistentcalculationofgeneral,nonequilibriumheatingandcoolingratesgivenspeciesabundancessetbyequilbriumPDRconditionsforgivenextinction,densityandequilibriumtemperature.ThekeyPyPDRresultsforTeq,H2,andCOabundancesareshowninFig. 2-3 .ArraysofheatingandcoolingrateswerecreatedusingbothPyPDR(T=2.7Kto104K)andCloudy(104Kto105K),thensmoothlyjoinedalongthetemperaturedimensionusingthefunction: R(T)=10.0log10[RC(T)(T)]+log10[RP(T)(1.0)]TJ /F12 7.97 Tf 6.58 0 Td[((T))](2{3)whereR(T)isthenal,smoothlycombinedrate,calculatedfromTthegastemperature,RCtheCloudyrate,RPthePyPDRrate,andtheFermi-Diracsmoothingfunction: (T)=1 1+exp[)]TJ /F5 11.955 Tf 9.3 0 Td[(10.0(log10T)]TJ /F5 11.955 Tf 11.96 0 Td[(4.0)].(2{4) 41

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Figure2-3. (top)PyPDRequilibriumtemperatureasafunctionofdensity.ThedensitycorrespondstoavalueofAVfromfromFig. 2-2 .Detailsarediscussedinx 2.3.3 .Linesofconstantpressureareplottedingraytomoreeasilyshowregionsofthermalinstability.(middle)H2fractionasafunctionofdensity.HydrogenbecomesessentiallyfullymolecularatdensitiesabovenH'80cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3.(bottom)COfractionasafunctionofdensity.ThecarbonbecomesfullymolecularintheformofCOatdensitiesabovenH'2103cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3. 42

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ThisjoinedthefunctionsatT=104K,wheregoodagreementstilloccurredbetweenthemodels.Fromtheresultingnalarraysofheatingratesandcoolingrates,abilinearinterpolationisperformedtoderiveratesforanydensityandtemperaturecombination.Thenal,combined2Dinterpolationplotsforcooling,heating,andnetheatingasfunctionsofdensityandtemperaturearedisplayedinFig. 2-4 .Theseplotsshowthetotalcooling,heating,andnetrateatalldensitiesandtemperatures.Note,thatfromT=105KuptoT=108K,weignoreheatingandadoptthecoolingratesderivedby Sarazin&White ( 1987 ).Valuesbeyondthearraydomainadoptthelimitingvalues.Thus,foranycellinourEnzosimulation,thedensityandtemperaturearereadinandcoolingandheatingratesarereturned. 2.3.4HeatingandCoolingComponentsAbreakdownofspecicheatingandcoolingcomponentsattheequilibriumtemperatureisshowninFig. 2-5 .Photoelectricheatingofdustgrainsisthedominantheatingsourceforlow-densitygasupuntilnH102cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.Abovethisdensity,thehigherdustextinctionblocksexternalFUVphotonsandthusreducesphotoelectricheating.Theubiquitousuxofcosmicraysthenbecomesthemainheatingcomponentinhigh-densitygas.H2formationalsocontributesasthecloudbecomesfullymolecular.Themaincoolantsinthelowdensity,ionized/atomicregion(nH<1cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)areLy-andHydrogenrecombinationlines.Asdensityincreases,variousatomiclines(OI,CII,CI)becomedominantcoolants.ThesespeciesinelasticallycollidewithHandHe,excitinginternaldegreesoffreedomandsubsequentlydecayingthroughphotonemission.Molecularlines(CO,13CO)providelargecontributionsincoolingasdensityincreases,temperaturedecreases,andthegasreacheshighlevelsofmolecularabundance.Atthehighestdensities(>104cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3),gas-graincoolingdominatesascollisionsbetweendustgrainsandgasmoleculesleadtoemissionofinfraredphotonsfromthedecayoflatticevibrations. 43

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Figure2-4. Densityandtemperaturedependentinterpolatedarraysof(topleft)cooling,(topright)heating,and(bottom)ratioofheating/cooling.Thecontoursshowconstantrates(topleftandtoprightpanels)andratios(bottompanel),e.g.,intheratiomap,the100contourrepresentstheequilibriumtemperature. 44

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Figure2-5. Componentbreakdownofthemaincooling(top)andheating(bottom)ratesperunitvolumeasafunctionofdensityattherespectiveequilibriumtemperatures(giveninFig. 2-3 ). 45

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2.3.5ObservationalDiagnosticsInadditiontoprovidingabetterunderstandingofthedominantphysicalprocessesoccurringatdierentdensitiesandtemperatures,theheating/coolingcomponentbreakdownalsoenablesthecreationofobservationaldiagnosticsintheformoflineemissivities.Herewefocusonapreliminaryinvestigationintohigh-JCOtoseeiftheyaregooddiagnosticsofshocksarisingfromcloudcollisions.ThePDR-derivedcoolingdataincludecontributionsfromtherst40rotationallinesforboth12COand13CO.Similartothemethodofcreatingthecoolingandheatingfunctions,tablesofdensityandtemperaturedependentemissivitieswerecompiledtoallowcalculationofobservablequantitiesintheformofintegratedintensitymapsandspectra.Viapost-processing,integratedintensitymapscanbederivedfromthevolumeemissivityfunctionscoupledwithsimulationoutputs.Weassumeaxed1pcthicknessofthesimulationvolumeforcalcuationofthesemaps.Giventhissimplistic,highly-idealized2Dgeometryofcloudstructurespresentedinthisinitialpaper,forsimplicitywedonotcalculateradiativetransferoftheemissivitiesfromeachcell,butsimplysumtheircontributionsasiftheiremissionreacheduswithnegligibleattenuation.However,notethattheemissivitiesoflinesfromPyPDRdoalreadyaccountforanidealizedcloudopticaldepthviaanescapeprobabilityformalismthroughthePDRlayer(seex 2.3.3 ).Furtherdetailedstudyofobservationaldiagnosticsofcloud-cloudcollisionsbasedon3Dsimulationsandincludingfullradiativetransferwillbedeferredtoafuturepaper.ForeaseofcomparisonwithGalacticclouds,weassumeaducialclouddistanceofd=3kpcanddepthofz=1pc.WeusethelinevolumeemissivitiesderivedfromthePyPDRtodetermineanintegratedintensityforeachcellinthesimulation.Integratedintensitiesarederivedvia: I=ZId=2k 2ZTmbd.(2{5) 46

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whereIisthespecicintensity,isthewavelengthofthechosenmolecularline,andTmbisthemainbeamtemperature.Changingvariablesfromtovandsubstituting,wehave ZTmbdv=3 2kI=3jV 8kd2.(2{6)wherejisthevolumeemissivity,Visthecellvolume,andisthesolidanglesubtendedbythecell.Whilevaluesofzanddareassumedinordertoprovidesomeobservationaloutputs,theintensitymapscanbescaledforanydesiredthickness,giventheoptically-thinassumption.IntegratedintensitymapsofCOlinesandlineratioswithrotationalexcitationsJ=2-1,3-2,and8-7usingthismethodarepresentedanddiscussedinx 2.5 .Inadditiontointegratedintensitymaps,spectraofthecorrespondingobservationalvolumescanbecreated,simplybyplottingthedistributionofspecicintensityasafunctionoflineofsightvelocity.Syntheticspectraofthe13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)linesforanisolatedGMCandaGMCcollisioncase,viewedalongsightlineswithinthe2Dsimulationplane,arecompared.Velocitygradientsderivedfromthesespectraaredescribedaswellinx 2.5 . 2.4Results 2.4.1Out-of-planemagneticeldsHereweassumethemagneticeldsareorientatedorthogonaltothe2Dsimulationplaneandthusthecollisionvelocity.Usingthevirialtheorem, Chandrasekhar&Fermi ( 1953 )showedthatmagneticeldssupportthecloudpreventinggravitationalcollapseiftheaveragemagneticeldstrengthexceeds Bcrit=2RG1=2,(2{7)whereistheaveragedensityofthecloud.Notethisassumestheexternalmagneticeldtobenegligible.Wesystematicallyvarythemagneticeldstrengthtoprobethesub-andsupercriticalregimesandtounderstandthetransitionfromsub-tosupercritical. 47

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2.4.1.1IsolatedcloudThesimplestcasetoconsiderisanisolatedcloud.Forouradoptedparameters(seeGMC1valuesofTable 2-1 andruns1.A.xinTab. 3-2 ),thecriticalmagneticeldis27.9G.Weinitializethecloudwithauniformout-of-planemagneticeld,samplingvaluesof10,20,27.9and40Gandsettingtheambienteldto10G.Wealsocarryoutanunmagnetizedsimulation.Cloudevolutionisfollowedfor10Myr,morethan2freefalltimes,t=(3=[32G])1=2,whichis'4.35Myrfortheadoptedcloudvalues.Notethatthisexpressionforthefree-falltimeisforauniformsphereandnotforaninnite,uniformcylinder.Thisisanintentionalchoicetouseacommondenition,aswewillextendthisworkto3Dinfuturestudies.Figure 2-6 showstheevolutionoftheaverageclouddensityforeachmodel,trackedusingtheadvectivescalarmethod(seex 2.2.2 ).Fortheunmagnetized,purehydrodynamicalmodel,theline-massofthecloudexceedsthecriticalvalue22=Gandthuscollapsesunimpeded.Allofthecloudmassendsupintoasinglecellinaboutafree-falltimeandthencontinuestoslowlyaccretemassfromtheexternalmedium(asseenintheshallowatslopeofthemeandensityat5Myr).Notethataftert'6Myr,thecloudmaterialisnolongertrackedwell,likelytheresultofanumericalartefactduetonumericaldiusion.Notethatwetrackthecloud(orclump,asinlatercases)byadvectingascalareldSwhichwesetto1insidethecloudand0outside.ThecloudisdenedbymaterialwithS>0.5.Bythetimethecloudcollapses,mostofthemassiswithinasmallnumberofgridcells.Asevolutioncontinues,cloudandambientmaterialmixessothatthescalarisnowbelowthedenedvalueanditsmassisnolongeraccountedfor.Ifmagneticeldsarepresent,themagneticpressuresupportsthecloudagainstgravitationalcollapse.Theoscillationisduetothetransitiontowardsanequilibriumdensityandmagneticelddistribution.Formagneticeldvaluesbelowthecriticalvalue,thecloudisinitiallysupercriticalandthuscollapses.Theaveragedensityfollowsthesameevolutionasforthepurehydrodynamic 48

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Figure2-6. AveragedensityofthecloudovertimeforinitialBstrengthsof0,10,20,28,and40G.Thebluedash-dottedlinemarkswhentheB=0Gcaseisaectedbynumericaleects.CriticaleldstrengthoccursatBcrit=28G.Thedottedverticallinedenotesthefreefalltimeofthecloud.Thedottedhorizontallinesshowcritpredictedforeachmodel. model.However,thecloudsdonotcollapsecompletely,evenforeldstrengthsclosetotheexternalmagneticeldvalue.Actually,aslongasamagneticeldispresent,thecollapseofthecloudisimpeded.Thiscanbeeasilyunderstoodfromconservationofmagneticuxandmassina2Dgeometry.Boththeaveragemagneticeldanddensityareproportionalto1=R2.Thecriticalmagneticeld,however,isproportionalto1=RasBcrit/R(seeEq. 2{7 ).Thus,asthecloudcollapses,theaveragemagneticeldinthecloudincreasesfasterthanthecriticalmagneticvalue.Whiletheinitialmagneticeldistooweaktosupportthecloud,subsequentcontractioncausestheeldtoeventuallybecomestrongenoughtohaltcollapse.Thus,thecloudtransitionsfromasupercriticalregimetoasubcriticalone. 49

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Usingtheinitiallinemassandmagneticuxofthecloud,themeandensityatwhichthetransitionfromsupercriticaltosubcriticaloccurs,isgivenby crit=4m3lG 2.(2{8)ForB=10GandnH=100cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,wendncrit=776cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.Figure 2-6 indeedshowsthatthegravitationalcollapseoscillatesclosetothisvalueforB=10G,graduallysettlingtowardsanequilibriumstate.Thenaldensitiesareslightlyhigherthanpredicted,presumablyduetoexternalpressurefromtheambient,magnetized,infallinggas.Thisresultisspecictothe2Dcylindricalgeometryadoptedhere.Forasphericalcloud,thecriticalmagneticeldstrengthisgivenby Chandrasekhar&Fermi ( 1953 ) Bcrit2.5RG1=2.(2{9)Notethesimilaritywiththeexpressionofthecriticalvalueforacylindricalcloud(eq. 2{7 ).Ifthecloudisinitiallysupercritical,wecanassumenearlyisotropiccollapse.Then,thedensityisproportionalto1=R3,sothatBcrit/1=R2.BecauseofmagneticuxfreezinginidealMHD,themeanmagneticeldofthecloudisproporptionalto1=R2.Thismeansthatthecriticalmagneticeldandthemeanmagneticeldhavethesameproportianlityandthecloudremainssupercriticalduringthecollapse.Itisclearthat,ifhighgravitationalcollapseistobeachievedin2D,owalongeldlines(alongthedirectionofcollapse)orowthrougheldlines(dueto,e.g.,ambipolardiusionorturbulentreconnection)mustoccur.Alternateeldgeometriesarediscussedinlatersections. 2.4.1.2IsolatedcloudwithembeddedclumpWenowembedaclumpwithintheclouddiscussedintheprevioussection.Thecriticalmagneticeldfortheclumpis'65G,whilethecriticalvalueforthecloudhasincreasedto'40G(astheaveragedensityofthecloudishigherwiththeembeddedclump).Weexaminetheeectofvariousmagneticeldstrengthsinthecloudandclump.First,wekeepthetheclumpmagneticeldconstantandvarythecloudvalue.Thistellsusmoreaboutthe 50

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Figure2-7. Averageclumpdensity(toppanel)andtemperature(bottompanel)versustimeforconstantGMCmagneticeldB1=40GandvaryingBcl=40,55,65,75G.CriticaleldstrengthoccursatBcl=65G.ThesolidlinerepresentstheaveragevalueintheclumpdenedbythescalarvalueS>0.5,whiletheshadedregionsshowtheaveragesbetweenS>0.25andS>0.75.Thisconventionforclumpdenitionisfollowedthroughouttheremainderofthepaper. evolutionofanequilibriumclumpinasub-orsupercriticalcloud.Then,wekeepthecloudmagneticeldconstantwhilevaryingtheclumpvalue.Thesecorrespondtoruns1.B.xinTab. 3-2 .Althoughwearerestrictedwithourcloudandmagneticeldgeometry,theseresultsareusefulforunderstandingmorecomplexsimulations.ResultsareshowninFigures 2-7 and 2-8 .ForaconstantBGMCnearitscriticalvalue,theevolutionoftheclumpisentirelydeterminedbytheratioofitsgravitationalandmagneticenergy(itsthermalenergyis 51

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Figure2-8. Averageclumpdensity(toppanel)andtemperature(bottompanel)overtimeforconstantclumpmagneticeldBcl=65GandvaryingGMCeldstrengthasB1=10,20,40,65G.CriticaleldstrengthoccursatB1=40G. negligible).Usingeq. 2{8 ,wendthat,forBcl=40G,theaveragedensityoftheclumpincreasesbyafactorof2.7.However,Figure 2-7 showsanincreasetwicethisvalue.Thisisduetotheinitialcontractionofthecloudbetween0-2Myrasittriestosetupanequilibriumdistribution.Afterthisinitialadjustmentphase,theaveragedensityoftheclumpdropstoafewtimestheinitialvalueasexpected.Forhigherinitialmagneticeldsintheclumpthedensityincreasesbyasmallerfactor,asalsoexpectedfromeq. 2{8 .ForaconstantBcl,changesintheaverageclumpdensityaredrivenbyexternalpressurefromthesurroundingGMCmaterial.ThisexternalpressureisrelativelylargerforthelowerGMCmagneticelds.Inthesecases,theGMCisinitiallysupercriticalandstartstocontract 52

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gravitationally.Theaveragedensityoftheclumpincreasesmaximallybyafactorof5.Theclumpmagneticeldisstrongenoughtoresistgravitybuttheclumpisfurthercompressedtohigherdensitiesbecausetheexternalpressurecontributesnon-negligiblytothegravity.ForstrongerGMCmagneticelds,however,thedensityoftheclumpisnotincreasingbecauseofthepressureexertedbytheGMC.Instead,theclumpisinitiallynolongersubcritical.Theexternal(i.e.,GMC)magneticeldisnotnegligibleandshouldbetakenintoaccountwhenderivingthecriticalvalue.ForhighGMCmagneticelds,thecriticalvalueoftheclumpisactuallygreaterthan65G,andthusitinitiallycollapsesgravitationally.However,itisnothighlysupercriticalsothedensityincreaseisquitemodest.Atthesametime,GMCswithhighermagneticeldsexpandafter2-2.5Myr(seeprevioussection).Theexternalmagneticeldthendecreases,aswellasthecriticalmagneticeldoftheclump.Thisresultsinre-expansionoftheclumptonearitsinitialvalue.Ourresultssuggestthatincreasingexternalpressuresisapossiblewaytotriggerasub-to-supercriticaltransition. 2.4.1.3Collidingclouds:head-oncollisionsAsignicantsourceofadditionalpressurecanbeprovidedbyrampressureofcloudcollisionsandtheresultingthermalandmagneticpressurereleasedinshocks.Therampressuredependsontherelativecollisionspeed,vrel2.Weinvestigatedierentcollisionspeeds,i.e.,vrel=5,10,20,and40kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1(seeruns1.C.1.xinTable 3-2 ).Densityandtemperatureslicesatdierentstagesoftheevolutionareshownforvrel=10kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1inFigure 2-9 .Thetwocloudsareinitiallyseparatedsuchthatthecollisionoccursat4Myr,whichallowsforaninitialredistributionofthedensityinthecloud(seeFigures 2-10 and 2-12 ).Thecloud-cloudcollisioncompressesthecloudsandtheclump,leadingtohigherdensities.Thecollisionalsogivesrisetomanyshockspropagatingthroughtheclouds.Suchshockscontributetoraisingthepressurearoundtheclump.High-temperatureshockfrontsarepresentwithintheotherwisecold(15K)clouds.Themagnitudeofthemagneticeldalsoincreasesasmaterialiscompressed.Thisincreaseinmagneticpressurepreventstheclumpfromcollapsingcompletely,evenwiththeadditionalexternalpressureofthecollision. 53

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Figure2-9. Evolutionofcloudscollidinghead-on(zeroimpactparameter)withsnapshotsshownat2.05,4.01,4.99,5.96,and7.92Myr(seerun1.C.0inTable 3-2 .)Here,magneticeldsarenearcriticalvaluesanddirectedout-of-plane.Bcl=65G,B1=40G,andB0=10G.(toprow)MapsofnHand(bottomrow)temperature,withblackvectorsrepresentingvelocityareshown.Theadvectivescalardeningtheclumpisshownbygreycontourlines,representingthescalarvalueS=0.25,0.5,and0.75. Figure 2-10 showstheevolutionoftheaverageclumpdensityandtemperaturefordierentcollisionspeedscomparedtothenon-collidingcase.Notethat,forvrel=20and40kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,thecollisionswereperformedinthereferenceframeoftheclump,toavoidhighowvelocityinducednumericaldiusioneectsthatcanhavemodesteectsonclumpboundarydenitions,mostlyaectingmeasurementofclumptemperature.Duetotheutilizedset-up,acollisionfrontbetweenthelow-densityambientenvelopesarisesinbetweentheclouds.Beforethecloudsdirectlyinteract,theyarebeinginuencedsomewhatbythishighpressurepost-shockcollisionregion.However,thepressurehereismuchlessthantherampressureresultingfromtheGMC-GMCcollision,giventhefactorof10dierenceinGMCtoambientdensity.TheeectsoftheshockedambientmediumontheclumpcanbeseeninFig. 2-10 ,att/4Myr.Bothdensityandtemperatureareaected,morenoticeablyat20and40kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1,buttheensuingGMCcollisiondominatesthe 54

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Figure2-10. Averageclumpdensity(Toppanel)andtemperature(2ndpanel)overtimecomparingtheeectsofcollisionvelocityforout-of-planeeldgeometries(seeruns1.C.1.x).Here,out-of-planemagneticeldsarenearcritical(Bcl=65G,B1=40G,andB0=10G).Collisionvelocitiesvrel=5,10,20,40kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1areshown,alongwiththeevolutionoftheisolatedGMCwithclump.Theratiosofthecollidingcasescomparedtotheisolatedcaseforaveragedensity(3rdpanel)andtemperature(bottompanel)arealsoshown. 55

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Figure2-11. Timeevolutionofcollidingcloudsat2.05,4.01,4.99,5.96,and7.92Myrwithb=0.5R1(seerun1.C.2.2inTable 3-2 .)Here,out-of-planemagneticeldsarenearcritical(Bcl=65G,B1=40G,andB0=10G).(toprow)MapsofnHand(bottom)mapsoftemperaturewithblackvectorsrepresentingvelocityareshown.Theadvectivescalardeningtheclumpisshownbygreycontourlines,representingthescalarvalueS=0.25,0.5,and0.75. subsequentclumpevolution.Theseeectsduetotheshockedambientmediumcanbeseeninthedensityandtemperatureevolutionforcollidingcasesinsubsequentruns,discussedbelow.Asexpected,thedensityandtemperatureoftheclumpresultingfromtheGMCcollisionincreasewithcollisionspeed,ashighervelocitiesinducestrongershockswithlargercompressions.However,evenforvrel=40kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1,theincreasesinclumpdensityareonlymodest:aboutafactorof2to3timesgreaterthantheisolatedcase.Ofcourse,someofthisisduetothespecicgeometryweadopthere.Forothercloudgeometries,e.g.,sphericalcloudsin3D,andmagneticeldgeometries,e.g.,moreparalleltocollisionvelocities,thisextrapressuremayyetbesucienttotriggerthetransitionfromsub-tosupercritical.Thecollisionmodelsdoshowlargerexcursionsinclumpmeantemperatures,whichwouldbeexpectedtohaveanimpactonastrochemicalprocessesintheclump. 2.4.1.4Collidingclouds:o-axiscollisionsO-axiscollisions,inwhichtheimpactparameterwasvaried,werealsoexplored.GMC2wasplacedatdierentperpendiculardistances,b,fromGMC1'slineofsymmetryand 56

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Figure2-12. Averageclumpdensity(Toppanel)andtemperature(2ndpanel)overtimecomparingtheeectsofimpactparameterforout-of-planeeldgeometries(seeruns1.C.2.x).Here,out-of-planemagneticeldsarenearcritical(Bcl=65G,B1=40G,andB0=10G).Impactparametersofb=0.5,1.0,and1.5R1wereexplored.Theratiosofthecollidingcasescomparedtotheisolatedcaseforaveragedensity(3rdpanelandtemperature(bottompanel)arealsoshown. 57

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themeandensityoftheclumpmaterialwastrackedover10Myr.Figure 2-11 displaysthemorphologyofthecollisionforb=0.5R1.Thecloudsinteractat4Myrinanasymmetricmanner,creatinglamentarystructuresandimpartingangularmomentumonthecoalescedstructure.Comparedwiththeon-axishead-oncollisions,theresultingstructuresaremorphologicallymorelamentarybutthelevelofgravitationalcontractionisroughlyequivalent.Thelackofcompletegravitationalcontractionisexpectedbecauseoftheux-freezinglimitationofout-of-planeeldsdescribedabove.Inaddition,anyangularmomentuminthenalstructurealsohelpstosupporttheclump,furtherreducingthedegreeofcontraction.TheaverageclumpdensitiesforvariousimpactparametersarecomparedinFigure 2-12 .Collisionsat4Myrshowvaryingfactorsofdensityincrease,withhigheraveragedensitiesforsmallervaluesofb(moredirectcollisions).Aswiththecaseofheadoncollisions,clumpdensitiesareonlyincreasedbyatmostafactorofafew. 2.4.2In-planemagneticeldsTheprimaryinhibitorofcompletecollapseintheout-of-plane(Bz)magneticeldrunsisuxfreezing,i.e.,gascannotmoveacrossmagneticeldlines.Therefore,inthissection,wechangethedirectionofthemagneticeldfromorthogonaltotheplanetobewithintheplane.Contrarytotheout-of-planeeldmodelswherethemagneticeldvalueishigherinsidethecloudthanoutsideit,weassumeauniformmagneticeldacrossthecloudandexternalmedium.Forsuchclouds,gravitationalcollapseproceedspreferentiallyalongthemagneticeldlines.Whileforcessupportingthecloudaremuchgreaterperpendiculartothemagneticeldlines, Tomisaka ( 2014 )showedthatauniformin-planeeldgeometrycanyieldmagneticallysubcriticalcongurationsforinnitecylinders.Themaximumlinemasswasevaluatedas max'22.4R0 0.5pcB0 10GMpc)]TJ /F4 7.97 Tf 6.59 0 Td[(1+13.9cs 0.19kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1Mpc)]TJ /F4 7.97 Tf 6.59 0 Td[(1 (2{10) fortheisothermalcase. 58

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Multipleeldstrengthswereexplored,samplingvaluespreviouslyusedintheout-of-planecasestokeepthetotalmagneticpressurecomponentconsistent.WeapplyjBj=10,40,and65Gandanalyzetheeectsonisolatedandcollidingcases.Thesemodelscorrespondtoruns2.xinTable 3-2 . 2.4.2.1IsolatedcloudwithembeddedclumpWithuniformBxandByelds,theGMCandclumpcollapsealongthedirectionoftheeldtoformdensesheetsperpendiculartotheeldlines.Thetimescalesassociatedwiththeircontractionareoftheorderofthesphericalfree-falltimet,i.e.,'1.6Myrfortheclumpand4.4MyrfortheGMC.Aftertheinitialcollapseparalleltothemagneticeld,thegasstartstocontractperpendicularly.Completecollapseoftheclumptakesmuchlongerasthegasmotionsareperpendiculartothemagneticeld.Theisolatedcaseismostsimilartothemodelsof Tomisaka ( 2014 ).However,theembeddedoverdenseclumpdominatesthegravitationalcollapseofthecloud.Thelinemassoftheclumpis3450Mpc)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Equation 2{10 yieldsmax1660Mpc)]TJ /F4 7.97 Tf 6.58 0 Td[(1for65G,andevensmallervaluesfor10and40G.Thus,themaximumsupportedlinemassbyin-planemagneticeldsisexceeded,andoursimulationsagreewiththeseresults.Aeldstrengthof135Gcouldbeusedtosupporttheclump,butthiscasewasnotexplored. 2.4.2.2CollidingcloudsForcollidingcloudsweagainadoptaducialrelativevelocityof10kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1andstudytwodierentin-planemagneticelddirections,i.e.,parallel(i.e.,Bx)andperpendicular(i.e.,By)totheconvergingow.Herewesetthecollisiontimeatt=0Myrasthereisnomorestablestatetobereached.Further,weonlystudyasinglecollisionspeedasthedynamicsaredominatedbythegravitationalcollapseofthecloudsandclump.Similartotheisolatedmodel,thelinemassoftheclumpandcloudsexceedsthemaximumsupportablebythermalandmagneticpressures.Thecloudscollapseintoattenedsheetsperpendiculartothemagneticeldlines.Thetimescalesofgravitationalcollapseareagainoftheorderofthefree-falltime. 59

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Inthesehighlycollapsedscenarios,theclumpisnolongerwelltrackedatlatetimesduetonumericaleects. 2.4.3MixedFieldGeometriesWhiletheprevioussectionsdescribetwoextremes,i.e.,eitherthecloudismaximallysupportedbymagneticelds(out-of-planemagneticeld)orminimally(in-planemagneticeld),wenowinvestigateacombinationofthetwogeometries.Itrepresentsamorerealisticsituationasexpectedin3D,wherethemagneticeldprovidessomesupportagainstgravitationalcollapse,butcannothaltitcompletely,ifthecloudissupercritical.Inthesecases,weassumeauniformin-planemagneticeldstrengthof10G(alongthex-axis(Fig. 2-13 )orthey-axis(Fig. 2-14 )).Theout-of-planecomponentsarechosensuchthatthetotaleldstrengthhasamagnitudeequaltoitscriticaleldstrength(seeTable 2-1 andruns3.xinTable 3-2 ).Theexternalmediumhaszeroout-of-planemagneticeldcomponent,preservingthetotaleldstrengthofjB0j=10G.Suchaeldisbothdensity-dependent(asobservedby Crutcher ( 2012 ))andisdivergence-free. 2.4.3.1IsolatedcloudwithembeddedclumpAstheout-of-planemagneticeldisnear-criticalandstrongenoughtostabilizetheGMCandclump,theearlyevolutionissimilartotheout-of-planecase(seeFigure 2-10 ).Adensity(andmagnetic)gradientisquicklyestablishedtoformanequilibriumstructure.However,gasalsoowsalongthein-planemagneticeld.Thenthelinemassofthecloudincreaseswhilethemagneticuxremainsconstant.TheclumpandGMCgraduallycontract,althoughtheassociatedtimescaleismuchlongerthanthefree-falltime.Foralargerratioofin-planetoout-of-planemagneticeld,theevolutionisfasterastheout-of-planemagneticeldislessdominant. 2.4.3.2Collidingclouds:head-oncollisionsWeperformsimulationsofcloudscollidinginthismixed-eldgeometry,againinvestigatingtheeectofcollisionspeed(vrel=5,10,20,and40kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1).Additionally,thedirectionofthe 60

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Figure2-13. TimeevolutionofcollidingGMCsat2.05,4.01,4.99,5.96,and7.92Myrforthex-directedmixedeldgeometry(seerun3.C.1.0inTable 3-2 .)Here,thetotalB-eldmagnitudeisnearcriticalwhileanadditionalin-planeuniformeldofBx=10Gisappliedthroughoutthesimulation.(toprow)MapsofnHwithmagneticeldsrepresentedbystreamlinesand(bottomrow)mapsoftemperaturewithblackvectorsrepresentingvelocityareshown.Theadvectivescalardeningtheclumpisshownbygreycontourlines,representingthescalarvalueS=0.25,0.5,and0.75. in-planecomponentofthemagneticeldisvariedwithrespecttocollisionvelocity(seeruns3.C.1.xand3.C.2.xinTab. 3-2 .)Similartothemixed-eldisolatedcloudcase,thecollidingcloudsthreadedbyamixofout-of-planeandin-planemagneticeldsexperiencealargercompressioncomparedtothepurelyout-of-planeclouds.However,thedirectionoftheuniformcomponentofthemagneticeldaectsthelate-timebehavioroftheclump.Forpartialeldsparalleltothecollisionvelocity(i.e.,x-direction),therearetemporarydensityincreasesofafactorof2)]TJ /F5 11.955 Tf 12.59 0 Td[(3duringthecollision,buttheaverageclumpdensityactuallydecreasesslightlyat5Myrandbeyond,relativetotheisolatedcase(seeFigure 2-15 ).Thisreboundeectisgreaterforhighervelocities.Theshocksinitiallycompresstheclump,thensubsequentlydistortit,formingasickle-likeshape.FromFigure 2-13 ,weseethattheoriginalclumpisbrokenapartduetothecollision.Thetemperatureoftheclumpmaterialisaectedmoresignicantlyashighvelocityshocksdominatethemeanclump 61

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Figure2-14. TimeevolutionofcollidingGMCsat2.05,4.01,4.99,5.96,and7.92Myrforthey-directedmixedeldgeometry(seerun3.C.2.0inTable 3-2 .)Here,thetotalB-eldmagnitudeisnearcriticalwhileanadditionalin-planeuniformeldofBy=10Gisappliedthroughoutthesimulation.(toprow)MapsofnHwithmagneticeldsrepresentedbystreamlinesand(bottomrow)mapsoftemperaturewithblackvectorsrepresentingvelocityareshown.Theadvectivescalardeningtheclumpisshownbygreycontourlines,representingthescalarvalueS=0.25,0.5,and0.75. temperature,temporarilyraisingittofewhundredK.ThematerialcoolstotensofKintheaftermathofthecollision.Forpartialeldsperpendiculartothecollisionvelocity(i.e.,y-direction),thebehaviorisnearlyidenticalforpre-collisiontimest<4Myr.However,thedierentmagneticeldgeometrycausestheclumptobecompressedinadierentmanner(seeFigures 2-14 and 2-16 ).Inthiscase,thecollisioninducesnosickle-shapedstructure,butrathertheclumpstaysrelativelycompact,withtheaveragedensityincreasing,butnotrebounding.ThematerialinthecollisionalowinterfaceregionfreelyfallsintotheoverdenseremnantsofthecloudandclumpduetotheorientationoftheB-eld.Shocksarecontinuallycreatedastheglobalowandinfallingmaterialinteract,regulatedbythemagneticelds.Latetimebehaviorafterthecollisionrevealscontinuouslyincreasingclumpdensitiesduetoinfall,withelevated(T50)]TJ /F5 11.955 Tf 11.95 0 Td[(100K)butroughlyleveltemperatures. 62

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Figure2-15. Averageclumpdensity(Toppanel)andtemperature(2ndpanel)overtimecomparingtheeectsofcollisionvelocityfortheBmixeldgeometrycase(seeruns3.C.1.x).Here,out-of-planemagneticeldsarenearcritical(Bcl=65G,B1=40G,andB0=10G)whileanadditionalin-planeuniformeldofBx=10Gisappliedthroughoutthesimulation.Collisionvelocitiesvrel=5,10,20,40kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1areshown,alongwiththeevolutionoftheisolatedGMCwithclump.Theratiosofthecollidingcasescomparedtotheisolatedcaseforaveragedensity(3rdpanel)andtemperature(bottompanel)arealsoshown. 63

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Figure2-16. Averageclumpdensity(Toppanel)andtemperature(2ndpanel)overtimecomparingtheeectsofcollisionvelocityfortheBmixeldgeometrycase(seeruns3.C.2.x).Here,out-of-planemagneticeldsarenearcritical(Bcl=65G,B1=40G,andB0=10G)whileanadditionalin-planeuniformeldofBy=10Gisappliedthroughoutthesimulation.Collisionvelocitiesvrel=5,10,20,40kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1areshown,alongwiththeevolutionoftheisolatedGMCwithclump.Theratiosofthecollidingcasescomparedtotheisolatedcaseforaveragedensity(3rdpanel)andtemperature(bottompanel)arealsoshown. 64

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2.4.3.3Collidingclouds:o-axiscollisionsOurnalmodelisacloud-cloudcollisioninthemixed-eldgeometrywithanin-planeuniformeldofBx=10G.Wehavevrel=10kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1andadditionallyapplyb=0.5R1toGMC2(see3.D.0inTab. 3-2 ).Wedesignatethisasour\ducialcase"andrunthestandardresolution,alongwithoneandtwoadditionallevelsofAMR,givingamaximumeectiveresolutionof0.0625pc.WecomparetheeectsofdierentresolutionsinFigure 2-17 .Pre-collisiondensitiesarequitewellconverged,butbegintodeviateastheshockwavesandclumpcompressionarerealizedatdierentresolutions.Largerinitialdierencesareseeninthetemperatures,wherehigherresolutionsleadtogenerallyloweraverageclumptemperatures.Thisislikelyduetotheinitialshockcreatedattheboundariesoftheuniformclumpasthedensitygradientisestablished.Athigherresolutions,thepost-shockregioncontributeslesstotheoverallclumpmaterial.Additionally,inspectionofclumpcontoursatthevariousresolutionsrevealedslightlydierentclumpboundariesarisingfromthecollision.Thiscouldpartiallyaccountforthegreaterdiscrepanciesatlatertimes.Whiletheseresolutioneectsarenotinsignicant,thekeyresults{relativechangesofacloudcollisionwithrespecttotheisolatedcase{retaingoodagreementthroughoutthemajorityofthesimulation(upto8Myr).Figure 2-18 summarizestheentireducialrun,showingtimeevolutionformapsofdensity,temperature,andcommonobservationalbandsof13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)aswellasthe12CO(J=8-7)/13CO(J=2-1)lineratio.Theseintegratedintensitymaps,basedonoutputsfromthePDRmodelingaspotentialobservationaldiagnostics,arediscussedinx 2.5 .Broadlyspeaking,theeectofaniteimpactparameterfortheGMCcollisionresultsinashearingvelocityeldandasymmetricmorphologiesasvariousareasoftheclumparecompressedanddistorted.GMC2canbeseencontractinggravitationallyasitapproachesthemoremassiveGMC1.Priortothecollision,partsofGMC1andtheclumpareslightlycompressedbytheboundingshocksarisingfromthecollidingregionoftheambientmaterial. 65

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Figure2-17. Aresolutionstudycomparingtimeevolutionofaverageclumpdensity(Toppanel)andtemperature(2ndpanel)fortheducialcase(seerun3.D.0).Modelsatthestandardresolution(10242)arecomparedwiththoserunwithoneandtwoadditionallevelsofAMR.Theratiosforaveragedensity(3rdpanel)andtemperature(bottompanel)comparedtotheisolatedcaseattheparticularresolution,arealsoshown. 66

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Thecollisionitselfcompressespartsofthecloudsevenfurther,asGMC2entersGMC1andimpactstheclumpfromthenorth.Fromthedensityandtemperaturemaps,shockscanbeseenpermeatingthecloudmaterialandpassingthroughtheclumpthroughouttheentirecollisionprocess.Atlatertimes,theoriginalclumpmaterialisdistortedgreatlyandevenbreaksapartintoafewpieces,butthedensestmaterialremainsinsidethemainclumpregion.Peakcompressionduetothecollisionoccursnear5Myr(thirdcolumninFigure 2-18 ).Weinvestigatethisfurtherbyzoominginontheclumpatthistimestepandmappingvariouskeyquantities.ThisisshowninFigure 2-19 .Thedensity,temperature,magneticelds,andvelocitygradientintheregionssurroundingandincludingtheclumpareanalyzed.Integratedintensitymapsarealsoshowninthisgureanddiscussedinx 2.5 .Theclump,initiallyauniformcylinder,remainsrelativelydistinctandcontiguous,thoughatthistimestepitisundergoingcompressionanddistortionduetothecloudcollision.WhatwasonceGMC2canbeseenasthedenser(few103cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)materialthathaspunchedintoGMC1andisimpactingtheclumpfromthenorth.TheaverageclumpdensityisnH104cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3,embeddedinGMCmaterialof102{103cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.Theclumptemperature,ontheotherhand,isnotparticularlydistinctfromthesurroundingmaterial,generallyatafew10sofK.Shocksofafew100sofKareseenpropagatingthroughtheclumpandcloud.Thehightemperaturematerial(104K)duetothestrongshockcreatedbythecollisionwithGMC2haspenetratedGMC1,buthasnotreachedtheclump.ThemagneticeldscanbeseencorrespondingcloselytothedensitymorphologyoftheGMC,witheldstrengthgenerallyincreasingwithdensity.TheB-eldshavestrengthsof100GinthecompressedGMCmaterialandpeakatafewhundredGwithintheclumpandnearbyregions.Theinitialin-planeelds,uniformanddirectedalongthecollisionaxis,remainmostlyuniform,exceptforwheretheGMCshavebeendisrupted.Complexeldstructuresarisewithintheclumpandcloudmaterial.Inthiscase,thereisaloosecorrelationbetweenmagneticelddirectionandthedirectionofinfallinggasowtotheclump. 67

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Figure2-18. TimeevolutionofcollidingGMCsat2.05,4.01,4.99,5.96,and7.92Myr(1levelAMRversionofrun3.D.0inTable 3-2 .)Here,out-of-planemagneticeldsarenearcritical(Bcl=65G,B1=40G,andB0=10G)whileanadditionalin-planeuniformeldofBx=10Gisappliedthroughoutthesimulation.Furthermore,GMC2isosetatb=0.5R1.(Row1):MapsofnHwithmagneticeldsrepresentedbygreystreamlines.(Row2):Mapsoftemperaturewithblackvectorsrepresentingvelocity.(Row3):13CO(J=2-1)integratedintensitymapsusingPDR-based,temperatureanddensitydependentvolumeemissivities.(Row4):Similarlyderived13CO(J=3-2)lineintensitymaps.(Row5):Similarlyderived12CO(J=8-7)lineintensitymaps.(Row6):12CO(J=8-7)/13CO(J=2-1)lineintensityratiomaps.Theadvectivescalardeningtheclumpisshownbyblackorwhitecontourlines,representingthescalarvalueS=0.25,0.5,and0.75. 68

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Figure2-19. Zoomedinmapsoftheclumpatt=4.99Myr,nearthetimeofmaximumcompressionduetothecollision.Thisisthex-directedmixedeldgeometrycasewithb=0.5R1(2levelAMRversionofrun3.D.0inTable 3-2 .)Here,thetotalB-eldmagnitudeisnearcriticalwhileanadditionalin-planeuniformeldofBx=10Gisappliedthroughoutthesimulation.(left4gures)Mapsofdensity(nH),temperature,B-eldmagnitude,andvelocitygradientmagnitudeareshown.Greystreamlinesindicatemagneticeldstructurewhilevelocitiesarerepresentedbytheblackvectors.(right4gures)Mapsof13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)intensity,aswellasamapof12CO(J=8-7)/13CO(J=2-1)lineintensityratioareshown.Theadvectivescalardeningtheclumpisshownbyblackorwhitecontourlines,representingthescalarvalueS=0.25,0.5,and0.75. Thevelocitygradientmapshowsdetailedstructureofthemanyshockspropagatingthroughoutthecloud.ThestrongestgradientscanbeseencorrespondingwiththeshockedGMC-envelopeinterface,aswellastheGMC-GMCcollisionregion.Thevelocitymagnitudesshowsometurbulentmotionbeingproducedbythecollision.Toillustratetheeectsofourtreatmentofnonequilibriumheatingandcooling,Figure 2-20 comparesthedierencesintemperaturesbetweenthenonequilibriumcooling/heatingfunctionsdevelopedinthispaperandacooling/heatingcurvethatassumesequilibriumtemperatures.Dierencesprimarilyoccurintheshockedregions,asmaterialisshockheatedoutofequilibrium.Thetemperaturemaps,uponwhichtheobservationaldiagnosticsheavily 69

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Figure2-20. Amapoftheratioofactualsimulationtemperaturetothedensity-basedequilibriumtemperatureatt=4.99Myrforthe2levelAMRducialcase.TheadvectivescalaratvaluesS=0.25,0.5,and0.75deningtheclumpisshownbyblackcontourlines. depend,wouldexhibitverydierentbehaviorhadonlyasimpleequilibriumcooling/heatingcurvebeenused. 2.5ObservationalDiagnosticsHerewebrieyoutlinetwopotentialmethodsofobservationallydiagnosingGMCcollisions,basedonemissionofhigh-JCOlines.However,giventheidealized2Dnatureofthesimulationspresentedsofar,wedefermoredetaileddiscussiontoafuturepaperthatwillconsidertheoutputsfrom3Dsimulations. 2.5.1IntegratedIntensityMapsUsingtheoutputsfromourPDRmodeling(methoddescribedinx 2.3.5 ),wecreateCOintegratedintensitymapsfromthesimulationoutputs.NotethatthelocalemissivityofCO 70

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linesdoestakeintoaccounttheopticaldepthofanassociatedPDRlayer,ofgiventotalcolumndensitythatdependsonlocalvolumedensity.Toillustratethemethod,weperformpost-processingonthecollidingcase(vrel=10km=s)withanimpactparameterofb=0.5R1andBx-orientedmixedelds,ourducialmodel.ThediagnosticsportionsofFigures 2-18 and 2-19 showintegratedintensitymapsofcommonobservationalbandsof13CO(J=2-1and3-2)and12CO(J=8-7)aswellasthe12CO(J=8-7)/13CO(J=2-1)lineratio.Thesemapsassumeadepthof1pcinthezdirectionandaclouddistanceof3kpc.Notealsothattheadoptedabundanceratioof13Cto12Cis1/60.WeseethattheCOemissionlinestracemoleculargasingeneral,withthehigher-Jlinesindeedprobingmorestronglyshockedregions.AsJincreases,highertemperaturematerialistraced,withshockfrontsofvaryingstrengthsbeingfollowed.ThisoccursevenforlowvaluesofnH.Whiletheselineemissivitiesaremoststronglyaectedbytemperature,theyarealsotracersofhighdensityduetothehighercriticaldensityofthehigh-JtransitionsandthedependenceofnCOonnH.Thus,lowertemperature,highnHgasisalsorevealed.13CO(J=2-1)and13CO(J=3-2)intensitymapsshowfairlysimilarstructures,primarilytracinghigh-densitymaterialaswellashighertemperatureregions.The12CO(J=8-7)map,however,accentuatesmorestronglyshockedregions,closelytracingthehigh-temperaturedenseregions.Stronglyshocked,hightemperature,highdensitygas{potentiallyasignatureofcloud-cloudcollisions{producesthestrongestintensityofhigher-levellines.EmissivitiesatcertainJlevelsaswellastheirratioscanactasdiagnosticsofawiderangeofconditionsandpotentiallydetermineshockpropertiesandphysicalconditionsintheaectedgas.Thenallineratiomapfurthertraceshigh-temperature,high-densitymaterial,andde-emphasizeslow-temperature,high-densitymaterial.The12CO(J=8-7)/13CO(J=2-1)lineratiocouldbeanecienttracerofcloudcollisions.Figure 2-21 exploresthispotentialcloud-collisionsignature.Theaverage12CO(J=8-7)to13CO(J=2-1)lineintensityratiowithintheclumpiscalculatedandfollowedovertimeforaset 71

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ofisolatedandcollidingcases.Fromtheseresults,weseethatthisparameterisanexcellenttracerofcloudcollisions.Whiletheclumpintheisolatedcase(onceitsettlesintoarelativelystablestate)retainsavalueofthisintensityratioof1)]TJ /F5 11.955 Tf 12.35 0 Td[(10,aclumpexperiencingaGMCcollisionseesmuchlargervaluesofthelineratio,evenreaching>103forvrel=40kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Collisionvelocitiesaslowasvrel=5kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1showanexcessofafactorof10withrespecttotheisolatedcase. 2.5.2SpectraFromthesimulations,syntheticspectrawerecreatedinordertoprovideamoredirectcomparisonwithobservedcloudkinematics.Whiletheinitialconditionsand2Dgeometryarefairlyidealized,weexpectthesediagnosticmethodstobeofgeneraluse,e.g.,onceoutputsfrom3Dsimulationsareavailable.EmissionlinespectraofvariousobservationalvolumeswithinthesimulationboxfortheisolatedandcollidingducialcaseareshowninFigure 3-14 .TheisolatedcaseshowsanarrowvelocityrangeofdensegastracersThereisalsoarelativelystrongpeakin12CO(J=8-7)asthecloudpinchesinonitselfduetothepresenceofin-planemagneticelds,buttheseshocksoccuratlowvelocities.Thechosenvolumehaslittleeectonthespectraasthemainfeaturesarelocalizedaroundtheclumpregion.Thesamefeaturesarepresentinbothlinesofsight,withgreaterasymmetryinthex-velocitysimplyduetotheo-centerinitialpositionoftheclumprelativetoGMC1.ThespectraforthecollidingcaseshowamuchwidervelocityspreadineachoftheCOemissionlines.Inthe20pc20pcbox,theemissionpeaksin12CO(J=8-7)atmultiplenarrowvelocitybandscorrespondtothestrongestshocksasseeninFig. 2-19 .Thehighemissivityfeaturein12CO(J=8-7)forthey-velocityindicatesstrongshockstravelingnorthwardaroundthecollisionregion.Thestrongfeaturespresentinthe8pcby5pcregionbutnottheclumpmaterialrepresentshockscompressing,butnotyetpropagatingthrough,theclump.Theseshocks,directedinthenegative-xandydirections,indicatethecollisionwithGMC2.Nextwemeasureline-of-sightvelocitiesandvelocitygradientsinthe8pcby5pcrectangularregionaroundtheclumpintheducialsimulationatthetimeofmaximum 72

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Figure2-21. Average12CO(J=8-7)/13CO(J=2-1)lineintensityratio(top)overtimecomparingtheeectsofcollisionvelocityfortheBmixeldgeometrycase(seeruns3.C.1.x).Here,out-of-planemagneticeldsarenearcritical(Bcl=65G,B1=40G,andB0=10G)whileanadditionalin-planeuniformeldofBx=10Gisappliedthroughoutthesimulation.Collisionvelocitiesvrel=5,10,20,40kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1areshown,alongwiththeevolutionoftheisolatedGMCwithclump.Theratiosofthecollidingcasescomparedtotheisolatedcase(bottom)arealsoshown. 73

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Figure2-22. Syntheticspectrafor13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)areshownfor(topsix:(a)-(f))theisolatedcaseand(bottomsix:(g)-(l))collidingcase,att=4.99Myr.Thesubplotsdenoteemissionanalyzedfromdierentvolumes(xyvalueslistedbelow,andassuming1pcextentinthezdirection)inthesimulation:a20pc20pcboxcenteredontheclump,asmaller5pc8pc(isolatedcase)or8pc5pc(collidingcase)regioncontainingtheclump,andcontributionsolelyfromtheclumpmaterial,denedbythescalarvalueS>0.5.Theleftcolumnshowsspectraderivedfromvx(i.e.,aviewalongthecollisionaxis),whiletherightcolumnshowsspectraderivedfromvy(i.e.,aviewperpendiculartothecollisionaxis).Velocitybinsof0.25kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1areused. 74

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compressionusingthe13CO(J=2-1)spectra.Wecomparegradientsderivedfromthetotalmassdistributionandthosederivedfromtheintensitiesof13CO(J=2-1),13CO(J=3-2)and12CO(J=8-7)spectra.Figure 2-23 showsthemeanvelocitiesandderivedvelocitygradientsoftheclumpmaterialalongorthogonallinesofsight.Themeangradientsare0.97and-0.81kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1pc)]TJ /F4 7.97 Tf 6.58 0 Td[(1forspectrameasuredalonglinesofsightperpendicularandparalleltothecollisiondirection,respectively.SomewhatsmallergradientsarederivedfromlowerJCOlines,andlargergradientsfromhigherJlines.VelocitygradientshavebeenmeasuredobservationallywithinIRDCsandGMCs.Forexample, Raganetal. ( 2012 )foundvelocitygradientsof2.4and2.1kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1pc)]TJ /F4 7.97 Tf 6.58 0 Td[(1withinsub-pcregionsofIRDCsG5.85-0.23andG24.05-0.22,basedonobservationsofNH3(1,1). Henshawetal. ( 2014 )foundvaluesof0.08,0.07,and0.30kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1pc)]TJ /F4 7.97 Tf 6.59 0 Td[(1on2pc)]TJ /F4 7.97 Tf 6.59 0 Td[(1scalesandlargerlocalgradients(1.52.5kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1pc)]TJ /F4 7.97 Tf 6.59 0 Td[(1)onsub-parsecscalesinIRDCG035.3900.33,basedoncentroidvelocitiesofthedensegastracerN2H+(1-0).?derivedameanvelocitygradientof0.24kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1pc)]TJ /F4 7.97 Tf 6.58 0 Td[(1of10IRDCclumps,basedon13CO(1-0)emission.ThegradientsseeninoursimulatedclumparesomewhatlargerthanthoseobservedtowardsIRDCsby?,whichmayindicatetheseIRDCsarenotbeingdisturbedkinematicallybythekindofcollisionmodeledinourducialsimulation.However,theresultsofarangeof3Dsimulationsandawidervarietyofviewinganglesareneededbeforemoredenitiveconclusionscanbedrawnfromsuchcomparisons. 2.6DiscussionandConclusionsWehaveexploredawiderangeofparameterspaceofmagnetizedGMC-GMCcollisions.Weperformedidealized2DsimulationsfromtheGMC-scaledownto0.1parsecscales,allowingustostudyindetailthestructureofGMCsundergoingcollisions.Inparticular,wefocusedonaclumpembeddedinaGMC,aimingtoisolatetheeectsofvariousparametersontheevolutionofclumpmaterial.Webeganbydevelopingnewheatingandcoolingfunctionsthatdependondensity,temperatureandextinction,basedonthemethodofVLBT2013.Wecombinedtheresults 75

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Figure2-23. Meanvelocitiesofan8pcby5pcrectangularregionaroundtheclumpatt=4.99Myr,alongthe(top)x-directionand(bottom)y-direction.Blacklinesrepresentlineofsightvelocitiesweightedbythemassdistributionoftheregion.Bluecrossesareintensity-weightedmeanvelocitiesderivedfrom13CO(J=2-1)spectraof1pcwidestripsthatevenlydividetheregionalongthelineofsight.Greenandredcrossesdenotesimilarlycalculatedmeanvelocitiesfrom13CO(J=3-2)and12CO(J=8-7),respectively.Thecoloreddottedlinesshowthebestlinearttoeachcorrespondingsetofpoints,withthevalueofthisgradientdisplayedinparenthesisinthelegend. 76

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fromthePDRcodesPyPDRandCloudytocreatearraysofheatingandcoolingratesthatspantheatomictomoleculartransition,allowingtreatmentofamulti-phaseISMandincludingthethermalinstabilityofwarmandcoldatomicmedia.Ourheatingandcoolingfunctionsreturnself-consistentratesfromdensitiesrangingfromnH=10)]TJ /F4 7.97 Tf 6.58 0 Td[(3)]TJ /F5 11.955 Tf 12.75 0 Td[(106cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3andtemperaturesrangingfromT=2.7)]TJ /F5 11.955 Tf 12.38 0 Td[(105K.Thisenabledustostudynon-equilibriumtemperatureconditionsthatarepresentintheshockedmaterialofcollidingclouds.Further,wesimilarlyderivedemissivityarraysforvariouscommonobservationalbandsofCO,allowingustosimulatesyntheticobservationsviapost-processing.IntermsofMHDsimulations,ourmodelstrackedaninitiallymagneticallysubcriticalclumpembeddedwithinaGMC.Weinvestigateddierentcollisionvelocities,impactparameters,magneticeldstrengthsandorientationsandtheireectsoncollidingversusisolatedGMCs.Forthemaximallysupportiveout-of-planeB-eldcases,wereportedGMCcollisionsattypicalvelocitiescausingdensityincreasesofafactorof2)]TJ /F5 11.955 Tf 12.23 0 Td[(3,withareboundresultinginrelativelyloweraveragedensistiespost-collision.Duringthecollision,averageclumptemperatureswereincreasedbyafactorofupto10)]TJ /F5 11.955 Tf 12.59 0 Td[(20duetoshocksdominatingtheclumpmaterialbeforesettlingbackto15)]TJ /F5 11.955 Tf 12.05 0 Td[(30K.CollisionswithimpactparameterbetweentheGMCsproducedsimilarlevelsofcontractionwithlessexaggeratedeectsforhigherimpactparameters.However,thesetypesofcollisionsinvolvestronglyshearingvelocityeldsthatproducedasymmetriesandmorelamentarystructure,aswellasimpartingangularmomentumtotheresultingcloud.Mixed-eldgeometriesresultedinrelativeincreasesofdensityandtemperatureatlevelssimilartotheout-of-planecase.However,late-timebehaviorofthecloudsshowedeventualcontraction,asmaterialisabletoowalongtheeldlinesandslowlyaccumulateontotheclump.AnalysisofCOlineemissivitiesprovidedawaytotrackshocksofvariousstrengths.Inparticular,theaveragevalueofthe12CO(J=8-7)/13CO(J=2-1)ratiowithinaclumpthatwasundergoingacollisionversusoneinanisolatedcloudresultedindierencesofafactorofupto 77

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104fortypicalcollisionvelocities.Evenslowcollisionsofvrel=5kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1showedexcessesofafactorof10inthisparameter.Thismaybeausefuldiagnosticsignatureofcloudcollisions.Spectraandvelocitygradientsofmolecularlineemissionarounddensegasclumpsmayalsoprovidetestsofcloudcollisionsasatriggeringmechanismfortheirformation.OnecaveatofthepresentedmodelsisthatalltheshocksareinthecontextofidealMHD.Also,theeectsofinitialGMCturbulence,ambipolardiusion,starformation,andstellarfeedbackhavenotbeenaddressedinthisstudy,butareplannedinfuture3Dmodels.However,starformationandstellarfeedbackarenotlikelytobetooimportantincomparingsimulationoutputswithsomeISMclouds,suchasInfraredDarkClouds.AmorecompletestudyofobservationaldiagnosticswithcomparisontocasesintheGalaxyisplannedinasubsequentpaperthatwillanalyze3DsimulationsandincludeinitialGMCturbulence. 78

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CHAPTER33DTURBULENT,MAGNETIZEDSIMULATIONSWeinvestigategiantmolecularcloud(GMCs)collisionsandtheirabilitytoinducegravitationalinstabilityandthusstarformation.Thismechanismmaybeamajordriverofstarformationactivityingalacticdisks.Wecarryoutaseriesofthreedimensional,magnetohydrodynamics(MHD),adaptivemeshrenement(AMR)simulationstostudyhowcloudcollisionstriggerformationofdenselamentsandclumps.Heatingandcoolingfunctionsareimplementedbasedonphoto-dissociationregion(PDR)modelsthatspantheatomictomoleculartransitionandcanreturndetaileddiagnosticinformation.Thecloudsareinitializedwithsupersonicturbulenceandarangeofmagneticeldstrengthsandorientations.Collisionsatvariousvelocitiesandimpactparametersareinvestigated.Comparingandcontrastingcollidingandnon-collidingcases,wecharacterizemorphologiesofdensegas,magneticeldstructure,cloudkinematicsignatures,andclouddynamics.Wepresentkeyobservationaldiagnosticsofcloudcollisions,especially:relativeorientationsbetweenmagneticeldsanddensitystructures,likelaments;13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)integratedintensitymapsandspectra;andcloudvirialparameters.WecomparetheseresultstoobservedGalacticclouds. 3.1IntroductionCollisionsbetweengiantmolecularclouds(GMCs)withintheinterstellarmediumhavebeenproposedasamechansimfortriggeringstarformation( Loren , 1976 ; Scovilleetal. , 1986 ; Tan , 2000 ),potentiallyevensettingglobalstarformationrates(SFRs)ofdiskgalaxies.Itisanattractivemechanismbecauseitisaprocessthatisexpectedtocreateparsec-scaledensegasclumpsthatarepronetogravitationalinstabilityandaretheprecursorstostarclusters, ReprintedwithpermissionfromWu,B.,Tan,J.C.,Nakamura,F.,etal.2016,ArXive-prints,arXiv:1606.01320 79

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whileatthesametimebeingsensitivetoglobalgalacticdynamics,suchastheshearrate( Tan , 2000 ; Tasker&Tan , 2009 ; Tan , 2010 ; Suwannajaketal. , 2014 )andthepresenceofspiralarms( Dobbs , 2008 ).SuchaconnectiontoorbitalshearnaturallyexplainsthedynamicalKennicutt-Schmidtrelation( Kennicutt , 1998 ; Leroyetal. , 2008 ),SFR/gaswhereSFRandgasaresurfacedensitiesofstarformationrateandtotalgasandistheorbitalangularfrequency.Globalgalacticsimulationshaveshownthatinaatrotationcurvedisk,GMCcollisiontimescalesarerelativelyfrequent,attcoll'0.2torbit( Tasker&Tan , 2009 ; Dobbsetal. , 2015 ).MoststarformationisobservedtooccurwithinGMCs,whicharegenerallydenedtohavemasses104M,withmeanmasssurfacedensities100Mpc)]TJ /F4 7.97 Tf 6.59 0 Td[(2,andmeanvolumedensitiesnH'100cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3,butwithlargevariationandsubstructureintheformoflaments/clumps/cores(e.g., McKee&Ostriker , 2007 ; Tanetal. , 2013 ).AverageradiiofGMCsrangefrom6)]TJ /F5 11.955 Tf 12.53 0 Td[(100pc,althoughtheyaretypicallynotwelldescribedbyasimplesphericalgeometry.Rather,lamentaryand/orcomplexirregularmorphologiesareoftenobserved(e.g., Jacksonetal. , 2010 ; Roman-Duvaletal. , 2010 ; Raganetal. , 2014 ; Hernandez&Tan , 2015 ).Attypicalmolecularcloudtemperaturesof10)]TJ /F5 11.955 Tf 12.7 0 Td[(20K,thermalpressuresupportisinsucientforpreventinggravitationalcollapseofGMCsandtheirprotoclustergasclumps.Magneticelds(e.g., Mouschovias , 2001 ; Crutcher , 2012 ; Lietal. , 2014 )andturbulence(e.g., Krumholz&McKee , 2005 ; Padoan&Nordlund , 2011 ; Federrath&Klessen , 2012 ; Padoanetal. , 2014 )arebothlikelytobemoreimportantininuencingthegravitationalstabilityofmoleculargasandthustheregulationofstarformation.MagneticeldstrengthshavebeenmeasuredintheISMviatheZeemaneect,revealingamagnitudethatisdensity-dependent.InthediuseISM,themagneticeldhasbeenmeasuredtobe62Glocallyand103Gat3kpcGalactocentricdistance( Beck , 2001 ).Withinmolecularclouds,clumpsandcoreswithnH>300cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3thedistributionofmagneticeldstrengthshasbeeninferredtobeboundedbyarelationthatscalesas 80

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Bmax=B0(nH=300cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)2=3,whereB0=10G( Crutcheretal. , 2010 ),whileatlowerdensities,Bmax=B0=10G.Werefertothisasthe\Crutcherrelation."Kinematically,GMCshaveinternalvelocitydispersionssimilartothevirialvelocity,whichisatleastanorderofmagnitudelargerthanthesoundspeed(cs0.2km/sfor10Kgas)(e.g., Solomonetal. , 1987 ; Roman-Duvaletal. , 2010 ; Hernandez&Tan , 2015 ).ThusGMCsareexpectedtobepermeatedbysupersonicturbulence.RandombulkvelocitiesofGMCshavebeenobservedintheGalaxytobe5)]TJ /F5 11.955 Tf 12.12 0 Td[(7kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1(e.g., Lisztetal. , 1984 ; Stark , 1984 ).However,actualinteractionvelocitiesareexpectedtobesetbytheshearvelocityat1-2cloudtidalradii,whichmaybeseveraltimesfaster( Gammieetal. , 1991 ; Tan , 2000 ).OnscalesofGMCsandclumpsconversionofgasintostarshasbeenproposedtobeaslowandinecientprocessrelativetolocaldynamicaltimescales( Zuckerman&Evans , 1974 ; Krumholz&Tan , 2007 ; DaRioetal. , 2014 ).Fasterconversionrateshavebeenproposedforsomeofthemostactivestar-formingregionsintheGalaxy( Murrayetal. , 2010 ; Leeetal. , 2015 ).Starformationisseentobehighlylocalizedinspaceandtime,withrelativelyhigheroveralleciencieseventuallyachievedwithintheseclusters(e.g., Lada&Lada , 2003 ; Gutermuthetal. , 2009 ).Thereareanumberofobservationalcandidatesfortriggeringofstarformationbycloudcollisions.Themostcommoncriteriaforidentifyingcandidatesisthepresenceoftwodistinctvelocitycomponentsofmoleculargas(tracedbyCOrotationallinespectra),surroundingpopulationsofdensecoresoryoungstars.PotentialexamplesincludeNGC133( Loren , 1976 ),LkH198( Loren , 1977 ),W75-DR21( Dickeletal. , 1978 ),GR110-13( Odenwaldetal. , 1992 ),Westerlund2( Furukawaetal. , 2009 ; Ohamaetal. , 2010 ),M20( Toriietal. , 2011 ),CygnusOB7( Dobashietal. , 2014 ),andN159West( Fukuietal. , 2015 ).However,problemsremaininvericationofcollisions.Itcanbediculttoruleoutchancealignmentsofmultiple,independentvelocitycomponentsthatareseeninprojection.Itisalsoverychallengingtodiscerntheoverall3Ddistributionofcloudstructuresfromposition-position-velocitydata. 81

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ThebasicquestionweseektoansweriswhetherrealisticmodelsforGMC-GMCcollisions,i.e.,convergingowsofmoleculargasthatarealreadypronetogravitationalinstability,resultindensegasstructuresandstarformationactivitythatcanexplaintypicalobservedstar-formingregions.Inourrstpaperinthisseries, Wuetal. ( 2015 ,hereafterPaperI),wepresentedidealized2DsimulationsofGMCcollisionsandtheireectonapre-existingdense,magnetizedclump.PaperIintroducedmanyofthemethodsthatwillbeadoptedhere,includingphoto-dissociationregion(PDR)-basedheatingandcoolingfunctions.Theseallowpredictionofmolecularlinediagnosticsofcloudcollisions:e.g.,collisionsleadtohighratiosof12CO(J=8-7)tolowerJlineintensities.HereinPaperII,wewillextendthesemodelsto3D,turbulentGMCsandfocusonthepropertiesofdensegascreatedinGMC-GMCcollisions.PaperIIIwillexplicitlymodelthestarformationthatmayresultfromsuchcollisions.Ourworkispartofagrowingbodyofnumericalstudiesthathaveinvestigatedcloud-cloudcollisions.Earlysimulationstypicallyinitializedtwosphericalcloudsandstudiedthephysicaleectsofcollisions.Itwasshownthatcollisionsproducebowshockswhichleadtocompressionofgasandgravitationalinstability( Habe&Ohta , 1992 ),bendingmodeinstabilitiesandhighlyinhomogeneoushigh-densityregions( Klein&Woods , 1998 ),thin-shellandKelvin-Helmholtzinstabilitiesduetoshear( Anathpindika , 2009 ),andlamentformationfromashock-compressedlayer( Balfouretal. , 2015 ).Recentsimulationsofturbulent,unmagnetizedcloudsshowedcoreformationatthecollisioninterfacewithpropertiesfavorabletomassivestarcreation( Takahiraetal. , 2014 ),andwithobservationalsignaturespotentiallyfoundinposition-velocitydiagrams( Haworthetal. , 2015a , b ).Ourworkisdistinguishedfromtheabovestudiesbymodelingmagnetized,turbulentclouds,withrealisticheatingandcoolingfunctions.Theseenableustofocusonanumberofdiagnosticsignaturesofcloudcollisionsthatcanbecomparedagainstobservedclouds.Section 4.2 describesournumericalmethodsandinitialsetup.Section 4.3 discussesourresults,whichincludemorphologies(x 3.3.1 ),magneticelds,(x 3.3.2 ),probabilitydistribution 82

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functions(x 3.3.3 ),integratedintensitymaps(x 3.3.4 ),kinematics(x 3.3.5 ),anddynamics(x 3.3.6 ).WepresentourconclusionsinSection 4.4 . 3.2NumericalModel 3.2.1InitialConditionsWechooseinitialconditionstomatchpropertiesofobservedGMCs.WeincludephysicalprocesseslikelytobedominantintheformationandevolutionofstructurewithinGMCs:self-gravity,supersonicturbulence,andmagneticelds.Wethenfocusontheeectsofcollidingtwocloudsthatareconvergingatagivenvelocityandwithagiveninitialimpactparameter.Oursimulationvolumeisa128pc-sidedcubecontainingtwoidentical,initiallysphericalGMCswithuniformdensitiesofHnucleiofnH,GMC=100cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3andradiiRGMC=20.0pc,givingeachGMCamassMGMC=9.3104M.Thecloudsareembeddedinambientgas,representingtheatomiccoldneutralmedium(CNM).ThismaterialissettohavenH,0=10cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.WeintroducesupersonicturbulenceintheGMCs,creatingthevelocityeldviaa3Dpowerspectrumfollowingtherelationv2k/k)]TJ /F4 7.97 Tf 6.58 0 Td[(4,wherek==disthewavenumberforaneddydiameterd.TheGMCgasisinitializedwithvirialscaleMachnumberMs=cs=23(forT=15Kconditions).Wechosetheminimumk-modetobethatspanningourclouddiameters,i.e.,settingthelargest-scaleturbulentvelocities,andthemaximumk-modetobetentimesgreatersothatourducialrangeforbothcloudsis2
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virialparameters,1(e.g., Roman-Duvaletal. , 2010 ),especiallywhenconsideringtheirposition-velocityconnected,13CO-emittingstructures(Hernandez&Tan2015).OurchoiceofinitializingwithalargerkineticenergycontentismotivatedbythedesiretonothaverapidglobalcollapseofthecloudswithintherstfewMyr,i.e.,thetimescaleofthecollision.Thesimulationboxisinitializedwithalarge-scaleuniformmagneticelddirectedatanangle()relativetothecollisionaxisoftheclouds.Theducialdirectionis=60,thoughvariousorientationsareexplored.Theducialmagneticeldstrengthissettobe10G,followingZeemanmeasurementsofGMCeldstrengths( Crutcher , 2012 ).Additionally,wetestnon-magnetizedaswellasmorestronglymagnetized(30G)casestoexploretheeectsofmagneticeldstrength.Wedenemagneticcriticalityviathedimensionlessmass-to-uxratio GMC=M= 1=(2G1=2)(3{1)Inthiscase,wecalculatethemass-to-uxratiobyaveragingoverthecrosssectionofoneGMCthroughthevolumeofthebox,includingambientgas.ThisyieldsBcrit=43G.ThusourGMCsaremagneticallysupercriticalandsoshouldbeabletoundergoglobalcollapseiftheirinternalturbulenceisatasmallenoughlevel.Thedefaultrelativecollisionvelocityofthecloudsischosentobevrel=10kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,thoughvaluesof5and20kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1arealsoexplored.TheCNMenvelopeofeachGMCisassumedtobeco-movingwiththecloudandthusisalsocollidingatthesamerelativevelocity.Intermsofthesimulationdomain,halfthevolumeisinitializedwithavelocity+vrel=2whiletheotherhalfmoveswith)]TJ /F3 11.955 Tf 9.3 0 Td[(vrel=2.Generally,thesimulationsarerunfor5Myr.Thefreefalltimefortheadoptedinitialdensityofthecloudsist=(3=[32G])1=2'4.35Myr,buttforthedensersubstructurescreatedbyturbulenceismuchless.Mostoftheanalysisisperformedatatime4Myrafterthebeginningofthesimulations,thoughthetime-evolutionofvariouscloudpropertiesisalsoexplored. 84

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Table3-1. Initialsimulationproperties GMCambient nH(cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3)10010R(pc)20-M(M)9.3104-T(K)15150t(Myr)4.35-cs(km/s)0.230.72vA(km/s)1.845.83vvir(km/s)4.9-(km/s)5.2-Ms23-MA2.82-k-mode(k1,k2)(2,20)-vbulk(km/s)55B(G)10104.31.50.0150.015 Table3-2. Summaryofsimulationsandexploredparameterspace modelnamevrelBbkms)]TJ /F4 7.97 Tf 6.59 0 Td[(1(G)()(RGMC) 1aColliding1010600.52Non-Colliding010600.53vrel=5km=s510600.54vrel=20km=s2010600.55=0101000.56=301010300.57=901010900.58b=0RGMC10106009B=30G1030600.510B=0G,Col.100-0.511B=0G,Non-Col.00-0.5 aIncludesadditionalrunsexploringlowerresolutionsusing1and2levelsofAMR. Theinitialconditionsoftheset-upareshowninFigure 3-1 andtheirpropertiesaresummarizedinTable 4-1 .Acompletelistofmodels,illustratingtherangeofparameterspaceexplored,isshowninTable 3-2 .Inoursubsequentdiscussion,weshallrefertoModels1and2asthe\ducialcolliding"and\ducialnon-colliding"models,respectively,whiletheremainingmodels(3-11)willbecollectivelyreferredtoasthe\parametermodels." 85

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Figure3-1. Fiducialinitialconditions.Toppanel:Masssurfacedensity,showntogetherwithmagneticeldstructure(graylines).Bottompanel:Mass-weightedtemperature,showntogetherwiththevelocityeld(blackvectors;velocityscaleinthetopright).GMCs1(left)and2(right)haveidenticaldimensionswithaninitialseparationoftheircentersof2RGMCinthex-directionand0inthez-direction.Inthey-direction,theyareosetbyanimpactparameterb=0.5RGMC. 86

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3.2.2NumericalCodeWeusethenumericalcodeEnzo1,amagnetohydrodynamics(MHD)adaptivemeshrenement(AMR)code( Bryanetal. , 2014 ).ThiscodesolvestheMHDequationsusingtheMUSCL2nd-orderRunge-KuttatemporalupdateoftheconservedvariableswiththeHarten-Lax-vanLeerwithDiscontinuities(HLLD)methodandapiecewiselinearreconstructionmethod(PLM).Thehyperbolicdivergencecleaningmethodof Dedneretal. ( 2002 )isadoptedtoensurethesolenoidalconstraintonthemagneticeld( Wang&Abel , 2008 ).Forourmainresults,weuseatoplevelrootgridof1283and3additionallevelsofrenement,givingaminimumgridcellsizeof0.125pcandeectiveresolutionof10243.Twoadditionalmodelsoftheducialcollidingcasewith2and1levelofAMR,respectively,areruntoinvestigatetheeectsofresolutiononourresults.Weperformtheequivalentanalysisforeachresolutioncaseandcompareanynoteworthydierencesintherespectivesections.Forallcases,acellisrenedwhenthelocalJeanslengthbecomessmallerthan8cells.ThisresultsinlargervolumesofhighlyrenedregionswithintheGMCswhencomparedtothe4cellstypicallyusedtoavoidarticialfragmentation(i.e.,theTruelovecriterion; Trueloveetal. 1997 ).However,wenotethatforourmagneticallysupportedgastheeective\magneto-Jeansmass"willbesignicantlylargerthanthethermalJeansmass.Wemakeuseofthe\dualenergyformalism"thatsolvestheinternalenergyequationinadditiontothetotalenergyequation.Thisisnecessaryforwhenthermalenergyisdominatedbymagneticandkineticenergy,asitisinourcase.Thismethodcalculatesthetemperaturefromtheinternalpressurewhentheratioofthermaltototalenergyislessthan0.001,andfromthetotalenergyotherwise.WealsouseamethodoflimitingtheAlfvenspeedinordertoavoidextremelysmalltimestepssetbyAlfvenwaves.Thiswasdonebysettingamagneticelddependentdensityoor,determinedbyachosenmaximumAlfvenvelocity,vA=B=p 0=1107cms)]TJ /F4 7.97 Tf 6.58 0 Td[(1. 1 http://enzo-project.org (v2.4-dev,changeset845edacb82b1+) 87

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Thus,forB10G,onlygasatdensitiesbelownH0.1cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3isaectedbythislimit.Inoursimulations,asmallfractionofgasventuresintothisregime,thuswedeterminetheoverallresultstobeessentiallyunaected. 3.2.3ThermalProcessesWeareprimarilyinterestedinthedenseinternalstructuresofGMCs.ThisgasisalmostentirelymolecularwithdensitiesnH&102cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3andequilibriumtemperaturesof15K.Forsimplicity,weuseaconstantvalueofmeanparticlemass=2.33mH.Wealsochooseaconstantadiabaticindex=5=3throughouttheentiresimulationdomain,followingmethodsadoptedinPaperI.WhilethisdoesnotaccountfortheexcitationofrotationalandvibrationalmodesofH2thatwouldoccurinsomeshocks,weconsiderthatthisisthemostappropriatesingle-valuedchoiceofforoursimulationsetup,givenourfocusonthedynamicsofthedensemoleculargas.WeimplementPDR-basedheatingandcoolingfunctionsthatwerecreatedanddescribedindetailinPaperI.Thesefunctionsincludeatomicandmolecularheatingandcoolingprocessesinnonequilibriumconditions,takingintoaccountextinction,density,andtemperature.AgainfollowingPaperI,weassumeaFUVradiationeldofG0=4(i.e.,appropriateforinnerGalaxyconditions,e.g.,atGalactocentricdistancesof4kpc)andbackgroundcosmicrayionizationrateof=1.010)]TJ /F4 7.97 Tf 6.59 0 Td[(16s)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Theheating/coolingfunctionsspanthedensityandtemperaturespaceof10)]TJ /F4 7.97 Tf 6.59 0 Td[(3nH=cm)]TJ /F4 7.97 Tf 6.58 0 Td[(31010and2.7T=K107(increasingtheupperlimitsfrom106cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3and105K,respectively,fromPaperI),encompassingourdesiredregimeofinterestandapproximatingamulti-phaseuid.TheresultingheatingandcoolingratesareincorporatedintoEnzoviatheGrackleexternalchemistryandcoolinglibrary2( Bryanetal. , 2014 ; Kimetal. , 2014 ).Theinformationisreadinviathepurelytabulatedmethodandmodiesthegasinternalenergy,Eint= 2 https://grackle.readthedocs.org/ 88

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Figure3-2. Top:Timeevolutionofmasssurfacedensityforthetheducialcolliding(model1,1strow)andnon-colliding(model2,2ndrow)cases.Bottom:Timeevolutionofmass-weightedtemperatureforthesamemodels(model1,3rdrow;model24throw).Snapshotsat1.0,2.0,3.0,and4.0Myrareshown.Mass-weightedmagneticeldsareshownasgraystreamlineswhilevelocitiesareshownasblackvectorswiththevelocityscaleshowninthetopright. p=()]TJ /F5 11.955 Tf 11.96 0 Td[(1),ofagivencellwithanetheating/coolingratecalculatedby H=nH[)]TJ /F2 11.955 Tf 12.95 0 Td[()]TJ /F3 11.955 Tf 11.95 0 Td[(nH]ergcm)]TJ /F4 7.97 Tf 6.59 0 Td[(3s)]TJ /F4 7.97 Tf 6.59 0 Td[(1,(3{2)where)]TJ /F1 11.955 Tf 10.67 0 Td[(istheheatingrateandisthecoolingrate. 89

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3.2.4ObservationalDiagnosticsAkeyoutputoftheaforementionedheating/coolingfunctionsisthedetailedinformationofspeciccomponentsthatcontributetothetotalheatingandcoolingrates(seePaperIforthefullmethod).Specically,byextractingrotationallinecoolingratesof12COand13CO,weareabletocreatesyntheticobservationsofself-consistentCOemissivitiesviapost-processing.PaperIintroducedanumberofobservationaldiagnostics,namelyhigh-Jtolow-JCOlineintensityratiosandvelocityspectra.Theanalysisinthispaperrevisitsthesemetrics,butnowfor3Dgeometriesandinitiallyturbulentclouds.Wenotethatwhileradiativetransferofemissivitiesisnotcalculatedduringpost-processing(i.e.,wesumcontributionsalongsightlinesthatisvalidintheopticallythinlimit),itisindirectlyincorporatedineachcellviatheheating/coolingfunctions.Self-shieldingandlineopticaldepthsareaccountedforinthePDRmodels,whichassumeaone-to-onedensity-extinctionrelation(seePaperI).Nevertheless,wechooselinesinwhichopticaldepthsshouldberelativelysmall.Theresultingintensitiesaresimplyintegrateddirectlythroughthesimulationdomain.WealsonotethatCOfreeze-outontodustgrainsisnottreatedinourPDRmodels.Amoredetailedstudywithcomparisonofourapproximatefunctionsto3DPDRmodelsandradiativetransfercalculationsiscurrentlyinpreparation(Bisbasetal.,inprep.).WewillpresentintegratedintensitymapsandspectraofCOlinesandlineratioswithrotationalexcitationsJ=2-1,3-2,and8-7inx 3.3.4 andx 3.3.5 ,respectively.Thedynamicalanalysisofx 3.3.6 isperformedonsynthetic13CO(J=1-0)maps. 3.3ResultsWeperformanalysisofthesimulations,focusingonthefollowingcategoriesofinterest:densityandtemperaturemorphologies(x 3.3.1 );magneticeldmorphologiesandstrengths(x 3.3.2 );masssurfacedensitydistributions(x 3.3.3 );COlinediagnostics(x 3.3.4 );kinematics(i.e.,spectraandvelocitygradients)(x 3.3.5 );anddynamics(i.e.,virialanalysis)(x 3.3.6 ).Primarily,weinvestigaterelativedierencesbetweentheducialcollidingandnon-collidingcases,withthegoalofunderstandingthephysicaleectsofGMC-GMCcollisionsand 90

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determiningpotentialdierentiatingobservationaldiagnosistechniques.Additionally,theremainingparametermodelsareanalyzedtosupplementthemainresultsbyunderstandingtheeectsofvariationsinthecollisionalparameters.Forvisualizationandanalysis,weoftenusearotatedcoordinatesystem(x0,y0,z0)relativetothesimulationaxes(x,y,z)suchthatx0,y0,andz0arerotatedbythepolarandazimuthalangles,respectively,(,)=(15,15)abouteachaxis.ThepurposeofthisistoremovebiasesfromanarticialcollisionalplanethatdevelopsasaresultofourinitialconditionsofcollidingowsofuniformCNM.ThisplanehasnegligibledynamicaleectsontheGMCs,butamagniedobservationalsignaturewhentheline-of-sightisdirectlyalignedalongthisplane.Insomecases,anon-rotatedcoordinatesystemdenotedby(x,y,z)issucientlyunaectedbytheinitialconditionsandisthususedforsimplicity. 3.3.1MassSurfaceDensityandTemperatureMorphologyThetimeevolutionofmasssurfacedensity(superposedwithmagneticeldlines)andtemperature(superposedwithgasvelocityvectors)structuresintheducialcollidingandnon-collidingcasesareshowninFig. 3-2 .SimilarplotsfortheremainingnineparametermodelsareshowninFigs. 3-3 and 3-4 fordensityandtemperature,respectively. 3.3.1.1FiducialmodelsBoththeducialcollidingandnon-collidingcasesdeveloplamentarydensitystructureswithintheGMCsasaresultoftheturbulentvelocityelds.Thespatialextentofthenon-collidingGMCsisgenerallyretainedoverthecourseof&1free-falltime,thoughthedensitydistributionevolvesfromaninitiallyuniformdensitytoanetworkofrelativelyslowlygrowinglamentsandwithincreasingdierentiationindensities.Forthecollidingcase,anelongatedlamentarysheet-likestructureofmuchhigherdensityquicklydevelopsnearthecollidingregion,withbothGMCmaterialandCNMgasbeingsweptupinthelargeshockscreatedbythecollidingows.Aprimarylamentaryregionresults,generallylyingintheplaneorientedperpendiculartothecollisionaxis,withsmallerlamentsextendingoutward.Structureswithmasssurfacedensitiesexceeding1gcm)]TJ /F4 7.97 Tf 6.58 0 Td[(2are 91

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Figure3-3. Timeevolutionofmasssurfacedensityfortheremainingsimulations(models3through11).Eachrowrepresentsaspecicmodelaslabeled,whilecolumnsaresnapshotsatt=1.0,2.0,3.0,and4.0Myrareshown.Mass-weightedmagneticeldsarerepresentedbygraystreamlines. 92

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Figure3-4. Timeevolutionofmass-weightedtemperaturefortheremainingsimulations(models3through11).Eachrowrepresentsaspecicmodelaslabeled,whilecolumnsaresnapshotsatt=1.0,2.0,3.0,and4.0Myr.Mass-weightedvelocitiesarerepresentedbyblackvectors,withthevelocityscaleshowninthetopright. 93

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morelocalizedandformatfractionsoftheoriginalt,muchmorequicklyrelativetothenon-collidingcase.Themasssurfacedensitystructureandmagneticeldsmutuallyaectoneanother.Inthenon-collidingcase,thedensestlamentsarequalitativelypreferentiallyalignedperpendiculartomagneticeldlines.Additionally,theturbulentmaterialdragsthemagneticeldswithit,creatingtwistedandmorecomplexmagneticstructuresfromaninitiallyuniformgeometry.Inthecollidingcase,thelarge-scaleowscompressthemagneticeldsintotheplaneperpendiculartothecollisionaxis,eectivelyre-orientingthemagneticeldsinanewlocallydominantdirection.RelativeorientationsbetweenmasssurfacedensitystructureandmagneticeldsmaybeanobservabledierentiatingfactorbetweenrelativelyisolatedturbulentGMCsandthosewhichhaveundergoneamajorbinarycollision.Amoredetailedanalysisquantifyingtheserelativeorientationsisdiscussedinx 3.3.2 .Thestrongcouplingbetweenmagneticeldanddensityinthesimulationsisexpectedfromux-freezinginidealMHD.Non-idealMHDeectssuchasambipolardiusionmaybecomedominantincertainregimeswithintheGMCsandwillbeexploredinasubsequentpaper.ThePDR-basedheating/coolingfunctions(describedinx 4.2.3 andPaperI)enableustoapproximatethethermalbehaviorofgasintheatomic-to-molecularregimeandmodelnon-equilibriumeects,specicallyshocks.Forbothmodels,thetemperatureisgenerallyneartheequilibriumtemperaturefortheparticulardensity:tensofKelvinatnH>100cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3and102Kto103KfornH.10cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3.Inthenon-collidingcase,thedeviationofactualgastemperaturefromtheequilibriumtemperaturecurveisgenerallysmall.Inthecollidingcase,largeshockwavesarecreated,resultinginahigh-temperatureshockfrontthatsweepsthroughGMCmaterialasitentersthepost-shockregion.Upondoingso,acentralregionoflowtemperaturelamentarygasdevelops,againstronglycorrelatingwithdensitystructures.ThisregionofT15Kgasgrowsinsizeasmoredensematerialaccumulates. 94

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3.3.1.2ParametermodelsNext,wediscusshowvariationsinthecollisionparametersaectthemorphologiesofmasssurfacedensityandtemperaturethroughtheirsubsequentevolution.Figs 3-3 and 3-4 provideadirectcomparisonbetweenthesemodels.Collisionvelocitiesofvrel=5and20km/sareexploredinmodels3and4,respectively.Byt=4Myr,Model3hasnotyetproducedgasof>1gcm)]TJ /F4 7.97 Tf 6.59 0 Td[(2butcontainsmorphologicalfeaturessomewhatinbetweenthenon-collidingandcollidingducialmodels.Arelativelydenselamentcanbeseenforminginthecentralcollisionregion,whileaseparateregionwithinGMC2hasbeguntoformaseconddenselament.Bothregionscorrespondspatiallywithdensestructuresthatforminthenon-collidingcase,whichpointstoturbulenceasthedominantformationmechanism,buttheirdensitiesarefurtherenhancedatearliertimesduetothecollision.Theseregionsarealsositesofthelowesttemperatures,coolingto15K.Model4createsastrongershock,higher-densitycollisionregion,andhigher-densityclumpsatearliertimes.Themainlamentarysheetappearsmorelocalizedtothecentralcollisionregion,andmanydensecore-likestructuresarecreatedalongthelengthofthisgenerallamentrelativetothefewer,moreelongatedstructurescreatedinmoreslowlycollidingcases.Thehighercollisionvelocityalsocreatedhigh-temperature(T>1000K)shockfrontspropagatinganti-paralleltotheincomingowaswellasobliqueshockscreatedattheGMCboundariescorrespondingtotheimpactparameter.Initialmagneticeldorientationsof=0,30,and90areexploredinmodels5,6,and7,respectively.Asmagneticpressureactsindirectionsperpendiculartotheeldlines,itisexpectedthatsmallervaluesofshouldresultinlessinhibitedowandyieldhigherdensitygas.Whileturbulencedoesstirupthemagneticeldlines,thelarger-scaleuniformdirectionandbulkowdominatetheresultingmorphology.Thus,higherdensitygasisformedatearliertimesforsmaller,withtheextentofgeneralGMCsubstructuresgreatestalongthedirectionofthelarge-scalemagneticelds.Thetemperatureswithinthedenseregionsarenearequilibrium,asidefromregionsthroughwhichshocksareactivelycrossing.Among 95

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thesemodels,ambientgasnearthecollisionalregionexhibitdierencesinthetemperaturemorphologyduetothedensityofpost-shockmaterial.Moreperpendicularvaluesofresultinpost-shockregionswithdensitiesspreadoverlargerextentscreatedbybuilt-upmagneticpressurefromtheows;thisproducesgrowingregionsofT100KgassurroundingtheGMCmaterial.Model8explorestheeectsofahead-oncollision(b=0).Comparedtotheducialcollidingcase,thehead-oncollisionproducesfairlysimilarstructuresindensityandtemperature,thoughthefeaturesexhibitgreatermorphologicalsymmetry:dense,coldclumpsandlamentsarecreatedatbothpositiveandnegativey-valuesasopposedtopredominantlypositivey-valuesfortheb=0.5RGMCcases.Model9exploresacaseofstrongermagneticeld,withB=30G,resultinginGMCswithamass-to-uxratioGMC=1.43,onlyslightlymagneticallysupercritical,andCNMwith0=0.5,distinctlymagneticallysubcritical.Thisthreefoldincreaseinmagneticeldstrength,however,createsroughlyanorderofmagnitudeincreaseinmagneticpressure(P/B2.)Thenalresultisanevolutioninwhichthecloudsarecompressedbythebulkows,butmergingisinhibited.Theresultinglamentsstillaccumulatetowardsthecentralcollidingregionbutaremoredispersedthanintheducialcase.Unmagnetizedcasesareexploredinmodels10and11,therespectivecollidingandnon-collidingsimulations.Inbothmodels,deviationsindensitystructuresarisequicklyintheevolutionastherearefewerforcesinhibitingcollapse.Denserlamentsformmorequickly,whichinturncollapseintoclump-likestructuresontheorderoft.Thecollisionactstolocalizetheresultingclumpsinthecentralregion,whilethenon-collidingcloudsformclumpsatfairlyevenlyspatiallydistributedregionsthroughouteachparentcloud.Thedensityandtemperaturecontrastsaresharperforthenon-magnetizedclouds,comparedtothesmoother,moreconnectedstructuresofthemagnetizedcases.Amoredetailedquantitativeanalysisinvestigatingmasssurfacedensitydistributionandevolutionusingprobabilitydistributionfunctions(PDFs)isdiscussedinx 3.3.3 . 96

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Figure3-5. Visualizationofmasssurfacedensityandprojectedmagneticeldpolarizationvectorsfor(left)theducialcollidingand(right)non-collidingsimulations.Masssurfacedensityisrepresentedbytheunderlyingcolors,whilethemagneticeldsare"painted"alongtheirpolarizationdirectionusingtheLICmethod.Thedomainshownrepresentsaphysicalprojectedareaof64pc2. 3.3.2MagneticFieldsInterstellarmagneticeldsandtheircomplexinteractionswithbothturbulenceandgravitylikelyplayanimportantroleintheformationandevolutionofGMCs,laments,andeventuallystars.However,theirdynamicalimportanceisnotwell-determined.Twoimportantmagneticeldparametersthatinuencegasdynamicsaremagneticeldorientationandstrength.Observationally,theprojectedmagneticeldorientationaveragedalongtheline-of-sightcanbestudiedviadustpolarizationmaps(assumingaparticulargrainalignmentmodel),whiletheline-of-sightcomponentofthemagneticeldstrengthcanbecalculatedfrommolecularlinesplittingduetotheZeemaneect.Recently,theabilitytounderstandmagneticeldorientationsinGalacticmolecularcloudshasbeengreatlyexpandedbythePlanckspaceobservatory,withitsall-skycapabilityofmeasuringbothdustpolarizationandopticaldepth,andresolutiontoprobetheinteriorsofnearby(d<450pc)clouds(see PlanckCollaborationetal. ( 2016 ,hereafterPlanckXXXV)).FromoursimulationsincorporatingmagnetizedturbulenceontheGMC-scale,wecanperformsimilartypesofanalysisinordertobetterunderstandobservablemagneticeld 97

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Figure3-6. Diagramofangledenitions.ForamagneticeldBandanobserverviewingalongthe-zaxis,istheinclinationanglebetweenBandtheplane-of-sky,while isthepositionanglebetweenB?(theplane-of-skymagneticeldcomponent)andthe\north"direction(inthiscase,y).Theintegratedpolarizationpseudo-vectoryieldsanangle. signaturesandtheirconnectionswithunderlyingphysicalprocesses.Werstanalyzemagneticeldorientationrelativetomasssurfacedensitystructuresandtheninvestigatemagneticeldstrengthrelativetogasvolumedensity.Fig. 3-5 usesthelineintegralconvolution(LIC,rstproposedby?)methodtocombinevisualizationofcolumndensityandprojectedmagneticeldstructurefortheducialcollidingandnon-collidingcases. 3.3.2.1Relativeorientations:Bvs.iso-NHTostudymagneticeldorientations,weutilizetheHistogramofRelativeOrientations(HRO, Soleretal. 2013 ).TheHROisastatisticaltoolthatquantiesthemagneticeldorientationrelativetothegradientofthecolumndensity.Itcanbeperformedonpolarizationobservations(e.g.,PlanckXXXV)aswellasnumericalsimulations(e.g., PlanckCollaborationetal. , 2015 ; Chenetal. , 2016 )tostudythemutualdependenceofmagneticeldsondensitystructures. 98

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Figure3-7. Leftpanels:Columndensitymaps,log10(NH=cm)]TJ /F4 7.97 Tf 6.59 0 Td[(2),withblackvectorsrepresentingthenormalizedplaneofskypolarizationeld.Thecollidingcaseisshowninthetopgure,whilethenon-collidingcaseisinthebottomgure.Rightpanels:HistogramsofRelativeOrientations(HROs)comparingtheanglebetweenthepolarizationpseudo-vectorpvs.iso-NHcontourspixel-by-pixelintheducialcolliding(top)andnon-colliding(bottom)simulations.Theprojectedmapisdividedinto25columndensitybinsofequalpixelcount.HROsforthelowest(1stbin;black),middle(12thbin;blue),andhighest(25thbin;red)NHbinareshown,usinganglebinsof15.Thehistogramcolorcorrespondswiththecoloredcontoursthatboundlow(black),intermediate(blue),andhigh(red)columndensityregionsoftheprojectionmap.Histogramswithpeaksat0correspondtoppredominantlyalignedwithiso-NHcontours(i.e.,B-eldsalignedalonglaments).Histogramswithpeaksat90correspondtoppredominantlyperpendiculartoiso-NHcontours(i.e.,B-eldsalignedperpendiculartolaments). 99

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TheHROinvestigatestheanglebetweenthepolarizedemissionpandNHiso-contours: =arctanrNHp jrNHpj(3{3)pisapseudo-vectordenedby p=(psin)^x+(pcos)^y(3{4)wherepisthepolarizationfractionandisthepolarizationangle.Thus,onecanthinkofalsoasbeingtherelativeanglebetweenthemagneticeldandthelamentaryaxisofstructuresseeninmasssurfacedensitymaps.NotethattheconventionweadoptforfollowsPlanckXXXVbutisdierentfrom Soleretal. ( 2013 )and Chenetal. ( 2016 ).Weassumeaconstantpolarizationfractionp=0.1(though PlanckCollaborationetal. ( 2015 )and Chenetal. ( 2016 )usevariousgrainpolarizationfractionmodelsintheiranalysis)whileisthepolarizationanglederivedfromtheStokesparameters.TherelativeStokesparameterscanbecalculatedfollowingpreviouswork( Lee&Draine , 1985 ; Fiege&Pudritz , 2000 ; Kataokaetal. , 2012 ; Chenetal. , 2016 ): q=Zncos2 cos2ds(3{5) u=Znsin2 cos2ds(3{6)whereistheanglebetweenthelocalmagneticeldrelativetotheplaneofthesky,whileistheangleofthemagneticeldontheplaneoftheskyrelativetothe\north"axis(seeFig. 3-6 ).Foracoordinateorientationwherethey-axiscanbedenedas\north"withthelineofsightdirectedalongthez-axis,therelativeStokesparameterscanbewrittenas(see Chenetal. ( 2016 )): q=ZnB2y)]TJ /F3 11.955 Tf 11.95 0 Td[(B2x B2ds(3{7) u=Zn2BxBy B2ds(3{8) 100

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Finally,wecancalculate,thepolarizationangleontheplaneofthesky: =1 2arctan2(u,q)(3{9)wherearctan2isthearctangentfunctionwithtwoarguments,returningangleswithin[)]TJ /F8 11.955 Tf 9.3 0 Td[(,]basedonthequadrantoftheinputs.Todistinguishcloudstructurefrombackgroundstructure,PlanckXXXVselectedpixelsinregionswherethemagnitudeofthecolumndensitygradientexceededthemeangradientofareferencediusebackgroundeld.Inourcase,thegradientthresholdwaschosentobe0.25theaveragevalueoftheducialcollidingcaseinordertobettercapturetheGMCmaterial.Weapplythisvalueforeachcaseandadditionallyapplyacutofthelowestcolumndensityvalues(NH<21.5cm2).(Note:weassumenHe=0.1nH,givingamassperHof2.3410)]TJ /F4 7.97 Tf 6.59 0 Td[(24g.)isthencalculatedforeachremainingpixelintheprojecteddomain.Thisdomainisdividedinto25binsofNHranges,eachcontaininganequalnumberofpixels.ForagivenNHrange,anHROplotcanbecreated,comparingthedistributionofcellsforeachangle)]TJ /F5 11.955 Tf 9.3 0 Td[(90<<90.WecreateHROsforthelowest,intermediate,andhighestcolumndensitybinstoinvestigatehowthemagneticeldorientationchangesasafunctionofcolumndensity.Thismeanshistogramspeakingat=0correspondtopmostlyalignedparalleltolamentarystructure,whilepeaksat=90correspondtoperpendicularalignmentofmagneticeldswithlaments.Theleft-handcolumnofFig. 3-7 showscolumndensitymapsoftheducialcollidingandnon-collidingcasesover-plottedwithmagneticeldvectorsandcoloredcontoursdeningthethreeaforementionedNHranges.Theright-handcolumnshowstherespectiveHROs,representingmaterialwithinthespeciccolumndensityrange.Intheducialcollidingcase,theHROpeaksnear0especiallyforthelowcolumndensitybins,whiletheintermediateandhighcolumndensitybinsshowslightpreferencetothisvalue.Thissigniesapredominantlyparallelalignmentofpwithiso-NHcontoursforthecollidingcase.Likewise,theducialnon-collidingcaseexhibitsstrongpeaknear0forthelowcolumndensitybin,butisroughly 101

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atformoderatecolumndensitieswhilepeakingat=90forthehighestcolumndensities.Thissigniesashiftfrompredominantlyparallelalignmentofpwithiso-NHcontoursatlowdensitiestoapredominantlyperpendicularalignmentathighdensities.Inordertodistinguishtrendsalongtheentirecolumndensityrangeandcomparemodelswithvariouscollisionalparameters,wefurtherquantifyHROsusingthehistogramshapeparameter,whichisdenedas(see Soleretal. ( 2013 )andPlanckXXXV): =Ac)]TJ /F3 11.955 Tf 11.96 0 Td[(Ae Ac+Ae,(3{10)whereAcistheareawithinthecentralregion()]TJ /F5 11.955 Tf 9.3 0 Td[(22.5<<22.5)undertheHRO,whileAeistheareawithintheextrema()]TJ /F5 11.955 Tf 9.29 0 Td[(90<<)]TJ /F5 11.955 Tf 9.3 0 Td[(67.5and67.5<<90)oftheHRO.Thusisindependentoftotalbinnumberandnormalizesrelativedierenceswithintheindividualhistogram.>0isindicativeofaconcavehistogram(ppreferentiallyparalleltoiso-NHcontours),while<0isindicativeofaconvexhistogram(ppreferentiallyperpendiculartoNH).FromPlanckXXXV,uncertaintiesintheHROswerefoundtobedominatedbyhistogrambinning,whichweincludeinouranalysishere.Thekthbininthehistogramhasvariance 2k=hk1)]TJ /F3 11.955 Tf 16.16 8.09 Td[(hk htot(3{11)withhkandhtotbeingthenumberofsamplesinthekthbinandtotalnumberofsamples,respectively.Thetotaluncertaintyof,givenby,isthencalculatedfrom 2=4(A2e2Ac+A2c2Ae) (Ac+Ae)4.(3{12)AlsofollowingPlanckXXXV,wecanstudytrendsinvslog10(NH=cm2)byttingalinearfunction =CHRO[log10(NH=cm2))]TJ /F3 11.955 Tf 11.96 0 Td[(XHRO].(3{13)CHROandXHROcanbeusedasquantitativeparameterstocomparegeneralrelationshipsbetweenallthesimulationmodels.AnegativeslopeCHROrepresentspbecomingmore 102

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Figure3-8. Comparisonofthehistogramshapeparameter,,vscolumndensity,NH,amongthemagnetizedsimulations.>0representsapreferentiallyparallelorientationbetweenmagneticeldlinesandiso-NHcontours,while<0representsapreferentiallyperpendicularorientation.Theblue,green,andredlinesrepresentlinesofsightfromthex0,y0,andz0axes,respectively.TheparametersCHROandXHROforthebestlineartforeachlineofsightareindicatedintherespectivecolor. parallelwithlamentsasNHincreases,whileapositiveCHROwouldsignifyanincreasinglyperpendicularrelativeorientation.XHROrepresentsthecrossovervalueofNHatwhichpswitchesfromperpendiculartoparalleltoiso-NHcontours.Figure 3-8 showsvs.NHforourmagnetizedruns(models1-9).Thisrelationdoesnotappeartohavestrongdependenceonlineofsight,agreeingfairlywellforeachmodelalongthey0andz0viewingdirections.Viewingfromthex0-directiondoesresultinoccasionaldeviations,butforthemostpartitiswell-correlated.ThesemodelsaregenerallytwithCHRO<0andXHRO22,whichagreewiththeobservationalresultsfrom PlanckCollaborationetal. ( 2016 ).Fromthe10molecularcloudsintheirstudy,meanvaluesofCHRO=)]TJ /F5 11.955 Tf 9.3 0 Td[(0.41andXHRO=22.16werefound,withuncertaintiesingenerallyinthetensofpercentrange. 103

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However,betweenthevariousmodelsthemselves,therearenotabledierences.Theducialnon-collidingcasehasafairlyatslope,withCHRO)]TJ /F5 11.955 Tf 23.14 0 Td[(0.1,resultinginarelativelylargespreadforXHRO.Incomparison,theducialcollidingcasehasasteeperslope,withCHRO)]TJ /F5 11.955 Tf 23.06 0 Td[(0.3,andamoreconsistentXHRO.Thephysicalinterpretationisthatthecollisioninuencestheoverallpreferentialalignmentofmagneticeldsrelativetogaslaments,specicallydrivingthevalueofmorepositiveforlowercolumnstructures(i.e.,moreconcaveHRO;ppreferentiallyparalleltolowNH),andmorenegativeforhighercolumnstructures(i.e.,moreconvexHRO;ppreferentiallyperpendicularhighNH).Thisisemphasizedwhenvaryingcollisionalvelocitiesareexplored(models3and4).Theintermediatecollisionvelocity(vrel=5km=s)resultsinaslightincreaseinCHRO,whilethehighcollisionvelocity(vrel=20km=s)increasestheslopestrongly,withCHROassteepas-0.83.ThevalueofseemsmostaectedatlowNH,whilestayingrelativelysteadyat/0forhighNH.Thex0line-of-sightinthiscasedoesnotcapturemuchoftheeectofthecollisiononthemagneticeldpolarization.Theeectsofinitialmagneticeldorientation(models5,6,and7)arelessdirect,butinitialorientationappearstoprimarilyinuencethevalueofCHRO,with=0resultinginpositiveCHRO.Ahead-oncollision(model8)appearstohaveasmalleectontheoverallvsNHrelationwhencomparedtotheducialcollidingmodel.ThereisaslightupwardshiftinvaluesofXHRO,buttheoverallshapeisgenerallysimilar.Theimpactparameter,whilesignicantontheGMCscale,wouldnotbeexpectedtogreatlyinuencethebehaviorofcollisionsbetweensmallerindividualsubstructuresthatdeterminethelocalB-eldpolarization.Lastly,thestronger-eldcaseofB=30G(model9)hasnotableeectsontheslope,withCHRO=)]TJ /F5 11.955 Tf 9.29 0 Td[(0.73inthez0lineofsight,aswellasamoderatecrossoverpointXHRO22.ThismodelproducesthemostpreferentiallyperpendicularalignmentofB-eldandlamentarystructureathighNH. 104

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Figure3-9. PhaseplotsexaminingjBjvs.nHfor(left)theducialcollidingand(right)non-collidingsimulationsatt=4.0Myr.Thecolorbardisplaysthetotalgasmassateachpoint.Thedashedlinerepresentsthe\Crutcherrelation,"whereBmax=B0=10GfornH<300cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3andBmax=B0(nH=300cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)2=3otherwise.ThecutointhelowdensityregionsisduetotheAlfvenlimiter. TheresolutionanalysisofHROresultsyieldedsimilarvaluesforalllinesofsightintheducialcollidingmodel,withsignsofconvergencewhenincreasingresolutionfrom1-2AMRlevelsto2-3.HROsandsubsequenthistogramshapeparameteranalysismaybeausefultoolfordierentiatingbetweennon-collidingandcollidingcloudsgiventhestrongcorrelationswithcollisionvelocityandB-eldstrengthand,toalesserextent,variousothercollisionalparameters. 3.3.2.2Magneticeldstrengths:jBjvs.nHThemagneticeldstrengthasafunctionofdensityinGMCsisanotherpropertythatispotentiallyimportantfortheevolutionofsubstructure.Figure 3-9 exploresthejBjvs.nHrelationfortheducialcollidingandnon-collidingGMCs.Thecollidingcaseinvolvescreationofregionsofbothhighdensityandhighermagnetizationthanthenon-collidingcase.ThemajorityoftheoverallgasmassremainsneartheinitializedvaluesofBandnH,butthecollisiongenerallyproducesstrongereldstrengthsforagivendensity.Theconcentrationofgasmassfrom10
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thenon-collidingcase,thegasmassmostlystaysconcentratedneartheinitializedlevels,withespeciallytheambient,CNMgasevolvinginamostlyquiescentmanner.Althoughoursimulationsareinitializedwithrelativelyidealizedconditions,bothducialmodelsdevelopaBvs.nHbehaviorapproximatelyconsistentatleastingeneralshapewiththe\Crutcherrelation"( Crutcheretal. , 2010 )whereBmax=B0=10GfornH<300cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3andBmax=B0(nH=300cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)2=3,fornH>300cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.OurmodelsexhibitrelativelystrongerjBjoverall,exceedingthemaximumvaluesstatisticallydeterminedbyobservationscomprisingtherelation.ThegasinthecollidingcasereachesmGstrengthsatnH106cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3astheaccumulationofgastohigherdensitiesinturncompressesthemagneticeldsalongwithit.However,atdensitiesnear300cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3,thereisindeedaslightelbowseeninthephaseplot,asthemajorityofgasbelowthatrangeretainsroughlyconstantvaluesofjBjinthetensofGrange.Thenon-collidingcasealsoexhibitstheelbowintherelation,withasmalleroverallrangeindensityandjBj.ThedeviationsbetweenjBjfoundinourmodels,especiallythehighlymagnetized,low-densitygasofthecollidingcase,butthismaybeattributabletotheparticularchoiceofourinitialeldstrengthsandothersimulationparameters.ThedicultZeemanmeasurementsof Crutcheretal. ( 2010 )wereperformedforrelativelynearbyobjects,soitisconceivablethatregionsofhighermeanmagneticeldstrengthmayleadtoslightlymodiedjBjvs.nHrelations. 3.3.3MassSurfaceDensityProbabilityDistributionFunctionsPDFsofmasssurfacedensity(orNHorAV)havebeenusedastoolstostudythephysicalcharacteristicsofobservedmolecularcloudsandIRDCs(e.g. Kainulainenetal. , 2009 ; Kainulainen&Tan , 2013 ; Butleretal. , 2014 ).Mechanismssuchasturbulence,self-gravity,shocks,andmagneticeldsallcontributetotheresultingdistributionof.Forturbulentclouds,the-PDFisgenerallycharacterizedaslog-normalatlowerNHranges,whileathigherNHanadditionalpowerlawtailcomponentisoftenmeasuredandattributedtocompressionduetoself-gravity.Thewidthofthelog-normalcomponentis 106

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expectedtocorrelatewiththestrengthofturbulence,i.e.,theMachnumberoftypicalshocks.Thefractionofmassinthehigh-powerlawtailmaycorrelatewiththedegreeofgravitationalinstabilityandtheeciencyofstarformation.Wepresentarea(pA())andmass-weighted(pM())PDFsof(32pc)3extractedregionsprojectedalongthez0-directionthrougheachofourmodels.Foreachdistribution,wealsondthebest-tlog-normalfunction: p()=A (2)1=2lnexp)]TJ /F5 11.955 Tf 10.49 8.09 Td[((ln)]TJ ET q 0.478 w 304.94 -149.29 m 324.87 -149.29 l S Q BT /F5 11.955 Tf 304.94 -159.27 Td[(ln)2 22ln(3{14)wherelnisthestandarddeviationofln.AscalefactorAisincludedtoallowforadjustmentbetweendieringPDFnormalizationschemes.AsummaryofthetparametersforeachrunisshowninTable 3-3 .Figure 3-10 showsthetimeevolutionofareaandmass-weighted-PDFsfortheducialcollidingandnon-collidingcases.Foreachcase,theregioniscenteredonthepositionofmaximumattherespective4Myrtimesteptocapturetheevolutionofthedenselament.Astheregionevolves,bothcasesexhibitabroadeningofthedistribution,withln,Aincreasingover3Myrfrom0.200to1.079forcollidingcloudsand0.143to0.600fornon-collidingclouds.Likewise,ln,Mincreasesfrom0.215to1.413(colliding)and0.142to0.691(non-colliding).Thevaluesfor Astayrelativelyconstant,withslightincreasesforthecollidingcase. Mincreasesforbothcases,withamuchstrongerincreaseinthecollidingcaseduetothehighdensitiescreated.Boththeareaandmass-weighted-PDFsaregenerallywell-twithasinglelog-normal,thoughthecollidingcaseat1.0Myrand4.0Myrandnon-collidingcaseat4.0Myrexhibitslightexcessesatthehigh-end.InFigure 3-11 ,wecalculateareaandmass-weighted-PDFsfortheparametermodelsatt=4Myr.Theregionsarecenteredatthepositionofmaximumineachcase.Theguresareorganizedbymodelscomparingcollisionvelocity(models3,4),magneticelddirection 107

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Figure3-10. Area-weighted(leftcolumn)andmass-weighted(rightcolumn)-PDFsof(32pc)3regionsfromtheducialcolliding(top)andnon-colliding(bottom)casesastheyevolveintime.-PDFsforeachcaseatt=1.0,2.0,3.0,and4.0Myrareshowninblue,green,red,andcyan,respectively.Thebestlog-normaltsforeachcaseareplottedasdash-dottedlinesofthesamecolor.Ineachpanel,the-PDFsfromobservationsofamassiveIRDCfrom Limetal. ( 2016 )isshowninmagenta.TheshadedregiondenotesareasofAV<3mag,matchingthecompletenesslevelstheobservedIRDCs. (5,6,7),andimpactparameter(8)andmagneticeldstrength(9),respectively.Theducialcollidingandnon-collidingcasesarealsoincludedforreferenceineachgure.Thegreatestdierencesarisefromthecollisionvelocity.Highervaluesofvrelcreategreaterrelativeamountsofgasatbothhighandlowmasssurfacedensities,resultinginincreasinglyhighervaluesoflnAandlnM. Aand Malsoshowmonotonicincreaseswithcollisionvelocity.Aninspectionofinitialmagneticeldorientationyieldsfairlysimilar-PDFsandcorrespondingPDFparametersforeachcase.Thus,althoughthevariationofleadstoquitedierentdensityandtemperaturemorphologies,theresulting-PDFsaremuchlessaected. 108

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Figure3-11. Area-weighted(leftcolumn)andmass-weighted(rightcolumn)-PDFsof(32pc)3regionsfromtheparametermodelsforeachcategoryof(top)vrel,(middle),and(bottom)jBjandb.-PDFsforeachcaseatt=4MyrareshownTheducialcollidingandnon-collidingcasesatt=4Myrareplottedindarkandlightgray,respectively,forreferenceineachgure.Thebestlog-normaltsforeachcaseareplottedasdash-dottedlinesofthesamecolor.Ineachpanel,the-PDFsfromobservationsofamassiveIRDCfrom Limetal. ( 2016 )isshowninmagentaandtheshadedregiondenotesareasofAV<3mag,matchingthecompletenesslevelstheobservedIRDCs. 109

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ThevariationofbandjBjresultedininsignicantchangestothe-PDFs,thoughtheunmagnetizedcollidingcasereachedthehighestmasssurfacedensities.However,thePDFparametersforeachofthesecollidingcasesarerelativelysimilar.Whencomparedwiththeunmagnetized,non-colliding,case,thedierencesin-PDFsduetocollisionvelocityareemphasizedfurther. Butleretal. ( 2014 )and Limetal. ( 2016 )havepresentedthe-PDFofa30pcscaleregioncenteredonamassiveIRDCthatisembeddedinaGMC.Near+midinfraredextinctionmappingandsub-mmdustcontinuumemissionmethodshavebeenusedtoderivethePDF.Theregioncontainsaminimumclosecontourof=0.013gcm)]TJ /F4 7.97 Tf 6.59 0 Td[(2(AV=3mag),soisexpectedtobecompleteforhighervaluesof.Thearea-weightedPDF(weightingbythetotalareaofthosepixelswithAV3mag)iswelltbyasinglelog-normalwith A=0.039gcm)]TJ /F4 7.97 Tf 6.58 0 Td[(2andln,A=1.4.Thereisarelativelylimitedfractionofmaterialathigh'sinexcessofthelog-normal,i.e.,pl.0.1.ThesefeaturesarequitesimilartosomeofthesimulatedPDFs,especiallythecollidingcaseat4Myr,whichiswell-twith A=0.021gcm)]TJ /F4 7.97 Tf 6.58 0 Td[(2andln,A=1.1.Thevrel=20kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1,=0andb=0RGMCmodelsalsohavesimilarvalues.Whilethisdoesnotproveanyparticularscenario,thecollidingcasesingeneraldemonstratestrongconsistencywithobservations.Instudyingresolutioneects,the-PDFsarewell-converged,withhistogramnoisedecreasingasresolutionincreasesandoverallvaluesoflog-normaltparametersinagreementwithinafewpercent. 3.3.4IntegratedIntensityMapsFromthePDR-basedheatingandcoolingfunctions,weextract12COand13COmolecularlinecoolinginformationtocreateself-consistentsyntheticintegratedintensitymapsviapost-processing.12COand13COlineemissivitiesatdierentJlevelsareaectedtovariousextentsbydensityandtemperature.Generally,weexpectthelower-JCOlinestoactasatracerofthebulkofthemoleculargas,whilehigher-Jlinesprobehighertemperature,densergas.Thesemid-tohigh-JCOlinesareoftensignaturesofshockedregionsandhavebeen 110

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Table3-3. Propertiesof-PDFs nameln,A Aln,M M(gcm)]TJ /F4 7.97 Tf 6.58 0 Td[(2)(gcm)]TJ /F4 7.97 Tf 6.58 0 Td[(2) Colliding(1.0Myr)0.2000.0170.2150.018Colliding(2.0Myr)0.5670.0200.5390.028Colliding(3.0Myr)0.8500.0230.8350.048Colliding(4.0Myr)1.0790.0211.4130.071Non-Col.(1.0Myr)0.1430.0140.1420.014Non-Col.(2.0Myr)0.5030.0090.6910.008Non-Col.(3.0Myr)0.5860.0130.5450.018Non-Col.(4.0Myr)0.6000.0150.6910.020vrel=5km/s1.0040.0160.8760.043vrel=20km/s0.9860.0380.8180.086=01.0450.0220.9690.061=300.8930.0270.8830.058=901.2550.0171.1230.077b=0RGMC0.9820.0380.6100.079B=30G0.4070.0191.8680.027B=0G,Col.1.3170.0141.4230.070B=0G,Non-Col.1.0070.0051.1190.013 studiedinGMCsandIRDCs( Ponetal. , 2015 ).ThegeneralstrengthoftheshockcanbefollowedwithincreasingvaluesofJ.PaperIfoundthe12CO(J=8-7)/13CO(J=2-1)lineintensityratiotobeagoodtracerofcloudcollisionsduetothestrongshockscreatedincollidingcasesbutnotinisolatedscenarios.UsingsimilarmethodsasPaperI,weassumeaducialdistancetotheGMCsofd=3kpc.Fromthis,wedetermineuxcontributionsfromeachcellinthesimulationandcalculateintegratedintensitiesusing I=ZId=2k 2ZTmbd.(3{15)whereIisthespecicintensity,isthelinewavelength,andTmbisthemainbeamtemperature.Tocalculatethetemperaturecontributionofthecells,weuse ZTmbd=3 2kI=3jV 8kd2.(3{16) 111

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Figure3-12. TimeevolutionoftheducialcollidingGMCmodel,simulatingvariouslineemissivitiesat1.0,2.0,3.0,and4.0Myr.IntegratedintensitymapsderivedfromthePDR-basedcoolingfunctions:Row1:[CII].Row2:13CO(J=2-1).Row3:13CO(J=3-2).Row4:12CO(J=8-7). wherejisthevolumeemissivity,Vthecellvolume,andthesolidanglesubtendedbythecell.Figures 3-12 and 3-13 showthetime-evolutionofmapsof[CII],13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)integratedintensityfortheducialcollidingandnon-collidingcases,respectively.[CII]actsasaprobeforthelowerdensity,PDRgasenvelopingGMCs.ThisregioncontainsgastransitioningtothemolecularphaseandjoiningtheGMCmaterial.Oursyntheticmapsof[CII]showemissioninextendedregionssurroundingthedensergas.Thecollidingcaseexhibitshigher[CII]intensities,butoverasmallervolumeconcentratedabouttheconverging 112

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Figure3-13. SameasFig. 3-12 exceptforthenon-collidingcase,simulatingvariouslineemissivitiesat1.0,2.0,3.0,and4.0Myr.IntegratedintensitymapsderivedfromthePDR-basedcoolingfunctions:Row1:[CII].Row2:13CO(J=2-1).Row3:13CO(J=3-2).Row4:12CO(J=8-7). ows.TheoriginalGMCsshowI[CII]1Kkm=s,withsubsequentevolutionreachingupto4Kkm=s.Thenon-collidingcaseremainsat1Kkm=sthroughouttheevolution,keepingafairlyconsistentdistribution.Theemissionisextendedandencompassesthedensermoleculargas.13CO(J=2-1),13CO(J=3-2)areseentobegoodtracersofcold,densegas.Asbothcollidingandnon-collidingcloudsevolve,denselamentsformandbecometraceablebytheselow-JCOlines.Notingthedierencesinintegratedintensityscalesbetweenthetwomodels,thedensitiesinthecollidingcasereachsignicantlyhigherlevelsatearliertimescomparedtothenon-collidingcaseandcanbetracedthroughCO.Themorphologiesofthestructures 113

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dier,asoneprimarydenselamentaryregioncanbeseenbeingformedattheinterfaceofthecollidingows,whiledistinct,distributedlamentsareformedforthenon-collidingcase.TheprimarylamentarystructureinthecollidingcaseexhibitsdenseclumpsreachingI80Kkm=s,whiletheseparatelamentsevolvinginthenon-collidingcasereachvaluesofI20Kkm=sforboth13CO(J=2-1)and13CO(J=3-2).Starkdierences,however,canbeseenin12CO(J=8-7),wherehighintensitiesareproducedlaterintheevolutionoftheducialcollidingcase,asthedenselamentsinbothGMCscollideandmerge.Thesebegintobecomevisibleatt3Myrandreachlevelsof103Kkm=s.Inthenon-collidingcase,thereisalmostnoemissionatthisrotationallevel,indicatingalackofstrongshocks.Bythet4Myrmark,onlyI12CO(J=8)]TJ /F4 7.97 Tf 6.59 0 Td[(7)0.2Kkm=scanbedetected. 3.3.5KinematicsSyntheticspectrawerecreatedtogainmorequantitativecomparisonsbetweenthevariousemissionlinesaswellastounderstandthekinematicsofthemodels.Additionally,line-of-sightvelocityspectracanbedirectlycomparedtothosemeasuredfromobservedclouds.ThemajorityofcloudcollisioncandidateshavereliedprimarilyonmultiplevelocitycomponentsdeducedfromCOspectrainconjunctionwithcoherentdensitystructuresand/oryoungstarsasevidencefordetection.ThecurrentstudyoersauniquemethodofdirectlyreproducingvariousCOspectraforcloudsundergoingcollisionsandcomparingthemwithnon-collidingscenarios. 3.3.5.1SpectraInFigure 3-14 ,wehavecreatedspectraof13CO(J=2-1),13CO(J=3-2),and12CO(J=8-7)(sameastheintegratedintensitymaps)throughsquarepatchesofarea(25.6pc)2projectedthroughthex,y,andzlinesofsightforboththeducialcollidingandnon-collidingcases.Eachspectrumcorrespondstotherespectivemasssurfacedensitymap,onwhichtheprojectedpatchisindicated.Thepatchescenteronthehighestmasssurfacedensityregionsforbothcases. 114

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Figure3-14. Top:Masssurfacedensitymapsareshownforvariouslinesofsightdirectedthroughtheducialcollidingcase(toprow:(a)-(c))andnon-collidingcase(bottomrow:(d)-(f)).Theblackboxesboundequal-volumeregionscontainingtheprimarylamentineachsimulationatt=4.0Myr.Bottom:Syntheticvelocityspectrafor13CO(2-1),13CO(3-2),12CO(8-7)fromtherespectiveselectedregionsshownintheuppergures.Notelargedierencesin12CO(8-7)integratedintensitiesrelativeto13CO(2-1)and13CO(3-2)betweenthecollidingandnon-collidingmodels. 115

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Therstmaindierenceseeninthespectrabetweenthecollidingandnon-collidingcasesisthewidthofthevelocityranges.Thenon-collidingcaseexhibitsfairlynarrow(v.10km=s)velocitywidthsforeachlineofsight.Thecollidingcase,ontheotherhand,hasbroader(v15)]TJ /F5 11.955 Tf 12.91 0 Td[(20km=s)velocitywidthsandwhatmaybeinterpretedasmultiplecomponents,atleastforthevxandvydirections,buttoalesserextentvzaswell.AnotherkeyresultistherelativestrengthofthevariousCOlines.Throughouteachofthenon-collidinglinesofsight,thestrengthoftheintegratedintensityfollowsthetrendof I13CO(2)]TJ /F4 7.97 Tf 6.58 0 Td[(1)>I13CO(3)]TJ /F4 7.97 Tf 6.59 0 Td[(2)>I12CO(8)]TJ /F4 7.97 Tf 6.58 0 Td[(7)(3{17)Themagnitudesareoftheorder2,1,and210)]TJ /F4 7.97 Tf 6.58 0 Td[(3Kkm/s,respectively.Forthecollidingcase,theexactoppositetrendisseen: I13CO(2)]TJ /F4 7.97 Tf 6.58 0 Td[(1)
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Figure3-15. Position-velocitydiagramsfortheducialcollidingcase(leftcolumn)andnon-collidingcase(rightcolumn).Thescalingisderivedfromsynthetic13CO(J=1-0)lineintensitiesthroughvelocitybinsofv=0.212kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Theblackcrossindicatesthepositionofthecenterofmassandthesolidblacklineshowstheintensity-weightedlinearvelocitygradient(dvlos=ds)acrosseachcloud. Weinvestigatetheducialcollidingandnon-collidingcasestransformedfromour3Dspatialdatatop-p-v-spaceforeachofthex,y,andzlinesofsight(seeFig. 3-15 ).Thevelocitydispersionwasdenedusingtheintensity-weightedrms1Dvelocitydispersionofthecorrespondingregion.Velocitygradientswerecalculatedalongeachspatialdirectionforcoordinateaxesorthogonaltothechosenlineofsight(e.g.,fordvz dx,thebestlineartwasdeterminedthrougheachintensity-weightedcellin(x,vz)space).Table 3-4 summarizesthevelocityinformationfortheducialcollidingandnon-collidingcases,foreachlineofsight.Strongdierencesbetweenthetwomodelsarerevealedthroughthevelocitydispersion,withthecollidingcaseshowingindicationsofmuchgreaterdispersion.Thelargestvelocitydispersionof3.7km/sisseenalongthecollisionaxis,whiletheorthogonaldirectionsalsoexperiencegreaterdispersionrelativetothenon-collidingcase.TheRMSvelocitydispersion 117

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Table3-4. Velocitygradients CaseLoSdvlos ds(kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)(kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1pc)]TJ /F4 7.97 Tf 6.58 0 Td[(1) Collidingx3.65880.0581y2.76110.1648z2.47600.0278Non-Collidingx1.49260.0864y1.19960.0110z1.96490.0948 overthe3linesofsightis3.01km/sforthecollidingcaseand1.58km/sforthenon-collidingcase.Thevelocitygradientsrevealdierencesaswell.Thelargestvelocitygradientoccurswhenlookinginthedirectionofthecollisionalimpactparameter,at0.16km/s/pc.However,thegradientsalongtheremainingdirectionsaresimilarinmagnitudeandevensomewhatsmallerwhencomparedwiththenon-collidingcase.TheRMSvelocitygradientoverthe3linesofsightis0.1022km/s/pcforthecollidingcaseand0.0743km/s/pcforthenon-collidingcase.Overall,thekinematicsmeasuredintheducialcollidingcaseareinroughagreementwiththetenobservedIRDCsandassociatedGMCsfromHT15,inwhichvelocitydispersionsoforderfewkm/sandvelocitygradientsgenerallyat0.1(butupwardsof0.6-0.7)km/s/pcwerefound,thoughtheseresultsdonotnecessarilyprecludethenon-collidingcase.However,thekinematicsofobservedIRDCs,especiallythosewithhighermeasuredvaluesofvelocitygradientanddispersion,maysuggestamoredynamicformationscenariowithcompressionofGMCmaterial. 3.3.6DynamicsVirialanalysisofcloudscomparestherelativeimportanceofself-gravitywithinternalmotionsandcanrevealdynamicalpropertiesofthematerialand,inturn,provideevidenceforrecentkinematichistory.HT15performedvirialanalysisontenobservedIRDCsandassociatedGMCsbasedon13CO(J=1-0)emissionandfoundthatIRDCshavemoderatelyenhancedvelocitydispersionsandvirialparametersrelativetoGMCs,potentiallyindicatingmoredisturbedkinematicsofthedensestgas.IfGMCcollisionsindeedtriggertheformation 118

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Figure3-16. Timeevolutionmapsof13CO(J=1-0)integratedintensityfortheducialcollidingcaseat2.0,3.0,and4.0Myr.ThedierenteectiveradiicalculatedforthevirialanalysisareplottedascoloredcircleswithradiidenedbyRM(blue),RA(green),andR1=2(red). ofIRDCsandthenstarclusters,virialanalysismaybeanotherimportantdiagnosticfortheproductsofcloudcollisions.Wefollowthe\simpleextraction(SE)"and\connectedextraction(CE)"techniquesdetailedinHT15,applyingthemtoourducialcollidingandnon-collidingmodels.First,wecalculatethecloudcenterofmassinp-p-v-spacebasedon13CO(J=1-0)intensity.SEselectsallvoxelswith13CO(1-0)emissionouttoradiiofR=5,10,20,and30pcandwithinav015kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1line-of-sightvelocityrange.CE,ontheotherhand,selectsvoxelsdirectlyconnectedface-wiseinp-p-v-space.Eachmustexceedthesame13CO(1-0)intensitythresholdofTB,v1.35KasinHT15,i.e.,theGalacticRingSurvey(GRS)( Jacksonetal. , 2006 )5rmslevel.Theconnectedvoxelmustalsoliewithina30pcradiusand15kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1velocity.Allconnectedstructuresinthep-p-vdomainarefoundviatheestablishedgraphtheorymethodofconnectedcomponentsofundirectedgraphs,withcellsmeetingtheabove-mentionedcriteria 119

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Figure3-17. Fromtoptobottomrows:Timeevolutionofthetotalmass,velocitydispersion,virialradiiasdenedbythearealradiusRA,andthecorrespondingvirialparameter.Thecolumnscomparethevariousmodels,asindicatedbytherespectivecolorandlabel.Thethreeprimarylinesofsightarealsoinvestigatedforeachmodel,denotedassolid(x),dashed(y),anddotted(z)lines.Theshadedregioniscenteredonvir=1withafactorof2toeachside,roughlytherangeseenbyHT15. actingasthenodes.Thesubgraphwiththelargestnumberofnodesisdesignatedastheconnectedextraction,andfurtheranalysisisperformedonthissubsetofvoxels.ForCE,threedierentradiiarecalculated,basedonvariousdenitions:themass-weightedradius(RM;themeanprojectedradialdistanceofcloudmassfromthecenterofmass),arealradius(RA;fromthetotalprojectedareaA=R2A=NpAp,whereNpandAparethepixelnumberandarea,respectively,ofthedenedcloud),andhalf-massradius(R1=2;theradiusfromthecenterofmassthatcontainshalfthetotalcloudmass).Tostudyvirializationofthecloud,weusethedimensionlessvirialparametervirfrom Bertoldi&McKee ( 1992 ) vir=52R GM,(3{19)whereisthemass-averagedline-of-sightvelocitydispersion. 120

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Figure 3-16 showsthetimeevolutionofthe13CO(J=1-0)integratedintensitymapsfortheducialcollidingandnon-collidingcasesandthecorrespondingvirialradii.Forbothmodels,the13CO(J=1-0)structuresgrowinextentandencompassmorematerial,leadingtoincreasingeectiveradii.Acentraldominantlamentarystructureformsinthecollidingcase,whereasthenon-collidingcasecontainsanumberofsmaller,morespatiallyseparatedlaments.The13COemissionisgenerallyweakerandmoredispersedinindependentstructuresinthenon-collidingcase.Thechosenmethodforextractionsuccessfullytracksthesamesinglelargestlamentarystructureovertimeasitevolvesinbothcases.Thevirialparameterandconstituentvariablesforallmodelsforthethreex,y,andzlinesofsightaredisplayedinFig. 3-17 .ThesevariableswithintheCEshowdistinctivetrendsovertimeaswellassystematicdierencesbetweenvariousmodels.Thetotalmassofthemainconnected13CO-denedstructuregrowssteadilyovertime.Theducialcollidingcaseproducesstructuresthatgrowfrom103tojustunder105Mover3Myr.Thenon-collidingcasegrowsatasimilarrate,butgenerallycontains10timeslessmass.Thevrel=20km/smodelcreateshigher-massstructuresatearliertimes,butconvergestojustover105Mbyt=4.0Myr.Thevrel=5km/scasefollowsanintermediategrowthevolution.The=0,30,and90caseshavesimilarmassevolution,withslightlysmallermassescorrespondingtoincreasingvaluesof.Thetotalstructuremassfortheb=0RGMCandB=30Gcasesgrowinasimilarmanner.Thenon-magnetizedcollidingandnon-collidingcasesfollowsimilarevolutionastheducialcollidingandnon-collidingcases,respectively,butdogrowtoslightlylargermassesingeneralduetothelackofmagneticpressuresupport.Thevelocitydispersionsofthe13COemittingstructuresarefoundtogrowthroughoutthetimeevolutionforallcases,generallystartingnear/1km/sandreaching2-3km/s.Thecollidingcasesingeneralshowdistinctlyhighervelocitydispersions,especiallywhenviewingalongthecollisionaxis(x).Fastercollisionvelocitiesresultinlargervelocitydispersions,while 121

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theredoesnotseemtobemuchdependenceoninitialmagneticelddirection.Strongermagneticeldsappeartodampenthecollision,resultinginslightlysmallervaluesof.Themeasuredarealradiigenerallygrowinasimilarmannerasthemass,althoughthereisastrongdependenceonviewingdirection.Specically,thez-directedline-of-sight,inwhichtheplane-of-skyissensitivetoboththecollisionandimpactparameteraxes,showsamuchgreaterradiusinallcases.Alongthisdirection,theradiiaremeasuredtoincreasefromapproximately1pcto10pcinallcases,thoughcollidingcasesingeneralcreatedlargerstructuresbyafewpc.Thehighervelocitycollisionsgrowmuchfasterinitially,butreachsimilarnalspatialextents.Alongtheotherlinesofsight,therearesimilartrends,althoughtheinitialandnalradiiareapproximatelyafactorof10smallerinthesedirections.Thegeneraltrendforallmodelsisforthevirialparametertodecreaseovertime,whichappearstobemostlydrivenbytheaccumulationofmoreandmoremassintothestructures.Thecalculatedradiiofthestructureshaveastrongdependenceonviewingdirection,asdescribedabove,thusaectingviraswell.Inthezline-of-sight,wheremoreextendedstructureisdetected,thevirialparametervaluesbeginmoderatelysuper-virialbutevolvetoapproachthoseexpectedofvirialequilibrium,i.e.,vir1(recallvir<2impliesagravitationallyboundstructure,ignoringsurfacepressureandmagneticpressureeects).Forotherviewingdirections,virofthestructureisgenerallysmaller,oftenalreadysub-virial.Systematicdierencesinvirbetweenmodelsarelessdistinctthanfromviewingdirection,withvirialparametersdecreasingbyfactorsofafewovertime.Despitethesmalldierences,thesmallestvaluesofvirarepresentinthenon-magnetizedcases.Overall,someofthesestructuresthemmaybeundergoingrapidglobalcollapse,butmorelikelyinthemagnetizedcasestheB-eldsareprovidingsupportthatmaykeepthemclosertovirialequilbrium.Weexpectthat:(1)thestructureswillcontinuetoaccumulatemassandbecomeevenmoregravitationallybound;(2)theyarelikelytocontainhighlygravitationallyunstablesubstructures,e.g.,thedenselamentsandclumpsthatappearfrom3to4Myrintheducialcollidingcase. 122

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Resultsfromthe10IRDCs/GMCsstudiedinHT15showrelativelylargevariationofderivedvirialparameterdependingontheanalysismethod:inparticular,themostrelevantmethodforcomparisonwithouranalysisisCE,,i.e.,connectedextractionofastructurewhereanopticaldepthcorrectionhasbeenassessed,andwherethevelocitydispersionismeasureddirectlyfromthesecondmomentofthespectrum.Thismethodndsvaluesofvir1,butwithsignicantdispersionofaboutafactoroftwo.Stillthesevaluesaresomewhatlargerthanthoseseeninmostofoursimulationsatt4Myr.InthecontextoftheGMC-GMCcollisionscenario,thismayindicatethattherelevanttimescaleforcomparisonisatearliertimes,e.g.,t1to2Myr,orthatthetypicallineofsighttoGMCsisinadirectionthatincludesasignicantcomponentofthecollisionvelocityaxis(whichislikelyforcollisionsmediatedbyshearintheGalacticdisk).Whilethevaluesofviraresimilarbetweenallofthesimulations,rangingfromslightlytostronglygravitationallyboundobjects,thetotalmassesandvelocitydispersionarenotablylargerforthecollidingcases.Thusweconcludethat,incomparisontothe13COemittingstructuresformedinnon-collidingsimulations,thoseformedviaGMCcollisionsaremorelikelytoleadtotheconditionsnecessaryformassivestarclusterformation. 3.4DiscussionandConclusionsWehaveinvestigatedphysicalpropertiesassociatedwithandpotentialobservationalsignaturesofmagnetized,turbulentGMCscollisions.OurmethodhasutilizedPDR-basedheatingandcoolingfunctions,developedinourpreviousstudywith2Dsimulations,toallowournew3Dsimulations,withresolutionof0.125pc,tofollowthemulti-phase,non-equilibrium,thermalevolutionoftheclouds,includingtheirshockstructures.WehaveexploredtheparameterspaceofGMCcollisions,includingtheeectsofcollisionvelocity,impactparameter,magneticeldorientationandstrength.Wehavealsocarriedoutdetailedcomparisonsoftheresultsofotherwiseidenticalcollidingandnon-collidingclouds.Wehavefoundthattherelativeorientationsbetweenmagneticeldsandmasssurfacedensitystructuresmaybeusedtodiagnoseacloudcollision.HROsandsubsequenthistogram 123

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shapeparameteranalysisrevealdistinguishingbehaviorresultingfromcloudcollisionscomparedwithnon-collidingclouds.Inparticular,thecollisionvelocityappearstohaveastrongeectontheHROshapeparameter.Thedependenceonlineofsightisfairlylow,strengtheningthe vs.diagnostic.ThejBjvs.nHrelationfoundinourmodelsrevealssomewhatstrongermagneticeldstrengthwhencomparedtothe\Crutcherrelation",althoughthegeneraltrendappearstofollowBmax/(nH)2=3athigherdensitieswhilestayingnearroughlyconstantjBjatlowerdensities.Thisbehaviorislikelysensitivetoourchoicesofinitialconditions,butmayberepresentativeofregionsofslightlyhighermeaneldstrengthcomparedtotherelativelynearbyobjectswhichcomprisethe\Crutcherrelation".Areaandmass-weighted-PDFsshowlargedierencesamongourmodels,withstrongdistinguishingfactorsbetweencollidingandnon-collidingcases.Althoughitisjustasinglecase,acomparisonwiththe-PDFofanobservedIRDCndsthattheevolvedGMCcollisioncaseshavemoresimilar-PDFsthantheresultsofnon-collidingsimulations.IntensitymappingofCOspectra,especiallythe12CO(J=8-7)/13CO(J=2-1)lineintensityratio,isanotherpotentiallystrongdiagnosticofcloudcollisions.Fromsyntheticspectraofourmodels,theintegratedintensities,aswellasthevelocityspread,aredierentiatorsbetweencollidingandnon-collidingGMCsandbothappeartobegenerallyindependentoflineofsightorientation.Kinematically,thevelocitydispersionofthecollidingcasewasfoundtobemuchhigherthanthatofthenon-collidingcase,atalmostafactorof2higher,reaching>3.5kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1whenmeasuredalongthecollisionaxis.Velocitygradientsarealsoenhancedduetocollisions,withthehighestvaluesinthecollidingcasemeasuredwhenviewingorientationisalongthesamedirectionthatthecloudsareosetviatheimpactparameter,atdvlos=ds=0.20kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1pc)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Finally,studyofthe13CO-denedstructuresformedinthecollidingandnon-collidingscenariosarequitedierent.Inallofthecollidingcases,theyaremuchmoremassivewith 124

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generallylargervelocitydispersion.Bothcollidingandnon-collidingcasesaregravitationallybound.ThissuggestsapotentialroleforGMCcollisionsinthetriggeringofmassivestarclusterformation. 125

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CHAPTER4DENSITYANDMAGNETICALLYREGULATEDSTARFORMATIONWestudygiantmolecularcloud(GMCs)collisionsandtheirabilitytotriggermassivestarclusterformation.Wefurtherdevelopourthreedimensionalmagnetized,turbulent,collidingGMCsimulationsbyimplementingstarformationsub-gridmodels.Twosuchmodelsareexplored:(1)\Density-Regulated,"i.e.,xedeciencyperfree-falltimeaboveasetdensitythreshold;(2)\Magnetically-Regulated,"i.e.,xedeciencyperfree-falltimeinregionsthataremagneticallysupercritical.Variationofparametersassociatedwiththesemodelsisalsoexplored.Betweencollidingandnon-collidingcases,wecomparethestarformationrateovertime,thespatialclusteringofthestarsviaaminimumspanningtree(MST)method,andtheresultingkinematicsofthestarparticlesincomparisontothenatalgas. 4.1IntroductionMoststarsforminclusterswithingiantmolecularclouds(GMCs),whichhavetypicalhydrogennumberdensitiesofnH=100cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3,diametersoftensofparsecs,massesofupto106M,andaveragetemperaturesof10)]TJ /F5 11.955 Tf 11.96 0 Td[(30K.InfraredDarkClouds(IRDCs)arerecognizedasbeingthelikelyprecursorstostarclusters( Rathborneetal. , 2006 ; Tanetal. , 2014 ).IRDCs,locatedwithinGMCs,havesuchhighmasssurfacedensities(&0.1gcm)]TJ /F4 7.97 Tf 6.59 0 Td[(2)thattheyaredarkatmid-IR(10m)andevenfar-IR(70m).Theirlowtemperatures(10)]TJ /F5 11.955 Tf 12.58 0 Td[(20K)(see,e.g., Pillaietal. , 2006 ; Wangetal. , 2008 ; Sakaietal. , 2008 ; Chiraetal. , 2013 ),highvolumedensities(nH>105cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3),relativelycompacysizes(fewpc),andmasses(102)]TJ /F5 11.955 Tf 12.43 0 Td[(104M)indicatethattheymaybethehigh-massanaloguetotherelativelyisolated,extinctedclumpsthathavebeenidentiedassitesofsomelowmassstarformation(e.g.,Bokglobules; Bok&Reilly , 1947 ).Currently,thedominantprocessesthatinducethecollapseandfragmentationofGMCsintostar-formingclumps,suchasIRDCs,arepoorlyunderstood.Varioustheoreticalmodelsincludetriggeringbyspiralarmpassage(e.g., Wyse&Silk , 1989 ; Tamburroetal. , 2008 ),instabilitiesfromtheglobalgalacticdisk(e.g., Elmegreen , 1994 ; Lietal. , 2006 ),regulation 126

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byturbulence(e.g., Krumholz&McKee , 2005 ),regulationbymagneticelds(e.g., VanLooetal. , 2015 ),triggeringbystellarfeedback(e.g.,supernova; Inutsukaetal. , 2015 ),triggeringbyconvergingatomicows(e.g., Heitschetal. , 2009 ),andtriggeringviaconvergingmolecularows,i.e.,GMC-GMCcollisions(e.g., Scovilleetal. , 1986 ; Tan , 2000 ; Wuetal. , 2015 , 2016 ). Wuetal. ( 2015 ,hereafterPaperI)and Wuetal. ( 2016 ,hereafterPaperII)developedanumericalstudyofGMC-GMCcollisions,focusingonunderstandingthephysicalmechanismsaswellasprovidingobservationaldiagnostics.Comparingstronglymagnetized,supersonicallyturbulentGMCsincollidingandnon-collidingcasesoverawideparameterspaceandinvestigatingavariedarrayofpotentialobservationalsignatures,theyfoundthatanumberofindicatorssuggestsimilaritiesbetweenthecollidingscenariostoobservedGMCsandIRDCs.Further,dynamicalvirialanalysissuggestedthatdense13CO-denedstructurescreatedthroughGMCcollisionsweremorelikelytocollapseandformmassivestarclusterswhencomparedwithmorequiescentlyevolvingstructures.Onekeypieceofthepuzzlemaylieintheperiodjustafterstarclustersareformed.Thegoalofthisstudyistoanswerthequestion:DorealisticmodelsofGMCcollisionscreatestarclustersthatcloselymatchthepropertiesofobservedyoungstar-formingregions?WeapproachthisquestionbyfurtherbuildinguponourpreviousmodelsofGMCsthroughtheimplementationofstarformationsub-gridmodels,includingdevelopmentofanew,magnetically-regulatedsub-gridmodel.Wethenleverageourexistinggas-focusedobservationaldiagnosticmethodswithadditionalinformationfromthepopulationofstarparticles.Thus,wehopetoprovideacontinuous,self-consistentlinkbetweenIRDC-typestructuresandtheformationofyoungstarclusters.Section 4.2 describesournumericalsetupandthevariousstarformationmodels.WethenpresentourresultsinSection 4.3 ,whichinclude:gasandclustermorphologies,(x 4.3.1 )resultingstarformationrates(x 4.3.2 ),spatialclustering(x 4.3.3 ),andstarparticlekinematics(x 4.3.4 ).InSection 4.4 wediscussourconclusions. 127

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4.2NumericalModelWeusethenumericalframeworkdevelopedinPaperIIasafoundationandfurtheraddvariousstarformationroutines.Againwefocusoncomparisonsbetweentheducialcollidingandnon-collidingcaseswithineachofthesestarformationmodels. 4.2.1InitialConditionsOurGMCsareidenticaltothoseinitializedinPaperII,whicharemotivatedbyobservedGMCproperties.Thecloudsareself-gravitating,supersonicallyturbulentandmagnetized.Theircollisionisinitializedwithanimpactparameter.Thecloudsareembeddedinanambientmediumoftentimeslowerdensity(i.e.,anatomiccoldneutralmedium,CNM),whichforthecollidingcase,isconvergingalongwiththeGMCs.Thesimulationdomainis(128pc)3andcontainstwoneighboringGMCs.TheGMCsareinitiallyuniformspheres,withHydrogennumberdensitiesofnH,GMC=100cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3andradiiRGMC=20.0pc.ThisgiveseachGMCamassMGMC=9.3104M.Theambientgasrepresentstheatomiccoldneutralmedium(CNM)andhasadensityofnH,0=10cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.ThecentersoftheGMCsareosetby2RGMCinthecollisionaxis(x),0inthey-axis,andb=0.5RGMCinthez-axis.TheGMCsareinitializedwithasupersonicturbulentvelocityeldfollowingthev2k/k)]TJ /F4 7.97 Tf 6.59 0 Td[(4relation,wherek==disthewavenumberforaneddydiameterd,conventionallywiththe\k-mode"normalizedtothesimulationboxlength.ThegaswithintheGMCisinitializedwithMachnumberMs=cs=23(forT=15Kconditions),ofordervirial.Wesetourducialk-modestobef2,...,20grepresentativeofthelarge-scaleturbulentvelocities(smallk)spanningourGMCdiametersandasmallenoughminimumscale(largek)whichisnumericallyresolved,butexpectedtocascadetosmallerscales.Wedonotdriveturbulence,insteadlettingitdecaywithinafewdynamicaltimes.NotealsothatturbulenceisinitializedonlywithintheinitialvolumeoftheGMCswhileweleavetheambientmediumnon-turbulent. 128

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Table4-1. Initialsimulationproperties GMCambient nH(cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3)10010R(pc)20-b(RGMC)0.5-M(M)9.3104-T(K)15150t(Myr)4.35-cs(km/s)0.230.72vA(km/s)1.845.83vvir(km/s)4.9-(km/s)5.2-Ms23-MA2.82-k-mode(k1,k2)(2,20)-vbulk(km/s)55B(G)1010()60604.31.50.0150.015 Alarge-scaleuniformmagneticeldofstrength10Gisinitializedthroughouttheboxatanangle=60withrespecttothecollision(x-)axis.ThischoiceifjBjismotivatedbytheZeemanmeasurementsoftypicalGMCeldstrengths,summarizedby Crutcher ( 2012 ).Intheducialcollidingcase,thebulkows(includingboththeambientgasandtheGMCs)havearelativevelocityofvrel=10kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1.Inthenon-collidingcase,thereisnobulkvelocityow.Thesimulationsarerunfor5Myrtoinvestigatetheonsetofstarformation.NotethatthefreefalltimegiventheinitialuniformdensityGMCsist=(3=[32G])1=2'4.35Myr.However,tforthedensersubstructurescreatedbyturbulenceismuchshorter. 4.2.2NumericalCodeOurmodelsarerunusingEnzo1,amagnetohydrodynamics(MHD)adaptivemeshrenement(AMR)code( Bryanetal. , 2014 ).WeusetheDedner-MHDmethod,whichsolves 1 http://enzo-project.org (v2.4-dev,changeset845edacb82b1+) 129

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Figure4-1. (Toptworows:)Timeevolutionofmasssurfacedensityfortheducialcolliding(noSF-col)and(bottomtworows:)thenon-colliding(noSF-nocol)caseswithnostarformation.Snapshotsat0.0,1.0,2.0,3.0,4.0,and5.0Myrareshownforeachcase.Mass-weightedmagneticeldsareshownasgraystreamlines. 130

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thesolvestheMHDequationsusingtheHarten-Lax-vanLeerwithDiscontinuities(HLLD)methodandapiecewiselinearreconstructionmethod(PLM).ThetimeisevolvedusingtheMUSCL2nd-orderRunge-Kuttamethod.TherB=0solenoidalconstraintofthemagneticeldismaintainedviaahyperbolicdivergencecleaningmethod( Dedneretal. , 2002 ; Wang&Abel , 2008 ).Thesimulationdomainisrealizedwithatoplevelrootgridof1283with3additionallevelsofAMR.Ourmodelsthushaveaneectiveresolutionof10243,withaminimumgridcellsizeof0.125pc.WerenesolelyonthelocalJeanslength,settinganecessaryrequirementofresolvingby8cells.ThisisintentionalinordertomorehighlyresolvelargervolumesoftheGMCgaswhencomparedtothe4cellstypicallyusedtoavoidarticialfragmentation(i.e.,theTruelovecriterion; Trueloveetal. 1997 ).Further,asthisJeanscriterionassumespurelythermalsupport,ifourgasismagneticallysupported,thentheeective\magneto-Jeansmass"willbesignicantlylargerthanthethermalJeansmass.Duetotherelativelyhighbulkvelocitiesandemphasisofmagneticelds,werequiretheuseofthe\dualenergyformalism",whichseparatelysolvestheinternalenergyequationaswellasthetotalenergyequation.Iftheratioofthermaltototalenergyislessthan0.001,thenthetemperatureiscalculatedfromtheinternalpressure.Otherwise,thetotalenergyisused.Additionally,weemploythe\Alfvenlimiter"(describedinPaperII)toavoidexceedinglysmalltimestepssetbyAlfvenwaves.ThisactsbychoosingamaximumAlfvenvelocity,vA,max=B=p 0min=1107cms)]TJ /F4 7.97 Tf 6.59 0 Td[(1,andsettingadensityoorthatisdeterminedbythemagneticeld.Thispredominantlyaectsonlysmallpocketsofverylow-densitygaswithwhichwearelessinterested,andthusthedynamicalresultsaredeemedunaectedbythislimiter. 4.2.3ThermalProcessesWeassumeaconstantmeanparticlemass(=2.33mH)throughoutthesimulationdomainforsimplicity,asourfocusisonthedensemoleculargasofGMCs.Wealsochooseaconstantadiabaticindex=5=3.Notethatthisessentiallyignorescertainexcitationmodesof 131

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Table4-2. Starformationmodels NameStarFormationvrelCellSizenH,sftMin.CellMassM?,minc1Model(kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)(pc)(cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)(yr)(M)(M) noSF-colnone100.125-----noSF-nocolnone00.125----SF-05-coldens.reg.100.1250.51066.21043210-SF-05-nocoldens.reg.00.1250.51066.21043210-SF-1-coldens.reg.100.1251.01064.31046310-SF-1-nocoldens.reg.00.1251.01064.31046310-SF-2-coldens.reg.100.1252.01063.110412610-SF-2-nocoldens.reg.00.1252.01063.110412610SF-Breg-05-colmag.reg.100.125---100.063SF-Breg-05-nocolmag.reg.00.125---100.063SF-Breg-1-colmag.reg.100.125---100.126SF-Breg-1-nocolmag.reg.00.125---100.126SF-Breg-2-colmag.reg.100.125---100.252SF-Breg-2-nocolmag.reg.00.125---100.252 H2thatmayberelevant(i.e.,shocks),butitisstillthemostappropriatesingle-valuedchoiceof,givenourfocusonthedynamicsofcoldH2.Also,weassumenHe=0.1nH,givingamassperHof2.3410)]TJ /F4 7.97 Tf 6.59 0 Td[(24g.ThePDR-basedheatingandcoolingfunctionsdevelopedinPaperIareagainusedinthesesimulations.Theassumptionsare:(1)FUVradiationeldofG0=4(i.e.,appropriateconditionsfortheinnerGalaxy,e.g.,atGalactocentricdistancesof4kpc)and(2)abackgroundcosmicrayionizationrateof=1.010)]TJ /F4 7.97 Tf 6.58 0 Td[(16s)]TJ /F4 7.97 Tf 6.58 0 Td[(1.Theheating/coolingfunctionstracetheatomictomoleculartransitionandrecreateamulti-phaseISM.Theyspandensityandtemperaturerangesof10)]TJ /F4 7.97 Tf 6.59 0 Td[(3nH=cm)]TJ /F4 7.97 Tf 6.59 0 Td[(31010and2.7T=K107,respectively.WeusetheGrackleexternalchemistryandcoolinglibrary2( Bryanetal. , 2014 ; Kimetal. , 2014 )toincorporateourheating/coolingfunctionsintabularformintoEnzo,modifyingtheenergyequation. 2 https://grackle.readthedocs.org/ 132

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4.2.4StarFormationWeutilizetheparticlemachineryofEnzotomodelstarformation.Specically,starparticles(i.e.,collisionless,dimensionlesspointswithmassM?)formwithinasimulationcellifcertainlocalcriteriaaremet. 4.2.4.1Fixedstarformationeciencyperfree-falltimewiththresholddensityOurbasestarformationroutineisa\density-regulated"model,basedon VanLooetal. ( 2013 ).Inthismodel,thedensitywithinthecellmustexceedaducialstarformationthresholdvalueofnH,sf=106cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3.FornH>nH,sf,starparticlesareproducedataxedstarformationeciencyperfree-falltime.Thedensitythresholdisafreeparameterofourmodeling,anditschoicedependsontheminimummassthatisallowedforstarparticlesandtheminimumcellresolution(seeTable 4-2 ).Inourmodel,,thexedstarformationeciencyperlocalfree-falltime,isanotherfreeparameter.Weassumeaducialchoiceof=0.02,motivatedbyobservationsofGMCsandtheirstar-formingclumpswhichsuggestfairlylowanddensity-independentvaluesof(see,e.g., Zuckerman&Evans , 1974 ; Krumholz&Tan , 2007 ).Notethatwedonotimposecertainrequirementsusedinotherstarformationroutinessuchasthepresenceofaconverginggasoworthatthegasstructuremustbegravitationallyboundinorderforstarformationtoproceed.However,wenecessitatethatonlycellsbothatthenestlevelofAMRandwithtemperatureslessthan3000Kareallowedtoformstars.Thispreventsstarformationfromoccurringinthehot,densematerialofshockfronts.WhenacellreachesthethresholdnH,sf,astarformationrateisassessedandthenthemassofstarsthatshouldbeformedinagiventimestepiscomparedtotheminimumparticlemass.Themassofthestarparticleisdeterminedby M?=x3 tt,(4{1)whereisthegasdensity,x3isthecellvolume,tisthenumericaltimestep,andtisthefree-falltimeofgasinthecell(wheret=(3=32G)1=2isused). 133

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Topreventanextremelylargenumberoflow-massparticlesfromformingandgreatlyslowingthecalculation,weemployanadditionalrequirementofaminimumstarparticlemass,M?,min.IfthecalculatedM?1)the(stochastic)starformationprocessisallowedtooccuratxedeciencyperlocalfree-falltime.However,ifthecellismagneticallysubcritical(i.e.,<1),themagneticpressureisdeemedstrongenoughtowithstandgravitationalcontraction,preventinganystarsfromformingwithinthatcell.Notethattheothercriteria(i.e.,nestrenementlevel,T<3000K,M?>M?,min)areretained. 134

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Wenotethatalthoughthetruemass-to-uxdependsonthegeometryoftheentireuxtubeandcannotbecompletelyconnedtoalocalizedquantity,thisstillactsasarst-ordercorrection.Further,wesampledierentvaluesofc1inourvariousmagnetically-regulatedstarformationmodels,eectivelyaccountingforvariousgeometriesthroughthisparameter.Ultimately,wecomparemodelswiththreedierentrealizationsofstarformation:(\noSF")nostarformation,(\SF")density-regulatedstarformation,and(\SF-Breg")magnetically-regulatedstarformation.Withinthe\SF"suiteofmodels,weexploreanarrayofnH,sfvalues,whilethe\SF-Breg"studyvariesvaluesofc1.Table 4-2 listsallrunsperformedinthisstudy. 4.2.4.3StarparticledynamicsOncethestarclusterparticlesarecreated,theirmotionsarecalculatedasacollisionlessN-bodysystem.Notethesearenotsinkparticles:thereisnogainofmassbygasaccretion(whichweexpecttoberealisticduetotheactionofstellarwindsfromtheyoungstars).Theyinteractgravitationallywiththegasviaacloud-in-cellmappingoftheirpositionsontothegridtoproduceadiscretizeddensityeld.Note,however,thatgravitationalinteractionsbetweenstarclusterparticlesarethussoftenedtotheresolutionofthegrid.Inrealitythedistributionofstellarmassrepresentedbythestarclusterparticlewouldbespreadout,butbyamountsthatarenotsetbythelocalgasdensity.Thusthedetailedstructureofgravitationallyboundstarclusters,madeupofmanysimulationstarclusterparticles,isnotespeciallywellmodeledinoursimulations.However,theearlystagesofthespatialandkinematicdistributionofthestars,especiallyingas-dominatedregions,shouldbemoreaccuratelyfollowed. 4.3ResultsWeperformanalysisofeachthesimulations,comparingandcontrastingstarformationmodelsaswellascollidingvs.non-collidingcases.Inparticular,wediscuss:morphologyofclusters(x 4.3.1 );starformationrates(x 4.3.2 );spatialclustering(x 4.3.3 );andstarkinematics(x 4.3.4 ). 135

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Figure4-2. TimeevolutionofmasssurfacedensityforallcollidingcaseswithSF.Thetopthreerowsdisplaythedensity-regulatedSFrunswhilethebottomthreerowsdisplaythemagnetically-regulatedSFruns.Snapshotsat2.0,3.0,4.0,and5.0Myrareshown.Starparticlesareoverplottedasblackpoints. 4.3.1ClusterMorphologyThemorphologyofthegasandthestarsareshowninFigs. 4-2 and 4-3 .FortheSF-colcases,starclustersbegintoformnearthet=4.0Myrmark,eachofwhichislocatedwithinthemaincollidinglamentaryregion.Theseclustersappeartoforminrelativelyevenlyspacedintervalsandareco-locatedwithoverdenseclumpsattheintersectionoflaments. 136

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Figure4-3. Timeevolutionofmasssurfacedensityforallnon-collidingcaseswithSF.Thetopthreerowsdisplaythedensity-regulatedSFrunswhilethebottomthreerowsdisplaythemagnetically-regulatedSFruns.Snapshotsat2.0,3.0,4.0,and5.0Myrareshown.Starparticlesareoverplottedasblackpoints. Byt=4.5Myr,thenorthwestclustershavegrownandmergedintoonedominantstarclusterlocatednear(x,y)=(5pc,10pc).ThislargeclusterappearstocontainmultiplepopulationsofsmallerstarclustersthathavemergedtogetherthroughacombinationofthegravitationalattractionandlargescaleowsoftheGMCcollision.Thespatiallyseparatedclustersfromearliertimeshavegrowninpopulationandaremovingtowardthemaincluster, 137

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whileafewsmallerclustersarecontinuingtoformalongthestill-collidingdenselamentarygas.Byt=5.0Myr,themaincluster,whichhasgrowntoafewthousandstars,isco-locatedwiththemajorityofthedensegas,asmorestarclustersareformedinthevicinity.Thereexistsasmallpopulationofindividualstarsthathavepresumablybeendisruptedandhaveleftthemaincluster.ThefactoroftwovariationsinnH,sfdonotgreatlyaltertheoverallclustermorphology.However,therearesmalldierencesintotalclusternumberaswellasclustersizecorrespondingtothedensitythreshold,withincreasingthresholdsleadingtoreducedstarandclusterformation.Asanexample,byt=5.0Myr,thecollapsinglamentlocatednear(7pc,15pc)hasformedtwoclustersinSF-05-col,oneclusterinSF-1-col,andnoneinSF-2-col.Incontrast,theB-reg-colmodelsresultinmuchearlierstarformation,initializingpriortothet=2.0Myrmarkineachcase.Starsalsoforminamuchlessclusteredmanner,butarestilllocatedalonglamentaryregions.Theonsetofstarformationinthemagnetically-regulatedcasesoccursdirectlyatthecollisionalinterfacebetweenthetwoGMCs.Astimeprogresses,starscontinuetoformprimarilyinthepost-shockcollidingregions,butwithsomestarformationscatteredthroughouttheGMCs.Byt=4.0Myr,alargeprimaryclusterhasformedaroundthedenselamentaryregionnear(5pc,10pc)andalongthemaincollisionallament.ThiscontinuestogrowandcollapsealongwiththegasfromtheGMCs.WithintheB-reg-colmodels,increasingvaluesofc1resultinreducedstarformationoverall,thoughthelocationswherestarformationiscentereddonotchange.Relativetothedensity-regulatedmodels,themagnetically-regulatedroutinesresultinmuchgreaterstarformationandamuchlargercentralcluster.ComparedtotheGMCcollision,theSF-nocolcaseisrelativelyquiescentuntilmuchlaterintothesimulation,asstarformationisinitiatedaftert=4.0Myrasopposedtobefore.Thestarsforminconcentratedclustersatthedensitypeakslocatedwithinthelamentarystructuresformedbyturbulence.Again,smallvariationsexistbetweenthedierentnH,sfthresholds,butthesitesofstarformationaremoreorlessconsistentbetweenSF-colmodels. 138

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Byt=5.0Myr,solitaryclustershaveformedinlamentsnear()]TJ /F5 11.955 Tf 9.3 0 Td[(14pc,)]TJ /F5 11.955 Tf 9.3 0 Td[(31pc)and()]TJ /F5 11.955 Tf 9.3 0 Td[(6pc,15pc).Inthemorestronglyconcentratednetworkoflamentscenteredabout(25pc,15pc),veclustershaveformedinSF-05-nocol,threeinSF-1-nocol,andnoneinSF-2-nocol.ComparedtocaseswheretheGMCsarecolliding,thestarformationisspatiallymuchmorespreadoutandisolated.TheSF-B-nocolcasesalsoresultinreducedstarformationwithlaterinitializationtimeswhencomparedtothemagnetically-regulatedcollidingcases.ThestarformationisnotconcentratedatanyGMCinterface,butoccursinwithinlaments.TheSF-Breg-05-nocolcaseresultsinsmallamountsofstarformationbyt=2.0Myr,whileSF-Breg-1-nocolbarelyhasanyandSF-Breg-2-nocolhasnone.Thistrendcontinuesthroughthetimeevolution,withstarformationcenteringonthedensernetworksoflamentsanddecreasingwithincreasingvaluesofc1.Again,thereismuchgreaterstarformationrelativetothedensity-regulatedmodels. 4.3.2StarFormationRatesandEcienciesThetotalstarformationrateandoveralleciencyofvariousscenariosareimportantquantitiesthatmayinformusofthemainconstituentsoftheglobalgalaxystarformationrateandeciency.Foreachofthestarformationmodels,weshowstarformationratesandecienciesinFig. 4-4 .Wecalculatethetotalmassofthestarparticlesovertime,measuredrelativetopost-collisionevolutionaswellasint=4.35Myr.Inaddition,thetotalmassisnormalizedtoanoverallstarformationeciencyofthetwooriginalGMCs.Weseethatforthedensity-regulatedcollidingcases,starclusterformationinitiatesatt=3.3Myrafterthecollisionwithaspreadof0.1Myrdependingontheparticulardensitythreshold.TheSFRgrowsatafairlyrapidpace,reachingamaximumstarformationrateof0.08M=yrat4.3Myr(t).TheSF-2-colcase,whilebeginningstarformationslightlylater,actuallyreachesthehighestSFR,thoughalldensity-regulatedSF-colmodelsconvergeneartforbothSFRandtotalstarmass.Atthistime,thestarformationeciencyhasreached7%ineachdensity-regulatedcase.Behaviorchangesnotablyafter1.0t.Thestarformationratesdropdownto0.02)]TJ /F5 11.955 Tf 12.03 0 Td[(0.03M=yrthenagainincreasesto0.05M=yr.This 139

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Figure4-4. (Top:)Thestarformationrateovertime.TheSF-colcaseisshowninblue,whiletheSF-nocolcaseisshowningreen.(Bottom:)Thetotalmassinstarsovertimeforeachcase,inbothphysicaltimesincetheinitialconditionsaswellasfreefalltime.ThestarformationeciencyisnormalizedrelativetothetotalinitialmasswithinthetwoGMCs(1.86105M). shiftinSFRisalsoseeninthetotalstarmass,withtotalstarformationeciencyincreasingmoreslowlyto12%by5.0Myr.Forthemagnetically-regulatedcollidingcases,starformationinitiatesnear1Myr.ThetotalstarmassandSFRvarybyfactorsofafewbetweenthevariousSF-Bregcases,butbyt,themodelsarealsorelativelywell-convergedat0.06M=yr.Relativetothedensity-regulatedruns,theSFRisgreaterpriortojustbefore4Myr,thenoscillatesslightlyandreturnstothesamevalueby5Myr.Theoveralltotalstarmassis1.2timesthatofthedensity-regulatedcases,resultinginastarformationeciencyof15%.IntheSF-nocolcases,starformationinitiatesmuchlater,att=4.6Myr,withSFRsoforder10)]TJ /F4 7.97 Tf 6.58 0 Td[(3M=yrgrowingbyafactorofafewuntilthesimulationendtimeoft=5.0Myr.Thesemodelsdonotconverge,withroughlyfactorsoftwoinSFRseparatingeachmodel,and 140

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showslightoscillations.ThestarformationeciencyfollowsasimilarincreaseastheSF-colcase,butreachingjust0.01-0.1%bytheendofthesimulation.Themagnetically-regulatednon-collidingmodelsinitiatestarformationearlierwhencomparedtothedensity-regulatednon-collidingmodels,withanonsetbeginningneart=2.0-2.5MyrfortheSF-Breg-1-nocolandSF-Breg-2-nocolmodels,respectively,whiletherststarsinSF-Breg-0.5-nocolbeginmuchearlier,aroundthesametimeasthecollidingcounterpart.Despitetheselargeinitialdierences,theSFRsandtotalstarmassesgrowinasimilarmannerandconvergeovertime.Byt,themodelsarewithinafewpercentofeachother,withSFRsof0.05M=yrandSFecienciesof1%.Notably,thestarformationbehaviorremainsconstantthroughthettransition,unlikebothcollidingstarformationmodels. 4.3.3SpatialClustering 4.3.3.1Minimumspanningtree Figure4-5. MSTfortheSF-col(left)andSF-nocol(right)casesatt=5.0Myrwhenviewedfromthez-direction.EachstarparticleisrepresentedbyablackdotwhilebranchesoftheMSTareshowninred.N?isthetotalnumberofstars,while m, s,andQarethenormalizedmeanedgelength,normalizedcorrelationlength,andtheratioofthetwo,respectively. Onemethodofstudyingthehierarchicalstructureofclustersisthroughtheuseoftheminimalspanningtree(MST).TheMST(developedbyBarrow,Bhavsar&Sonoda1985)isatechniqueborrowedfromgraphtheoryinwhichalloftheverticesofaconnected,undirected 141

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Figure4-6. Qvs.time.TheevolutionofQisshownforeachmodel,asdenotedbythelabelcolor.Calculationstakenasviewedfromx,y,andzareshownassolid,dashed,anddash-dottedlines,respectively.ThethresholdofQ0=0.785isshownasthedottedblackline. grapharejoinedsuchthatthetotalweightingforthegraphedgesisminimized.Inthecaseofstarclusters,theprojectedeuclideandistancesbetweentheindividualstarsactsastheedgeweight.Tostudythehierarchicalstructureofacollectionofstars, Cartwright&Whitworth ( 2004 )introducedadimensionlessparameter,Q,whichcandistinguishandquantifybetweenradialclustering(i.e.,morecentrallyconcentrated)vs.fractaltypeclustering(i.e.,moresubstructure).Specically, Q= s m.(4{4)Thenumeratoristhenormalizedcorrelationlength s= d Rcluster,(4{5)where disthemeanpairwiseseparationdistancebetweenthestarsandRclusteristheoverallclusterradius,calculatedasthedistancefromthemeanpositionofallstarstothefarthest 142

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Table4-3. Parametersofobservedclusters clusterQ s m Taurus0.470.550.26IC23910.660.740.49Chameleon0.670.630.42Opiucus0.850.530.45IC3480.980.490.48 star.Thedenominatoristhenormalizedmeanedgelength m=PN?)]TJ /F4 7.97 Tf 6.59 0 Td[(1iei (N?)]TJ /F4 7.97 Tf 6.58 0 Td[(1) q N?A (N?)]TJ /F4 7.97 Tf 6.59 0 Td[(1),(4{6)whereN?)]TJ /F5 11.955 Tf 12.22 0 Td[(1isthetotalnumberofedges,eiisthelengthofeachedge,andA=R2clusteristheclusterarea.ThethresholdofQ0=0.785determinesaquantitativethresholdofeitherradialclustering(Q>Q0)orfractalclustering(Q
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Figure4-7. Position-velocitydiagramsforthedensity-regulatedstarformationcollidingcase(SF-col;leftcolumn)andnon-collidingcase(SF-nocol;rightcolumn)at5.0Myr.Thestarparticlesareoverplottedinblack.Thescalingisderivedfromsynthetic13CO(J=1-0)lineintensitiesthroughvelocitybinsofv=0.212kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Thegraycrossindicatesthepositionofthecenterofmassandthesolidwhitelineshowstheintensity-weightedlinearvelocitygradient(dvlos=ds)acrosseachcloud. concentration.Qbeginsasteadyincreasefrom0.2to0.4untiltheendofthesimulationatt=5.0Myr.TheSF-nocolcase,ontheotherhand,hastherststarclusterformingatt=4.6MyrwithQ0.6.ThissubsequentlydropsinasimilarmannerastheSF-colcase,assmallstarclustersformfromwithinthespatiallyseparateddenselamentsoftheGMCs. 4.3.4KinematicsThekinematicsofyoungstarsandtheirsurroundinggashasbeenstudiedinordertotrytoshedlightontheinitialconditionsoftheirorigin.Oursimulationsoerauniqueopportunitytoinvestigatetheresultingkinematicsofboth13CO-denedgasaswellasthestarsthatformundervariousstarformationscenarios. 144

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Table4-4. Gasandstarkinematics CaseLoSdvlos dsgasstars vgas vstars v(kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1pc)]TJ /F4 7.97 Tf 6.58 0 Td[(1)(kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)(kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)(kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)(kms)]TJ /F4 7.97 Tf 6.59 0 Td[(1)(kms)]TJ /F4 7.97 Tf 6.58 0 Td[(1) SF-colx0.19173.802210.00-0.21190.8434-1.0553y0.26784.39239.690.4313-1.30831.7396z0.27244.08639.80-0.5662-1.36450.7983RMS0.2474.1019.830.4291.1951.262SF-nocolx0.08841.77611.521.00350.49890.5046y0.01351.23460.92-0.1468-0.43020.2834z0.06642.07351.66-1.1875-1.90250.7150RMS0.06431.7301.400.9021.1620.531 Ourgasstructuresaredenedusingsynthetic13CO(J=1-0)emission,basedonthesameobservationalassumptionsasPaperII(i.e.,GMCsareatadistanced=3kpcandwebinwithaspectralresolutionof0.212kms2).Fig. 4-7 showsposition-velocitydiagramsfortheSF-colandSF-nocolcases.Fromthisinformation,wecancalculatevelocitygradientsofthegas,thevelocitydispersionofthegasandthestars,the13CO-weightedaveragevelocitiesofthegas,themass-weightedaveragevelocitiesofthestars,andtheosetbetweenthetwo.Table 4-4 summarizesthevaluesfordvlos ds,gas,stars, vgas, vstars,and vwhenviewedfromthex,y,andzdirections.ThevelocitygradientfortheSF-colcasehasanRMSvalueof0.247km/s/pcwhiletheSF-nocolcase0.0643km/s/pc,approximately4timessmaller.Thevelocitydispersionsshowasimilardistinction,withgasintheSF-colcaseat4.101km/swhilegasintheSF-nocolcasehas1.730km/s.TheSF-colcaseformsstarswithstars,RMS=9.83km/swhiletheSF-nocolcaseformsstarswithstars,RMS=1.40km/s.Withafactorof7dierenceinstars,thisparametermaybeanimportantclueintothestarformationhistoriesofclusters.IntheSF-colcase,the13CO-weightedaveragevelocitiesarefoundtobe vgas,RMS=0.429km/swhiletheSF-nocolcasehasvelocitiesat vgas,RMS=0.902km/s.However,themass-weightedaverageaveragestarvelocitiesintheSF-colcasewere vstars,RMS=1.195km/sandintheSF-nocolcasewere vstars,RMS=1.162km/s.Investigatingtheresultingoset 145

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betweenmeangasandstarvelocitiesrevealdierences,with( v)RMS=1.262km/sinthecollidingcaseand0.531km/sinthenon-collidingcase.DaRioetal.(inprep.)observedintheOrionNebulaClusterosetsbetweengasandstarvelocitiesofapproximatelyvr)]TJ /F5 11.955 Tf 22.43 0 Td[(0.5km/s,butupto)]TJ /F5 11.955 Tf 9.3 0 Td[(1.0to)]TJ /F5 11.955 Tf 9.3 0 Td[(1.5km/sinsomeregions.Whileindividualkinematicpropertiesofthegasandstarsobservedinvariousclustersmaybeexplainedbyothermeans(e.g.,turbulentmotionsorstellarfeedback),wepresentsignsthat,whentakenasawhole,mayprovidesignaturesofaformationscenarioviaGMCcollision. 4.4DiscussionandConclusionsWehaveimplementedtwoclassesofstarformationsub-gridroutinesintotheMHDcode:adensity-regulatedmodelandanewmagnetically-regulatedmodel.Varyingkeyparametersforeachstarformationroutine,weexploredthestarformationratesovertime,thespatialclusteringofthestars,andstellarkinematics.Inthedensity-regulatedcases,collidingmodelsresultedinindividualstarclusters,locatedinclumpswithinlaments,mergingtoformonelarge,dominantclusterwithapopulationofapproximately5000stars.Magnetically-regulatedcollidingmodelsledtostarformationthatwaslessclusteredbutstilloccurredalonglaments.Thenon-collidingcasesweremuchmorequiescent,withdensity-regulatedroutinesformingstarsrelativelylater,injustafewseparatedclustersoftensofstarparticleseach.Themagnetically-regulatednon-collidingcasesalsosawquiescent,dispersedstarformation,stillfollowingthelamentaryregions,butatafairlylowrate.Overall,themagnetically-regulatedmodelsledtohigherstarformationrelativetothedensity-regulatedmodels.Wealsofoundthatinallmodels,amuchgreaternumberofstarsarecreatedinthecollidingGMCsscenario.Thecollidingcasesformstarsapproximately1Myrearliercomparedtothenon-collidingcasesandcreatealargecentralclusterwith10timeshigherSFRsandSFeciencies.TheMSTQparameterwasusedtoinvestigateclusteringpropertiesofthestar,ndingboththeSF-colandSF-nocolcasetohavefairlystrongfractalclustering.However,the 146

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collidingcaseshowsatrendtowardsradialclusteringasitevolves,whilethenon-collidingcasestaysatverylowQvalues.Kinematically,thevelocitygradientsofthecluster-formingcollidingcaseisshowntobeafactorof4timesgreaterthanthatofthenon-collidingcase.Thevelocitydispersionsarealsosimilarlydistinct,withthegasinthecollidingcloudsatovertwicethevelocitydispersionasgasinnon-collidingclouds,andstarvelocitydispersionofalmost10timesthatinthecollidingcasevs.thenon-collidingcase.Finally,anosetbetweentheaveragegasandaveragestarvelocitiesisfoundtobetwiceasgreatinthecollidingcasewhencomparedtothenon-collidingcase.Weconcludethatmuchlarger,morekinematicallydisrupted,andmorecentrallypeakedstarclustersforminGMCcollisions,whilenon-collidingGMCsformstarsinamuchmoreisolatedandquiescentmanner.GiventhesameinitialGMCs,acollisionmaytriggeranotherwiseearlieronsetofstarformation,withstarformationecienciesofupto10%perfree-falltimewithinthedenseregion. 147

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CHAPTER5CONCLUSIONSANDFUTUREAPPLICATIONS 5.1SummaryandConclusionsInChapter2,wedevelopedthenumericalframeworkfortestingGMCcollisions.PDR-basedheatingandcoolingfunctionswerecreated,enablingtreatmentofnon-equilibriumtemperaturestatesandprovidingestimatesofemissivitiesofvariouscoolinglineswithwhichtomakeobservationalpredictions.Fromouridealized2DMHDmodelsofGMCcollisionsandtheireectonapre-existingoverdenseclump,weinvestigatedhowtheevolutiondependedonmagneticeldstrength,magneticeldgeometry,collisionvelocity,andimpactparameter,comparingisolatedversuscollidingclouds.Wefoundfactorsof2)]TJ /F5 11.955 Tf 11.1 0 Td[(3increaseinmeanclumpdensityfromtypicalcollisions,withstrongdependenceoncollisionvelocityandmagneticeldstrength,butwereultimatelylimitedbyux-freezingin2Dgeometries.Forgeometriesenablingowalongmagneticeldlines,wesawgreaterdegreesofcollapse.Fromour13COintegratedintensitymapsandspectra,wefoundthattheratioofJ=8-7tolower-JemissionisapowerfuldiagnosticprobeofGMCcollisions.InChapter3,weexpandedourmodelto3Dandaddedsupersonicturbulenceaspartoftheinitialconditionoftheclouds,exploringasimilarbutreducedparameterspace.Weanalyzeddensityandtemperaturemorphologies,relativeorientationsbetweenmagneticeldsandlamentarystructures,themagneticeldstrengthtodensityrelation,PDFsofmasssurfacedensity,integratedintensities,gaskinematics,andvirialparameters.Weprovidedavariedsuiteofdiagnosticsofcloudcollisionsandconcludedthat,comparedtostructuresformedinnon-collidingGMCsimulations,thoseformedfromcollisionswerermorelikelytoleadtoconditionsnecessaryforcreationofdense,self-gravitatinggasclumpsandthusstarclusterformation.InChapter4,weimplementedvariousstochasticstarformationroutinesintotheMHDcode,especiallydevelopingnewmagnetically-regulatedstarformationsub-gridmodels.We 148

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exploredthestarformationrateovertime,thespatialclusteringofthestars,andstellarkinematics.Insummary,wehavecarriedoutthemostrealisticsimulationstodateoftheGMCcollisionprocessandhowthismaytriggerstarformation.Herewebrieydiscussseveralapplicationsandfuturedirectionsofthiswork. 5.2FutureApplicationsThecloudcollisionmodelsdevelopedinthisdissertationcanbeextendednumericallyaswellasfurthertestedobservationally.Inthissection,wediscussongoingprojectsinwhichthisworkisbeingapplied,aswellaspotentialfutureprojects.Implementationofnon-idealMHDbyincludingambipolardiusionwillexpandonthephysicsofthemodel,moreproperlytreatingtheseparatepopulationsofionsandneutralsinthegas.ComparisonofobservedIRDCsusingthe[CII]tracercanprovideinsightintogasattheboundariesofGMCsandactasadditionalmodesofcomparisonbetweencollidingandnon-collidingGMCs.WedescribeanongoingStratosphericObservatoryforInfraredAstronomy(SOFIA)projecttomap[CII]inIRDCs.AseparatecomparisonfortheSerpensSouthIRDCisplanned.SerpensSouthisayoungclusterformingregionandacandidateofcollisionsbetweenlamentarystructures.Finally,oncestarshaveformed,PaperIIIpredictsdistinctkinematicpropertiesoftheresultingstars.WeaimtocompareresultswiththeINfraredSpectraofYoungNebulousClusters(IN-SYNC)survey. 5.2.1AmbipolarDiusionInnature,themass-to-uxratioisnotxedasitisinideal-MHDsimulations.Duetothedriftbetweenthepopulationofionsvs.neutrals,called\ambipolardiusion",themagneticeldcandiuseandasgasowsperpendiculartotheeldlines.Thisprocessmaybecomeimportantinhighdensityregions,expeditingthecollapseofgas.Workiscurrentlyunderway(Christieetal.,inprep.)toimplementambipolardiusionintotheENZOcodeandtocomparethecurrentducialmodelswithnon-idealMHDmodels. 149

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5.2.2[CII]MappingofIRDCsWehaveproposedtousethemappingcapabilitiesoftheSOFIAupGREATinstrumenttomap[CII]emissionaroundasampleof4IRDCs(Fig. 5-1 ).Theseobjectshavebeenpreviouslystudiedextensivelybyourresearchgroup,focusingprimarilyonthedensegascomponents.However,thelowerdensitymaterialhasnotbeeninvestigated,thusmotivatingourproposal.[CII]tracesthePDR,whichexistsintheregionsenvelopingGMCsandIRDCs.Thusitcanprobethegasthatisjoiningthecloudandbecomingmolecular.ThekinematicsignaturesofthelowerdensitymaterialmayplayacriticalroleintheformationofIRDCsandmaybeusedtohelpdierentiatebetweendierenttheoreticalmodelsofIRDCformation.Inparticular,wewishtocomparethe[CII]integratedintensitymapsandspectrawithoursimulations,checkingthepredictionsbetweenrelativelyisolateddecayingturbulencevs.triggeringbyconvergingmolecularowsfromGMC-GMCcollisions. 5.2.3ApplicationtoSerpensSouthOneimportantpredictionfromourGMCcollisionmodelsliesintherelationshipbetweenmagneticeldmorphologyandlamentarygasstructures.Thus,aregionofparticularinterestisSerpensSouth,averyyoungcluster-formingIRDC(0.5Myr).WithinSerpensSouth,thereexistsahighfractionofClassIprotostarsandabundantCCS.CCSisamoleculartracerofgasintheprestellarphase.Thedynamicalstate( Tanakaetal. , 2013 )ofSerpensSouthhasbeenstudiedindetail.Extensivepolarizationmeasurementsofthemagneticeldorientationhasalsobeenperformedonthisregion( Sugitanietal. , 2011 ,seeFig. 5-2 ).Perhapsmostnoteworthyisthatithasispotentiallyasiteofactivelamentcollisions( Nakamuraetal. , 2014 ).MultiplepeaksinthePDF,aswellasextendedblue-skewedvelocityproleshavebeenmeasured,indicatingthatadynamicinteractionisoccurringinthisregion. Nakamuraetal. ( 2014 ),suggeststhatdenselamentswereformedfromthemergingofsmallerlamentscreatedbylocalturbulence,whichthemselvesareanaturaloutcome.The 150

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Figure5-1. (from Kainulainen&Tan 2013 )NIR+MIRextinctionmapsofIRDCsC(topleft),F(topright),G(bottomleft)andH(bottomright),chosenfortheSOFIA[CII]mappingproposal.Thegreenellipsesshowthe Simonetal. ( 2006a )-denedIRDCregion(fromMSXdata),whilethedottedsquaresandrectanglesshowtheregionsusedbyKainulainen&TantomeasureprobabilitydistributionfunctionsofcolumndensitiesthatarecompleteforAV>7mag.Thesizesoftheregionsofproposed[CII]mappingapproximatelycorrespondtothegreenellipses. 151

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Figure5-2. (from Sugitanietal. 2011 )H-bandpolarizationvectormaptowardSerpensSouth,superposedonthe1.1-mmdust-continuumimageofASTE/AzTEC( Gutermuthetal. , 2011 ).YSOsidentiedby Gutermuthetal. ( 2008 )and Bontempsetal. ( 2010 )arenotincluded,butthoseidentiedby Gutermuthetal. ( 2008 )areindicatedbyred(class0/I)andblue(classII)opencircles. 152

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mergingofsmallerlamentsappearstobemoredominantthanmassaccretionalongthelamentsintermsoflassloadingtocluster-formingregions.Thus,directcomparisonandnumericalmodelingspecictothepropertiesobservedinSerpensSouthmayprovideacasestudyforobservationalpredictionswithboththemolecularlinetracersaswellasthepolarizationmodels. 5.2.4ApplicationtoIN-SYNCTheIN-SYNCprogramisapartoftheSDSS-IIIApachePointObservatoryGalacticEvolutionExperiment(APOGEE),ahigh-resolutioninfraredspectroscopicsurveyspanningallGalacticenvironments.ThegoalofIN-SYNCistostudythekinematicsinstarformingregions.Thisisdonethroughaccuratelymeasuringtheradialvelocityofthousandsofyoungstarsandusingthemastracersofthephysicalprocessesgoverningtheformationandearlyevolutionofstars,planets,andstellarclusters.Thevelocitiesofyoungstarscanrevealhowdynamicswithinamolecularcloudinuenceprotostellarmassaccretionandtheonsetofmasssegregationandevaporationinstellarclusters.IN-SYNCiscurrentlyconductingkinematicalsurveysofthePerseusMolecularCloudandtheOrionstarformingregion.Throughthousandsofspectra,acompletekinematiccensusoftheyoungstellarpopulationofthesetworegionswillbetaken.Specically,itwillsearchfordynamicalsub-clusteringasevidenceofseparatestarformingevents,andcomparethedynamicsofthestarswiththatofthesurroundinggas.OnepreliminaryresultoftheIN-SYNCsurveyoftheOrionregion(DaRioetal.,inprep.,seeFig. 5-3 )istheobservationofasystematicosetinvelocityofthemeanradialvelocityofyoungstarscomparedtothatof13COemittinggas.Themagnitudeoftheosetisabout1km/s.Thesizeoftheosetsbetweenyoungstarsand13COemittinggascanalsobeexaminedinoursimulationsthatincludethestarformationsub-gridmodels. 153

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Figure5-3. (fromDaRioetal.,inprep.)Leftpanel:spatialdistributionoftheIN-SYNCtargets,overplottedona13COmapfrom Nishimuraetal. ( 2015 ).Redsymbolsindicateknownmembersfromtheliterature,magentasymbolsindicateknowncandidatemembersfrom DaRioetal. ( 2016 ),bluesymbolsindicatetheremainingsources,likelynon-members.Middleandrightpanels:position-velocitydiagramsforthetargets,comparedtoeither13COand12COdata,respectively. 154

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BIOGRAPHICALSKETCHBenjaminWuwasborninNorthridge,CA,in1987.In2001,hemovedtoOviedo,FLandattendedSeminoleHighSchool,graduatingin2005.HethenenrolledatDukeUniversityandgraduatedwiththeclassof2009withaBachelorofSciencedegreeinmathematicsandphysics.In2010,heenteredtheDepartmentofPhysicsgraduateprogramattheUniversityofFlorida.HereceivedhisMasterofSciencedegreeinphysicsin2012andreceivedhisPh.D.inphysicswithanastronomyminorinthesummerof2016. 161