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Probing The Initial Conditions of Massive Star and Star Cluster Formation

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Title:
Probing The Initial Conditions of Massive Star and Star Cluster Formation A Combined Approach of Mid-Infrared Extinction Mapping and Numerical Simulation
Physical Description:
1 online resource (166 p.)
Language:
english
Creator:
Butler, Michael J
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Astronomy
Committee Chair:
Tan, Jonathan Charles
Committee Members:
Telesco, Charles Michael
Lada, Elizabeth Anne
Fry, James N

Subjects

Subjects / Keywords:
dust -- extinction -- filaments -- gmcs -- irdcs -- ism
Astronomy -- Dissertations, Academic -- UF
Genre:
Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Understanding the formation processes of massive star and star clusters in giant molecular clouds (GMCs) is of vital importance to the subject of galaxy evolution, but despite this importance many open questions remain. In order to address these topics, an understanding of the initial conditions from which massive stars and star clusters form is needed. We investigate these initial conditions from two directions: first, an observational study focused on massive starless (or early stage) clumps and cores within GMCs that reveal themselves as Infrared Dark Clouds (IRDCs), and second, a theoretical/numerical study focused on the formation and dynamics of these structures. An important aspect of this thesis is the convergence and comparison of the results from these two approaches. We present a method of mid-infrared extinction mapping of IRDCs, which are thought to represent the initial conditions of massive star and star cluster formation. This technique involves modeling the diffuse Galactic background intensity at 8 microns behind the dark cloud, assessing the foreground emission, and then using the observed cloud intensities to calculate the optical depth through the cloud. The optical depth is then converted to the mass surface density by assuming a dust opacity and gas-to-dust ratio. We present extinction maps for ten of the most massive, high contrast IRDCs from the sample of Rathborne et al. (2006). The masses derived from our extinction maps are then compared to those derived from millimeter emission, finding generally good agreement. The second part of the thesis presents the results of a numerical study of cloud formation and evolution that utilizes the adaptive mesh refinement hydrodynamic code Enzo to simulate a kiloparsec-scale box extracted from a global galaxy disk simulation. By following the evolution of this region to high ~ 0.1 pc resolution, the structure and dynamics of clumps within GMCs can be analyzed and compared to our observational results. We explore the effects of realistic heating and cooling functions that include the effects of molecular line and dust cooling (e.g. tracking the atomic to molecular phase transition) down to the low temperatures observed in real clouds of T ~ 5 - 10 K. We do not yet include magnetic fields or local stellar feedback, deferring these potentially important processes to future studies.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
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.
Statement of Responsibility:
by Michael J Butler.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Tan, Jonathan Charles.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045942:00001

MISSING IMAGE

Material Information

Title:
Probing The Initial Conditions of Massive Star and Star Cluster Formation A Combined Approach of Mid-Infrared Extinction Mapping and Numerical Simulation
Physical Description:
1 online resource (166 p.)
Language:
english
Creator:
Butler, Michael J
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Astronomy
Committee Chair:
Tan, Jonathan Charles
Committee Members:
Telesco, Charles Michael
Lada, Elizabeth Anne
Fry, James N

Subjects

Subjects / Keywords:
dust -- extinction -- filaments -- gmcs -- irdcs -- ism
Astronomy -- Dissertations, Academic -- UF
Genre:
Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Understanding the formation processes of massive star and star clusters in giant molecular clouds (GMCs) is of vital importance to the subject of galaxy evolution, but despite this importance many open questions remain. In order to address these topics, an understanding of the initial conditions from which massive stars and star clusters form is needed. We investigate these initial conditions from two directions: first, an observational study focused on massive starless (or early stage) clumps and cores within GMCs that reveal themselves as Infrared Dark Clouds (IRDCs), and second, a theoretical/numerical study focused on the formation and dynamics of these structures. An important aspect of this thesis is the convergence and comparison of the results from these two approaches. We present a method of mid-infrared extinction mapping of IRDCs, which are thought to represent the initial conditions of massive star and star cluster formation. This technique involves modeling the diffuse Galactic background intensity at 8 microns behind the dark cloud, assessing the foreground emission, and then using the observed cloud intensities to calculate the optical depth through the cloud. The optical depth is then converted to the mass surface density by assuming a dust opacity and gas-to-dust ratio. We present extinction maps for ten of the most massive, high contrast IRDCs from the sample of Rathborne et al. (2006). The masses derived from our extinction maps are then compared to those derived from millimeter emission, finding generally good agreement. The second part of the thesis presents the results of a numerical study of cloud formation and evolution that utilizes the adaptive mesh refinement hydrodynamic code Enzo to simulate a kiloparsec-scale box extracted from a global galaxy disk simulation. By following the evolution of this region to high ~ 0.1 pc resolution, the structure and dynamics of clumps within GMCs can be analyzed and compared to our observational results. We explore the effects of realistic heating and cooling functions that include the effects of molecular line and dust cooling (e.g. tracking the atomic to molecular phase transition) down to the low temperatures observed in real clouds of T ~ 5 - 10 K. We do not yet include magnetic fields or local stellar feedback, deferring these potentially important processes to future studies.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
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.
Statement of Responsibility:
by Michael J Butler.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Tan, Jonathan Charles.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045942:00001


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Iwouldliketothankmyfamilyfortheirencouragementandsupportthroughoutthecourseofthisstudy.Ithankthechairandmembersofmysupervisorycommitteefortheirvaluableinsightsandsuggestionsindevelopingthisdissertation.Inaddition,Iwouldalsoliketothanktothankthefacultyandpost-docsattheUniversityofFloridawhohavecontributedinvariouswaystothiswork,specicallyPeterBarnes,ElizabethTasker,andSvenVanLoo. 4

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page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 11 CHAPTER 1ANINTRODUCTIONTOMASSIVESTARANDSTARCLUSTERFORMATION 13 2MIDINFRAREDEXTINCTIONMAPPINGOFINFRAREDDARKCLOUDSI.PROBINGTHEINITIALCONDITIONSFORMASSIVESTARSANDSTARCLUSTERS ...................................... 20 2.1Introduction ................................... 21 2.2IRDCSampleSelection ............................ 23 2.3IRDCExtinctionMappingMethods ...................... 24 2.3.1CorrectionforForegroundDustEmission .............. 25 2.3.2BackgroundEstimation ......................... 26 2.3.2.1Large-scalemedianlter(LMF) .............. 26 2.3.2.2Small-scalemedianlter(SMF) .............. 27 2.3.2.3OrthogonalstripsacrosslamentaryIRDCs ........ 28 2.4Results ..................................... 29 2.4.1MassSurfaceDensityMapsandDistributions ............ 29 2.4.2CloudandCoreMasses ........................ 32 2.4.3CorrelationsofCoreMmm=MSMFwithDensityasEvidenceforGrainGrowth .................................. 34 2.5Conclusions ................................... 36 3MIDINFRAREDEXTINCTIONMAPPINGOFINFRAREDDARKCLOUDSII.THESTRUCTUREOFMASSIVESTARLESSCORESANDCLUMPS ..... 52 3.1Introduction ................................... 53 3.2Saturation-BasedMIRExtinctionMapping .................. 57 3.3Results ..................................... 61 3.3.1IRDCProperties ............................ 61 3.3.2MassiveStarlessCoresandClumps ................. 61 3.3.2.1Locatingthecores ...................... 61 3.3.2.2Coreandclumppropertiesatthe60Menclosedmassscale ............................. 64 3.3.2.3Best-tpowerlawcores ................... 67 3.3.2.4Best-tBonnor-Ebertcores ................. 69 3.4Discussion&Conclusions ........................... 69 5

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..................... 92 4.1Introduction ................................... 93 4.2Methods ..................................... 94 4.2.1MIREXMappingwithMulti-frameArchivalIRACImages ...... 94 4.2.2CoreIdentication ........................... 97 4.3Results ..................................... 97 4.3.1OverallCloudMass ........................... 97 4.3.2Core&ClumpStructure ........................ 98 4.3.3ColumnDensityPDFAnalysis ..................... 99 4.4DiscussionandConclusions .......................... 101 5KILOPARSEC-SCALESIMULATIONSOFSTARFORMATIONINDISKGALAXIESI. ............................................ 106 5.1Introduction ................................... 106 5.2MethodsandNumericalSet-up ........................ 108 5.2.1SimulationCodeandInitialConditions ................ 108 5.2.2StarFormation ............................. 110 5.3CoolingandHeatingFunctions ........................ 112 5.3.1Extinction-DependentHeatingandCoolingFunctions ........ 113 5.3.2InitialConditions ............................ 115 5.3.3Results ................................. 116 5.4DiscussionandConclusions .......................... 117 6KILOPARSEC-SCALESIMULATIONSOFSTARFORMATIONINDISKGALAXIESII.STRUCTUREANDDYNAMICSOFFILAMENTSINGIANTMOLECULARCLOUDS ....................................... 123 6.1Introduction ................................... 124 6.2MethodsandNumericalSet-up ........................ 125 6.3PhysicalPropertiesoftheISM ........................ 127 6.4FilamentStructureandDynamics ...................... 128 6.4.1FilamentWidth ............................. 129 6.4.2ColumnDensityPDFsofFilaments .................. 130 6.4.3ClumpSeparation ........................... 131 6.4.4DynamicalStateofFilaments ..................... 132 6.5DiscussionandConclusions .......................... 134 7DISCUSSIONANDCONCLUSIONS ........................ 154 REFERENCES ....................................... 161 BIOGRAPHICALSKETCH ................................ 166 6

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Table page 2-1IRDCsample ..................................... 50 2-2Spitzertelescopebandandbackground-weighteddustopacitiespergasmass 50 2-3IRDCcores ...................................... 51 3-1IRDCsample ..................................... 74 3-2Clumpproperties ................................... 89 3-3Besttpowerlawcoreproperties .......................... 90 3-4PropertiesofIRDCcoreandclumpsample .................... 91 4-1IRDCclumpproperties ............................... 103 4-2Best-tpowerlawcores ............................... 104 5-1Setofsimulations .................................. 120 5-2ListoftheinitialGMCs ............................... 120 6-1Filamentproperties ................................. 136 7

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Figure page 2-1Backgroundspectrum ................................ 38 2-2SpitzerIRAC8mimageofcloudC ........................ 39 2-3DistributionofpixelintensitiesforCloudC ..................... 40 2-4Backgroundintensitycomparison .......................... 41 2-5GLIMPSE8mimageofcloudH .......................... 42 2-6ResultsofLMFandSMFstripanalyses ...................... 43 2-7SpitzerIRAC8mimagesofIRDCA-D ...................... 44 2-8IRDCsE-G ...................................... 45 2-9IRDCsH-J ...................................... 46 2-10Mass-weightedPDFsoftheIRDCsample ................... 47 2-11Mass-weightedPDFscomparedtosimulations .................. 48 2-12Comparisonofcoremassestimates ........................ 49 2-13Comparisontommdustemissioncoremasses .................. 50 3-1Radiativetransfermodel ............................... 74 3-2Effectofnitelterwidthonestimatesof 75 3-3mapsofIRDCsA-F ................................ 76 3-4mapsofIRDCsG-J ................................ 77 3-5PowerLawandBonnor-Ebertproletting .................... 78 3-6mapsofcoresA1,A2,A3,B1,B2,andC1 ................... 79 3-7mapsofCoreC2,C3,C4,C5,C6,andC7 ................... 80 3-8mapsofCoreC8,C9,D1,D2,D3,andD4 ................... 81 3-9mapsofCoreD5,D6,D7,D8,D9,andE1 ................... 82 3-10mapsofCoreE2,E3,F1,F2,F3,andF4 .................... 83 3-11mapsofCoreG1,G2,G3,H1,H2,andH3 ................... 84 3-12mapsofCoreH4,H5,H6,I1,I2,andJ1 ..................... 85 8

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.................. 86 3-14MasssurfacedensityversusmassdiagramsfortheIRDCcores ........ 87 3-15MasssurfacedensityvsmassdiagramsforallIRDCcores ........... 88 4-1CoreC1-9maps .................................. 103 4-2CoreC10-15maps ................................ 104 4-3PDFforcloudC .................................. 105 5-1gmapsoverthegalacticdiskofTT09 ...................... 120 5-2Visualextinctionvsdensityrelationship ...................... 121 5-3galongthez-axisforRun7 ............................ 121 5-4VolumerenderednumberdensityofRun7 .................... 122 5-5Starformationrateasafunctionofthegassurfacedensity ........... 122 6-1projectionsofthesimulationregionalongthez-axis .............. 137 6-2projectionsofthesimulationregionalongthey-axis .............. 138 6-3projectionsofthesimulationregionalongthex-axis .............. 139 6-4StarformationratehistoryforrunSF ........................ 140 6-5projectionsforFilamentaat3.0Myr ....................... 141 6-6projectionsforFilamentbat3.0Myr ....................... 142 6-7projectionsforFilamentcat3.0Myr ....................... 143 6-8projectionsforFilamentdat3.0Myr ....................... 144 6-9DensityslicesforFilamentaat3.0Myr ...................... 145 6-10DensityslicesforFilamentbat3.0Myr ...................... 146 6-11DensityslicesforFilamentcat3.0Myr ...................... 147 6-12DensityslicesforFilamentdat3.0Myr ...................... 148 6-13Mass-weightedcolumndensityPDFsforFilamentsa-d 149 6-14Meanprolesacrossthetenregions(seeFigure 6-15 )perpendiculartolamentc 150 6-15MassandvelocityprolesalongFilamentc 151 9

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152 6-17Fiege-PudritzdiagramalongFilamentc 153 10

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2-1 .Apartfrombeingrelativelynearby,thissub-sampleisinfactfairlyrepresentativeofthefull38cloudsampleofRathborneetal.(2006).Simonetal.(2006a)tellipsestoeachcloudbasedonMSXimages.WhiletheseellipsesareoftennotparticularlyaccuratedescriptionsoftheIRDCshapes,wewillutilizethemasconvenientmeasuresoftheapproximatesizesandshapesoftheclouds,especiallyforthesmallscalemedianltermethodofestimatingthebackgroundradiation(x ).TheSpitzertelescopehasanangularresolution(PSFFWHM)ofabout2arcsecat8m,whichcorrespondstoalinearscaleof0.029pcforacloudatadistanceof3kpc. 23

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2-1 &Table 2-2 ).Uncertaintiesinthedustmodelsincludetheextenttowhichicemantleshaveformedonthegrainsandtheextenttowhichthegrainshaveundergonecoagulation.TheIRbackgroundinthewavelengthrangeprobedbytheIRACbandsreceivesitsgreatestcontributionfromthediffuseISM(transientlyheatedsmallgrains)atBand4,i.e8m,comparedtothatfrombackgroundstars.IndividualstellarsourcesbecomemuchmoreprominentintheGLIMPSEimagesattheshorterwavelengths.ThusinthispaperwerestrictouranalysistoBand4images,leavinganalysisatotherwavelengthsandthewavelengthdependenceofextinctionforafuturestudy.Inthe8mband,weestimatearangeofdustopacitiespergasmassof6.311cm2g1,andadopt=7.5cm2g1,whichisformallyclosesttothemodelofOssenkopf&Henning(1994)withthinicemantlesthathaveundergonecoagulation 24

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.WeevaluateI,1fromtheobservedintensitiesderivedfromthecloudimages.Firstweconsidertheeffectsofforegrounddustemission. HR,(2)whereRisthegalactocentricradiusandHR=3.5kpcistheradialscalelength.ForeachIRDC,givenitsdistanceandGalacticlongitude,wecalculatetheratioofthecolumnofhotdustbetweenthesolarposition(atR=8kpc)andthetotalcolumnextendingouttoagalactocentricradiusof16kpc.ThisForegroundIntensityRatio,ffore,islistedinTable 2-1 foreachIRDC.Thenwederiveanestimateofthetrueintensityoftheradiationeldjustbehindthecloud,I,0,fromthatmeasuredviainterpolationofthecloudimages,I,0,obs,via 25

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2.3.2.1Large-scalemedianlter(LMF)ArelativelysimplewayofestimatingthediffuseIRbackgroundatagivenlocationbehindanIRDCistotakeamedianaverageofaregion(i.e.lter)centeredonthelocationofinterestandthatislargecomparedtothecloud.ThismethodwasappliedbySimonetal.(2006a)tomodeltheGalacticbackgroundfromMSXimagestothenidentifyIRDCsashighcontrastfeatures.Thismethodwillonlycapturebackgrounductuationsonscaleslargerthanthecloud.Indeedifthelterbecomestoosmall,i.e.withasizecomparabletothecloud,thenthederivedbackgroundwillbecomeinuencedbytheclouditselfandwillbeunderestimated.Forsimplicity,weadoptasquare-shapedlterforthismethod.AftersomeexperimentationandgiventhesizesoftheIRDCsinoursample,wechosealtersize 26

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2-2 .ThedistributionofpixelintensitiesisshowninFigure 2-3 .NotethattherewillbesomeregionswheretheestimatedvalueofI,1isgreaterthanthatofI,0.Thiscanarisebecauseofforegroundorbackgroundstars,orbecauseofsmalluctuationsinthetruebackgroundintensitythatarenotcapturedbythelargescaleaveragingusedinthemodel.ExaminingthedistributionofintensitiesintheLMF,wendtheFWHMofthedistribution.WesetthosepixelswithI,1>I,0+0.5FWHM,equaltoI,0sothatthederivedatthislocationiszero.Theseregionsaretypicallystarsorbrightemissionregions.TheremainingpixelswithI,1>I,0areallowedtoyieldanegativevalueof,whichhelpspreventsmallscaleuctuations(whichcanincludeinstrumentnoise)frombiasingthetotalmassinaregiontopositivevalues. 27

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)isrepeatedfortheregionoutsidethecloudellipse.ForeachimagepixelinsidetheIRDCellipseweestimateI,0,obsbyinterpolatingfromvaluesofI,0,obsoutsideoftheellipsethatarewithinanangulardistanceequaltothesemi-majoraxisoftheellipse,weightingbytheinversesquareoftheangularseparation,sothattheinnermostannulidominatetheaverage.ThisSmall-ScaleMedianFilter(SMF)methodisillustratedforcloudCintheright-handpanelsofFigure 2-2 .Here,andalsoinFigure 2-4 ,wecomparetheLMFandSMFestimatesofI,0,ndingtypicalvariationsatthelevelof.10%.A10%uncertaintyinI,0correspondstoamasssurfacedensityof0.013gcm2.Weconcludethatsystematicuncertaintiesinbackgroundestimationsetaminimumthreshold,belowwhichthemid-IRextinctionmappingmethodbecomesunreliable.Here,wealsonotethattheGLIMPSEimagesareoccasionallypronetocertainartifacts,e.g.changesindiffuseintensityalongdiagonalbandsandstripes,whichwillintroduceadditionaluncertaintiesintheseregions.TheSMFmethodimprovesupontheLMFmethodinreducingtheeffectoftheseartifacts. 2-5 ).Themedianimageintensitiesareevaluatedalongthesestrips(Figure 2-6 ).AlineartfortheIRbackgroundisttoregionsofthestripjudgedtobefreeofcloudmaterial.Thisisasomewhatsubjectiveprocess,sinceitishardtodistinguishbetweensmall-scalebackgroundvariationsandadditionalabsorbingcomponents.Nevertheless,weexpectthisestimateofthebackgroundintensityjustbehindthelamenttobemoreaccuratethantheLMFandSMFmethods,becausetheinterpolationbehindthelamentisoveraverysmallangular 28

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2-6 .Wealsoshowthederivedcolumndensities.Weseethatthevariationsinthebackgroundestimatesarerelativelysmall,atapproximatelythe10%level,similartothevariationsbetweentheLMFandSMFmethodsseenincloudC,andagaincorrespondingtomasssurfacedensityuncertaintiesof'0.013gcm2. 2.4.1MassSurfaceDensityMapsandDistributionsThemasssurfacedensitymapsderivedusingtheSMFmethodfortheremaining9cloudsarepresentedinFigures 2-7 2-9 withauniformscalerangein.TheseIRDCsexhibitavarietyofmorphologies,rangingfromverylamentary(cloudsFandH)tothosewithmoreapparentlysphericaldistributions(cloudsCandE).Thederivedmasssurfacedensitiesrangeupto'0.35gcm2,whichislikelytobedependentontheangularresolutionoftheimages.Asisapparentfromthe8mimages,someofthecloudshaveafewapparentlyembeddedsources,whichcauselocalizedregionsinthecloudstobeIR-bright,andthusnotamenabletoourextinctionmappingtechnique.InFigure 2-10 weshowthemass-weightedprobabilitydistributionfunctions(PDFs)with(evaluatedwiththeSMFmethod)ofthe10IRDCsusingtheregionsinsidetheirSimonetal.(2006a)ellipses.HerewedeneM0asthemassfraction,normalizedoverthedistributionofpixelswith>0.InFigure 2-11 weshowthesamePDFbutnowasafunctionof=,whereisthemean(area-weightedoverpixelswhichhave>0).ThevaluesofarelistedinTable 2-1 .Thedistributionsof=showthemostsimilarityfor=<0.5.Thehigh-sideofthedistributionsdoshowawidevarietyofproles:thereisalargerangeofmassfractionsatmasssurfacedensitiesthatare,forexample,3timesgreaterthanthemean. 29

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2-11 wemakeaqualitativecomparisonoftheseresultswiththeshapesof=PDFsresultingfromdifferentastrophysicalsourcesofturbulenceasmodeledintwosetsofpublishednumericalsimulations.Offner,Klein,&McKee(2008)presentedsimulationsofisothermaldriventurbulencetomaintainamean1DMachnumberofabout5inwhichself-gravitywasthenturnedonataparticulartime.OneexpectscloudswithhigherMachnumberturbulencetohavebroaderPDFsof=,asstrongershocksleadtogreatercontrastsbetweenregionsofcompressionandrarefaction.Cloudsthataremorestronglyself-gravitatingalsohavebroaderPDFs.Self-gravityalsotendstoskewthePDFstowardsthehigh-valueside.Figure 2-11 showstwoexamplesfromthesesimulations:oneisbeforeself-gravityhasbeeninitiated,soisrepresentativeofthe=PDFfromhydrodynamicMach4.7(1D)driventurbulencewithaBurgersP(k)/k2powerspectrum;theother,whichhasasimilarMachnumberof4.9,isafterself-gravityhasbeenallowedtodevelopstructuresforabout1meansimulationfree-falltimewhiletheturbulenceisstillbeingdrivenandissomewhatbroaderasaresult(14.2%ofthegasmasshascollapsedintosinkparticlesbythistime;thePDFisnormalizedtothetotalremaininggasmass).Nakamura&Li(2007)presentedsimulationsofmagnetizedprotostellaroutowdriventurbulence.Thedrivingscaleisrelativelysmallcomparedtothesimulationbox,andthesourcesarecentrallyconcentratedinthebox.Theirformationissporadicastheglobalclumpcollapses:weshowresultsafter1.5globalgravitationalcollapsetimes,whenabout80protostarshaveformed.Furthermorethereisalargescaledirectiontotheinitialmagneticeld,whichhasameandimensionlessux-to-massratioof0.52(in 30

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2-11 ;thesedistributionscorrespondtothemodelsshowninFigure7ofNakamura&Li[2007]).Acomparisonoftheobservedandsimulated=PDFsshowsthattheensembleoftheobserveddistributionscanbequalitativelyaccountedforbytherangeofsimulationsshown,althoughtheobservedIRDCsgenerallyhavenarrowerdistributions.However,wearenotabletoexcludethepossibilitythatothernumericalmodelsinvolvingdifferentphysics,e.g.alargerdegreeofmagneticsupport,and/orotherparameterscouldnotalsoexplaintheobservedclouds.SincemostoftheIRDCshaverelativelynarrowPDFscomparedtotheMach5turbulencemodels,thismayindicatethatthesecloudshavesmallerturbulentvelocitydispersionsand/orthatdynamicallyimportantmagneticeldsarepresent.Theprotostellaroutowdriventurbulencemodelsgenerallyhavebroader=PDFsthantheobservedIRDCs,andthismayindicatethesemodelsaremoreapplicabletolaterevolutionarystagesofstarclusterformation.However,theydoillustratetheeffectsofdynamicallyimportantlarge-scalemagneticeldsincreatingnarrower=PDFsforviewingdirectionsalongtheeldlines.ObservationsofthevelocitystructureoftheseIRDCsastracedbymolecularlineemissioncanhelptofurthertestthenatureofturbulencepresentintheearlystagesofstarclusterformation.Theextinctionmappingtechniquewehavepresentedalsoopensupthepossibilityofstudyingthe=PDFasafunctionofIRDC,Mandembeddedstellarcontent.Wedeferamorequantitativestudyofthesedependenciesandaquantitativecomparisonofthe=PDFstothoseformedinnumericalsimulationstoafuturestudy. 31

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2-1 welistthetotalcloudmassesderivedbytheLMFandSMFextinctionmappingmethods.Note,thesearethemassesinsidetheellipticalregionsdenedbySimonetal.(2006a)fromMSXimages,andthusarenotnecessarilyparticularlycloserepresentationsofthemorphologiesrevealedbySpitzerIRAC.Wendameanfractionaldifferenceof35%betweenthesetwomassestimates.WeregardtheSMFmassestimateasbeingmoreaccurate.Uncertaintiesinbothmethodswillgrowforlargercloudswithlowermeanmasssurfacedensities(i.e.smallercontrastsagainstthebackground).NotealsothisextinctionmappingtechniqueisnotsensitivetoauniformscreenofmatterthatcoversboththeregionoftheIRDCandtheregionwherethebackgroundisestimated.Acomparisonofextinction-derivedcloudmassesandmasssurfacedensitieswiththepropertiesinferredbymolecularlineemission,suchas13CO,willbepresentedinaseparatestudy(A.K.Hernandez&J.C.Tan,inprep.).Theextinctionmassestimatesareexpectedtobecomemoreaccurateathighvaluesof.EachoftheIRDCsinoursamplecontainsdensecoresstudiedbytheirmmdustcontinuumemissionbyRathborneetal.(2006).Werstidentifythosecoreswhichareamenabletoextinctionmapping(i.e.donotcontainbright8memission).CoresidentiedbyRathborneetal.(2006)asbeingmid-IRbright(labelled(e)inTable 2-3 )wereexcluded.WealsoexcludedcoresoverlappingwithfainterIRsources,iftheareaaffectedbythesourceswasgreaterthanabout10%ofthecore.Finally,weexcludedcoreswithverylowsurfacedensities,<0.02gcm2,sincetheextinctionmapping 32

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2-3 andFigure 2-12 wecomparethemmdustemissionandmid-IRdustextinctionmassestimates.Wendgenerallyverygoodagreementbetweenthesedifferentmethods.ThedispersionintheratiosoftheLMFandSMFestimatesisabout15%.Comparingtothe 33

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2-13 .Thebesttpowerlawrelationis(Mmm=MSMF)/n0.33H,SMF.ConsideringtheSpearmanrank-ordercorrelation,theprobabilityofachancecorrelationis0.0036.SinceMSMFandnH,SMFarecorrelatedviatheobservableSMF,wealsoexaminethecorrelationof(Mmm=MSMF)withMSMF,SMF(Figure 2-12 ),coreradius,r,andcoredistance(Figure 2-13 ).Wendprobabilitiesofchance(anti)correlationof0.28,0.018,0.99,and0.43respectively,i.e.thereisnosignicantcorrelationof(Mmm=MSMF)withMSMF,r,anddistance,andthereisamarginallysignicantanticorrelationwithSMF.Themostsignicanttrendistheanticorrelationof(Mmm=MSMF)withdensity.Onepossibleexplanationforthisobservedtrendisasystematicchangeindustopacitiesat8mand1.2mmcausedbygraingrowth,sinceMmm=MSMF/8m=1.2mm.Forexample,thethinicemantlemodelofOssenkopf&Henning(1994)predictsIRAC8m=1.2mmdecreasesbyafactorof0.68aftercoagulationforapproximately106yratadensityofnH=105cm3(or107yratadensityofnH=104cm3).Theratiodecreasesonlyslightlyinthelimitoffurthercoagulation.ComparisonoftheuncoagulatedbaregrainandthinicemantlemodelsofOssenkopf&Henning(1994)showsthat8m=1.2mmdecreasesbyaboutafactorof0.75bytheformationoficemantles.Thusatotalfactorofabout0.5decreaseinMmm=MSMF,i.e.aboutthatobservedinourcoresasthemeandensitychangesfrom104cm3to105cm3,couldbeexplainedbyacombination 34

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2-2

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DistributionofpixelintensitiesforCloudC.ThesolidlineshowsthedistributioninsidetheLMF(13arcminutesby13arcminutes)centeredontheIRDC.ThedottedlineshowsthedistributioninsidetheIRDCellipseandthedashedlineshowsitoutsidetheellipse(foraregion24arcminutessquare). 40

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Backgroundintensitycomparison.Distributionoftheratio(I,0,LMF=I,0,SMF)ofbackgroundintensitiesderivedfromofLMFandSMFmethods.Thedottedanddashedlinesshowthedistributioninsideandoutside(foraregion24arcminutessquare)thecloudellispse,respectively. 41

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GLIMPSE8mimageofCloudHwith3arcminutesscalebar.Thestripsconsideredinx arealsoshown(logarithmicintensityscaleinunitsofMJysr1). 42

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ResultsofLMFandSMFmethodswiththinstripanalysesforstripa(leftcolumn)andstripb(rightcolumn).Toppanels:MedianI,1,obsalongthestrip(solidlines),LMFestimateofI,0,obs(dottedlines),SMFestimateofI,0,obs(dashedlines),estimatefromstripintensityprole(longdashedlines).Positioncoordinateincreasesfromlower-leftendofstrips(seeFig. 2-5 ).Middlepanels:RatioofLMF(dotted)andSMF(dashed)estimatesofI,0,obscomparedtoestimatefromthestripintensityproles.Bottompanels:EstimatesofviaLMF(dotted),SMF(dashed),andstripanalysis(longdashed)methods. 43

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2-3 ,andthehorizontallineshowingascaleof3arcminutes.Therightcolumnshowsextinctionmapsmadebythesmall-scalemedianlteringmethod(SMF).Fromtoptobottom,thecloudsare:CloudA(G018.8200.28),CloudB(G019.27+00.07),CloudD(G028.5300.25).

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SameasFigure 2-7 ,butnow,fromtoptobottom,thecloudsare:CloudE(G028.67+00.13),CloudF(G034.43+00.24),CloudG(G034.7700.55). 45

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SameasFigure 2-7 ,butnow,fromtoptobottom,thecloudsare:CloudH(G035.3900.33),CloudI(G038.9500.47),CloudJ(G053.11+00.05). 46

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Comparisonofcoremassestimates.TopLeft:RatioofcoresmassesdeterminedviaextinctionmappingwithLargeandSmallMedianFiltermethods(MLMF=MSMF)versuscoremass.Topright:Samedataplottedasafunctionofcore(estimatedviatheSMFmethod).Middlepanels:Ratioofmmemissionmass(Rathborneetal.2006)toMLMF.Bottompanels:RatioofmmemissionmasstoMSMF. 49

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Table2-1. IRDCsample Spitzertelescopebandandbackground-weighteddustopacitiespergasmass

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IRDCcores A1(MM4)18.7900.2860.7212190.08290.08131631570.232A2(MM6)18.7990.2940.8141710.08050.07102111880.193A3(MM5)18.8060.3030.6981410.08050.07491561420.230A4(MM3)(e)18.7010.2270.582194-----A5(MM1)(e)18.7350.2260.535736-----A6(MM2)(e)18.8330.2990.465201-----B1(MM2)19.2880.08240.43194.50.06560.063157.351.30.354B2(MM1)19.3110.06750.33793.70.07740.068732.225.70.370C1(MM9)28.3240.06770.8243300.1650.1944015390.532C2(MM4)28.3450.05970.5092740.2340.3042393031.26C3(MM11)28.3520.10080.9213710.1990.2352432790.197C4(MM6)28.3550.07260.4851920.1620.1862042481.20C5(MM14)28.3560.05660.29130.00.1880.23866.171.11.59C6(MM10)28.3620.05320.8242960.07570.08574655840.576C7(MM16)28.3670.12031.073710.2030.2563524060.183C8(MM17)28.3880.03810.7271640.07890.08923293870.556C9(MM1)(e)28.3990.08120.6309520.1550.1832482910.643C10(MM8)(e)28.2440.01270.751343-----C11(MM7)(e)28.2920.00650.582253-----C12(MM3)(e)28.3220.01010.558400-----C13(MM5)(e)28.3250.16130.412147-----C14(MM12)(e)28.3280.03881.02395-----C15(MM2)(e)28.3370.11700.533449-----C16(MM15)(e)28.3390.14240.630111-----C17(MM18)(e)28.4170.007260.824135-----C18(MM13)(e)28.4190.13911.02385-----D1(MM5)28.5260.25030.6361940.08730.09951171260.271D2(MM7)28.5380.27571.244210.07990.09424164410.127D3(MM3)28.5430.23691.5516900.07220.08446727290.108D4(MM8)28.5430.26510.7461540.05650.06691191270.169D5(MM2)28.5590.22741.5517600.08170.09247538130.121D6(MM4)28.5590.24121.226630.07070.07393243800.116D7(MM1)28.5650.23500.91210000.06030.06552803180.232D8(MM10)28.5790.23031.133600.07080.08364354470.171D9(MM9)28.5890.22850.7181380.08290.09591401600.239D10(MM6)28.5570.23820.49798.6-----E1(MM7)28.6440.13750.74272.20.1090.1192062300.311E2(MM5)28.6500.12600.74285.40.06320.07741932210.298E3(MM2)28.6610.14560.9403270.08720.1003593980.264E4(MM4)28.7170.14560.71796.20.09530.1061401690.254E5(MM3)28.5800.14560.544101-----E6(MM6)28.6470.11430.76693.7-----E7(MM1)28.6880.17820.495119-----F1(MM8)34.4220.247920.55689.60.05560.049772.867.80.217F2(MM7)34.4380.247590.50272.20.05730.051755.849.80.217F3(MM6)34.4480.250910.6641040.06250.059197.088.40.166F4(MM9)34.4540.254950.6991300.05830.051311689.70.145G1(MM3)34.7340.56700.22511.60.06060.062210.49.770.474G2(MM2)34.7830.56830.6891560.05150.05041121050.177G3(MM4)34.7840.56080.50658.00.06670.068264.164.60.275G4(MM1)34.7120.59460.323138-----H1(MM9)35.4780.30960.38034.80.08420.086978.769.90.705H2(MM4)35.4830.28580.47889.60.1130.11469.971.90.364H3(MM5)35.4830.29540.52097.90.06020.06211191220.477H4(MM8)35.4910.28300.40848.90.08300.085436.037.40.304H5(MM6)35.4970.28630.52058.80.06020.062957.865.30.257H6(MM7)35.5220.27240.54879.60.1330.13889.892.00.308I1(MM1)38.9570.46590.38097.00.1110.12457.363.60.640I2(MM3)38.9710.45880.1579.120.1350.14212.811.61.65I3(MM2)(e)38.9370.45780.32760.5-----I4(MM4)(e)38.9490.43850.43239.8-----J1(MM4)53.1280.05030.38437.30.03240.021917.112.20.118J2(MM3)(e)53.0920.12010.1669.94-----J3(MM5)(e)53.1360.02830.20910.8-----J4(MM1)(e)53.1410.07170.183103-----J5(MM2)(e)53.1570.06720.28836.5-----

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gcm2.(3)FromthevarietyofdustmodelsconsideredbyBT09,weexpect30%uncertaintiesintheabsolutevalueof8m.WithinaparticularIRDC,wecanexpectsomesystematicvariationin8mduetodifferentdegreesoficemantlegrowth,buttheseshouldbeatmost20%(Ossenkopf&Henning1994),andprobablymuchlessafteraveragingoverconditionsonalineofsightthroughthecloud.ApartfromthechoiceofMIRopacity,therearetwomainsourcesofuncertaintyinvolvedinMIRextinctionmapping.First,theintensityoftheMIRemissionbehindthecloudisassumedtobesmoothandmustbeestimatedbyextrapolationfrom 55

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weintroducethemethodofsaturation-basedMIRextinctionmapping.Inx wepresenttheresultsofapplyingthismethodtostudythestructureof42massivestarlessandearly-stagecore/clumpslocatedin10IRDCs.Inx wediscusstheimplicationsoftheseresultsformassivestarandstarclusterformationtheories. 57

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3-1 ) 58

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3-1 ):1)DenearegionoftheskyastheIRDC.FollowingBT09,weusetheellipsesfromthecatalogofSimonetal.(2006),whichwerebasedonMSXimages.2)UsingGLIMPSE8mimages,ndtheminimumvalueofI,1,obsinsidetheIRDC,I,1,obs(min).3)SearchforallpixelsintheIRDCwithI,1,obs(min)
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3-1 .Theyrangefrom(sat)=0.33to0.52gcm2asoneprogressesalongtheGalacticplanetowardsl=0,wherethebackgroundisbrightest.Anadditionaluncertaintyresultsfromouruseofasingleeffectivevalueof8m=7.5cm2g1averagedovertheSpitzerIRAC8mband,weightingbythelterresponsefunction,thespectrumoftheGalacticbackgroundandthedustopacitymodel(BT09).Sincethesefunctionsvaryoverthiswavelengthrange(seeFig.1ofBT09),atlargeopticaldepthstheactualtransmittedintensitywillbegreaterthanthatpredicted,beingmoredominatedbytheregionofthespectrumwiththelowestopacity.Theneteffectisanunderestimationofthetruemasssurfacedensity,giventheobservedratiooftransmittedtoincidentintensities.WehaveinvestigatedthesizeofthiseffectbyintegratingthetransferEquation 3 overtheaboveweightingfunctions(seeFig. 3-2 ).Forourducialdustmodel(themoderatelycoagulatedthinicemantlemodelofOH94),whichhasarelativelyatMIRopacitylaw,theeffectissmall:justafewpercenteffectuptovalueof1gcm2,risingtoabouta10%effectby=10gcm2.Forillustrativepurposes,Fig. 3-2 alsoshowstheresultsfortheDraine(2003)RV=3.1dustmodel,moreappropriateforthediffuseISM,whichhasbaregrainsandstrongervariationofopacityacrossthiswavelengthrange.Nowtheeffectleadstoanunderestimationofbyuptoseveraltensofpercentfor1gcm2.Otherdustmodelswehaveconsidered,suchastheDraine(2003)RV=5.5model,havesomewhatsmallerunderestimationfactors. 60

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3.3.1IRDCPropertiesFollowingtheabovealgorithm,wendthatall10IRDCsoftheBT09sampleexhibittheeffectsofsaturation.Inhindsight,thisisnottoosurprisingsincethesecloudswereselectedtohaverelativelyhighcontrastagainstthebackground.ThemapsofthecloudsareshowninFigs. 3-3 and 3-4 .ThepropertiesofthesecloudsarelistedinTable 3-1 ,wherewealsocomparetheirpropertiestothosederivedwiththeSMFmethodofBT09withtheanalyticmodelofforegroundestimation.Usingthesaturation-basedestimateofforegroundemission,wendI,foreandthusfforehasincreasedinalltheclouds.Thusthehighestvaluesofthatweinferhaverisenfrom0.10.3gcm2inBT09to0.40.6gcm2inthispaper.Themeanvalues,SMFrisebysmallerfactors,sothatthetotalcloudmassesrisebyonaverageafactorof2.0.AcomparisonoftheglobalpropertiesoftheseIRDCwiththepredictionsoftheoreticalmodelsoftheinterstellarmediumwillbepresentedinaseparatepaper. 3.3.2.1LocatingthecoresThecoresweareconsideringareasubsetofthoseoriginallyidentiedbyRathborneetal.(2006)basedontheirmmdustcontinuumemission,observedwiththeIRAM-30mTelescopeat11arcsecFWHMangularresolution.BT09selected43coresfromtheRathborneetal.sample,excludingthosewithsignicant8memissionandthosewithlow-contrastagainsttheMIRbackground(i.e.with.0.02gcm2).Here,wehaveexcludedoneoftheBT09cores,E4,becauseitsGLIMPSEimagesuffers 61

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,weexpectourderivedvaluesoftobehigher(andmoreaccurate)thanthoseofBT09.ComparingthecoremassesofBT09withthosederivedhereforthesameregions,wendtheyhavetypicallyincreasedbyafactorofabout2.2.Inthispaper,wenowredenethecorecentertobethecenterofthehighestpixelinsidethepreviouscoreboundary.Iftherearetwoormoreadjacentsaturatedpixelsatthecorecenter,thentheiraveragepositionisusedtodenethecenter.Infact,17ofthe42coresexhibitsaturation.Occasionally,afterinspectingthe8mGLIMPSEand24mMIPSGALimages,wenotethepresenceofMIRsourcesnear(<7.5arcsec)thecorecenter.Thisoccursin9ofthe42cores(B2,C6,C8,D5,D6,D8,E2,E3,I1).Inordertofocusonmassivestarlessandearly-stagecores,weshiftthecentertoanew,nearby(.3arcsec)maximumtoavoidanymajorsourcesofMIRemissionwithinaradiusof7.5arcsecofthenewcenter.Inseveralcases(C4,D4,F2,J1),themapinsidetheRathborneetal.coreboundarydoesnotexhibitawell-denedhighpeak.InthesecasesweselectanewcorecenterascloseaspossibletotheRathborneetal.core:normallythisiswithinafewarcsecondsoftheboundary,butforF2itisabout10arcsecoutside.Figure 3-5 showsthemapofcoreA1,extractedfromthelargerimageofIRDCA,showninFig. 3-3 .Pixelssufferingfromsaturationaremarkedwithsmallwhitesquares.Thecorecenterismarkedwithacross.Similarimagesofall42coresareshowninFigs. 3-6 to 3-12 .Wenotethat5oftheIRDCs(B,E,G,H,J)onlyhaveonecorethatexhibitssaturation.ThisispossiblebecausetheconditiontodetermineifanIRDCissaturated 62

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3-5 showscl(r)withblueopensquaresymbols,plottedattheradiicorrespondingtothecenterofeachannulus.Thetotalenclosedmass,whichwerefertoastheclumpmassMcl(r),isindicatedbythebluelong-dashedline. 3-5 andthesecorepropertiesarelistedinTable 3-2 andTable 3-3 .CoreA1happenstobeoneofthemostextensivelysaturatedcoresatthescaleofanenclosedmassof60M(alongwithC2,H1,I1,I2,J1),sothesenumbersarelikelytobesignicantlyaffectedbysaturation(whichcausesustounderestimate),soactuallytheradiusenclosing60Mwouldbesmallerandlarger.Thedistributionsoftheradii,Rcl,andmeanmasssurfacedensities,cl,ofthe42core/clumpsattheMcl=60MscaleareshowninFigure 3-13 (withthe6 64

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3-4 ).Wenexttapowerlawdensitydistribution, Rclk,cl,(3)wheres,cl=HnH,s,cl(withH=2.341024g)isthedensityatthesurfaceoftheclump,Rcl.Weprojecttheabovedistributiontoderivecl(r),whichwethenconvolvewithaGaussianwithaFWHMof2arcsec(toallowfortheSpitzerIRAC8mPSF).Wethentthismodeltotheobservedcl(r)prole,excludingannulithataresignicantly(>50%)affectedbysaturatedpixels.ForCoreA1,k,cl=1.40andnH,s,cl=2.47105cm3.Forthewholesample,themean/median/dispersionvaluesofk,cl=1.09=1.10=0.236andnH,s,cl=(1.76=1.85=0.852)105cm3.ThesedistributionsareshowninFig. 3-13 withthebluedottedhistograms.ThevaluesforindividualcoresarelistedinTable 3-2 andTable 3-3 .Theaboveanalysisissomewhatsimplisticinthatithasassumedthestructureexistsinisolation.Inreality,weseethatthesehighobjectsaresurroundedbyregionsthatalsohavesignicantmasssurfacedensities.Thusnextwemodelthecoreswithasimilarpowerlawdensitystructure, Rck,c,(3)butnowwhencomparingtotheobservedmapsweaccountforthemasssurfacedensityofthesurroundingclumpmedium,cl,env.Weestimatecl,envusingtheobservedvalueintheannularregionfromRcto2Rc.Thischoiceismotivatedbythedesiretosamplearegionoftheclumpthathasascalecomparabletothecoreinbothsize 65

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3-13 ,andTable 3-2 ).Comparedtotheclumpresults(i.e.derivedfromthetotalproles),above,fortheenvelope-subtractedcorepropertieswenecessarilyndsmallersurfacedensities,steeperdensityprolesandsmallervolumedensities.Thepowerlawtsignoreannuliaffectedbysignicantsaturation,whereisunderestimated.Thuswealsoestimateacoremass,Mc,PL,basedonextrapolationofthepowerlawtstothecenterofthecore: 3k,cnH,s,c ). 66

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3-13 andTable 3-2 andTable 3-4 ). 67

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3-5 .Thelocationofthepeakvalueof2indicatesthebest-ttingpowerlaw(PL)coreradius,whichoccursat0.251pcwithavalueof2=1.62.Acircleofthisbest-tcoreradiusisshowninthemapofthecoreinFig. 3-5 .ThetotalenclosedmassatthisscaleisMcl=303M,thecoremassisMc=194M,themeancoremasssurfacedensityisc=0.204gcm2andtheclumpsurroundingthecorehascl,env=clc=0.115gcm2.ThecoremassbasedonintegratingthepowerlawproleisMc,PL=204M,yieldingaslightlyhighermeanmasssurfacedensityofc,PL=0.214gcm2.Thebest-ttotalcl(r)=c(r)+cl,envmodelproleisshownbythesolidlineinFig. 3-5 (thedottedcontinuationintheinnerregionindicateswhereannuliaffectedbysaturationarenotusedinthetting).Figure 3-5 showstheclumpenvelopesubtractedproleofc(r),togetherwithvariousprojectedpowerlawts,includingthebest-tvalueofk,c=1.88.Theparametersofthebest-ttingpowerlawplusclumpenvelopemodelarelistedinTable 3-2 andTable 3-3 .ThedistributionsofRc,cl(whichisthemeantotalovertheareaofthecore),c,PL,k,cl,k,c,nH,s,cl,nH,s,c,MclandMc,PLareshowninFigure 3-13 andsummarizedinTable 3-4 .ThevaluesforeachcorearelistedinTable 3-2 andTable 3-3 .Itisimportanttonotethatthesebest-tvaluesmaynotnecessarilybethemostaccuratedescriptionofthecorestructures.Theyarebasedonazimuthally-averagedquantities.Themapofaparticularcoreshouldbeinspectedtogaugethevalidityofthisassumption.Also,thevaluesof2asafunctionofradiusshouldbecheckedtogaugethereasonablenessanduniquenessofthet. 68

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3-5 .ThishasRc=0.670pc,Mc=353M,c=0.0523gcm2,cs=0.275kms1andP0=k=8.9107Kcm3.However,thevalueof2=8.75,whichissignicantlylarger,i.e.worse,thanthebest-tpowerlawplusclumpenvelopemodelt(forwhich2=1.62).AlsothesizeoftheBonnor-Ebertttedcoreismuchlargerthanthepowerlawmodel:ascanbeseefromFig. 3-5 ,ontheselargerscalestheassumptionofsinglemonolithicandazimuthallysymmetricstructurebecomeslessvalid.CarryingouttheBonnor-Ebertanalysisforall42cores,wendthetsaregenerallyworsethanforthepowerlawmodels.Thebest-ttingBonnor-Ebertradiiaretypicallylargerthanthoseofthepowerlawcoremodels.Forthesereasons,wedonotconsidertheBonnor-Ebertmodelsfurtherinourdiscussion. 69

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3-14 weshowthe42core/clumpsontheversusMdiagram(followingTan2007).Here,ismeasuredfromthetotalobservedmassinsideagivenradialdistancefromthecore/clumpcenter.InFigure. 3-15 wecomparetheseprolestothepropertiesofthe31star-formingclumpswhoseIRandsub-mmdustcontinuumemissionwasobservedandmodeledbyMuelleretal.(2002).Notethatthesepropertiesdependonthe(1D)modeledtemperaturestructure,dustemissivity(theyusedthesameOssenkopf&Henning(1994)dustmodelthatwehaveadoptedforourMIREXmaps)andgas-to-dustratio(wehavescaledMuelleretal.'smassesbyafactor1.56tobeconsistentwithouradoptedgas-to-dustratio).TheIRDCcores/clumpsoverlaponlywiththelower-rangeofthestar-formingcore/clumpsample,perhapsindicatingthereisa(physicallyplausible)evolutionarygrowthincore/clumpdensityasstarformationproceeds.However,notethatmany(indeedmost)star-formingcoresandclumpshave<1gcm2.Alternatively,thelackofstarlesshighcore/clumpsmaybeduetothesomewhatsmallervolumeoftheGalaxythatwehaveprobedwithournearbyIRDCsample,comparedtotheMuelleretal.star-formingcore/clumpsample.Muelleretal.(2002)founddensitypowerlawindicesofk,cl=1.80.4,slightlysteeperthanourderivedvaluesforIRDCcoresofk,c'1.6,butsignicantlysteeperthanourvalueforclumpsofk,cl'1.1.Again,thislatterdifferencemayindicateanevolutionincloudpropertiesasstarformationproceeds.Consideringtheseresults,wesuggestthattheinitialconditionsoflocalmassivestarformationintheGalaxymaybebettercharacterizedwithvaluesofcl'0.2gcm2ratherthan1gcm2,whichwouldimplysmalleraccretionratesandlongerformation 72

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0.2gcm23=4yr.(3)Inthiscaseofmassivestarformationatrelativelylowvaluesof,weexpectfragmentationofthecoresispreventedbymagneticelds,i.e.ifthecoremassisequaltothemagneticcriticalmass(Bertoldi&McKee1992) Z2B R2=3nH 3 isthen190G.Sucheldstrengthsaresimilartothoseobservedinregionsofactivemassivestarformation(e.g.Crutcher2005).Indeed,Crutcher(2005)notedtheobservedmasstouxratiosscatteredaboutthecriticalvalue.Numericalsimulationsofthecollapseofmarginallymagneticallycritical(ratherthansupercritical,e.g.Wangetal.2010;Hennebelleetal.2011)coresarerequiredtoinvestigatethisscenarioforformingmassivestars,and,moregenerally,forexplainingthehigh-masstailoftheinitialmassfunction(Kunz&Mouschovias2009). 73

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IRDCsample

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).Thecolorscaleisindicatedingcm2.Thedashedellipse,denedbySimonetal.(2006)basedonMSXimages,denestheregionwherethebackgroundemissionisestimatednotdirectlyfromthesmall-scalemedianlteraverageoftheimageintensity,butratherbyinterpolationfromnearbyregionsjustoutsidetheellipse.Thelocationsofthemassivestarlesscoreswehaveselectedforanalysis(x )aremarkedwithcrosses.BrightMIRsourcesappearasarticialholesinthemap,wherewehavesetthevaluesof=0gcm2.

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3-3 )ofIRDCsG-JderivedfromMIREXmappingusingSpitzerIRAC8mimages.

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3-3 ).Thecorecenterismarkedwithacross.Saturatedpixels,forwhichisalower-limitofthetruevalue,aremarkedwithsmallwhitesquares.Theblackdashedcircleshowstheradiusenclosingatotalmassof60M.Theredsolidcircleshowstheextentofthecorederivedfromthebest-tpowerlaw(PL)coreplusenvelopemodel(seetext).(b)BottomLeft:RadialprolesofCoreA1:observedlogcl=(gcm2)(blueopensquares,plottedatannulicenters)derivedfromthemapshownin(a);totalprojectedenclosedmass,Mcl,(bluelong-dashedline[seerightaxis]);coremass,Mcafterclumpenvelopesubtraction(reddashedline[seerightaxis]);indexofcorePLdensityprole,k,c,(redcrosses);log2(redtriangles)ofthePLplusenvelopet(best-thasamaximumorlocalmaximumvalue[seetext]);thebest-tPLplusenvelopemodel(bluesolidline;dottedlineshowsrangeaffectedbysaturationthatwasnotusedinthetting);logc=(gcm2)ofbest-tcoreafterenvelopesubtraction(redsolidsquares)andPLt(redsolidline;dottedlineshowsrangeaffectedbysaturationthatwasnotusedinthetting).(c)TopRight:c(r),i.e.afterclumpenvelopesubtractionforthebest-tmodel(redsolidsquares;opensquaresshowresidual,post-subtractionenvelopematerial).PLmodelswithvariousvaluesofk,careindicated(dashedlines),includingthebest-tmodelwithk=1.88(solidline).(d)BottomRight:Asfor(c)butforBonnor-Ebert(BE)plusenvelopetting.c(r),i.e.afterclumpenvelopesubtractionforthebest-tmodel(redsolidsquares).Best-tBEmodel(solidline)andmodelsvaryingcs(long-dashedlines)andP0(dashedlines)byfactorsof2fromthisareshown(seetext).

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3-5 )andazimuthallyaveragedradialprolegures(notationasFig. 3-5 ).

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3-5 )andazimuthallyaveragedradialprolegures(notationasFig. 3-5 ).

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3-5 )andazimuthallyaveragedradialprolegures(notationasFig. 3-5 ).

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3-5 )andazimuthallyaveragedradialprolegures(notationasFig. 3-5 ).

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3-5 )andazimuthallyaveragedradialprolegures(notationasFig. 3-5 ).

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3-5 )andazimuthallyaveragedradialprolegures(notationasFig. 3-5 ).

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3-5 )andazimuthallyaveragedradialprolegures(notationasFig. 3-5 ).

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3-14 ,nowcombiningall42corestogether(coloredlines).Theblacksymbolsandlinesshowthemassesof31activelystar-formingcore/clumpsfromMuelleretal.(2002),withtrianglesindicatingthemassesaboveadensitythresholdofnH3104cm3(wehavescaledthemassesbyafactor1.56tobeconsistentwithouradoptedgas-to-dustmassratio)andthesquaresindicatingthemassesinsidethedeconvolvedsourcesize.Note,thepropertiesofthecloudsonthisinnerscalearenotdirectlyresolved,butareinferredbasedonsimple1Dradiativetransfermodeling.TheIRDCcores/clumpsoverlaponlywiththelower-rangeofthestar-formingcore/clumpsample,perhapsindicatingthereisanevolutionarygrowthincore/clumpdensityasstarformationproceeds.

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Clumpproperties

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Besttpowerlawcoreproperties

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PropertiesofIRDCcoreandclumpsample

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4.2.1MIREXMappingwithMulti-frameArchivalIRACImagesAsdescribedinBT12,theMIREXmappingtechniquerequiresknowingtheintensityofradiationdirectedtowardstheobserveratalocationjustbehindthecloudofinterest,I,0,andjustinfrontofthecloud,I,1.Thenfornegligibleemissioninthecloudanda1Dgeometry,I,1=eI,0,wheretheopticaldepth=,whereisthetotalopacityatfrequencyperunitgasmassandisthegasmasssurfacedensity.However,becauseofforegroundhotdustemissionbetweenourlocationandtheIRDC,weactuallyobserve 94

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4-1 ).Inoverlappingregions,thedatahasbeenco-added,sothetotalexposuretimeforeachregionisdeterminedbyhowmanypointingsoverlapwithinit.Thisexposuretimesetsthe1noiselevelforeachregion.Foreachindependentregionwithanareagreaterthan500pixels,wesearchforlocalsaturation.Todothis,wecompletethefollowingsteps:1)Deneasetofregions,determinedbytheoverlappingIRACpointings.2)Usingthe8mimage,ndtheminimumvalueofI,1,obsinsideeachregion,I,1,obs(min).3)SearchforallpixelsinaregionwithI,1,obs(min)
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4.3.1OverallCloudMassWeusethesameIRDCellipticalboundary(effectiveradiusof15.4arcmin,e=0.632)adoptedbyBT09andBT12toevaluateamean=0.0951(ignoringregionsaffectedbyMIR-brightsources).Weassumethereisa30%uncertaintyinthisestimateduetouncertaintiesintheopacityperunitmass,whichincludesdustopacityanddust-to-gasmassratiouncertainties(seeBT12).Thisresultcompareswiththevalueof=0.0610gcm2fromBT12and=0.0721gcm2fromKT13.Givenourestimateofandthekinematicdistanceof5.0kpc(Simonetal.2006),forwhichweassume20%uncertainties,wethenevaluatethetotalIRDCmassinsidetheellipseregion(witheffectivecircularradiusofRe=7.7pc)asM=73,200M.Thiscompareswithourpreviousestimatesof45,000M(BT12)and53,200M(KT13).Ifweextendourintegrationtoalargereffectiveradiusof8.3pc,whichenclosesthewholerighthandsideoftheMIREXmap,wederiveatotalmassof70,200M. 97

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Rclk,cl,(4)wheres,cl=HnH,s,cl(withH=2.341024g)isthedensityatthesurfaceoftheclump,Rcl.Weprojecttheabovedistributiontoderivecl(r),whichwethenconvolvewithaGaussianwithaFWHMof2arcsec(toallowfortheSpitzerIRAC8mPSF).Wethentthismodeltotheobservedcl(r)prole,excludingannulithataresignicantly(>50%)affectedbysaturatedpixels.WelisttheclumpandcorepropertiesforboththeMcl=60Mcaseandthebest-tpowerlawcaseinTable 4-1 andTable 4-2 98

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6-13 thelog-normaltsoftheBT12cloudsA,B,C,D,F,G,H,andJfromKT13.Wenotethat,unlikethetpresentedforcloudCinthispaper,thesetsweredonewithoutknowingthepeakpositionofthecolumndensityPDF.Asaresult,thetsarelessconvergentandshouldbeconsideredasarst,suggestiveefforttomeasuretheshapeofthemean-normalizedPDF.Wealsonotethatthelog-normalfunctionprovidesaverygooddescriptionoftheobservedPDFofcloudC.Thedeviationathigh,islikelyduetothesaturationlimitoftheMIREXmap,withsat'0.8gcm2.Thisprovidesapowerfulconstraintfortheoreticalmodelsoftheinitialconditionsofstarclusterformation,inparticularfortherelativeimportanceofturbulence(anditsdrivingscale),magneticelds(includinglargeandsmallscalecomponents)andself-gravity.Inparticular,sinceasinglelognormalfunctionprovidesaverygoodt,thereisnoindicationforthepresenceofaseparatehigh-endpowerlawtail,whichhasbeenclaimedtoindicatethepresenceofaseparateself-gravitatingcomponentwithinacloud(e.g.Kainulainenetal.2011).Sincethe 100

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5.2.1SimulationCodeandInitialConditionsTheglobalgalaxysimulationsofTT09followedtheformationandevolutionofthousandsofGMCsinaMilky-Way-likediskwithaatrotationcurvewithvelocitymagnitudeof200kms1.However,withaspatialresolutionof8pc,onlythegeneral,globalpropertiesoftheGMCscouldbestudied.Inordertoprobetheinternalstructureanddynamicsoftheseclouds,wemustpushtohigherresolution.Duetothecomputationalresourcecostofperformingsuchalargesimulationtohighresolution,wecannotsimulatetheentiregalaxy,butmustfocusonalocalregion.Weextracta1kpcby1kpcpatchofthedisk,extending1kpcaboveandbelowthemidplane,centeredataradialdistanceof4.25kpcfromthegalacticcenter(seeFig. 5-1 )atatimeof250MyrafterthebeginningoftheTT09simulation,afterthediskhasfragmentedintoarelativelystablepopulationofGMCs.VanLooetal.(2013)thenfollowtheevolutionoftheISMandtheGMCsinthisregionfor10Myrto0.5pc 108

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2v2c,0ln"1 109

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2.5log"1 66Xi=1exp(2.5AV,i)#mag.(5)ThisapproximateeffectivevisualextinctioniscalculatedforeverycellfromthesimulationofVanLooetal.(2013)usingtheSanchez-Salcedocoolingfunctionat10Myr.Fromthis,adensityvs.columnextinctionrelationshipisderived.ThisrelationisthenusedtogenerateatableofcoolingandheatingratesasafunctionofdensityandtemperatureusingthephotodissociationcodeCloudy(Ferlandetal.1998).Firstly,foragivendensity,rangingfrom103to106cm3withstepsof1dex, 113

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5-2 .AlthoughtheCloudycoolingcurve(fornH<102cm3)hasasimilartemperaturedependencebetween300-6000KastheSanchez-Salcedoetal.curve,theequilibriumcurveonlyexhibitsaweakthermalinstability.Furthermore,theinstabilityisatlowerdensitiesthantheSanchez-Salcedoetal.curve.Theshiftoftheinstabilitytowardslowerdensitiesisduetoahighercolumnextinctioncomparedtothe1019cm2usedbyWolreetal.(1995).Atlowdensities,thethermalequilibriumissetbytheLycooling 114

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5-1 showsthecolumndensityintegratedalongthez-axisandwecanidentifyfourdistinctdensitystructures.Infact,theselectedregioncontainssixclouds.Thetwosmallclouds(A&B)areabouttointeractwithalargerone(C)andaretherefore 115

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5-2 listsalloftheclouds.Theirpropertiesspanalargerangeinsizesandmasses.Thesmallestcloudonlyhasaradiusof15pcandamassof6104M,whilethelargestcloudisahundredtimesmoremassive(7.47106M)and30timeslargerinvolume.Thetotalmassinthecloudsis1.2107Mwhichisabout70%ofthegasmassinthesimulationbox.Thecloudshavediameterssmallerthan100pc,andthushaveatmost12cells(x7.8pc)acrosseachlineardimension.Theinitialvelocitydispersionofthecloudsishighenoughtogivesomeapproximatebalanceagainstself-gravity.Themeanvirialparameterofthecloudsis1.32withstandarddeviationof0.35,closetothevalueof1.3withstandarddeviationof0.76forGalacticGMCsderivedbyMcKee&Tan(2003)fromanalysisoftheresultsofSolomonetal.(1997)Notethe13CO-selectedcloudsstudiedbyRoman-Duvaletal.(2010),whichtracesomewhathigherdensities,havemedianvirialparamterof0.46.Thevastmajorityofthegasintheinitialconditionshastemperaturesbelow350K,andisthereforeinthecoldphase.Thisgasislocatedwithinthegalacticdiskandrepresents99%ofthetotalgasintheinitialconditions.Theremaining1%ofthegashastemperaturesabove105Kandislocatedintheregionssurroundingthedisk.TT09onlyallowthegastocoolto300Kwiththeonlyheatingoccurringasaresultofshocksinthegas. 5-4 showsavolumerenderingofrun7,highlightingtheseGMCandclumpdensitythresholds.ThestarformationratesinRun7dependonthechosenvalueoftheefciency,aswellasM,minandnH,sf.Theseparameterswerevaried,anditwasfoundthatwhile 116

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5-3 showsthemasssurfacedensityforrun7,withthestarclusterparticlesoverplotted.Theseparticlesareconcentratedwithinthemolecularclouds,butcanbeejectedifsufcientangularmomentumisinjectedfrom,forexample,acollisionwithanothercloudorclump.Theadditionofstarformationdoesnotchangemuchoftheglobaldensitystructureordynamics,butdoesreducethemaximumdensityvaluesreachedinthesimulationsbyaboutanorderofmagnitudecomparedtotherunswithoutstarformation.However,thesevaluesremainanorderofmagnitudehigherthananymasssurfacedensitiesseeninrealcloudsstudiedwithextinctionmapping.Ofthegaswithinmolecularclouds50-60%isindenseclumpswithnH>105cm3.ThisvalueismuchhigherthanobservedinnearbyGMCs,e.g.90%ofthecloudsintheBolocamGalacticPlaneSurveyhavearatioofclumpmasstocloudmass,orclumpformationefciency,between0and0.15(Edenetal.2012).Thehighclumpformationefciencyispartlyduetoourresolutionlimit.WedonotproperlycapturetheformationofindividualPSCs.sothattheturbulentdissipationrangeisnotfullyresolved.Theclumpsthenlackturbulentsupportagainstself-gravityherebyattaininghigherdensitiesandaccumulatingmoremass.InButler&Tan2013(inprep.),wefollowthegasto 118

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Viewofthegasmasssurfacedensity,g,overthe20kpcdiametergalacticdiskofTT09250Myrafterstartofthesimulation.Thesquareisa1kpcsidedregion,enlargedintherightimage,showingseveralGMCs.Thesearetheinitialconditionsforthesimulationsofthispaper.TheintialcloudslistedinTable 5-2 aremarked. Table5-1. Setofsimulations RunAMRaHeatingCoolingStarformation 1NoNoRBb1.27No2YesNoRB1.27No3YesPERB1.27No4YesPESSc1.27No5YesCloudyCloudy1.27No6YesCloudyCloudy2.33No7YesCloudyCloudy2.33Yes Table5-2. ListoftheinitialGMCs CloudMasscenterMassaRbcvirposition(x,y,z)(106M)(kms1)(pc) A0.921,0.164,-0.0040.093.617.91.70B0.865,0.249,0.0040.062.515.11.50C0.745,0.232,0.0137.4715.447.90.61D0.605,0.597,0.0052.5316.137.41.54E0.180,0.159,-0.0030.7910.521.51.26F0.089,0.588,-0.0031.0010.827.01.32 120

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MeanlogarithmicvisualextinctionasafunctionofthedensityasderivedusingtheSanchez-Salcedoetal.simulation.Theerrorbarsshowthedispersiononthemean,whiletheshadedareashowsthedistributionofallcolumnextinctionsinthenumericaldomain.Thesolidlinerepresentstheminimumcolumnextinctionduetoabsorptionwithinthecellitself. Figure5-3. Gasmasssurfacedensityalongthez-axisafter10Myrforrun7.Thewhitedotsrepresentthestarparticles. 121

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VolumerenderednumberdensityofRun7.TheGMCthresholdvolumedensity,nH100cm3,iscolouredblue,whiletheClumpthresholdvolumedensity,nH105cm3,gasiscolouredred. Figure5-5. 122

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6-1 ,Figure 6-2 ,andFigure 6-3 )thatwasusedinVanLooetal.(2013,VLBT13hereafter).VLBT13followedtheevolutionofthisregionfor10Myrwithamaximumresolutionof0.5pc.Inordertoresolvestructuresonthescaleofindividualstar-formingclumps,higherresolutionisneeded.Thefollowingsimulationscontain6levelsofAMRontopoftheoriginal7.8pcbasegridresolution,whichwedenefromtheoutputoftheTT09simulation.Thusweachieveamaximumresolutionof0.12pc.TheheatingandcoolingfunctionsutilizedarethosederivedfromthephotodissociationcodeCloudy(Ferlandetal.1998)byVLBT13fortemperaturesbetween5and105K.Thesefunctionsincludebothatomicandmolecularlinecoolingprocesses,includingtheformationanddestructionofH2andCO,amongothers.AtableofheatingandcoolingratesforarangeofdensitiesandtemperatureswasgeneratedbasedonthedensityversusmeanextinctionrelationshipderivedinVLBT13.FortemperaturesaboveT=105K,weopttousethecoolingcurveofSarazin&White(1987)andsettheheatingratetozero.Fordensitiesandtemperaturesaboveorbelowthelimitsofthetable,weusethelimitingrate.Formoredetailsonthederivationofthisfunction,see 125

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6-1 ,Figure 6-2 ,andFigure 6-3 ).WenotethattheZeussolver(Stone&Norman1992),ratherthanaGodunovsolver,hasbeenusedforthesesimulations.Thisintroducesrelativelylargeheatingratesduetonumericalviscosity,butmakesthecalculationmorenumericallystable. 6-1 ,Figure 6-2 ,andFigure 6-3 fortheinitialconditions,RunnSF,andRunSF.TheprimarydifferenceinthegaspropertiesbetweenRunnSFandRunSFcanbeseeninthegasmassanddensityvalues.Ourmethodofstarformationconvertsthedensestgas(nH>106cm3)intostarparticles,sothepeakdensity,aswellastheoverallgasmass,arewillbelowerforRunSF.ForRunnSF,thetotalgasmassinthesimulationvolumeis1.67107M.InRunSF,asaresultofstarformation,themassfallsby10%to1.37107Mduringthecourseofthesimulation.ThemassinstarparticlesinRunSFis2.89106M,composedof1.46105particles,resultinginameanstarparticlemassof19.8M.ThepeakgasdensityisnH=1.53109cm3inRunnSFandnH=4.53108cm3inRunSF,morethan2timessmaller.Theaveragestarformationrateover3.0Myris0.96Myr1kpc1.ThisisverysimilartothemeanrateseenoverthesametimeperiodintheVLBT13simulation,indicatingthattheglobalstarformationpropertiesdonotdependonthesimulationresolutionorchoiceofthresholddensityandminimumstarparticlemass.WecomparetheSFRtimeevolutionofrunSFtothe0.5pcresolutionrunincludingstarformation 127

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6-4 .However,thisstarformationrateisabouttwoordersofmagnitudehigherthantherateinobserveddiskgalaxies(Bigieletal.2008).AsdiscussedbyVLBT13,thisislikelyduetotheinuenceofmagneticeldsand/orstellarfeedback.Thequantitativeeffectofmagneticeldsforthesamesimulationset-upasVLBT13isbeinginvestigatedbyVanLooetal.(inprep.). 6-5 ,Figure 6-6 ,Figure 6-7 ,andFigure 6-8 .ThinslicesshowingthedensityandvelocityeldscenteredoneachlamentareshowninFigure 6-9 ,Figure 6-10 ,Figure 6-11 ,andFigure 6-12 .Foreachlament,wecalculateseveralphysicalquantitiesinsmallstripsalongthelament.Wechooseastripsizewithx,yandzdimensionsof10pc5pc5pc,suchthateach50pc-longlamenthas10boxesalongitslengthintheydirection,extending5pcperpendiculartothelamentinthexcoordinate.Thisgeometryisadoptedbecausethefourchosenlamentstendtoextendperpendiculartothex-axis.ThephysicalpropertiescalculatedinthesestripsalongthelamentsarepresentedinTable 6-1 .Wendmeanlamentmassesof4.92104M,meandensitiesofnH=8270cm3,andvelocitydispersionsof=7.84km=s.Wealsoobservevelocitygradientsof1.40km/s1pc1acrosstheinnermostregionsofthelaments(see 128

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6-14 129

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6-1 )inrunSF.ThesearethencomparedtotwoofthemostlamentaryIRDCsstudiedinBT12,cloudFandcloudH(seeFigure 6-13 ).ThePDFsofthesimulatedcloudsshowabroaddistribution,includingapower-lawtailtohighvaluesof.NotethattheMIREXmappingtechniquehasanupperlimitofthatitabletoprobe,correspondingto0.5gcm2formostIRDCswithMIREXmapsconstructedfromGLIMPSEdata,andslightlyhigherfortheBTKmapofIRDCC.AlsotheMIREXmapsarenotsensitivetothelowerdensityregime(.0.01gcm2).ThiscanbecorrectedbycombiningtheMIREXmapwithaNIRextinctionmap,whichisshownforcloudC(BTK,inprep.).AllowingfortheinabilityoftheMIREXmapstoprobetoveryhighvalues,theoverallcomparisonisquitefavorable,especiallyfortheNIR-correctedmapofIRDCC.Lookingmorecloselyweseethatthesimulationstendtohavearelativelysmallerfractionofmaterialat0.1gcm2.Theyhaverelativelymorematerialat&0.5gcm2,althoughitisdifculttoassessthisexcessquantitativelybecauseoftheobservationallimitationoftheMIREXmaps. 130

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6-15 .Ingeneral,weobserverelativelysmall0.5km=s=pcvelocitygradientsonthescaleoftheoveralllaments.Thegradientonsmallerscalescanreachashighas5km/s/pc(Filamenta,forexample).Togetarepresentativegradientonthescaleofobservedclouds,wepresentinTable 6-1 thegradientcalculatedfortheinnerregionofthecloud,denedtobethelamentcenter5pc.Wendameangradientfortheinnerregionofthelamentsof1.4km/s/pc,comparabletothehigherendofrangeofvaluesseeninIRDCs.Inordertobringour 132

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6-16 .Thedifferenceinthenearandfarspectrashowevidenceofgasinfallontothelament.InFigure 6-17 ,weshowtheresultsofcomparingthepressureintheenvelopesurroundingthelamenttotheinternalpressure.Wedenetheinternalregiontobethea5pcregioncenteredonthelocalcenterofmassalongthelament,andtheenvelopetobethenext5pcextendingfromthisinternalregion.Themassperunitlengthisobserved,andthevirialmassperunitlengthisdeterminedbythevelocitydispersioninthelament.Inthislament,themajorityofthelamentliesabovethezeromagneticeldsupportline,consistentwiththeOuterFilamentresultsseeninHernandezetal.(2012).Thismayindicatethatthelamenthasnothadsufcienttimetoreachvirialequilibrium.Thevelocitydispersionsuptoafactoroftenhigherthanobservedvaluesarelikelytobethecauseofthiseffect.Weexpectthat,withtime,thelament'skinematicswillbecomemorequiescent,andasinfalldecreases,theenvelopepressureandvelocitydispersionwilldecrease,causingthelamenttoapproachvirialequilibrium. 133

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1kpcx1kpcprojectionsalongthez-axis(i.e.perpendiculartothediskplane)ofthesimulationboxfor(toptobottom)theinitialconditions,thenSFrunat3.0Myr,andtheSFrunat3.0Myr 137

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1kpcx1kpcprojectionsalongthey-axisofthesimulationboxfor(toptobottom)theinitialconditions,thenSFrunat3.0Myr,andtheSFrunat3.0Myr 138

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1kpcx1kpcprojectionsalongthex-axisofthesimulationboxfor(toptobottom)theinitialconditions,thenSFrunat3.0Myr,andtheSFrunat3.0Myr 139

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StarformationratehistoryforrunSF(white)andthe0.5pcresultsfromVLBT13(red). 140

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50pcx50pcdensityslicesalongthe(toptobottom)z,y,andx-axescenteredonFilamentaforthenSFrunat3.0Myr(left),andtheSFrunat3.0Myr(right).Velocityvectorsareoverplottedinblack. 145

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50pcx50pcdensityslicesalongthe(toptobottom)z,y,andx-axescenteredonFilamentbforthenSFrunat3.0Myr(left),andtheSFrunat3.0Myr(right).Velocityvectorsareoverplottedinblack. 146

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50pcx50pcdensityslicesalongthe(toptobottom)z,y,andx-axescenteredonFilamentcforthenSFrunat3.0Myr(left),andtheSFrunat3.0Myr(right).Velocityvectorsareoverplottedinblack. 147

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50pcx50pcdensityslicesalongthe(toptobottom)z,y,andx-axescenteredonFilamentdforthenSFrunat3.0Myr(left),andtheSFrunat3.0Myr(right).Velocityvectorsareoverplottedinblack. 148

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Meanprolesacrossthetenregionsperpendiculartolamentc(triangles).Thebest-tgaussiansforeachprolearealsoshown(redlines).Alinearoffsethasbeenappliedtoeachproleandtfordisplaypurposes. 150

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Top:projectionalongthey-axiswithlamentstripsshownaswhiterectangles.Middle:MassprolealongFilamentc.BlueXmarksshowthecentersofthelamentstrips.Bottom:LineofsightvelocityprolesalongFilamentc

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Mass-weightedradialvelocityspectrumforthenear(blue)andfar(red)sideofeachlamentrelativetothecenterofmass.Thetotalspectrumisalsoplotted(black). 152

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Comparisonoftheenvelopeandlamentpressuresandthevirialmassperunitlengthtotheobservedmassperunitlength.Thecasefornomagneticeldsupportisshownasadashedline(Hernandezetal.2012,Fiege&Pudritz2000). 153

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MichaelJ.ButlerwasborninPittsburgh,PAinJulyof1985.HemovedwithhisfamilytoSpringHill,FLin1993whereheattendedSpringsteadHighschool,graduatingin2004.HeattendedtheUniversityofFloridainGainesville,FLandgraduatedwithaBachelorofSciencedegreeinAstronomyandaBachelorofArtsdegreeinPhysicsinMayof2008.HecontinuedattheUniversityofFloridatoreceiveaMasterofSciencedegreeinAstronomyin2010,andreceivedhisPh.D.inAstronomyinAugustof2013. 166