The Initial Conditions and Early Evolution of Star-Forming Clouds

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The Initial Conditions and Early Evolution of Star-Forming Clouds
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Hernandez,Audra Kathl
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Doctorate ( Ph.D.)
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University of Florida
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Astronomy
Committee Chair:
Tan, Jonathan
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Lada, Elizabeth A
Eikenberry, Stephen S
Gonzalez, Anthony
Fry, James N

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astronomy
Astronomy -- Dissertations, Academic -- UF
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Abstract:
The formation of star clusters from giant molecular clouds (GMCs) is of fundamental importance for the evolution of the Milky Way and other galaxies and yet there are still many open questions. Why do certain localized regions of GMCs form star clusters, while the rest of the cloud shows little star formation activity? Is this process the result of spontaneous instabilities in the cloud, perhaps regulated by turbulence or magnetic fields, or triggered by external agents? Does the star cluster formation process take few or many dynamical times? What are the processes that control GMC formation and evolution? I have investigated the physical properties of molecular clouds in order to address these questions. First, using 13CO (1-0) molecular line emission data from the Galactic Ring Survey (GRS), I studied the dynamical state of two filamentary infrared dark clouds (IRDCs), which are expected to be representative of the initial conditions for star cluster formation. I compared mass surface densities, Sigma_13CO, with those derived from small medium filter (SMF) mid-infrared (MIR) dust absorption, Sigma_SMF, finding systematic trends that could be due to CO depletion from the gas phase due to freeze out onto dust grains or decreased excitation temperatures in the highest density regions. Furthermore, one of the filaments was observed at higher angular resolution with the IRAM 30m telescope in multiple molecular species. I analyzed J=2-1 and 1-0 lines of 13CO and C18O. The latter yielded an excitation temperature and mass surface density map, and by comparison with Sigma_SMF, a depletion map of the cloud. With a significance of 10 sigma, I confirmed that CO depletion is widespread in the cloud. An estimated several hundred solar masses are being affected, making this one of the most massive clouds in which CO depletion has been observed directly. Additionally, through ellipsoidal and filamentary virial analyses, I found that the filament is in a state consistent with some models of virial equilibrium, although surface pressure terms are still quite important. There is tentative evidence that the regions of the filament with the most star formation activity are more likely to be in virial equilibrium. Secondly, turning to the larger scales of GMC environments around IRDCs, I first studied a small sample of nine relatively nearby IRDCs and their associated GMCs using GRS 13CO emission data. I measured GMC mass, position angle of the rotation axis projected on the plane of the sky, and the virial parameter, alpha. I investigated how these results depended on the scale used to define the GMC and for different methods of defining the GMC boundary. I found masses ~10^5 M_sun, a broad range of projected rotation axis position angles and alpha ~ 10, suggesting quite disturbed kinematics of the molecular gas on these scales. No systematic trends were found between alpha with size scale or with the method used to identify the GMC. Next, I performed a similar study for much larger samples of GMCs. No significant differences were found in the GMC properties of these samples. Both show quite large values of virial parameter, ~1 - 100, again suggesting that the clouds have quite disturbed kinematics. Both samples show a broad range of projected rotation axis position angles, including about half with rotation in a direction retrograde compared to Galactic rotation. This may have major implications for the formation and evolution of GMCs, perhaps indicating that strong interactions and mergers between clouds occur quite frequently. Finally, I performed a pilot study with data on 16 clumps from the Census of High and Medium-mass Protostars (CHaMP) to understand the chemical evolution between quiescent and active star-forming systems, as measured by their bolometric luminosity to mass ratio. Using ~90 and ~115 GHz molecular line data I searched for trends in the abundances of HCO^+ and N_2H^+, sensitive to carbon and nitrogen chemistry, respectively. The clumps show a large dispersion in relative abundances, especially HCO^+ and N_2H^+.
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In the series University of Florida Digital Collections.
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Includes vita.
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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 Audra Kathl Hernandez.
Thesis:
Thesis (Ph.D.)--University of Florida, 2011.
Local:
Adviser: Tan, Jonathan.

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THEINITIALCONDITIONSANDEARLYEVOLUTIONOFSTAR-FORMING CLOUDS By AUDRAKATHLEENHERNANDEZ ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2011

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c r 2011AudraKathleenHernandez 2

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ToMorganandLugosi 3

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ACKNOWLEDGMENTS Iwouldliketothankmyfellowgraduatestudents,fortaking thislongjourneywith me.IwouldespeciallyliketothankLeahSimon,JoannaLevin e,SunMiChung,and JustinSchafer,fortheirundyingsupport.Iwouldliketoth ankmyfamily,Mom&Dad, ShilohandAdam,foralwaysbelievinginme,Iloveyouallsom uch.Muchlovegoesout toDeniseConnelly,AnneKondratick,PeteCeballo(RIP),Of cerJenReedy,the8330 Sbuxcrew,andCommonGrounds.AspecialthanksgoestoPhill ipGodwinandGrant Noskoforalltheireditingskills.Iwouldespeciallyliket oacknowledgemyundergraduate thesisadvisorEllenZwiebelforencouragingmetopursueth isdegree.Iwouldliketo thankPeterBarnesforallhishelpandinsightonvariousrad ioobservations.Ialsothank myadvisorJonathanTanforpushingmetoworkharderandtome etdeadlinesInever eventhoughtwerepossible.Mymostsincerethanksandgrati tudegoestoBrandon, whokeptmegroundedandneverletmelosetrackofwhatwasrea llyimportanttome. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 11 CHAPTER 1ANINTRODUCTIONTOSTAR-FORMINGCLOUDS ............... 14 1.1GiantMolecularClouds ............................ 14 1.2TheVirialTheorem ............................... 15 1.3DynamicalPropertiesofGMCs ........................ 16 1.4TheGMCMassFunction ........................... 18 1.5GMCFormationTheories ........................... 18 1.6InfraredDarkClouds .............................. 19 1.7TheoriesofStarClusterFormation ...................... 20 1.8SummaryofThisDissertation ......................... 20 2THEDYNAMICALSTATEOFFILAMENTRAYINFRAREDDARKCLOUDS .. 24 2.1Introduction ................................... 24 2.2MassSurfaceDensityEstimationFrom13 CO ................ 26 2.3Comparison 13COand SMF:PossibleTrendsinTemperature,CODepletion andDustOpacitywith ............................ 29 2.4TheDynamicalStateoftheIRDCFilaments ................. 33 2.4.1IRDCMassesfrom13 COEmissionandMIRDustAbsorption ... 33 2.4.2EllipsoidalCloudVirialAnalysis .................... 34 2.4.3FilamentaryCloudVirialAnalysis ................... 38 2.5Conclusions ................................... 40 3MAPPINGLARGE-SCALECODEPLETIONINAFILAMENTARYINFRARE D DARKCLOUD .................................... 50 3.1AnIntroductiontoCODepletioninaFilamentaryInfrare dDarkCloud .. 51 3.2MassSurfaceDensityfromMIRExtinctionMapping ............ 53 3.3MassSurfaceDensityfromC 18 OEmission ................. 55 3.3.1Observations .............................. 55 3.3.2MassSurfaceDensityandT exEstimates ............... 56 3.4Comparisonof C18Oand SMF:EvidenceforCODepletion ........ 58 3.4.1AlternativestoCODepletion ...................... 62 3.4.2CODepletionandImplications .................... 63 5

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4THEDYNAMICALSTATEOFANINFRAREDDARKCLOUD .......... 71 4.1MotivationtoStudytheDynamicalStateofanInfraredDa rkCloud .... 71 4.2MassSurfaceDensityfromSmall-Median-FilterMIRExti nctionMapping 72 4.330mIRAMObservations ............................ 73 4.4MassSurfaceDensitiesfromCOEmission ................. 74 4.4.1COColumnDensityEstimates .................... 74 4.4.2ExcitationTemperatureEstimates ................... 75 4.4.3C 18 OMassSurfaceDensitiesEstimates ............... 75 4.4.4VelocityDispersionEstimates ..................... 76 4.5MassesofIRDCHfromCOandMIRDustAbsorption ........... 76 4.6TheDynamicalStateofIRDCH ....................... 77 4.6.1EllipsoidalCloudVirialAnalysisofIRDCH .............. 77 4.6.2FilamentaryCloudVirialAnalysisofIRDCH ............. 80 4.7ConclusionsoftheIRDCHDynamicalState ................. 82 5IRDCFORMATIONANDGLOBALGMCPROPERTIES ............. 87 5.1MotivationforaStudyonIRDCFormationandGlobalGMCPr operties .. 87 5.2TheGRSSurvey ................................ 89 5.3GMCpropertiesAroundaSmallSampleofLocalIRDCs .......... 90 5.3.1TheNineCloudIRDCSample ..................... 90 5.3.2DeningGMCmorphology ....................... 90 5.3.3MassEstimationFrom13 CO ...................... 91 5.3.4EstimatesofGMCRotation ...................... 94 5.3.5EstimatesoftheVirialParameter ................... 96 5.4GMCRotationandVirialization ........................ 97 5.4.1LargeSampleSelection ........................ 97 5.4.2Results ................................. 98 5.5ConcludingRemarksonIRDCFormationandGlobalGMCProp erties .. 101 6ASEARCHFORASTROCHEMICALTRENDSINSTAR-FORMINGCLOUDS 119 6.1MotivationtoSearchforAstrochemicalTrendsinStar-F ormingClouds .. 119 6.2TheCHaMPSurvey .............................. 119 6.2.1Strategy ................................. 120 6.2.2MopraObservation ........................... 120 6.2.3DataReduction ............................. 121 6.3TheAnalysisofRegion26 ........................... 122 6.3.1IntegratedIntensityMaps ....................... 124 6.4AstrochemistryofStar-FormingClouds ................... 125 6.5SummaryofFindingsinAstrochemicalTrends ............... 128 7SUMMARYANDCONCLUSIONS ......................... 142 REFERENCES ....................................... 145 6

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BIOGRAPHICALSKETCH ................................ 150 7

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LISTOFTABLES Table page 2-1Escapeprobabilitiesandcriticaldensities ..................... 28 2-2IRDCellipsoidalvirialanalysis ........................... 34 2-3IRDClamentaryvirialanalysis ........................... 42 3-1Parametersofdepletionfactoranalysis ...................... 66 4-1IRDCellipsoidalvirialanalysis ........................... 80 4-2IRDClamentaryvirialanalysis ........................... 83 5-1GMCphysicalparametersfromMethods1and2 ................. 102 5-2GMCphysicalparametersfromMethod3 ..................... 103 6-1CHaMPclumpphysicalparameters ........................ 123 8

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LISTOFFIGURES Figure page 2-1Dependenceof andd N 13CO=d vwithT B .................... 43 2-2ColumndensityproleswithvelocityforIRDCsFandH ............. 44 2-3MorphologyofIRDCF ................................ 45 2-4MorphologyofIRDCH ................................ 46 2-5SubtractionofIRDCenvelopes ........................... 47 2-6Directcomparisonof 13COand SMFinIRDCFandH .............. 48 2-7P 0=Pversusm=m virforstripsinIRDCsFandH .................. 49 3-1MorphologyoftheIRDC ............................... 67 3-2DepletionmapsoftheIRDC ............................. 68 3-3VelocitystructureoftheC 18 OassociatedwiththeIRDCanditsenvelope .... 69 3-4EvidenceforCOdepletion .............................. 70 4-1MorphologyofthelamentaryIRDCH ....................... 84 4-2P 0=Pversusm=m virforstripsinIRDCH ...................... 85 4-3P 0=Pversusm=m virforstripsinIRDCHwithanincreasedabundanceratio .. 86 5-1MapsofCloudA ................................... 104 5-2MapsofCloudB ................................... 105 5-3MapsofCloudC ................................... 106 5-4MapsofCloudD ................................... 107 5-5MapsofCloudE ................................... 108 5-6MapsofCloudF ................................... 109 5-7MapsofCloudG ................................... 110 5-8MapsofCloudH ................................... 111 5-9MapsofCloudI .................................... 112 5-10 versusradius .................................... 113 5-11Thevirialparameterversusradius ......................... 114 9

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5-12Thedistributionof fortwocloudcatalogs ..................... 115 5-13Thedistributionofthepositionangle:Comparisonswi thnumericalsimulations 116 5-14Acomparisonofvelocitydispersionandcloudsize ................ 117 5-15Acomparisonoflog ()withlog ( M 13 CO=M) .................... 118 6-1TheCHaMPSurvey ................................. 129 6-2Region26asseenat8 m(Spitzer-GLIMPSE) .................. 130 6-3ThemainquiescentandactiveregionsofRegion26 ............... 131 6-4Mopra12 COintegratedintensitymap ........................ 132 6-5Mopra13 COintegratedintensitymap ........................ 133 6-6MopraC 18 Ointegratedintensitymap ........................ 134 6-7MopraHCO +integratedintensitymap ....................... 135 6-8MopraHCNintegratedintensitymap ........................ 136 6-9MopraN 2 H +integratedintensitymap ....................... 137 6-10LuminosityfunctionofRegion26 .......................... 138 6-11Meanspectraofvariousmolecularspeciesforthequies centandactiveclumps 139 6-12AcomparisonofHCO +andN 2 H +integratedintensities ............. 140 6-13AcomparisonofvariousabundanceratioswithL bol=M HCO + ........... 141 10

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy THEINITIALCONDITIONSANDEARLYEVOLUTIONOFSTAR-FORMING CLOUDS By AudraKathleenHernandez August2011 Chair:JonathanC.TanMajor:Astronomy Theformationofstarclustersfromgiantmolecularclouds( GMCs)isoffundamental importancefortheevolutionoftheMilkyWayandothergalax iesandyettherearestill manyopenquestions.WhydocertainlocalizedregionsofGMC sformstarclusters, whiletherestofthecloudshowslittlestarformationactiv ity?Isthisprocesstheresult ofspontaneousinstabilitiesinthecloud,perhapsregulat edbyturbulenceormagnetic elds,ortriggeredbyexternalagents?Doesthestarcluste rformationprocesstake fewormanydynamicaltimes?Whataretheprocessesthatcont rolGMCformationand evolution? Ihaveinvestigatedthephysicalpropertiesofmolecularcl oudsinordertoaddress thesequestions.First,using13 CO(1-0)molecularlineemissiondatafromtheGalactic RingSurvey(GRS),Istudiedthedynamicalstateoftwolame ntaryinfrareddarkclouds (IRDCs),whichareexpectedtoberepresentativeoftheinit ialconditionsforstarcluster formation.Icomparedmasssurfacedensities, 13CO,withthosederivedfromsmall mediumlter(SMF)mid-infrared(MIR)dustabsorption, SMF,ndingsystematictrends thatcouldbeduetoCOdepletionfromthegasphaseduetofree zeoutontodustgrains ordecreasedexcitationtemperaturesinthehighestdensit yregions.Furthermore, oneofthelamentswasobservedathigherangularresolutio nwiththeIRAM30m telescopeinmultiplemolecularspecies.IanalyzedJ=2-1a nd1-0linesof13 COandC 18 O.Thelatteryieldedanexcitationtemperatureandmasssurf acedensitymap, 11

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andbycomparisonwith SMF,adepletionmapofthecloud.Withasignicanceof 10 ,IconrmedthatCOdepletioniswidespreadinthecloud.Ane stimatedseveral hundredsolarmassesarebeingaffected,makingthisoneoft hemostmassiveclouds inwhichCOdepletionhasbeenobserveddirectly.Additiona lly,throughellipsoidaland lamentaryvirialanalyses,Ifoundthatthelamentisinas tateconsistentwithsome modelsofvirialequilibrium,althoughsurfacepressurete rmsarestillquiteimportant. Thereistentativeevidencethattheregionsofthelamentw iththemoststarformation activityaremorelikelytobeinvirialequilibrium. Secondly,turningtothelargerscalesofGMCenvironmentsa roundIRDCs,Irst studiedasmallsampleofninerelativelynearbyIRDCsandth eirassociatedGMCs usingGRS13 COemissiondata.ImeasuredGMCmass,positionangleoftherot ation axisprojectedontheplaneofthesky,andthevirialparamet er, .Iinvestigatedhow theseresultsdependedonthescaleusedtodenetheGMCandf ordifferentmethods ofdeningtheGMCboundary.Ifoundmasses 10 5 M ,abroadrangeofprojected rotationaxispositionanglesand 10,suggestingquitedisturbedkinematicsof themoleculargasonthesescales.Nosystematictrendswere foundbetween with sizescaleorwiththemethodusedtoidentifytheGMC.Next,I performedasimilar studyformuchlargersamplesofGMCs.Nosignicantdiffere nceswerefoundinthe GMCpropertiesofthesesamples.Bothshowquitelargevalue sofvirialparameter, 1100,againsuggestingthatthecloudshavequitedisturbedkine matics.Both samplesshowabroadrangeofprojectedrotationaxispositi onangles,includingabout halfwithrotationinadirectionretrogradecomparedtoGal acticrotation.Thismayhave majorimplicationsfortheformationandevolutionofGMCs, perhapsindicatingthat stronginteractionsandmergersbetweencloudsoccurquite frequently. Finally,Iperformedapilotstudywithdataon16clumpsfrom theCensusofHigh andMedium-massProtostars(CHaMP)tounderstandthechemi calevolutionbetween quiescentandactivestar-formingsystems,asmeasuredbyt heirbolometricluminosity 12

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tomassratio.Using 90and 115GHzmolecularlinedataIsearchedfortrends intheabundancesofHCO +andN 2 H +,sensitivetocarbonandnitrogenchemistry, respectively.Theclumpsshowalargedispersioninrelativ eabundances,especiallyHCO +andN 2 H +. 13

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CHAPTER1 ANINTRODUCTIONTOSTAR-FORMINGCLOUDS Itisourcurrentviewthatmoststars,perhapsincludingour ownSun,wereborn notinisolation,butinstarclusters( Lada&Lada2003 ; Gutermuthetal.2009 ),forming fromgas clumps withingiantmolecularclouds(GMCs)orbitingingalacticd isks.The environmentalconditionsintheseformingclustersarelik elytobequitedifferentfrom moreisolatedregions.Inparticular,themasssurfacedens itiesandpressuresare observedtobemuchgreater( McKee&Tan 2003 )andtheimpactoffeedback,suchas ionization,frommassivestarswillbeenhanced.Theseclus tersarethebasicbuilding blocksofthestellarpopulationsofgalaxies.Feedbackfro mtheirmassivestarscontrols theevolutionoftheinterstellarmediumandmayhelpregula rfurtherstarformation. Despitethisimportance,ourignoranceofstarclusterform ationisenormous. Thereislittleconsensusabouttheanswerstoevenverybasi cquestions,suchas: WhatinitiatesstarclusterformationwithinaGMC:someext ernaltriggeringmechanism orspontaneousgravitationalinstabilitiesdevelopingin ternallywithinthecloud?Is starclusterformationaslow,quasi-equilibriumprocesso rdoesitinvolverapidglobal collapseofthegasclumps( Elmegreen2000 ; Tanetal. ; Elmegreen2007 )?Whatsets theefciencyofstarformationonthescaleofaclumpandofa GMC?Theclustered natureofstarformationtellsusthatthisefciencyisgene rallyverylowformostofthe massandvolumeofGMCs,butthenbecomeslargeinverylocali zedregions.What arethelifetimesofGMCsandthemainphysicalprocessestha tcontroltheirevolution? WhatarethechemicalpropertiesofGMCsattheearlystageso fstarformation? 1.1GiantMolecularClouds GMCsarethemostmassiveobjectsintheplaneoftheMilkyWay .Theyarevast ensemblesofgas,mainlyH2,anddust,withmassesof 10 410 6 M ,numberdensities ofHnucleiofn H = 10 210 3 cm3,andphysicalscalesoftensofparsecs.Theyare 14

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knowntobemagnetizedandturbulent,andarelikelytobesel f-gravitating( Williams etal. 2000 ),althoughthisisnotuniversallyaccepted(e.g. Dobbsetal.2011 ). GMCsdonotgenerallyhavesimple,regularmorphologies.In stead,theirstructure, bothglobalandinternal,iscomplex.Theycontainmanyhigh erdensityconcentrations invariousshapessuchaslamentsandclumps. Williamsetal. ( 2000 )denedthe followingterminologywithrespecttoGMCsubstructure:Cl umpsarecoherentregions inl b vspaceandaregenerallyidentiedfromspectraofmolecular lineemission. Star-formingclumpsarethoseclumpsinwhichstarclusters form.Thesmallest,densest regionsofGMCsarecores,regionswhichevolvetoproducesi nglestarsorstarsystems (e.g.closebinariesandtriples). 1.2TheVirialTheorem Thedynamicalstateofacloud(e.g.anentireGMCoranintern alsubstructuresuch asaclumporlament)isdescribedbythevirialtheoremLetIbethemomentofinertia ofacloud,I =Rr 2 dm.Thevirialtheoremisexpressedby:1 2 d 2 dt 2 I = 2(TTs ) +M+ W .(1–1) Here, T isthetotalinternalkineticenergy(includingthermalkin eticenergy), M isthe netmagneticenergy,andWisthegravitationalbindingenergy.Thetotalkineticener gy termisgivenby: T=ZV2 3 P th + 1 2v 2dV3 2 PV .(1–2) Here,P thisthelocalthermalpressure,visthelocalturbulentvelocitydescribingthe non-thermalpressureofthecloud.,andVisthecloudvolume. Pisthemeanpressure ofthegasgivenbytheidealgaslaw( P = Nk B T=V).Theterm Tsofequation 1–1 isthe kineticenergythatwouldresultifthecloudsurfacepressu repervadedthecloudvolume. 15

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Forasphericalcloudwithuniformdensity,amassequaltoM, aradiusofR,the gravitationalbindingenergyWis:W =3 5GM 2 R.(1–3) Forthemagneticeld,B,thenetmagneticenergy M canbedescribedasthe differencebetweenthetotalmagneticenergywithintheclo udandthatatalarge distancefromthecloud. M isgivenby: M= 1 8 Z( B 2B 2 O ) dV .(1–4) Ifthepresenceofmagneticeldsisignored,thenastaticcl oud,i.e.onewhichisin virialequilibrium,isdescribedbyd 2 dt 2 I = I= 0.Ifwecanalsoneglectsurfacetermsthen equation 1–1 simpliesto2T+ W = 0.(1–5) Inthiscasethekineticenergyishalftheabsolutevalueoft hegravitationalenergyand thesystemisgravitationallybound. Oneexpectsacloudtoreachapproximatevirialequilibrium onceithasexisted forlongerthanafewsignalcrossingtimes,t s2 R= (where isthe1Dvelocity dispersion), and ifthesurroundingenvironmentisrelativelysteady,i.e.e volvingon timesscaleslongerthanthissignalcrossingtime.Aswewil lsee,forGMCsandtheir substructures,thesurfacetermsinthevirialtheoremaret ypicallyimportantsothat equation( 1–5 )cannotbeapplied. 1.3DynamicalPropertiesofGMCs ThedynamicsofGMCswererstcharacterizedby Larson ( 1981 ).Larson presentedthreerelationswhicharenowcommonlyrefereedt oas“Larson'sLaws”.The rstoftheselawsisthe linewidth-sizerelation andstatesthatformolecularcloudswith supersonicturbulence,theline-widthsincreaseasapower ofthesize, v/R p.Larson estimatedapower-lawindexofp0.38.Thisisclosetothe1=3valuedescribing 16

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incompressibleturbulentuids,eventhoughGMCsarecompr essible.Inlaterstudies, Solomonetal. ( 1987 )foundp = 0.50.05basedonGMCsinsidethesolarcircle fortherelation: /R p(where isthe1Dvelocitydispersionequalto v=2.35). However,morerecently Heyeretal. ( 2009 )foundthatforGMCs,thevelocitystructure function,denedastheratiobetweenthevelocitydispersi onandsquarerootofthe radius, =R 1=2,varieswiththemasssurfacedensity,,ofthemoleculargas.Thisresult disagreeswithLarson'sthirdrelationwhichstatesthatal lGMCshaveapproximately equalcolumndensities(discussedmorebelow),andtherefo reequals,implyingthat thereisnouniversalityofthevelocitystructurewithinGM Cs.Theauthorspointoutthat thedependenceof =R 1=2onwasnotdetectedinpreviousstudiesduetothelimited rangeofdensitiesobservedbyearlylowresolutiondataset s. ThesecondLarsonrelationisthatallGMCsaregravitationa llybound.This relationshipimpliesthattheobservedmassofthecloudise qualtothevirialmass givenby:M vir = 52 R G ,(1–6) wherethecloudsize,R,isdenedbyastheradiusofacirclewiththeequivalentare aof thecloud. Larson'sthirdrelationstatesthatallGMCshaveapproxima telyequalcolumn densities.Healsopointedoutthatonlytwooftheserelatio nsareindependent,(i.e. anyonerelationcanbederivedfromtheothertworelations) Solomonetal. ( 1987 ) foundthatGMCswithinthesolarcirclehave( N H22(1.50.3) R 0.00.1 pc ),where( N H22 = N H=10 22,i.e.masssurfacedensitiesofabout200 Mpc2.However,basedon the13 COmolecularlinedatafromtheBU-FCRAOGalacticRingSurvey( GRS),andthe cloudsizesfrom Solomonetal. ( 1987 ), Heyeretal. ( 2009 )foundalowermedianmass surfacedensityof42 Mpc2.Theauthorssuggestedthatmaybeunderestimated becauseofsubthermalexcitationinthe13 CO(the12 COlineis 5timesasbright as13 CO)andtheassumptionofaconstantabundanceratioofH 2to12 COintheir 17

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estimates.Theypointoutthatiftheseissueswereaccounte dfor,themasssurface densitycouldriseto80120 Mpc2. Roman-Duvaletal. ( 2010 )foundamedianmass surfacedensityof140 Mpc2,basedon750molecularcloudswithintheGRS.This studydidnotsufferanunderestimationinsincetheirestimateswereperformedwithin4contoursofthe13 COintegratedintensitywhichselectsthedensestregionsofG MCs. 1.4TheGMCMassFunction LargescaleMilkyWaysurveyshaveproducedcatalogsofGMCs (12 CO: Dame etal.1986 ; Solomonetal.1987 ;13 CO: Jacksonetal.2006 ). Williams&McKee ( 1997 ) describedthemassfunctionoftheseGMCswithapowerlaw:dN c d ln M c = N clM c M u c ,(1–7) forcloudswithM c
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fromatomicgas.Furthermore,theseinteractions,orcloud -cloudcollisions,maycreate overdenseregionsandthustriggerstarformationactivity 1.6InfraredDarkClouds InfraredDarkClouds(IRDCs)areaselectionofdense,coldc lumpsandlaments withinGMCs.Theyhavebeenproposedtobetheprogenitorsof massivestarsand starclusters( Eganetal.1998 ; Careyetal.1998 ; Rathborneetal.2006 ).IRDCswere rstidentiedasdarkextinctionfeaturesagainstthebrig htmid-infraredemissionofthe GalacticPlanethroughtheMSXandISOspacesatellites( Eganetal. ; Peraultetal. 1996 ).TheyarefoundpreferentiallytowardstheGalaxy's5kpcm olecularring,which containsalargefractionofthemolecularhydrogenintheGa laxy.Thestudyby Simon etal. ( 2006a )catalogednearly10,000IRDCsusing8 mdatafromtheMSXsatellite. However,duetoahighlyvariablebackground,manyofthesem aybespuriousfeatures. Morerecently, Peretto&Fuller ( 2009 )cataloged 11, 000IRDCsusingthe8 m MIR-datafromtheSpitzer-GLIMPSEsurvey.Duetotheincrea sedresolutionofSpitzer comparedtopastsurveys,80%ofthecloudswerepreviouslyundetected. TheirstrongextinctionintheMid-IRrequiresIRDCstohave highcolumndensities. Earlystudiesshowedthattheyarecold(T20 K)anddense(n H>10 5 cm3)( Egan etal.1998 ; Careyetal.1998 2000 ).Morerecently,thestudyby Rathborneetal. ( 2006 )showedthatIRDCshavetypicalsizesontheorderofafewpar secs,densities ofn H>10 4 cm3,andmasseswithinarangeofM10 310 4 M .Ithasthusbeen suggestedthatIRDCsaretheprecursorstomassivestarsand starclusters. TheformationofIRDCsisnotcurrentlyunderstood.Onetheo ryisthatIRDCs simplyformthroughthegravitationalcollapseofhigh-den sityperturbationswithin GMCs.Thismayberegulatedbyturbulenceormagneticeldsa nditmaytakejustafew ormanyfree-falltimes.AnothertheorysuggeststhatIRDCs aretheresultofatriggered collapseviaexternalperturbations,suchascloud-cloudc ollisionsorstellarionizationor supernovafeedback. 19

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1.7TheoriesofStarClusterFormation Thereisalsodebatesurroundingstarclusterformation.On escenariosuggests thatstar-formingclumps,orproto-clusters,areinastate ofquasi-virialequilibrium( Tan etal. 2006 ).Theopposingscenariosuggeststhatstar-formingclumps areundergoing rapidglobalcollapse( Elmegreen2000 ; Hartmann&Burkert2007 ).Thisdebateis alsorelatedtothetimescaleofstarclusterformation,i.e .whetheritislongorshort comparedtothefree-falltimescale( McKee&Ostriker 2007 ),t =3 32 G 1=2 = 1.3710 610 3 cm3 n H(1=2) yr .(1–8) 1.8SummaryofThisDissertation Thefollowingchaptersinthisdissertationare,oraimtobe ,self-containedjournal articles.Chapter2waspublishedinTheAstrophysicalJour nal,titled“TheDynamical StateofFilamentaryInfraredDarkClouds”( Hernandez&Tan 2011 ).Chapter3has beensubmittedforpublicationinTheAstrophysicalJourna l,titled“MappingLarge-Scale CODepletioninaFilamentaryInfraredDarkCloud”.Chapter s4through6havenotyet beensubmittedforpublication. Mydissertationfocusesonthekinematicsandphysicalprop ertiesofIRDCs, includingtheirsurroundingGMCs,astheyarebelievedtopo rtraytheinitialconditions ofstarandstarclusterformation.InChapter2( Hernandez&Tan 2011 )Ianalyze13 CO J = 10lineemissiondatafromtheGalacticRingSurvey(GRS)of Jacksonetal. ( 2006 )fortwohighlylamentaryIRDCs.Afterconsideringthemol ecularenvelopes surroundingthelaments,themasssurfacedensitiesderiv edfrom13 CO, 13CO,are comparedwiththosederivedfromthesmall-median-lter(S MF)mid-infrareddust extinctionmappingof Butler&Tan ( 2009 ), SMF.Thereisanapproximatelylinear relationshipbetweenthetwomethodsofmeasuringthemasss urfacedensityand evidencetheratio 13CO= SMFdecreaseswithincreasing SMF.Thisdecreasingtrend maybeduetoasystematicdecreaseinexcitationtemperatur e,increaseindustopacity, 20

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ordecreaseofthe13 COabundanceduetodepletioninregionsofhighcolumndensity Throughanellipsoidalandlamentaryvirialanalysisofbo thclouds,wendthatthe surfacepressuretermsappeartobedynamicallyimportantt othestructureofthe lamentandthus,theselamentsmaynotyetbeinvirialequi librium.Wendtentative evidencethattheregionsofthelamentwiththemoststarfo rmationactivityarecloser tovirialequilibrium. InChapter3( Hernandezetal. 2011 ),furtheranalysiswascarriedoutonone highlylamentaryIRDC(G035.39 00.33)usingmoresensitive,higherresolutionC 18 Oemissionlinedata,J = 10andJ = 21transitions,takenwiththeIRAM30m telescope.Iderivedtheexcitationtemperaturesasafunct ionofpositionandvelocityin thecloud,withtypicalvaluesof 7K.Themasssurfacedensities, C18O,werethen derivedassumingstandardgasphaseabundancesandaccount ingforopticaldepth intheline,whichcanreachvaluesof 1.Themasssurfacedensitiesreachvalues of 0.07gcm2.Theseresultswerethencomparedtothemasssurfacedensit ies derivedfrommid-infrared(MIR)extinctionmapping, SMF,from Butler&Tan ( 2009 ). Withasignicanceof10 ,wend C18O= SMFdecreasesbyaboutafactorof5as SMFincreasesfrom 0.02to0.2gcm2,whichweinterpretasevidenceforCOdepletion. InChapter4(Hernandezetal.inprep),thedynamicalstateo fthelamentaryIRDC (G035.39 00.33)isanalyzedusing13 COandC 18 O,J = 10andJ = 21transitions, molecularlineemissiondatafromtheIRAM30mtelescope.Us inginformationonthe lament'skinematics,anellipsoidalandlamentaryanaly sisisagainperformed.With thishigherresolution,multi-transitiondata,thelamen taryvirialanalysisnownds that,althoughthesurfacepressuretermsareimportant,th elamentisself-gravitating andmayinfacthavereachedvirialequilibrium.Thediffere ncebetweentheseresults andthoseofChapter2canbeunderstoodasbeingduetotheuse ofamoreaccurate estimateofT exoftheCOmoleculesandamoreaccurateaccountingfortheeff ectsof depletion. 21

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Chapter5embarksuponastudyoftheformationandevolution ofthelargescale GMCsinwhichIRDCsareembedded.UsingtwolargesamplesofI RDCsaspositional tracersofGMCstowardstheinnerGalaxy,Ianalyzedtheprop ertiesofthesurrounding GMCmaterial.Focusedondeterminingthecloud'sdegreeofr otationandvirialization, GRS13 COmolecularlinedatawasusedtoestimatethemassesandrotat ionalvelocities ofeachGMC.TwoindependentlyderivedsamplesofGMCs(cata logsfrom Simon etal.2006b and Kodaetal.2006 ),wereemployedtodetermineiftherewasany statisticaldifferencebetweenGMCsdetectedthroughexti nctionorthroughmolecular lineemission.Byinvestigatingthedistributionofpositi onanglesofcloudrotationaxes projectedontheplaneofthesky,wefoundthatthereisnosta tisticaldifferencebetween thetwocloudsamples,veriedbyaKSprobabilityof 0.30,andthatasubstantial fractionofthecloudsrotateinaretrogradesensecompared totheirGalacticorbits. Thisobservationisimportant,asintuitively,oneexpects thatifGMCsformrapidlyfrom large-scaledispersedgasthentheGMCrotationshouldtend tobeprograde,following thedirectionofthegeneralGalacticrotation.However,th epresenceofretrogradecloud rotationsuggeststhatsomecloudshavehadtimetointeract withtheirsurrounding environmentorothercloudsandthusaltertheirangularmom entum.Thisconclusion supportstheoreticalmodelsofcloudformationandevoluti onthroughconverging molecularowsandcloud-cloudcollisions. Thelastpartofmydissertation,Chapter6,includesworkdo neaspartofthe CensusofHighandMedium-massProto-stars(CHaMP)team.Th eCHaMPSurvey ( Barnesetal. 2011 ),ledbyDr.PeterBarnes,istherstlarge-scale,unbiased uniform mappingsurveyatsub-parsecresolutionofmassiveclumpsi ntheSouthernMilkyWay (280
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presentsapilotstudyaimedatunderstandingthechemicale volutionbetweenquiescent andactivestar-formingclouds. 23

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CHAPTER2 THEDYNAMICALSTATEOFFILAMENTRAYINFRAREDDARKCLOUDS Thedense,coldgasofInfraredDarkClouds(IRDCs)isthough ttoberepresentative oftheinitialconditionsofmassivestarandstarclusterfo rmation.Weanalyze13 CO J = 10lineemissiondatafromtheGalacticRingSurveyof Jacksonetal. ( 2006 ) fortwolamentaryIRDCs,comparingthemasssurfacedensit iesderivedfrom13 CO, 13CO,withthosederivedfrommid-infraredsmallmedianlterex tinctionmapping, SMF, by Butler&Tan ( 2009 ).Afteraccountingformolecularenvelopesaroundthelam ents, wendapproximatelylinearrelationsbetween 13COand SMF,i.e.anapproximately constantratio 13CO= SMFintheclouds.Thereisavariationofaboutafactoroftwo betweenthetwoclouds.Wendevidenceforamodestdecrease of 13CO= SMFwith increasing,whichmaybeduetoasystematicdecreaseintemperature,in creasein importanceofhigh13 COopacitycores,increaseindustopacity,ordecreasein13 COabundanceduetodepletioninregionsofhighercolumndensi ty.Weperformellipsoidal andlamentaryvirialanalysesoftheclouds,ndingthatth esurfacepressureterms aredynamicallyimportantandthatgloballythelamentsma ynotyethavereached virialequilibrium.Somelocalregionsalongthelamentsa ppeartobeclosetovirial equilibrium,althoughstillwithdynamicallyimportantsu rfacepressures,andthese appeartobesiteswherestarformationismostactive. 2.1Introduction Massive,highcolumndensityInfraredDarkClouds(IRDCs), typicallyidentied asbeingopaqueagainsttheGalacticbackgroundat 10m,arethoughttocontain thesitesoffuturemassivestarandstarclusterformation( e.g. Rathborneetal. 2006 ), sincetheirdensities(n H >10 4 cm3)andmasssurfacedensities( >0.1 g cm2)are similartoregionsknowntobeundergoingsuchformationact ivity( Tan 2007 ).Studiesof molecularlineemissionfromIRDCscanhelpdeterminetheir kinematics.Inparticular, wewouldliketoknowiftheyaregravitationallybound,ifth eyarenearvirialequilibrium 24

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andifthereisevidenceforcoherentgasmotionsthatmighti ndicatethatIRDCformation involvesconvergingatomicows( Heitschetal. 2008 )orconvergingmolecularows fromcloudcollisions( Tan 2000 ). Inthisstudyweuse13 CO J = 10lineemissiondatafromtheGalacticRing Survey(GRS; Jacksonetal.2006 )fortwolamentaryIRDCs,cloudsF(l = 34.437 ,b = 0.245 ,d = 3.7kpc)andH(l = 35.395 ,b =0.336 ,d = 2.9kpc)fromthesample of10relativelynearbymassiveanddenseIRDCsof Butler&Tan ( 2009 ;hereafter BT09),comparing13 CO-derivedmasssurfacedensities, 13CO,withsmallmedianlter (SMF)mid-infrared(MIR)(8m)extinctionmappingderivedmasssurfacedensities, SMF,usingthemethodofBT09appliedtothe Spitzer InfraredArrayCamera(IRAC) band4imagesoftheGalacticplanetakenaspartoftheGalact icLegacyMid-Plane SurveyExtraordinaire(GLIMPSE; Benjaminetal.2003 ).Weconsidersystematicerrors ineachofthesemethods,whichisnecessarybeforeanalyzin glargersamplesofclouds. WearealsoabletolookforevidenceofchangingCOabundance withcolumndensity, e.g.duetopossibledepletionofCOathighdensities.Wethe nperformavirialanalysis ofthecloudstodeterminetheirdynamicalstate. Therehavebeenanumberofotherstudiescomparing13 COderivedmasssurface densitieswiththosefromothermethods.Forexample, Goodmanetal. ( 2009 )compared nearinfrared(NIR)dustextinction,farinfrared(FIR)dus temissionand13 COline emissioninthePerseusgiantmolecularcloud(GMC),probin gvaluesofupto 0.02 g cm2(i.e.uptoA V'8mag).Evenafteraccountingfortemperatureandoptical depthvariationstheyconcludedthat13 COemissionwasarelativelyunreliabletracerof masssurfacedensity,perhapsduetothreshold,depletiona ndopacityeffects.Ourstudy probeshighervaluesof,from 0.01to 0.05 g cm2,andcompares13 COemission withMIRextinctioninordertoinvestigatetheseprocesses Battersbyetal. ( 2010 )used13 COemission,MIRextinctionandFIRdustemission methodstomeasureandthemassofclumpsin8IRDCs,oneofwhichisIRDCF 25

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ofourstudy.Theydidnotpresentaspeciccomparisonof 13COwithothermethods, althoughderivedclumpmasseswereinreasonableagreement .Theirsamplealso includedMIR-brightregions,associatedwithultra-compa ctHIIregions,forwhichthe MIRextinctionmethodcannotbeapplied.Aswedescribebelo w,ourapproachdiffers inanumberofways,includingbyfocusingonlamentaryandm ostlyquiescentregions ofIRDCsforwhichtheMIRextinctionmethodismostreliable andwhicharelikelyto beclosertotheinitialconditionsofthemassivestarandst arclusterformationprocess. WenotethatwhileIRDCFinparticulardoescontainsomeregi onsofquiteactivestar formation,includinganultra-compactHIIregion,hereweh aveconcentratedonitsmore quiescentportions. 2.2MassSurfaceDensityEstimationFrom13 COWeevaluatethecolumndensityof13 COmolecules,d N 13CO,inavelocityintervald vfromtheirJ = 1!0emissionviad N 13CO ( v ) d v = 8Q rot A3 0 g l g u 1exp h kT ex 1 ,(2–1) whereQ rotisthepartitionfunction,A = 6.3355108 s1istheEinsteincoefcient, 0 = 0.27204cm,g l = 1andg u = 3arethestatisticalweightsofthelowerand upperlevels, istheopticaldepthofthelineatfrequency ,i.e.atvelocityv,T existheexcitationtemperature(assumedtobethesameforall rotationallevels).For linearmolecules,thepartitionfunctionisQ rot =P 1J =0 (2 J + 1)exp(E J=kT ex )withE J = J ( J + 1) hBwhereJistherotationalquantumnumberandB = 5.510110 10 s1istherotationalconstant.Thusfor13 CO(1-0)wehaveE J=k = 5.289K.ForJ = 1,Q rot = 4.134, 6.018, 7.906forT ex = 10, 15, 20K. TheopticaldepthisdeterminedviaT B ,= h k [ f ( T ex )f ( T bg )]1e ,(2–2) 26

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whereT B isthebrightnesstemperatureatfrequency ,f ( T )[exp( h=[ kT ])1]1, andT bg = 2.725Kisthebackgroundtemperature.T B isderivedfromtheantenna temperature,T A,viaT A f clump T B ,where isthemainbeamefciency( = 0.48fortheGRS)andf clumpisthebeamdilutionfactorofthe13 COemittinggas,whichwe assumetobe1fortheIRDCswearestudying.However,itshoul dbenotedthatthe BT09MIRextinctionmapsoftheIRDCsdoshowthatthereisstr uctureonscales smallerthantheangularresolutionoftheGRSsurvey.Given theobservedT B and foranassumedT exwesolveequations( 2–1 )and( 2–2 )for andthusd N 13CO=d v(see Fig. 2-1 ).ForagivenT B, ,thisgureallowsustojudgethesensitivityofthederived columndensityperunitvelocitytotemperatureuncertaint ies. Whileweusetheaboveformulae,whichaccountforopticalde pth,tocalculateour columndensityestimates,forconveniencewealsostatethe irbehaviorinthelimitof opticallythinconditions.WehaveT B ,= ( h=k )[ f ( T ex )f ( T bg )] sothatd N 13CO ( v ) d v = 1.210 14 Q rot f ( T ex )f ( T bg ) [1e (h=kT ex ) ]1 T A=K f clump cm2 km1 s (2–3) !1.110 15 T A=K f clump cm2 km1 s ( T ex = 15 K). (2–4) Thelastcoefcientchangesto(0.9865, 1.347)10 15forT ex = 10, 20K. Devine ( 2009 )estimatesatemperatureof19KforcloudFbasedonVLA observationsofNH 3 (1, 1)and(2, 2).Forthiscloud,wethusadoptatemperatureof 20K.ForcloudHwechooseamoretypicalIRDCtemperatureof1 5K( Careyetal. 1998 ; Careyetal.2000 ; Pillaietal.2006 ).Wealsoconsidertheeffectofvaryingthese temperatures. TheGRShasanangularresolutionof46 00 ,withsamplingevery22 00 .Thevelocity resolutionis0.22km s1( Jacksonetal. 2006 ).Fromamorphologicalexamination ofthe13 COemissioninl b vspaceandcomparisontotheMIRextinctionmapsof BT09weidentifythevelocityrangeofthegasassociatedwit heachIRDClament(see Figs. 2-2 2-3 and 2-4 ).ForcloudFweconsiderassociatedgastobeatLSRvelociti es 27

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Table2-1.Escapeprobabilitiesandcriticaldensities IRDCSpectrumN 13CO 13COn H2n crit n H2=(n crit )(seeFig. 2-2 )(10 16 cm2)(g cm2)(cm3)(cm3) Fmean2.730.03440.873134016600.807 Fhigh4.940.06220.705243013401.81 Hmean2.750.03470.696285013222.15 Hhigh3.460.04360.587359011203.22 4865 km s1andforcloudHat4050 km s1.Thetotal13 COcolumnisthenevaluated overthevelocityrangeofthecloudN 13CO =RdN 13CO. ToconvertfromN 13COtototalmasssurfacedensity 13COwerstassumen 12CO n 13CO = 6.2 R gal kpc + 18.7(2–5) ( Milametal. 2005 ),whereR galisthegalactocentricradius.ForcloudsFandHwe estimateR gal = 5.37, 5.89kpc,respectively(assumingR gal,0 = 8.0kpc),whichwould yieldn 12CO=n 13CO = 52, 55,respectively.Forsimplicityweadoptn 12CO=n 13CO = 54for bothclouds.Wethenassumen 12CO n H2 = 2.0104 ,(2–6) similartotheresultsof Lacyetal. ( 1994 ).Theobservedvariationinthisabundance inGMCsisaboutafactoroftwo( Pinedaetal. 2008 ),andthisuncertaintyisamajor contributortotheoverallsystematicuncertaintyinoures timateof 13CO.Thusour assumedabundanceof13 COtoH 2is3.70106and 13CO = 1.26102 N 13CO 10 16 cm2 g cm2 ,(2–7) assumingamassperHnucleusof H = 2.341024 g. TheassumptionofLTEbreaksdownifthedensityofthegasisl owerthanthe effectivecriticaldensity, n crit,i.e.thecriticaldensityof13 CO(J=1-0),n crit = 1.910 3 cm3,allowingforradiativetrappingwithescapeprobability = e ,wherewe approximate asthecolumndensityweightedmeanvalueof .Note,foraspherical cloudwewouldset equaltotheaverageof =2,butweuse forthesecloudswith 28

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alamentarygeometrysinceweexpect seenalongourlineofsighttoberelatively smallcomparedtootherviewingangles. Heyeretal. ( 2009 )arguedsub-thermal excitationof13 COrotationallevelsmaybecommoninGMCs,causinglowervalue s oflineemissionthanexpectedunderLTEconditionsandthus causingestimates ofbasedonLTEassumptionstobeunderestimates.TheIRDClam entsweare consideringaregenerallyofhigherdensitythanthetypica lGMCvolumesconsidered by Heyeretal. ( 2009 ).FortheaverageandhighestintensityspectraineachIRDC (see Fig. 2-2 ),weevaluate (seeTable 2-1 ).Wealsoestimaten H2,assumingalament line-of-sightthicknessthatisequaltoitsobservedwidth .Acomparisonofn H2with n critshowsthatthedensitiesareclosetoorgreaterthantheeffe ctivecriticaldensities,thus justifyingtheassumptionofLTEconditions.Furthermore, weexpectthatthetypical densityatagivenlocationisgreaterthanourestimatedval uesduetoclumpingon angularscalesthataresmallerthanthe46 00 resolutionoftheCOobservations.Such clumpingisapparentintheMIRextinctionmaps(Figs. 2-3 & 2-4 ). 2.3Comparison 13COand SMF:PossibleTrendsinTemperature,CODepletion andDustOpacitywithThemorphologiesofIRDCsFandHareshowninFigures 2-3 and 2-4 ,respectively. The13 COemissionismoreextendedthanthestructuretracedbytheBT 09MIR extinctionmaps,whicharederivedbycomparingtheobserve d8mintensityatthe cloudpositionwiththeexpectedbackgroundintensityinte rpolatedfromnearbyregions. Uncertaintiesinthisestimationofthebackgroundleadtoa lackofsensitivityoftheMIR extinctionmapstomasssurfacedensitycontrasts.0.013 g cm2. Sincethereisasignicantamountofmoleculargasinthesur rounding“envelope” regionsaroundthelaments,tocomparetheratioof SMFand 13COinthelamentswe mustrstsubtractthecontributionto 13COfromtheenvelopes.Todothisweconsider orthogonalstripsacrosseachIRDClamentandmeasure13 COemissiononeitherside (seeFigs. 2-3 & 2-4 ).Thespectraofthese“off-source”,enveloperegionsarec orrected 29

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foropticaldeptheffects,asdescribedabove,averagedand thensubtractedfromthe central“on-source”,lamentregion(seeFig. 2-5 ).Wendtheenvelope-subtracted spectraaregenerallynarrowerthanthetotal.Wealsondth atthesizeofnegative residualscreatedinthesubtractionprocessarerelativel ysmall.However,thefactthat insomecasesweseequitesignicantvariationintheenvelo pespectrafromoneside ofthelamenttotheother,suggeststhatthisisoneofthema jorsourcesofuncertainty inmeasuringthemolecularemissionpropertiesoftheseemb eddedlaments.Afterthis procedure,wearenowinapositiontocomparetheenvelope-s ubtractedvaluesof 13COwiththosederivedfromtheSMFextinctionmappingmethodof BT09. WealsonotethattheMIRextinctionderivedvaluesofsufferfromtheirown systematicuncertainties,includingcorrectionsduetofo regrounddustemission( Butler& Tan 2009 ),scatteringintheIRACarray( Battersbyetal. 2010 ),adopteddustopacities anddusttogasratios.However,saturationduetolarge8mopticaldepthand/oran insufcientlysubtractedforegroundisnotanimportantso urceoferrorforourpresent study,sincethevaluesof SMFareinanycasereducedwhenthemapsaresmoothedto thelowerresolutionofthe13 COdata. AsnotedbyBT09,theMIRextinctionmappingtechniquefails forlocations wheretherearebrightMIRsources.Iftheintensityoftheso urceisgreaterthanthe backgroundmodel,thenformallyanunphysical,negativeva lueofisreturnedby thismethod.IntheanalysisofBT09,negativevaluesofarealloweduptoacertain thresholdvaluetoaccountfornoise-like,approximatelyG aussian,uctuationsinthe backgroundintensity.Forthemoreextremeuctuationscau sedbybrightsources, BT09set = 0.ThustheeffectofabrightMIRregionwithinanIRDCistocau sethe extinctionmappingmethodtounderestimatethetruemasssu rfacedensity.Formost point-likeMIRsources,thiseffectisquiteminorafterthe extinctionmapsareaveraged tothe22.14 00 pixelscaleoftheCOobservations.However,inIRDCFweiden tifytwo 30

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regions(indicatedinFig. 2-3 ),whicharesignicantlyaffectedbybrightMIRsourcesand excludethemfromthesubsequentanalysis. Thevaluesof 13CO(afterenvelopesubtraction)and SMFforeachpixelinthe lamentregionsofIRDCsFandHarecomparedinFigure 2-6 .Wenotethatboththese measuresofareindependentofthedistancetothecloud.Consideringju stthedata with 13COand SMF>0.01 g cm2,thebesttpowerlawrelation 13CO=g cm2 = A ( SMF=g cm2 ) has = 0.770.18, 0.320.28andA = 0.580.44, 0.0740.069for IRDCsFandH,respectively. Overtherange0.01< SMF=g cm2<0.07wendthat 13CO' SMFtowithin afactorof 2forthemeanvaluesineachIRDClament.Thedispersionwith inan individualIRDCfrompixeltopixelisalsoataboutthisleve l.Thesystematicoffsets mayreectrealsystematicvariationsoftheassumedtemper ature,13 COabundance, dustopacitiesorenvelopesubtractionmethodforeachIRDC comparedtoouradopted valuesandmethods.Thedispersionmayreectlocalsystema ticvariationsanderrors introducedbymeasurementnoise. InbothIRDCstheratio 13CO= SMFdecreaseswithincreasingmasssurfacedensity asmeasuredby SMF.Wegaugethesignicanceofthistrendbynotingthattheabo ve valuesof forIRDCsFandHdifferfromunityby1.3and2.4standarddevi ations, respectively,assumingerrorsaredistributednormally. Thereareseveralphysicalprocessesthatmaybecausingsuc hatrend.A systematictemperaturedecreasefromthelowercolumndens ity,outerregionsof thelamentstothehighercolumndensitycenterswouldlead ustosystematically underestimate 13COinthelatter,whilehavinglittledirecteffectondustopac ities (althoughtheremaybeanindirecteffectviaformationofic emantles,seebelow).For thetemperaturerangesweexpecttobepresent,i.e.from 10-20K(e.g. Pillaietal. 2006 -althoughnotethesearebasedonmeasurementsofNH 3,whichmaytrace differentconditionstothoseofthe13 CO),thiseffectbecomesimportantforvaluesof 31

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T B >4K(seeFig. 2-1 b).Weillustratethesizeofthiseffectforthehighest SMFpositionsinIRDCsFandHinFig. 2-6 .Asystematictemperaturedecreaseof5Kinthe highregionscouldremovemuchoftheobservedtrend. Anotherpossibilityisthatourcorrectionsfortheoptical depthofthe13 COemission aresystematicallyunderestimatedatthehighercolumnden sitypositions.Thiswouldbe expectedifasignicantamountofmassiscontainedinunres olveddensecores.The largestopticaldepthcorrectionsinthehighestcolumnden sitypositionspresentlylead toanincreaseintheestimatedcolumnbyfactors <2.Futurehigherangularresolution13 COandC 18 Oobservationsoftheselamentsarerequiredtoinvestigate thisissue further. DepletionofCOmoleculesontodustgrainsisknowntooccuri ncold,highvolume densitygas( Casellietal. 1999 ).Thisprocesscouldsystematicallyreducethegas phaseCOabundanceinthehighregionsoftheIRDCs.Fordepletiontobefully responsiblefortheobservedtrendsinIRDCsFandHwouldreq uireaboutafactorof2 depletionas SMFincreasesfrom0.01to0.05g cm2.Becauseofdepletion,COisnot expectedtobeanidealtracerofthedensest,coldestpartso fIRDCs.Highresolution studiesofothertracers,suchasNH 3,willlikelybeneededtomeasurethekinematicsof theseregions. ThedepletionofCOviaformationofCOicemantlesondustgra inswouldalsohave someeffectontheMIRopacitiesofthesegrains,thusaffect ingourmeasurementof SMF.Thegrainswouldbecomelargerandabsorptionfeaturesdue topre-existingwater icemantlesmaybecomeobscured.The Ossenkopf&Henning ( 1994 )grainmodels showa 50%increasein8mopacity, 8m,goingfrombaregrainstothosewiththick icemantles.TheBT09estimatesof SMFassumedaconstantvalueof 8mconsistent withthethinicemantlemodelof Ossenkopf&Henning ( 1994 ).Thustheobserved decreaseintheratioof 13CO= SMFwithincreasingmasssurfacedensitycouldbe 32

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causedbythickeningofgrainicemantles,causingustosyst ematicallyoverestimate SMF. Anotherpossibleexplanationforatrendofdecreasing 13CO= SMFwithincreasing masssurfacedensityisactivechemicalfractionation( Langeretal.1980 1984 ; Glassgoldetal.1985 ; Visseretal.2009 ),whichenhancestheabundanceof13 COinregionswhere13 C +ispresentviatheviatheion-moleculeexchangereaction( Watson etal. 1976 ),12 CO + 13 C +!12 C + + 13 CO + 35 K.FUVirradiationmaintainsarelatively highabundanceof13 C +intheouterregionsofthecloud,withA V.1mag.Therelative abundanceof13 COto12 COcanbeenhancedbyfactorsof 10.ForA V&2,the enhancementfactorisonlyabout20%(e.g.foramodelwithn H 2 = 10 3 cm3andT=20K; Glassgoldetal.1985 ).ForIRDCsFandH,thelamentsaretypicallyembeddedinsi de “envelope”gaswith 13CO'0.01 g cm2,i.e.N H'410 21 cm2.Thetrendof decreasing 13CO= SMFisobservedtooccuras SMFincreasesto 0.05 g cm2.13 COfractionationenhancementsshouldnotbevaryinginthisre gimebylargeenoughfactors toexplainourobservedresults.Itshouldalsobenotedthat eveninthelower-column densityregions,iftheFUVuxislargeenough,thenisotope selectivephotodestruction of13 COcomparedtotheself-shielded12 CO( Bally&Langer 1982 )mayreversethe fractionation-producedenhancementoftheabundanceof13 COto12 CO. 2.4TheDynamicalStateoftheIRDCFilaments 2.4.1IRDCMassesfrom13 COEmissionandMIRDustAbsorption WecalculateIRDCmassesusingtheobservedmasssurfaceden sitiesand angularsizes,andbyassumingnearkinematicdistances,si ncethecloudsareseenin absorptionagainsttheGalaxy'sdiffuseMIRemission.Wead optthekinematicdistances of Simonetal. ( 2006b ),whoassumedthe Clemens ( 1985 )rotationcurve.Thisleads toadistanceof3.7kpcforIRDCFand2.9kpcforIRDCH.Weassu meuncertainties of0.5kpc,whichcouldresult,forexample,fromlineofsigh tnoncircularmotionsof 8 km s1.Temperatureuncertaintiesof5Kwouldleadto 13COuncertaintiesof 33

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Table2-2.IRDCellipsoidalvirialanalysis CloudpropertyIRDCFIRDCH d(kpc)3.70.5 2.90.5R(pc)1.880.25 0.910.16 R obs(pc)3.520.48 1.210.21 yZ=R 3.930.6 2.060.3 13CO(g cm2)0.01470.003 0.01330.003 SMF(g cm2)0.00820.0016 0.02090.004 13CO (env)(g cm2)0.01960.004 0.02120.004 M 13CO(M )33001100 370150 M SMF(M )1900640 580230 M(M )2600870 480190 a 110/910/9a 20.5380.750W(10 46erg) 11.07.11.080.78 (km/s)1.460.15 1.200.12 t s = 2 R= (Myr)2.50.4 1.50.3T (10 46erg)16.46.4 2.060.91T0 ( A )(10 46erg)148 2.71.8T0 ( B )(10 46erg)7330 4.32.0 52 R=( GM ) 1.780.73 3.171.50 20%.Weestimatesimilarlevelsofuncertaintyin SMFduetoforegroundcorrection andbackgroundinterpolationuncertainties(BT09).Then, forIRDCF,the13 CO-derived massassumingT = 20Kintheon-sourcelamentregionafterenvelopesubtractio nisM 13CO = 33001100 M andthedustextinctionmassisM SMF = 1900640 M .For IRDCH,wendM 13CO ( T = 15 K) = 370150 M andM SMF = 580230 M .For ourcalculationsinvolvingthetotalmassofthecloudsweta keaveragesoftheabove estimateswhilestillassuming20%uncertaintiesintheave ragedvaluesof.Thuswe adoptM = 2600870 M forIRDCFandM = 480190 M forIRDCH.Theseresults aresummarizedinTable 2-2 2.4.2EllipsoidalCloudVirialAnalysis Following Bertoldi&McKee ( 1992 ),hereafterBM92,weconsideranellipsoidal cloudwithradiusRnormaltotheaxisofsymmetryandsize2 Zalongtheaxis.The aspectratioisdenedasyZ=R,whileR maxandR minarethesemimajorand 34

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semiminoraxesoftheellipseobtainedbyprojectingtheclo udontotheplaneofthe sky. IRDCsFandHbothhaverelativelythin,lamentarymorpholo gies:wesetR max=R min = 3.40, 1.78,respectively,i.e.thesameelongationastherectangular regions weconsidertodenethelaments(Figs. 2-3 & 2-4 ).Giventhesemorphologies,we expectthesymmetryaxesofthecloudstobeclosetotheplane ofthesky.Thusforboth weadoptaducialvalueoftheinclinationanglebetweenthe cloudsymmetryaxisand thelineofsightof = 60 .WeassumeR = R minandZ = R max=sin ,soy = 3.93, 2.06forIRDCsFandH,respectively.Anuncertaintyof15 ininclinationwouldcause 15%uncertaintiesiny.Itisalsousefultointroduceageometricmeanobservedrad ius,R obs( R max R min ) 1=2,whichisalsorelatedtoRvia,R obs = R cos 1=2[1 + ( y tan) 2 ] 1=4. BM92alsodeneR masthemeanvalueofR obsaveragedoverallviewingangles,but forourindividualcloudswewillexpressquantitiesinterm sofRandR obs.Itshouldbe notedthatthetreatmentoftheseIRDClamentsassimpleell ipsoidsisnecessarily approximate,andweconsiderthelamentaryanalysisofsec tion 2.4.3 tobemore accurate. Iftheclumpisinanenvironmentthatisevolvingwithatimes calelongerthanthe clump'sdynamicaltimescaleorsignalcrossingtimet s2 R= ,thenitshouldobeythe equilibriumvirialequation( McKee&Zweibel 1992 ):0 = 2(TT0 ) +M+ W .(2–8) Here, T istheclumpkineticenergy, T0isthekineticenergyresultingfromthesurface pressureontheclump, M isthemagneticenergyassociatedwiththecloud,andWis thegravitationalbindingenergy,whichforanellipsoidal cloudis(BM92)W =3 5 a 1 a 2 GM 2 R ,(2–9) 35

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whereforapower-lawdensitydistribution /rk ,a 1 = (1k =3)=(12 k =5)anda 2 = a rcsinh( y 21) 1=2 ( y 21) 1=2(2–10) forprolateclouds.Note,ourdenitionofWanda 2differsslightlyfromBM92sincewe donotneedtoconsiderR m.Weadoptk= 1(basedonastudyofthedensityproles inIRDCsButler&Tan2011 )sothata 1 = 10=9.Forourmeasuredvaluesofy,wehavea 2 = 0.53, 0.71forIRDCsFandH,respectively.Forthemassofthecloudweta kethe averagevaluesoftheestimatesfromMIRdustextinctionand13 COlineemission.Using thesevaluesweestimateW =(11.0, 1.08)10 46 ergforIRDCsFandH,respectively (seeTable 2-2 ).TheuncertaintiesinWarerelativelylargegiventhemeasurement errorsofandR. Theclumpkineticenergyis T= (3=2) M2,where istheaveragetotal1Dvelocity dispersion,whichwederivefromthe13 COlineemission(countingonlythoseparts oftheenvelope-subtractedspectrawithpositivesignalgr eaterthanorequaltoone standarddeviationofthenoiselevel)includingcorrectio nsforthemolecularweightof13 COandouradoptedcloudtemperatures.Weestimatethatwemeas ure toa10% accuracy.Wend T= (16.4, 2.06)10 46 ergforIRDCsFandH,withuncertaintiesat aboutthe40%level. Thesurfacetermforthekineticenergyis T0 = (3=2) P 0 V.Weestimatethis termintwoways.First(methodA),wecanmeasurethemasssur facedensityofthe surroundingmolecularcloudfromthe13 COemissionoftheenveloperegions.Wend 13CO (env) = 0.0196, 0.0212 g cm2forIRDCsFandH,respectively.Wescalethese valuesbyM=M 13CO,i.e.0.79and1.30.Iftheenvelopeisself-gravitating,it hasmean internalpressureP (env) = 1.85 G 2 (env),adaptingtheanalysisof McKee&Tan ( 2003 ) withparametersf g = 1(i.e.fullygasdominated), geomR 3 obs=( R 2 Z ) = 1.4(adopting anintermediatevalueforthetwoIRDCsaccuratetoabout20% ), B = 2.8(theducial valueof McKee&Tan ,measuringtheratioofthetotalpressureincludingmagnet ic 36

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eldstothatassumingtheywereabsent)and vir = 1.ThussettingP 0 = P (env) = (2.96, 9.38)1011cgsforIRDCsFandHandwiththecloudvolumeV = 4R 2 Z=3,we nd T0 ( A ) = (14, 2.7)10 46 erg. Second(methodB),weestimatethedensityintheenvelopere gion,assumingithas acylindrical,annularvolumewithouterradius2 RandinnerradiusR.ForIRDCsFand H,wenddensitiesof = 4(env)=(3R ) = (1.43, 3.20)1021 g cm3,equivalentton H (env) = (610, 1600) cm3.WeagainscalethesevaluesbyM=M 13CO,i.e.0.79and 1.30forIRDCsFandH,respectively.WethenequateP 0 =(env)2 (env),where (env)isthevelocitydispersionoftheenvelopegas(wend3.65, 1.89 km s1forIRDCsFand H)andevaluate T0 ( B ) = (3=2) VP 0!(73, 4.3)10 46 erg,withV = (4=3)R 2 Z. Theseresultsindicatethat,forbothIRDCs,thesurfacepre ssuretermofthevirial equationiscomparabletoormuchlargerthantheinternalki neticterm,althoughthe uncertaintiesarelarge.Assuming T0T ,thenforvirialequilbriumtobemaintained wouldrequire M(1=8)RV a ( B 2B 2 0 ) dVW,whereB 0isthemagneticeld strengthfarfromthecloudandV aisavolumethatextendsbeyondthecloudwherethe eldlineshavebeendistortedbythecloud.AssumingV aisthevolumeoftheenvelope regionsandassumingnegligibleB 0,wendB10, 13GforIRDCsFandH.Ifamore realisticvalueofB 0 = 10Gisadopted( Crutcher 2010 ),thenwendB14, 16G. Thusrelativelymodestmagneticeldenhancementscouldst abilizetheclouds. Bertoldi&McKee ( 1992 )deneadimensionlessvirialparameter, 52 R m=( GM )todescribethedynamicalstateofclouds.Weadoptaslightl yreviseddenition 52 R=( GM ) = a 1 a 2 2T = jWj ,witha 2denedasabove.ForIRDCsFandHwend = 1.78, 3.17.Whilethesevaluesarequiteclosetounity,especiallyfor IRDCF,which iscommonlytakentoinferthatself-gravityisimportant,t hisissomewhatmisleading sincethevalueofa 2isquitesmallfortheseelongatedcloudsandthesurfacepre ssure termsseemtobequiteimportant. 37

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ItispossiblethattheseIRDCshavenotyetreachedvirialeq uilibriumiftheir surroundingsareevolvingontimescales .t s afewMyr.Themeanvelocityofthe13 COemittinggasinthenorthandsouthenveloperegionsis55.72 ,56.10km s1, respectively,forIRDCF,and44.96,44.28km s1,respectively,forIRDCH.The north/southvelocitydispersionsare3.81/3.38km s1forFand1.69/2.07km s1for H.Thenorth/south 13CO'sare0.040/0.031g cm2forFand0.050/0.051g cm2forH. Theratiosofnorth/southpressures(estimatedbymethodB, /2)arethus1.64and 0.65forIRDCsFandH.Thepressuresappeartobefairlysimil aronthedifferentsides ofthelaments,althoughtheuncertaintiesaresuchthatva riationatthelevelofabouta factoroftwocouldbepresent.2.4.3FilamentaryCloudVirialAnalysis Fiege&Pudritz ( 2000 ),hereafterFP00,presentavirialanalysisoflamentary clouds.Theyderivedthefollowingequationsatisedbypre ssure-conned,nonrotating, self-gravitating,lamentary(i.e.lengths widths)cloudsthreadedbyhelicalmagnetic eldsthatareinvirialequilibrium:P 0 P = 1m m vir1 Ml jW lj .(2–11) HereP 0istheexternalpressureatthesurfaceofthelament,P =2istheaverage totalpressureinthelament,misthemassperunitlength,m vir22=Gisthevirial massperunitlength, Mlisthemagneticenergyperunitlength,andW l =m 2 Gisthe gravitationalenergyperunitlength. WedivideIRDCsF,Hinto7,4orthogonalstrips(seeFigs. 2-3 & 2-4 )withangular widths1.70 0 ,0.955 0 alongthelaments,respectively.Assumingaducialvalue ofthe inclinationanglebetweenthecloudsymmetryaxisandtheli neofsightof = 60 ,these correspondtophysicallengthsalongthelamentsof2.11,0 .930pc,respectively. InTable 2.5 ,foreachstripinIRDCsFandH,welistthevaluesof 13CO, SMF,M(calculatedfromthemeanofthesevaluesof),m, v, ,m vir,P, 13CO (env), (env) 38

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(calculatedafterscaling 13CO (env)by0.5( 13CO + SMF )= 13CO), v (env), (env)andP (env) (env)2 (env).WeequateP 0 = P (env). FollowingFP00,inFig. 2-7 weplotP 0=Pversusm=m vir.Therangeofmodels consideredbyFP00allowsforpositivevaluesof Ml= jW lj (i.e.poloidally-dominated B-eldsthatprovidenetsupporttothelamentagainstgrav itationalcollapse)and negativevalues(i.e.toroidally-dominatedB-eldsthatp rovidenetconnementofthe lament).Inallcases,P 0=P1.Incontrast,wendallofthelamentregionshaveP 0=P>1,i.e.thepressuresintheenveloperegionsappeartobegrea terthaninthe lament.Thisechoestheresultsfromtheellipsoidalviria lanalysis,whichfoundlarge surfacepressureterms.Assumingourmeasurementsofpress uresarereliable,e.g. arenotbeingadverselyaffectedbysystematiceffectsduet o,forexample,ourassumed lamentandenvelopegeometry,thentheseresultsimplytha tthelamentshavenotyet reachedvirialequilibrium. VerylargevaluesofP 0=PareinferredforstripsF1,F2andF3.Theseare consistentwiththelamentandenvelopespectrashowninFi g. 2-5 ,whichreveala relativelyweaklamentandrelativelystrongandvaryinge nvelopevelocityproles. StripsF6,F7andH2havethesmallestvaluesofP 0=P.2.Examiningthe IRAC8mimages(Figs. 2-3 & 2-4 ),thereissomeindicationthatthesearethesites ofrelativelyactivestarformation(especiallyF7andH2). Starformationrequires gravitationallyunstableconditionsinthelament,i.e.r egionswhereself-gravitystarts todominateoverexternalpressure.Ourresultsindicateth atthisalsorequiresthe localregionofthelamenttoreachapproximatevirialequi librium,althoughsurface pressuretermsstillremaindynamicallyimportant,i.e.m=m virissignicantlylessthan unity.Givenourmeasurementuncertaintiesandthefacttha ttheobservedregionsdo nothaveP 0=P<1,wearenotabletodeterminewhethertheeldgeometriesare more dominatedbypoloidalortoroidalcomponents.WenotethatF P00'sconclusionthat observedlamentsaredominatedbytoroidaleldsdependso ntheirassumptionthat 39

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thelamentsareinvirialequilibriumandontheirchoiceofP 0,whichwasnotdirectly measuredformostofthesourcestheyconsidered. Wecautionthatifindependentmolecularcloudsarepresent alongtheselinesof sightandwithsimilarvelocitiestothelaments,thenthis maycauseustooverestimate thevelocitydispersionandpressureintheenveloperegion saroundthelaments.From thespectrashowninFig. 2-5 wedonotexpectthisisoccurringinIRDCH,sincethe envelopespectrashareaverysimilarvelocityrangeasthe lament.Thesituationin IRDCFislessclearcut,sincethereappearstobeabroader,o ffsetcomponentthat dominatesmoreintheenveloperegion. 2.5Conclusions Wehavecomparedmeasurementsofmasssurfacedensity,,intwoIRDC lamentsbasedon13 COobservations, 13CO,withthosederivedfromMIRextinction mapping, SMF,ndingagreementatthefactorof 2level.Asystematicdecreasein 13CO= SMFwithincreasingmaybeduetoasystematicdecreaseintemperature, increaseinthecontributionofunder-resolvedhighoptica ldepthregions,increasein dustopacity,ordecreasein13 COabundanceduetodepletioninregionsofhigher columndensity.Futurestudiesthatspatiallyresolvethet emperaturestructureandMIR dustabsorptionpropertiescanhelptodistinguishthesepo ssibilities. Wehavethenusedthekinematicinformationderivedfrom13 COtostudythe dynamicalstateoftheIRDCs.Inparticularwehaveevaluate dthetermsofthe steady-statevirialequation,includingsurfaceterms,un dertheassumptionofellipsoidal andlamentarygeometries.Inbothcaseswendevidencetha tthesurfacepressure termsareimportantandpossiblydominant,whichmayindica tethatthelaments,at leastglobally,havenotyetreachedvirialequilibrium. Theseresultswouldbeconsistentwithmodelsofcompressio nofdensegasin collidingmolecularows,e.g.GMCcollisions. Tan ( 2000 )proposedthatthismechanism maytriggerthemajorityofstarformationinshearingdiskg alaxies.Theexpected 40

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collisionvelocitiesare 10 km s1.Itislessclearwhethercollidingatomicows, ( Heitschetal. 2008 ),whichformthemoleculargasaftershockcompressionofat omic gas,wouldalsoproducesuchkinematicsignatures:recallt hatweareinferringlarge surfacepressuresbasedon13 COemissionfromtheenvelopesaroundtheIRDC laments. Recentobservationsofextended,parsec-scaleSiOemissio n,likelyproduced inshockswithvelocities &12 km s1inIRDCHby Jim enez-Serraetal. ( 2010 )may alsosupportmodelsoflamentformationfromconvergingo ws.However,wecaution thattheobservedextendedSiOemissionisveryweakandmaya lsobeproducedby multipleprotostellaroutowsourcesformingintheIRDC(s ee Jim enez-Serraetal.2010 forfurtherdiscussion). Ourresolvedlamentaryvirialanalysisalsoindicatestha ttheregionsclosestto virialequilibrium(stripsF6,F7andH2)arethosewhichhav einitiatedthemostactive starformation.Thiswouldbeexpectedifmodelsofslow,equ ilibriumstarformation ( Tanetal.2006 ; Krumholz&Tan2007 )applylocallyintheseregions.Inthiscase, thesedenseregionsthathavebecomegravitationallyunsta ble,perhapsduetothe actionofexternalpressureand/orconvergingows,thenpe rsistformorethanonelocal dynamicaltimeandsoareabletoreachapproximatepressure andvirialequilibriumwith theirsurroundings.Inthisscenario,theyarestabilizedb ytherampressuregeneratedby protostellaroutowfeedbackfromtheformingstars( Nakamura&Li 2007 ). 41

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Table2-3.IRDClamentaryvirialanalysis CloudpropertyF1F2F3F4F5F6F7F totH1H2H3H4H tot 13CO(102 g cm2)0.2180.3380.8111.312.292.872.581.470.8641.671.561. 211.33 SMF(102 g cm2)0.4760.311-0.04320.8621.371.621.030.8231.381.941.9 73.282.09M(M )114107126357601737593264078.5126124157478m(Mpc1)54.050.759.716928534928117884.4135133169128 (1022 g cm3)3.293.093.6410.317.421.317.110.922.035.134.644.033 .3 v(km s1)59.1959.3458.8158.2658.3057.7757.7758.3945.0945.20 45.1344.7845.07 (km s1)1.361.271.071.441.591.862.271.461.521.341.030.9951 .20m vir(Mpc1)8567515369621170161024009861070840494460669P(1012 cgs)6.054.994.1921.343.873.888.323.150.763.436.843.647 .9 13CO (env)(102 g cm2)1.611.831.942.141.811.952.461.962.311.862.002.352. 12 (env)(1022 g cm3)18.712.96.7213.010.611.212.611.245.330.434.265.941 .2 v (env)(km s1)56.0355.8455.7856.5956.0455.6555.7255.9544.9744.78 44.5344.4044.67 ( env )(km s1)3.453.483.953.913.553.433.563.651.851.911.891.861. 89P (env)(1012 cgs)223156105199133132159149155110122229148 42

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A B Figure2-1.Theependenceof andd N 13CO=d vwithT B .(A)Dependenceof withT B (eq. 2–2 )assumingT ex = 10, 15, 20K(reddotted,bluesolid,green dashedlines,respectively).(B)Dependenceofd N 13CO=d vwithT B assumingT ex = 10, 15, 20K(reddotted,bluesolid,greendashedlines, respectively). 43

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A B Figure2-2.Columndensityproleswithvelocity.(A)ForIR DCF,thedashedlines showstheprolesassumingopticallythinemission,whilet hesolidlines showtheprolesaftercorrectionforopticaldepth.Atempe ratureof20K wasassumedforIRDCFand15KforIRDCH(seetext).Foreachcl oudthe upper,offsetproleisthatoftheaverageforthecloudandt helowerprole isthatofthehighestcolumndensityposition.(B)Sameas(A ),butforIRDC H. 44

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A B C D E F Figure2-3.MorphologyofIRDCF.(A) Spitzer GLIMPSEIRAC8 mimage,withlinear intensityscaleinMJysr1.Thehorizontallineshowsascaleof3 0 .The imagehas1.2 00 pixelsandthePSFhasaFWHMof2 00 (B)Masssurface density, SMF,withlinearintensityscaleing cm2,derivedfromtheprevious imageusingthesmallmedianlterMIRextinctionmappingme thodof Butler &Tan ( 2009 ).Theinner,redrectangle(centeredatl = 34.483 ,b = 0.276 withP.A.= +60 andsize0.0582 by0.198 )alongthelamentshowsthe “onsource”regionweconsidertocontainthemainlamentar ystructureof theIRDC.Theouter,bluerectangleextendsto“offsource”r egionswe considertoberepresentativeofthesurroundingGMCenvelo pe.These rectanglesaredividedinto7orthogonalstripstoaidinthe separationof componentsofCOemissionfromthelamentandGMCenvelope. (C)The sameextinctionmapconvolvedwithaGaussianof46 00 FWHMtomatchthe resolutionoftheCOmapsandpixelatedto22 00 onthesamegridastheGRS surveyimage.Thetwoblackhatchedsquaresshowregionswit hunreliable measuresof SMFbecauseofthepresenceofbrightMIRsources.These areexcludedfromthecomparisonwith 13CO.(D)Integratedintensitymap of13 CO(1-0)emissionoverthefullvelocityrangeof 5135 km s1ofthe GRSsurvey,withlinearintensityscaleinK km s1.(E)Integratedintensity mapof13 COoverthevelocityrangeof4865 km s1,i.e.thegaswe believeisassociatedwiththeIRDC,withlinearintensitys caleinK km s1. (F)Masssurfacedensityofthelamentderivedfrom13 COemission, 13CO, withlinearintensityscaleing cm2. 45

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A B C D E F Figure2-4.MorphologyofIRDCH.(A) Spitzer GLIMPSEIRAC8 mimage,withlinear intensityscaleinMJysr1.Thehorizontallineshowsascaleof3 0 .The imagehas1.2 00 pixelsandthePSFhasaFWHMof2 00 (B)Masssurface density, SMF,withlinearintensityscaleing cm2,derivedfromtheprevious imageusingthesmallmedianlterMIRextinctionmappingme thodof Butler &Tan ( 2009 ).Theinner,redrectangle(centeredatl = 35.517 ,b =0.275 ,withP.A.= +62.84 andsize0.0307 by0.0637 )alongthe lamentshowsthe“onsource”regionweconsidertocontaint hemain lamentarystructureoftheIRDC.Theouter,bluerectangle extendsto“off source”regionsweconsidertoberepresentativeofthesurr oundingGMC envelope.Theserectanglesaredividedinto4orthogonalst ripstoaidinthe separationofcomponentsofCOemissionfromthelamentand GMC envelope.(C)ThesameextinctionmapconvolvedwithaGauss ianof46 00 FWHMtomatchtheresolutionoftheCOmapsandpixelatedto22 00 onthe samegridastheGRSsurveyimage.(D)Integratedintensitym apof13 COoverthefullvelocityrangeof 5135 km s1oftheGRSsurvey,withlinear intensityscaleinK km s1.(E)Integratedintensitymapof13 COoverthe velocityrangeof4050 km s1,i.e.thegaswebelieveisassociatedwith theIRDC,withlinearintensityscaleinK km s1.(F)Masssurfacedensityof thelamentderivedfrom13 COemission, 13CO,withlinearintensityscaleing cm2. 46

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A B C D Figure2-5.SubtractionofIRDCenvelopes.(A)Filamentand envelopeofIRDCF,with spectracorrespondingtotheorthogonalstripsshowninFig ure 2-3 .Ineach, thedotted,redlineshowsthetotal13 COcolumndensitydistribution, includingopticaldepthcorrections,fromthelamentregi on.Thelong dashedanddot-dashed,bluelinesshowthespectrafromthen orthernand southernenveloperegions.(B)FilamentandenvelopeofIRD CH,withthe spectracorrespondingtotheorthogonalstripsshowninFig ure 2-4 .(C)Asin (A),wesubtracttheaverageofthenorthernandsouthernenv elopespectra (shortdashedbluelines)fromthelament(dottedredline) ,toleavean estimateofthematerialinthelament(solid,blackline). Theverticalsolid lineindicatesthemeanvelocity.(D)Sameanalysisandlabe lsas(C)for IRDCH. 47

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A B C D Figure2-6.(A)Directcomparisonof 13CO(afterenvelopesubtraction)and SMFin IRDCF.Thecrossesshowlocationswhereboth 13COand SMF>0.01 g cm2.Thedotsshowlocationsoflowersurfacedensities.The dottedlineshowstheonetoonelinearrelationandthelongd ashedline showsthebest-toffsetlinearrelation.Thesolidlinesho wsthebest-t powerlawrelation(seetext).(B)Sameas(A)butforIRDCH.( C)Ratioof 13COto SMFasafunctionof SMFforIRDCF.Thesolid(dashed)arrow showstheeffectonthehighestpositionofreducingtheassumed temperaturefrom20Kto15K(10K).(D)Sameas(c)butforIRDC H.The arrowshowstheeffectonthehighestpositionofreducingtheassumed temperaturefrom15Kto10K. 48

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Figure2-7.P 0=Pversusm=m virforstripsinIRDCsF(opensquaresjoinedbydottedline forF1toF7)andH(opentrianglesjoinedbydashedlineforH1 toH4).The smoothcurvesshowtheconditionssatisedbyequation( 2–11 )for Ml= jW lj <0(solidlines), Ml= jW lj= 0(dottedline),and Ml= jW lj >0(dashedlines).ThelargeobservedvaluesofP 0=Pmayindicatethatmostof theregionsinIRDCsFandHhavenotyetestablishedvirialeq uilibrium. ThosestripswiththelowestvaluesofP 0=P,i.e.F6,F7,andH2,appearto beundergoingmoreactivestarformation(seetextandFigs. 2-3 & 2-4 ). 49

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CHAPTER3 MAPPINGLARGE-SCALECODEPLETIONINAFILAMENTARYINFRARED DARK CLOUD Inthischapter,wecontinueworkingwiththelamentaryIRD CG035.39.-0033 (CloudH).Werevisitthemasssurfacedensityestimatesmad einChapter2,butusing moresensitive,higherresolutionC 18 Oemissionlinedata,J = 10andJ = 21transitions,takenwiththeIRAM30mtelescope.InChapter1 weshowedthattheratio 13CO= SMFdecreaseswithincreasing SMF.Hereweaddresstheprobablecausesof thattrendbyinvestigatingtheexcitationtemperature,in creaseindustopacity,andthe decreaseoftheC 18 Oabundanceduetodepletioninregionsofhighcolumndensity ThisworkhasbeenacceptedtoTheAstrophysicalJournalfor publication. InfraredDarkClouds(IRDCs)arecold,highmasssurfaceden sityandhighdensity structures,likelytoberepresentativeoftheinitialcond itionsformassivestarand starclusterformation.COemissionfromIRDCshasthepoten tialtobeusefulfor tracingtheirdynamics,butmaybeaffectedbydepletedgasp haseabundancesdue tofreeze-outontodustgrains.HereweanalyzeC 18 O J = 1!0andJ = 2!1emissionlinedata,takenwiththeIRAM30mtelescope,ofthe highlylamentaryIRDC G035.39.-0033.Wederivetheexcitationtemperatureasafu nctionofpositionand velocity,withtypicalvaluesof 7K,andthusderivetotalmasssurfacedensities, C18O,assumingstandardgasphaseabundancesandaccountingfor opticaldepthin theline,whichcanreachvaluesof 1.Themasssurfacedensitiesreachvaluesof 0.07 g cm2.Wecomparetheseresultstothemasssurfacedensitiesderi vedfrom mid-infrared(MIR)extinctionmapping, SMF,by Butler&Tan ( 2009 ),whichareexpected tobeinsensitivetothedusttemperaturesinthecloud.With asignicanceof &10 wend C18O= SMFdecreasesbyaboutafactorof5asincreasesfrom 0.02to 0.2 g cm2,whichweinterpretasevidenceforCOdepletion.Severalhu ndredsolar massesarebeingaffected,makingthisoneofthemostmassiv ecloudsinwhichCO 50

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depletionhasbeenobserveddirectly.Wepresentamapofthe depletionfactorinthe lamentanddiscussimplicationsfortheformationoftheIR DC. 3.1AnIntroductiontoCODepletioninaFilamentaryInfrare dDarkCloud SilhouettedagainsttheGalacticbackground,InfraredDar kClouds(IRDCs)are opaqueatwavelengths 10 m( Peraultetal.1996 ; Eganetal.1998 ),cold(T<20K; Careyetal.1998 ; Pillaietal.2006 ),anddense(n H10 310 5 cm 3; Teyssieretal. 2002 ; Rathborneetal.2006 ; Butler&Tan2009 ,hereafterBT09; Peretto&Fuller2009 ). Theyarelikelytobetheprecursorsofmassivestarsandstar clustersastheyhave similarphysicalconditions,suchasmasssurfacedensitie s,asregionswithsuchstar formationactivity( Rathborneetal.2006 ; Tan2007 ; Zhangetal.2009 ; Raganetal. 2009 ).COemissionfromthesecloudsmaybeusefulforunderstand ingtheirdynamics (e.g. Hernandez&Tan2011 ,hereafterHT11),butcouldbeaffectedbydepletedgas phaseabundancesduetofreeze-outontodustgrains,especi allyinthecoldest,highest densityregions. GasphasedepletionofCO,averagedalongthelineofsight,h asbeenobserved inthecold(T.10K)centersofrelativelylow-massandnearbystarlesscores (e.g. Willacyetal.1998 ; Casellietal.1999 ; Krameretal.1999 ; Berginetal.2002 ; Whittetetal.2010 ; BradyFord&Shirley2011 ).Typically,depletionischaracterizedby measuringthedepletionfactor,f D,denedastheratioofCOcolumndensity expected assumingstandardgasphaseabundancesgiventhecolumnofm aterialobserved fromeitherthemmdustcontinuumemissionornearinfrared( NIR)dustextinctionto the observed COcolumndensity(typicallyfromC 17 OorC 18 O). Casellietal. ( 1999 ) estimatedtheexpectedCOcolumnbasedonmmdustcontinuume mission,whichhas theadvantageofbeingabletoprobetohighcolumndensities ,butissensitivetothe adopteddusttemperatureandemissivity.Theyconcludedde pletionaffectedaregion atthecorecentercontainingabout2 M ofgas,wheren H&10 5 cm3,withdepletion factorsofupto 10wherethemasssurfacedensityis'0.6 g cm2. Krameretal. 51

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( 1999 )estimatedtheexpectedCOcolumnbasedonNIRextinction,w hichdoesnot requireknowingthedusttemperature,butdoesrequirether etobeasufcientareal densityofbackgroundstarsdetectableintheNIR.Theyfoun ddepletionfactorsofupto 2.5forregionswithA V2030mag,correspondingto0.10.15 g cm2. Massiveprotostellarcoresandclumpsaretypicallymoredi stantanddifcultto study,butCOdepletionhasbeenreportedby Fontanietal. ( 2006 )fromastudyof10 sourceswithmedianf D'3.2(butadispersionofaboutafactorof10), Thomas& Fuller ( 2008 )fromastudyof10sourceswithameanf D'1.3and Loetal. ( 2011 )from astudyof1sourcewithf D10.Theseresultsrelyonestimatesoftheexpected COcolumndensitybasedonmmdustcontinuumemission,arede rivedonlyfor singlepointingstothesources,andcandependonradiative transfermodelingof theunresolvedsourcedensityandtemperaturestructure( Thomas&Fuller2008 ; Loetal.2011 ).Sourcetosourcecomparisonsarehamperedbypossibleiso topic abundancevariationsaffectingtheserareCOisotopologue s.Theabovesourcesalready containmassiveprotostars,butitisnotclearifthedeplet ionsignalarisesfromthe immediatesurroundingenvelopeorfromnearbyunresolveds tarlesscores.Someofthe massiveprotostarsstudiedproduceultra-compactHIIregi onsandphotodissociationof moleculescouldbeoccurringinlocalizedregions,whichwo uldmimicdepletion. WeexpectCOdepletiontobewidespreadinthedenseregionso fIRDCs, potentiallyaffecting:thephysicalpropertiesonederive sfromCOemission;themid andfarinfraredopacitiesofdustgrainsasCOicemantlesbu ildup;andthustheinitial conditionsofstarandplanetformationintheseregions.In dividualresolvedIRDCs, assumedtohaveuniformisotopicabundances,mayalsobeuse fullaboratoriesinwhich tostudythedepletionprocessasafunctionoflocalgascond itions. Inthispaper,wepresentIRAM30mobservationsofC 18 O J = 1!0andJ = 2!1emissionfromthelamentaryIRDCG035.30-00.33(CloudHin BT09;nearkinematic distanceofd = 2.9kpc).Tolookforevidenceofdepletion,theC 18 O-derivedmass 52

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surfacedensity, C18O,iscomparedwiththesmallmedianlter(SMF)mid-infrared (MIR)extinctionmappingderivedmasssurfacedensity, SMF(BT09; Butler&Tan 2011 ,hereafterBT11).ThisworkismotivatedbythestudyofHT11 ,whoused13 COmolecularlineemissionfromtheGalacticRingSurvey(GRS) toestimatethemass surfacedensitiesoftwohighlylamentaryIRDCs,includin gFilamentH.Assuminga constantvalueofT ex = 15K,HT11foundtentativeevidenceforCOdepletion,but couldnotexcludethepossibilitythatothereffects,sucha ssystematicchangesinthe excitationtemperatureorthecontributionofhighopacity cores,werethecauseofthe observeddecreaseof 13CO= SMFwithincreasing.Withournewhigher-resolution, multi-transitionC 18 Odata,weareabletoexcludeormitigatetheseeffects,aswel las resolvinghighermasssurfacedensitystructurestoprobea largerrangeofconditions wheredepletionmaybeoccurring. 3.2MassSurfaceDensityfromMIRExtinctionMapping The8 mSMFmasssurfacedensity, SMF,mapwasderivedat2 00 resolution fromthe Spitzer IRACband4(GalacticLegacyMid-PlaneSurveyExtraordinai re [GLIMPSE]; Benjaminetal.2003 )imagebycomparingtheobservedintensityat eachpositionwiththeexpectedbackgroundintensity,esti matedbyinterpolatingthe intensitiesofsurroundingnearbyregionswheremedianlt ersmoothingisusedto denethebackgroundmodel(seeFigure1aand1b).Following BT09,adustopacityof 8m = 7.5 cm 2 g1wasadopted,similartothelterresponseandbackgroundsp ectrum weightedmeanIRACband4opacityexpectedfromthe Ossenkopf&Henning ( 1994 ) thinicemantlemoderatelycoagulatedgrainmodelwithagas -to-dustmassratioof156. Thisvalueissomewhathigherthanvaluesadoptedbyotherdu stmodels(e.g.125is usedforthe Weingartner&Draine2001 ),althougharecentestimatefromdepletion studiesndsagas-to-dustratioof141( Draine2011 ,p265).Inanycase,asdescribed below,ourstudyofCOdepletioncomparesrelativeabundanc esasafunctionofinthe IRDCandsoisindependentofthischoiceofoverallnormaliz ation. 53

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Acorrectionforforegroundemissionalsoneedstobeestima ted.BT09madethis correctionbyestimatingtheamountofforegroundemission fromaphysicalmodelof theMilkyWayandgivenameasuredkinematicdistance(assum edtobenear)ofthe cloud. Battersbyetal. ( 2010 )havepointedoutanadditionalsourceofforegroundfrom scatteringintheIRACarray.BT11havedevelopedamoreaccu rateempiricalmethod forestimatingtheforegroundemission,basedonthepresen ceofindependentsaturated (highopticaldepth)cores,andhereweusethisnewmethod.F ortheregionweanalyze inthisparticularIRDC,thevaluesof SMFareincreasedbyabout10%fromthose presentedbyBT09. SMFinthelamentisderivedfromcomparisonwithadjacentregi ons,which areassumedtohavenegligibleMIRextinction.Inreality,w eknowfrommolecular lineobservations(e.g.13 COfromtheGRSanalyzedbyHT11),thattheseregionsdo havesomematerialpresentassociatedwiththeIRDC.Werefe rtothisastheIRDC “envelope”.Thepresenceoftheenvelopeandothersystemat icuncertaintiesassociated withestimationoftheMIRbackgroundintensitymeanthat SMFbecomesunreliable when .0.01 g cm2.Forourcomparisonwiththemasssurfacedensityderivedfr omC 18 Oemission,the SMFmapisregriddedtothemuchlowerresolutionoftheCOdata (seebelow)andallpixelswith SMF<0.01 g cm2areexcludedfromtheanalysis. Methodsofaccountingfortheenvelopematerialarediscuss edfurtherin x 3.4 AsnotedbyBT09,wemustalsoaccountforlocationsofbright MIRemission. WherevertheobservedMIRintensityisgreaterthantheadop tedbackgroundmodel anunphysicalnegativevalueofwillbeestimated.Negativevaluesofareallowed uptolevelscomparablewiththeobservednoise,butmoreext remevalues,whichare mostlyduetodiscreteMIRbrightsources,have SMFsettozero.Thiscausesan underestimationofthemasssurfacedensityintheseregion s.Weidentifyandexclude fromfurtheranalysisremaining(i.e. 0.01 g cm2)pixelsin SMFmap(smoothedto theCOresolution)thathavemorethan20%oftheirareaoccup iedbyzeroornegative 54

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values.InFigure1b,theseexcludedpixelsareindicatedwi th“X”and“O”symbols fortheCO(1-0)andCO(2-1)resolutions,respectively.The irexclusionisdueeitherto thepresenceofaMIRbrightsourceorinregionswherethebac kgroundmodelingis inaccurate,whichcansometimesoccurneartheedgeofthel ament.Onlyarelatively smallnumberofpixelsareaffectedbythisexclusion.Infac t,ournalresultswouldnot havevariedsignicantlyifthisexclusionhadnotbeenimpl emented. 3.3MassSurfaceDensityfromC 18 OEmission 3.3.1Observations TheC 18 O J = 1!0andJ = 2!1linesweremappedusingtheIRAM (InstitutodeRadioastronomiaMilimetrica)30mantennain PicoVeleta,SpaininAugust andDecember2008.Anareaof20 40 wasmappedusingtheOn-The-Fly(OTF) methodtowardsG035.39-00.33withacentralpositionof ( J 2000) = 18 h 57 m 08 s, ( J 2000) = 021003000 (l = 35.517 ,b =0.274 ).WhiletheC 18 O J = 1!0transitionwasobservedwiththeABCDreceiverswithtypica lsinglesideband(SSB) rejections >10dB,theC 18 O J = 2!1linesemissionwasmappedbyusingtheHERA multi-beamreceiver.Off-positionsforbothtransitionli nesweresetto(183000 ,65800 ). Thebeamsizeat 110GHzfortheJ = 1!0transitionsis22 00 ,whileat 220GHztheJ = 2!1beamsizeis11 00 .TheVESPAspectrometerprovidedspectral resolutionsof20kHzand80kHzfortheJ = 1!0andJ = 2!1linesrespectively, whichcorrespondtovelocityresolutionsof 0.05 km s1and 0.1 km s1.Forthis study,allspectrawereresampledtothesamevelocityresol utionof0.2 km s1.The typicalsystemtemperatureswere150-220K.Intensitieswe recalibratedinunitsof antennatemperature(T A),andconvertedintoamainbeambrightnesstemperature,T B, ,viaT A f clump T B ,where isamainbeamefciencyandf clumpisthebeam dilutionfactor.Weuse = 0.64fortheJ = 1!0transition,and = 0.52fortheJ = 2!1transition.Thetypical1 RMSnoiseofthedatais0.2 K km s1overthe velocityrangeof4050 km s1.SincetheC 18 Oemissionisextendedoverthelament, 55

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weassumef clump = 1.Figure 3-1 cpresentsthemorphologyofFilamentHasseeninC 18 O J = 2!1emission. 3.3.2MassSurfaceDensityandT exEstimates WeestimatethecolumndensityofC 18 Omolecules,d N C18O,inthevelocityintervald v,fromtheiremissionthroughthegeneralequation:d N C18O ( v ) d v = 8 A3 0 g l g u 1exp (h=kT ex ) Q rot g l exp(E l=kT ex ) .(3–1) HereQ rotisthepartitionfunctionforlinearmoleculesgivenbyQ rot =P 1J =0 (2 J + 1)exp(E J=kT ex )withE J = J ( J + 1) hB,whereJistherotationalquantumnumberand BistheC 18 Orotationalconstantequalto5.489110 10 s1.h=k = 5.269, 10.54KforJ = 1!0andJ = 2!1transitions,respectively.At7.5K,Q rot = 3.205.Aisthe Einsteincoefcient,6.266, 60.11108 s1forJ = 1!0andJ = 2!1,respectively. 0isthewavelengthofthetransition,0.273, 0.137cmforJ = 1!0andJ = 2!1, respectively.g landg uarethestatisticalweightsofthelowerandupperlevels,an d is theopticaldepthofthelineatfrequency ,i.e.atvelocityv.Theexcitationtemperature,T ex,isassumedtobethesameforallrotationallevels.Details ontheestimationofT exaregivenbelow. Theopticaldepth, ,isderivedthroughthedetectionequation:T B ,= h k [ f ( T ex )f ( T bg )]1e (3–2) whereT B isthemainbeambrightnesstemperatureatfrequency ,f ( T )[exp( h=[ kT ])1]1,andT bgisthebackgroundtemperatureof2.725K.Fortheobservable,T B ,and foranassumedT ex, canbesolvedfordirectlythroughequation( 3–2 ).Therefore,we cansolveforthecolumndensityperunitvelocity,d N 18CO=d v,ateachl b vposition. Whilecareistakentoaccountfortheopticaldepthinourcol umndensityestimates, forreferencewealsostatethecaseoftheopticallythinlim itoftheC 18 O(J = 1!0) columndensity.If issmall,thenequation( 3–2 )reducestoT B ,= ( h=k )[ f ( T ex ) 56

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f ( T bg )] .Insertingintoequation( 3–1 )gives:d N C18O ( v ) d v = 6.57110 14 Q rot f ( T ex )f ( T bg ) [1exp(h=kT ex )]1 T A=K f clump cm2 km1 s (3–3) !9.75810 14 TA=K f clump cm2 km1 s ( T ex = 7.5 K). (3–4) AsinHT11,aninspectionoftheC 18 Oemissioninl b vspaceindicatesthatthe gasassociatedwiththelamentisintherangeof4050 km s1.Thetotalcolumn densityperpixelisthencalculatedovertheentirevelocit yrangeofthelament,N C18O =RdN C18O. Thecolumndensitiesforbothtransitions,N C18O,areconvertedtoatotalmass surfacedensity C18O,byassumingtheabundanceratiosofn 16O=n 18O = 327from Wilson&Rood ( 1994 )andn 12CO=n H2 = 2104from Lacyetal. ( 1994 ).Thus,our assumedabundanceratioofC 18 OtoH 2is6.12107andforeachpixelisthengiven by: C18O = 7.652102 N C18O 10 16 cm2 g cm2 ,(3–5) assumingamassperHnucleusof H = 2.341024 g,i.e. = 1 g cm2isequivalenttoN H = 4.2710 23 cm2. Inordertoaccuratelyderivethemasssurfacedensityofthe lament,anestimate oftheexcitationtemperature,T ex,isneeded.Toperformthisestimatethroughoutthe lament,wevariedtheassumedtemperatureateachl b vpositionuntiltheratio betweenthecolumndensitiesderivedfrombothtransitions wereinagreement.Todo this,werstdenedR 2,1astheratiobetweentheJ = 2!1andJ = 1!0column densities:R 2,1d N C18O,21 d N C18O,10 .(3–6) Thismethodissimilartotheoneusedin Krameretal. ( 1999 ),excepttheyaveraged overthevelocityproleoftheircloud.Thehigherresoluti onJ = 2!1datawas convolvedwithabeamof22 00 andregriddedtomatchtheresolutionandpixelscaleof 57

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theJ = 1!0data.Foralll b vpositionsaboveanoiselimitof3 inbothtransitions,R 2,1wascalculatedrstassumingaT ex = 30K.Then,T exwasiterativelydecreased untilR 2,1convergedtounity.Thisstepprovidedathreedimensionalg ridcontaining estimatesofT exforallpositionsabovethenoiselimit.Next,forallpositi onsbelowthe noisethreshold,theirT exwasestimatedbytakingthemeanexcitationtemperatureat thecorrespondingl bposition.Finally,foranyremainingl b vpositionswithoutan estimatedexcitationtemperature,themeanT exof7.2Kresultingfromtheprevious stepswasused.Positionsleftforthisnalsteparemainlyi ntheouterregionsofthe lamentwheretheemissionisweakand/orthenoiseishigh.T hecolumndensity weightedT exmapisshowninFigure 3-1 d. 3.4Comparisonof C18Oand SMF:EvidenceforCODepletion InFigure 3-1 ,wepresentthemorphologyofthelamentaryIRDCH.Thegoal of thissectionistocompare C18Oand SMF.Thesimplestwayofdoingthis,whichwe refertoasCase1,involvesastraightforwardpixelbypixel comparisonofthesevalues, smoothingthe SMFdatatotheresolutionoftheC 18 O(1-0)observations,forwhichwe havederivedaccurateexcitationtemperatureinformation .Note,thatonlypixelswith SMFand C18O0.01 g cm2areconsidered.Also,pixelsforwhich SMFisaffected bybrightMIRemissionareexcluded(see x 3.2 ).Wealsoperformacomparisonatthe higherangularresolutionoftheC 18 O(2-1)observations,whichwerefertoasCase1 HiRes,assumingT exatthishigherangularresolutioncanbeestimatedfromthev alues derivedatthe(1-0)resolution.ForboththeseversionsofC ase1,wereferto C18Oas C18O,TOT,sinceitisderivedfromalltheC 18 OemissionassociatedwiththeIRDCand itssurroundingGMC. However,asisapparentfromFigure 3-1 ,theC 18 Oemissionismoreextended thanthe8mextinctionmapfrom Butler&Tan ( 2009 ; 2011 ).Thisisbecause,as discussedabove,theextinctionmapisderivedfroman“on-o ff”comparisonwith adjacentregions,whichhelpdenethebackgroundMIRinten sitythatisexpectedto 58

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bebehindthelament.ThustheMIRextinctionmappingmetho dbecomesinsensitive tomaterialpresentintheseadjacent,lowercolumndensity (“envelope”)regions. Afaircomparisonbetween SMFand C18Owouldallowforthisenvelopematerial. Wethusdene“lament”and“envelope”regionsbasedonthe8 mimageofthe IRDC.FollowingHT11,thelamentisdenedtobearectangul arstripcenteredat ( J 2000) = 18 h 57 m 08.02 s, ( J 2000) = 0210035.700 ,2.05 0 wideinR.A.and4.47 0 long inDec.Theoutlineofthislamentregionisshownbyaredbox inthepanelsofFigure 1.Theenveloperegionisdenedtobemadeupoftwoadjacentr ectangularregions oneithersideofthelament.Theseareshownasbluerectang lesinFigure1and areeach0.56 0 wideinR.A.and4.47 0 longinDec.Note,thatbecauseofthelimited areamappedbyourobservations,theseenveloperegionsare narrowerthanthose consideredbyHT11. ForourCase2,weassumethattheC 18 Omaterialpresentintheenveloperegions isalsopresentatthesimilarlevelstowardsthelamentreg ion,andsoattemptto subtractthisemissionfromtheC 18 Ospectrumofthelament,beforethencomparing to SMF.Tocarryoutthissubtractionwedividethelamentandenve lopeintofourE-W strips(1to4fromNtoS)(seeFigure1).Ineachstrip,themea ncolumndensityper unitvelocityisevaluatedforthelament(basedon66C 18 O(1-0)pixels)andthetwo adjacentenveloperegions(basedon18C 18 O(1-0)pixelseach)(seeFigure 3-3 ),using theT exestimatesdescribedpreviously.Theenvelopespectraarea veragedandthen subtractedfromthelament.Thetotalcolumnofthisenvelo pe-subtractedspectrum isevaluatedandusedtoderive C18O,FIL.Thisisofcourseanapproximatemethodfor accountingfortheenvelopematerial:onecanseefromFigur e 3-3 thattheenvelope spectraoneithersideofthelamentcanbequitedifferent, especiallyforstrips1and2. Theuncertaintyintheenvelope-subtractedspectrumbecom eslargewhentheenvelope spectraareofsimilarstrengthasthatofthelament,asist hecaseforstrip1.Thuswe donotregardtheresultsofenvelopesubtractionforstrip1 asbeingreliable,andwe 59

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excludethesepixelsfromtheCase2analysis.AswithCase1, wealsoperformaCase 2HiResanalysis,using C18O,FILestimatedatthehigherresolutionoftheCO(2-1)data, adoptingvaluesofT exevaluatedattheCO(1-0)resolution. WiththeseCase1and2methods,wenowcomparethepixelbypix elvalues of C18Owith SMFderivedfromMIRextinctionmapping.AsnotedinHT11,these measurementsofareessentiallyindependentofclouddistanceuncertainti es. Figure 3-4 apresents C18O,TOTversus SMF,i.e.Case1ofnoenvelopesubtraction. ThebesttpowerlawrelationtotheCO(1-0)resolutiondata of C18O,TOT=g cm2 = A ( SMF=g cm2 ) has = 0.4520.054andA = 0.1460.023.ForCase1HiRes (i.e.attheCO(2-1)resolution,adoptingCO(1-0)resoluti onT exestimates)wend = 0.4630.025andA = 0.1510.010.TheseresultsaresummarizedinTable 3-1 Theseuncertaintiesarederivedassumingthattheerrorsof eachindividual measurementareasfollows:for C18O,axedvalueof0.0024 g cm2(derivedfromthe 1 RMSnoiseof0.2K km s1overthevelocityrangeof4050 km s1)anda20%error toaccountforuncertaintiesinT exassumedtobe1Katthetypicaltemperatureof7K; for SMF,a15%errorplusasystematicerrorof0.01g cm2(BT09).Attheresolution oftheCOpixels(11 00 forCO(1-0)and5 00 forCO(2-1)),the SMFmeasurementsare independent,butthe C18Oresultsarenotsincethetelescopebeamisabouttwice thepixelscale.Thustheabovequoteduncertaintiesofthep owerlawtsassume, conservatively,only25%ofthepixelsareused(althoughth ederivedvaluesofthe parametersarebasedontstoallofthepixels). Wearguebelowthat SMFisamoreaccuratemeasureofthetruemasssurface densityinIRDCsthan C18O,sinceonedoesnotexpectlargechangesinMIRdust opacitiesintheseenvironments,basedonthe Ossenkopf&Henning ( 1994 )dust models.Ifthisistrue,thenifC 18 Owerealsoanaccuratetracerofmasssurfacedensity, thenweshouldseeaone-to-onerelationbetween C18Oand SMF,i.e. '1,even ifA(thevalueof C18O= SMFwhen SMF = 1 g cm2)isnotexactlyunitybecause 60

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ofsystematicuncertaintiesintheabsolutevaluesofC 18 OabundanceorMIRdust opacities.Wemeasure = 0.4520.054forCase1and = 0.4630.025forCase1 HiRes,whicharesignicantly(10 and21 )differentfromone,andweinterpretthese resultsasbeingevidenceforCOdepletionfromthegasphase Toillustratethattheseresultsdonotdependonthechoiceo fdustopacityper unitgasmass,wehaverepeatedtheanalysisbutwithagas-to -dustmassratioof100 (ratherthanourducialvalueof156).Wend = 0.5090.073(about7 different from = 1)forCase1and = 0.5520.035(about13 differentfrom = 1)forCase 1HiRes.Notethatwedonotexpecttoderiveexactlythesamev aluesof asbefore sincewehaveaxedthresholdof0.01 g cm2toincludepointsintheanalysisand soreducingthegas-to-dustmassratiocausesustolosesome datapointsnearthis limit. Figure 3-4 bshowstheratio C18O,TOT= SMFversus SMFforourducialCase 1andCase1HiResanalyses,withthederivedpowerlawrelati onsoverlaid.For0.01< SMF=g cm2<0.03themeanvaluesof C18O,TOT= SMFare1.316and1.471for Case1andCase1HiRes,respectively.Bythetime SMF&0.1 g cm2, C18O,TOT= SMFhasdeclinedtovaluesof .0.4. InCase2weattempttoaccountfortheIRDCenvelope:weconsi derthatwecando thisreliablyonlyforstrips2,3and4,wheretheenvelopeis relativelyweakcomparedto thelament.Figure 3-4 cpresents C18O,FILversus SMFforCase2.Thebesttpower lawrelationtotheCO(1-0)resolutiondataof C18O,FIL=g cm2 = A ( SMF=g cm2 ) has = 0.2390.080andA = 0.0740.017.ForCase2HiRes(i.e.attheCO(2-1) resolution,adoptingCO(1-0)T exestimates)wend = 0.3170.038andA = 0.0900.010.Theseuncertaintiesassumethesamemeasurementuncertai ntiesas Case1,exceptanadditionalsystematicerrorof0.01gcm2hasbeenappliedto C18O,FILduetouncertaintiesassociatedwithenvelopesubtraction .Againtheseresultsindicate asignicant(10 and18 forCase2andCase2HiRes,respectively)departurefroma 61

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one-to-one( = 1)relation,whichweagaininterpretasevidenceforCOdeple tion.The resultswithagas-to-dustmassratioof100are = 0.3030.11(about6 differentfrom = 1)forCase2and = 0.3720.048(about13 differentfrom = 1)forCase2 HiRes. Figure 3-4 dshowstheratio C18O,FIL= SMFversus SMFforCase2andCase2 HiRes,withtheabovepowerlawrelationsoverlaid.For0.01< SMF=g cm2<0.03themeanvaluesof C18O,FIL= SMFare1.099and1.238forCase2andCase2HiRes, respectively.Thesevaluesaresmallerthantheirequivale ntsforCase1,asistobe expectednowthatweareallowingforthemolecularenvelope .Thevaluesarealsovery closetounity,suggestingthatouradoptedC 18 Oabundancesanddustopacityperunit gasmassarereasonable.Again,bythetime SMF&0.1 g cm2, C18O,TOT= SMFhas declinedtovaluesof .0.4. 3.4.1AlternativestoCODepletion Thereareseveralphysicalprocessesthatcouldberesponsi blefortheobserved trendofdecreasing C18O= SMFwithincreasing SMF.Onepossibilitycouldbethatour correctionsfortheopticaldepthoftheC 18 Oemissionaresystematicallyunderestimated nearthecenterofthelamentwherethecolumndensityislar ge.However,thelargest opticaldepthcorrectionsinthehighestcolumndensityloc ationsincreasethecolumnby only30%(thehighestopticaldepthsare 1,butlowerwhenaveragedoverthewhole column),sothiseffectisunlikelytobedrivingtheobserve dtrend. HT11suggestedtheirobservedtrendofdecreasing 13CO= SMFwithincreasing SMFcouldpotentiallyresultifatthesametimethereisasystem aticdecreaseinthe excitationtemperatureofabout5K.However,fromourT exestimates,wendnostrong negativetemperaturegradientwithintheIRDCtowardsthem asssurfacedensitypeaks. Infact,T exincreasesslightlytowardstothecenterofthelament,pro bablyasthe densitiesbecomegreaterthantheeffectivecriticaldensi tiesandthelowerCOlevels 62

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canthermalize.Thus,weexcludetrendsinT exascausingtheobservedvariationof C18O= SMF. FractionationofC 18 Ocouldinprinciplechangethelocalabundanceofthis molecule,butthemostimportantwayinwhichthiscanbeachi evedisviaisotope selectivephotodissociationatcloudedges,whichwouldno tbeabletoexplainthetrends ofdecreasingC 18 Oabundancethatweseerunningfrom'0.02 g cm2(A V'4mag) to '0.2 g cm2(A V'40mag). Anotherpossibilitytobeconsideredissystematicchanges in8mdustopacities forgasathigherdensities.Iftheopacitywastoincrease(e .g.duetograincoagulation and/oricemantleformationandgrowth),thenthiscouldexp lainourobservedtrend ofdecreasing C18O= SMFwithincreasing.The Ossenkopf&Henning ( 1994 )dust modelsdoshowanincreaseof 8mof19%goingfromtheuncoagulatedthinicemantle modeltotheuncoagulatedthickicemantle(allvolatilesde pleted)model.Maximal coagulation(correspondingtothatexpectedafter10 5yratdensitiesof10 8 cm3orafter 10 8yratdensitiesof 10 5 cm3,whichisprobablymorethatcanbeexpectedto haveoccurredsincetheobserveddensitiesofIRDCcoresare .10 5 cm3;BT09)raises 8mbyanadditional17%.Thus,icemantlegrowthandgraincoagu lationappearstobe abletoaccountforonlyasmallfractionoftheobservedvari ationof C18O= SMF. Weconcludethemostlikelycauseofthetrendofdecreasing C18O= SMFwith increasing SMFisCOdepletionduetofreezeoutontodustgrains.Thiswould causea systematicreductionintheamountofCOgasobservedinhigh ermasssurfacedensity regions,whicharelikelytoalsobeofhighervolumedensity 3.4.2CODepletionandImplications Followingthedenitionsof x 1andthenotationof Fontanietal. ( 2006 ),thedepletion factorisf DX E CO X O CO = SMF C18O ,(3–7) 63

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whereX E COistheexpectedabundanceofCOrelativetoH 2givenstandardgasphase abundances,X O COistheobservedabundanceandthelastequalityassumesthat SMFestimatedfromMIRextinctionmappingisanaccuratemeasur eofthetruemasssurface density(thisassumptionisdiscussedfurtherbelow).Give ntheuncertaintiesinthe absolutevaluesoftheC 18 OabundanceandtheMIRdustopacityperunitgasmass,we renormalizef DtobeunityfortheregionsoftheIRDCwith0.01< SMF=g cm2<0.03andrefertothisrenormalizedvalueastherelativedepleti onfactorf0D = Bf D,wherethe scalingfactor,B = 1.316, 1.471, 1.099, 1.238forCase1,Case1HiRes,Case2,Case2 HiRes,respectively.Weshowmapsoff0DforthesefourcasesinFigure 3-2 e-h.Wenote thatthevaluesoff0Dpresentedhere,peakingatvalues '5,aremasssurfacedensity weightedaveragesandthuslowerlimitstothemaximumvalue softhedepletionfactor thatapplyinthedensestregionsofthecloud. Weconcludethatwithhigh( 10 )signicance,widespreadCOdepletionis occurringinthisIRDC,withdepletionfactorsofupto 5(seeTable 3-1 ).Thesevalues arelargerthanthoseseentowardsmoreevolvedcoresandclu mpsalreadycontaining massiveprotostars( Fontanietal.2006 ; Thomas&Fuller2008 ).Ourmeasurementof COdepletionsuffersfromfewersystematicuncertainties, especiallysincewedonot requireknowledgeofthedusttemperature. Eachpixelinthelowerresolutiondepletionmaps(11 00 ,halftheC 18 O(1-0)angular resolution)correspondstoalengthof0.155pcatthecloudd istanceof2.9kpc,andso containsamassof11.4(=0.1g cm2 ) M .Thus,hundredsofsolarmassesappearto beaffectedbydepletionalongthelament(thetotalSMF-de rivedmassinthe4stripsis580230 M ,HT11),includingaparticularlyprominentmassivecoreor clumpinstrip2 andalargerclumppartiallyinstrip4andextendingtotheso uth. Thus,IRDCG035.30-00.33isoneofthemostmassivecloudsin whichCO depletionhasbeendetectedbydirectCO-basedandnon-CO-b asedmeasurements ofmasssurfacedensity.OurresultsalsosuggestthatCOdep letionwillbeacommon 64

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occurrenceinIRDCs,sincethevaluesof0.1 g cm2inthiscloudarequitetypical (e.g.BT09).COisthereforeanimperfecttracerofasignic antfractionofthemassof IRDCs(notjustthecoldest,densestcores).Accurateaccou ntingfordepletionand/or useofspeciessufferingminimaldepletion,suchasNH 3andN 2 H +,arerequiredfor moreaccuratedynamicalstudiesoftheseclouds. AnestimateoftheCOdepletiontimescaleduetofreeze-outo ntodustgrainsist D'8000=( n H 2 ,5 S ) yr,wheren H 2 ,5isthenumberdensityofH 2moleculesinunitsof10 5 cm3andSisthestickingprobability(oforderunity;e.g. Tielens&Allamandola 1987 forCOongrains.Wecanapplythistothethinnestregionofth eIRDC:the 500 (0.070pc)widelamentnearthecenterofstrip3,whichappe arstohavesignicant COdepletionwithf0D34.Assumingthedepthofthelament,whichhas SMF'0.2 g cm2,issimilartoitswidth,thenn H 2 ,5 = 2.0andt D'4000yr.Thisprovidesa lowerlimittotheageofthispartoftheIRDC.Thefree-fallt ime,t = (3=[32 G]) 1=2,for thisdensityis6.910 4 yr,i.e.muchlonger.However,ifthelamenthasbeencreated bylargerscalesupersonicows,thenonemightexpectthehi ghdensitygastohave beenpresentforabouttheowcrossingtimeacrossthewidth ofthelament.Velocities of 10 km s1mayberelevantinmodelsofGMC-GMCcollisions( Tan 2000 )orifthe large-scaleSiOemissionseentowardsthislament( Jim enez-Serraetal. 2010 )has beencreatedbysuchows.Theowcrossingtimeatthisspeed forthispartofthe IRDCisonly6800yr.ThusthefactthatweseeCOdepletionintheseverythinl aments oftheIRDCcanhelptoconstrainmodelsforthecloud'sforma tion.Formodelsinwhich thecloudlifetimeislessthantheowcrossingtimeacrosst helament,aconstraintis placedontheowspeed.ForthethinnestregionofthisIRDC, thiscorrespondstoow speeds .17 km s1. 65

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Table3-1.Parametersofdepletionfactoranalysis Case A B f0D(max) Case10.4520.054 0.1460.0231.3163.5(at SMF = 0.16 g cm2) Case1HiRes0.4630.025 0.1510.0101.4714.6(at SMF = 0.20 g cm2) Case20.2390.080 0.0740.0171.0993.8(at SMF = 0.16 g cm2) Case2HiRes0.3170.038 0.0900.0101.2384.9(at SMF = 0.20 g cm2) 66

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Figure3-1.MorphologyoftheIRDC. (a)Topleft:Spitzer GLIMPSEIRAC8 mimage, withlinearintensityscaleinMJySr1.Theimagehas1.2 00 pixelsandthe PSFhasaFWHMof2 00 (b)Bottomleft: Masssurfacedensity, SMF,with linearintensityscaleing cm2,derivedfromtheimageinpanel(a)usingthe smallmedianlter(SMF)MIRextinctionmappingmethodofBu tler&Tan (2009;2011).Regionswith SMF>0.01 g cm2butwhichare >20%affectedbyartifactsintheextinctionmap(e.g.duetoMIRb rightsources) areexcludedfromanalysisandshownby“X”'sand“O”'sforCO (1-0)and (2-1)resolutiongrids,respectively. (c)Topmiddleleft: Integratedintensity mapofC 18 O(J = 2!1)emissionoverthevelocityrangeof4050 km s1, i.e.thegasassociatedwiththeIRDC(HT11),inlinearunits ofK km s1and apixelscaleof5 00 (d)Bottommiddleleft: Themeanexcitationtemperature mapweightedbythecolumndensityinK,withpixelsizeof11 00 67

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Figure3-2.DepletionmapsoftheIRDC. (e)Topmiddleright: Relativedepletionfactor (f0D)mapforCase1(noCOenvelopesubtraction). (f)Bottommiddleright: Relativedepletionfactor(f0D)mapforCase1HiRes(noCOenvelope subtraction,derivedattheCO(2-1)resolution). (g)Topright: Relative depletionfactormapforCase2(COenvelopecontributiones timatedvia interpolationacrossstrips2,3and4thensubtracted;note weconsiderthis processunreliableforstrip1). (h)Bottomright: Relativedepletionfactormap forCase2HiRes. 68

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A B Figure3-3.VelocitystructureoftheC 18 OmoleculesassociatedwiththeIRDCandits envelope.Thecolumndensitydistribution,d N C 18 O=d v,hasbeenderivedfrom theC 18 O(1-0)and(2-1)spectra,localestimatesofT exandincludingoptical depthcorrections.(A)the4setsofproles(offsettodispl ayfromtopto bottomandlabeled1to4)correspondtothe4stripsshowninF igure 3-1 Thedotted,redlineisthesummedcontributionfromgasfrom thecentral regionofeachstrip,correspondingtotheIRDC“lament”(s eeFigure 3-1 andtext).Thedot-dashedandlong-dashedbluelinesshowsu mmed contributionfromthegasfromtheeasternandwesternenvel operegions, respectively.(B)Illustrationofenvelopesubtraction(C ase2,seetext).For thesamestripsasin(A),wesubtracttheaverageoftheeaste rnand westernenvelopes(short-dashedbluelines)fromthelame nt(dottedred lines),toleaveanestimateofthematerialinthelament(s olidblacklines). Weconsiderthisprocessunreliableforstrip1,wheretheen velopecontains asimilaramountofmaterialasthelament. 69

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Figure3-4.EvidenceforCOdepletion.(a)Comparisonof C 18 O,TOT(i.e.Case1)and SMFforallC 18 O(1-0)(crosses)andC 18 O(2-1)(dots)pixelsforwhichboth C18Oand SMF>0.01 g cm2andthepixelis <20%affectedby SMFartifacts.Thedottedlineshowsthecondition C 18 O,TOT = SMF.Thesolid, dashedlinesshowthebest-tpowerlawrelationstotheC 18 O(1-0),C 18 O(2-1)resolutiondata,respectively.(b)Ratio C 18 O,TOT= SMF(i.e.Case 1)versus SMF,withthesamesymbolandlinenotationasin(a).The horizontalsolid,dashedlinesfrom0.01< SMF=g cm2<0.03indicatethe meanvaluesofthedatainthisrangefortheC 18 O(1-0),C 18 O(2-1)resolution data,respectively.Thecrossintheupper-rightcornerind icatestypical estimateduncertainties.(c)Sameas(a),butnowestimatin g C 18 O,FILfor Case2.(d)Sameas(b),butforCase2.Both(b)and(d)showtha t C18O= SMFdecreasesbyuptoafactorof 5as SMFincreasesfrom 0.02 g cm2upto 0.2 g cm2. 70

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CHAPTER4 THEDYNAMICALSTATEOFANINFRAREDDARKCLOUD Inthischapter,wecontinueworkingwiththelamentaryIRD CG035.39.-0033 (CloudH).WerevisitthevirialanalysesmadeinChapter2,b utusingmoresensitive, higherresolutionC 18 Oemissionlinedata,J = 10andJ = 21transitions,taken withtheIRAM30mtelescope.Inchapter1,weshowedthatthes urfacepressureterms appearedtobedynamicallyimportanttothestructureofthe lamentandthus,these lamentsmaynotyetbeinvirialequilibrium.However,usin ghigherresolutiondata,we nowshowthatthehighdensitylamentwithinCouldHisactua llyconsistentwithbeing invirialequilibrium.Thisworkisnearreadyforsubmissio ntoTheAstrophysicalJournal. InfraredDarkClouds(IRDCs)arebelievedtorepresentthei nitialconditionsof massivestarandstarclusterformation.Informationonthe formationofIRDCs,suchas theirkinematics,canbegainedthroughstudyingmolecular lineemission.Weanalyze highresolutionC 18 Olineemissiondata,J = 1!0andJ = 2!1transitions,takenwith theIRAM30mTelescopeoftheInfraredDarkCloudH(G035.3900.33).Weperform ellipsoidalandlamentaryvirialanalysisofthehighlyl amentaryIRDC,ndingthat thelamentisconsistentwithbeinginvirialequilibrium. Weestimatedthatthesurface pressureofthecloudislessthantheinternalpressure.How ever,theratio

hasvaluesnear 0.4,indicatingthatthesurfacepressuretermsarestillimpor tantto theoverallsupportofthecloud.Thetworegionswhichappea rtobeclosesttovirial equilibriumalsoappeartobesiteswithactivestarformati on. 4.1MotivationtoStudytheDynamicalStateofanInfraredDa rkCloud Identiedasfeaturesofhighextinctionagainstthebright mid-infrared(mid-IR) backgroundoftheMilkyWay,InfraredDarkClouds(IRDCs)ar ebelievedtorepresent theinitialconditionsofstarclusterformation.Withthei rhighdensities(n H10 310 5 cm 3; Teyssieretal.2002 ; Butler&Tan2009 ,hereafterBT09; Rathborneetal. 2006 )theyaresimilartoregionsknowntocontainnewlyformings tellarclusters 71

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( Rathborneetal.2006 ; Tan2007 ; Zhangetal.2009 ; Raganetal.2009 ).Through studiesofmolecularlineemission,thekinematicsofIRDCs ofcanbedetermined.Such informationwillprovideinsightonwhetherstar-formingc loudsaregravitationallybound orinvirialequilibrium.Anyevidenceforcoherentgasmoti onwouldhelpuntangle theoriesofIRDCformation;i.e.convergingatomicows( Heitschetal. 2008 )or convergingmolecularowsfromcloudcollisions( Heitschetal. 2008 ). Inthispaper,wepresentIRAM30mobservationsof13 COandC 18 O,J = 1!0andJ = 2!1transitions,molecularlineemissionfromthelamentaryI RDCG035.30-00.33 (CloudHinBT09).Usingestimatesofmasssurfacedensity,m easuredfromtheC 18 Oemissionandmid-infrared(MIR)(8 m)dustextinctionmapping,weperformavirial analysisofahighlylamentaryIRDCtodetermineitsdynami calstate.Thisanalysis isdoneintwoways.First,weperformasimpleellipsoidalcl oudvirialanalysisbased onthemethodfrom Bertoldi&McKee ( 1992 ,hereafterBM92).Thesecondmethod isalamentarycloudvirialanalysisbasedonthe Fiege&Pudritz ( 2000 ,hereafter FP00)analysisofhelicalmagneticallythreadedlamentar ymolecularclouds.This workismotivatedbythestudyof Hernandez&Tan ( 2011 ,hereafterHT11).HT11 used13 COmolecularlineemissionfromtheGalacticRingSurvey(GRS) toestimate themasssurfacedensitiesoftwohighlylamentaryIRDCs,i ncludingFilamentH(the highdensitylamentofCloudH).HT11foundthroughtheirdy namicalanalysisthatthe surfacepressuretermsaredynamicallyimportant,suggest ingthatthelamentshave notyetreachedvirialequilibrium.However,theregionswh ichappeartobeclosetovirial equilibriumalsoappeartocontainproto-stellaractivity 4.2MassSurfaceDensityfromSmall-Median-FilterMIRExti nctionMapping The8 msmall-median-ltermasssurfacedensity, SMF,mapwasderivedat 2 00 resolutionfromthe Spitzer IRACband4(GalacticLegacyMid-PlaneSurvey Extraordinaire[GLIMPSE]; Benjaminetal.2003 )imagebycomparingtheobserved intensityateachpositionwiththeexpectedbackgroundint ensity.Themasssurface 72

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densitieswereestimatedbyinterpolatingtheintensities ofsurroundingnearbyregions (seeFigure1aand1b).Adustopacityof 8m = 7.5 cm 2 g1wasadopted,justas inBT09.Theextinctionmapsusedinthisstudyassumedagasto-dustratioof156 ( Weingartner&Draine 2001 ).Acorrectionfortheforegroundemissionwasmade basedonthepresenceofindependentsaturated(highoptica ldepth)cores( Butler& Tan 2011 ).AsdescribedinBT09, SMFinthelamentwasderivedfromcomparison withadjacent“envelope”regions,whichmaycontainasmall levelofmaterialasshown throughthemolecularlineobservations(e.g.13 COfromtheGRSanalyzedbyHT11). Therefore, SMFbecomesunreliableatmasssurfacesdensities .0.01 g cm2dueto theenvelopeandothersystematicuncertainties.Regionso fbrightMIRemission,where theextinctionmappingmethodfailsasnotedbyBT09,wereal soaccountedfor.Asdone in Hernandezetal. ( 2011 ,Chapter3,hereafterPaperI),weexcludegridded1100 SMFpixelscontaining30%ormore(byarea)zeroornegativevalu esfromtheoriginal SMFmapfromdensityestimatesusedinthevirialanalyses. 4.330mIRAMObservations TheJ = 1!0andJ = 2!1rotationaltransitionsof13 COandC 18 Owere mappedusingtheIRAM(InsitutodeRadioastronmiaMillimet rica)30mtelescopeinPico Veleta,SpainonAugust29th,2008.UsingtheOn-The-y(OTF)method,anareaof20 40 wasmappedtowardsFilamentHwithacentralpositionof ( J 2000) = 18 h 57 m 08 s, ( J 2000) = 021003000 (l = 35.517 ,b =0.274 ).Forallobservationstheoff positionsweresetto(183000 ,65800 ).Thetypicalsystemtemperatureswere150-220K. Theintensities,(TA),wereconvertedtoabrightnesstemperature,T Busingmainbeam efcienciesof0.64fortheJ = 1!0transition,and0.52fortheJ = 2!1transition.At 110GHz(J = 1!0),thebeamsizeis22 00 ,whileat 220GHz(J = 2!1)beam sizeis11 00 .Thevelocityresolutionsare 0.05 km s1and 0.1 km s1respectively. Forthisstudy,allspectrawasregriddedtoavelocityresol utionof0.2 km s1.Thetypical 1 RMSnoiseofthedatais0.2 K km s1overthevelocityrangeof4050 km s1.Since 73

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theC 18 Oemissionisextendedoverthelament,weassumef clump = 1.Figure 4-1 presentsthemorphologyofFilamentHasseenin8 memission(Spitzer-GLIMPSE), andmolecularlineemissionfrom13 COandC 18 O. 4.4MassSurfaceDensitiesfromCOEmission 4.4.1COColumnDensityEstimates Ourmethodforevaluatingthemasssurfacedensitiesfrom13 COandC 18 Owerethe sameasinPaperI.WeestimatethecolumndensityofC 18 Omolecules,d N C18O,inthe velocityintervald v,fromtheiremissionthroughthegeneralequation:d N CO ( v ) d v = 8 A3 0 g l g u 1exp (h=kT ex ) Q rot g l exp(E l=kT ex ) .(4–1) HereQ rotisthepartitionfunctionforlinearmoleculesgivenbyQ rot =P 1J =0 (2 J + 1)exp(E J=kT ex )withE J = J ( J + 1) hB,whereJistherotationalquantumnumber andBistherotationalconstantequalto(5.5101, 5.4891)10 10 s1for13 COandC 18 O, respectively.h=k = 5.289, 10.58Kfor13 COandh=k = 5.269, 10.54KforC 18 O,J = 1!0andJ = 2!1transitions,respectively.At7.5K,Q rot = 3.205.Aisthe Einsteincoefcient,wherefor13 CO,6.294, 60.38108 s1forJ = 1!0andJ = 2!1, respectively.ForC 18 O,6.266, 60.11108 s1forJ = 1!0andJ = 2!1,respectively. 0isthewavelengthofthetransition,for13 CO, = 0.272, 0.136cmforJ = 1!0andJ = 2!1,respectively.ForC 18 O, = 0.273, 0.137cmforJ = 1!0andJ = 2!1, respectively.g landg uarethestatisticalweightsofthelowerandupperlevels,an d is theopticaldepthofthelineatfrequency ,i.e.atvelocityv.Theexcitationtemperature,T ex,isassumedtobethesameforallrotationallevels.Details ontheestimationofT exaregivenbelow. AsinHT11andPaperI,theC 18 Ocorrespondingtothelamentfallswithinthe velocityrangeof4050 km s1.Thetotalcolumndensityperpixelisthencalculated overtheentirevelocityrangeofthelament,N C18O =RdN C18O. 74

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4.4.2ExcitationTemperatureEstimates AsinpaperI,weneededtoestimateanappropriateexcitatio ntemperatureateachl b vlocationtoaccuratelyestimatethecolumndensity.Tosumm arizeourmethod,the temperatureateachl b vpositionisdeterminedbyvaryingtheassumedtemperature untiltheratiobetweenmasssurfacedensitiesderivedfrom bothtransitionswerein agreement;whenR 2,1,theratiobetweentheJ = 2!1andJ = 1!0masssurface densities,wasequaltounity.TomatchtheresolutionoftheJ = 1!0data,thehigher resolutionJ = 2!1datawasconvolvedwithabeamof22 00 andregriddedtoapixel scaleof11 00 ForC 18 O,R 2,1wascalculatedforalll b vpositionsabovethe3 noiselimitinboth transitionsbyrstassumingaT ex = 30K.For13 CO,R 2,1wascalculatedforalll b vpositionsabovethe2 .Then,forbothmolecularspecies,T exwasiterativelydecreased from30KuntilR 2,1convergedto1.Thisprocedureresultedinathreedimension algrid containingestimatesofT exforallpositionsabovethenoiselimit.Next,forallpositi ons belowthenoisethreshold,theirT exwasestimatedbytakingthemeanexcitation temperatureatthecorrespondingl bpositionaveragedovervelocity.Finally,forany remainingl b vpositionswithoutanestimatedexcitationtemperature,we resettothe meanT exfromtheircorrespondinglamentorenveloperegion(seeFi gure 4-1 ). AsindicatedfromtheresultsofPaperI,thismethodofestim atingtheexcitation temperaturewassuccessfulfortheC 18 Omolecularlinedata.However,itwasfoundthat forthe13 COmolecularlinedata,R 2,1failedtoconvergefor60%ofthel b vpositions alongthelament.Weconcludedthatthefailuretoconverge wasdueto13 CObeing opticallythick.DuetotheC 18 OmolecularlinedataprovidingestimatesofT exthroughout theentireregion,werestricttherestofourvirialstudyto onlytheC 18 O. 4.4.3C 18 OMassSurfaceDensitiesEstimates ForonlytheC 18 Oemissionlinedata,thecolumndensitiesforbothtransitio ns,N C18O,areconvertedtoatotalmasssurfacedensity C18O,byassumingtheabundance 75

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ratiosofn 16O=n 18O = 327from Wilson&Rood ( 1994 )andn 12CO=n H2 = 2104from Lacyetal. ( 1994 ).Thus,ourassumedabundanceratioofC 18 OtoH 2is6.12107andforeachpixelisthengivenby: C18O = 7.652102 N C18O 10 16 cm2 g cm2 ,(4–2) assumingameanmassperHnucleusof H = 2.341024 g. FollowingthemethodusedinHT11,weestimated C18Obyrstsubtractingthe contributionof C18Ointheenvelopeofthelament.Bytracingfourorthogonalst rips acrossthelamentstructure(seeFig. 4-1 ),wemeasuredthecolumndensityperunit velocityonbothsidesofthelament(the“off-source”spec tra)usingthecolumndensity calculationdescribedabove.Finally,wesubtractthe“off -source”averagespectrafrom thecorresponding“on-source”lamentregion.4.4.4VelocityDispersionEstimates Weestimatetheaveragetotal1Dvelocitydispersion, ,foreachlamentand enveloperegionusingtheC 18 Olineemission.Thevariance, 2,isgivenby: 2 =RdN CO ( v v ) 2 dv RdN CO dv(4–3) where,dNCOisthemeancolumndensityand visthemeanvelocityinthecorresponding region.Wehaveincludedcorrectionsforthemolecularweig htsofC 18 Oandour estimatedcloudtemperatures. 4.5MassesofIRDCHfromCOandMIRDustAbsorption MassestimatesofthelamentaryIRDCHaremadeusingtheobs ervedmass surfacedensitiesandangularsizes.Wealsoassumeanearki nematicdistanceof2.9 kpcfrom Simonetal. ( 2006a ),whoassumedthe Clemens ( 1985 )rotationcurve.Near kinematicdistancesareappropriateduetothecloudbeingi dentiedthroughabsorption againstthediffuseMIRemissionoftheGalaxy.Theuncertai ntyofthedistanceis assumedtobe0.5kpcandismostlikelytheresultofnon-circ ularmotionsof 8 km s1. 76

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Temperatureuncertaintiesof5Kwouldleadtouncertaintiesof 20%.For SMF, weestimateanuncertaintyof 20%duetoforegroundcorrectionsandbackground interpolationuncertainties(BT09,2011).TheC 18 OmassisM C 18 O = 669201 M ,while thedustextinctionmassisM SMFis872230 M 4.6TheDynamicalStateofIRDCH 4.6.1EllipsoidalCloudVirialAnalysisofIRDCH Weperformanellipsoidalcloudvirialanalysisfollowingt heworkofBM92.Todo thisweconsiderIRDCHtobeanellipsoidalcloudwithradius Rnormaltotheaxisof symmetryandsize2 Zalongtheaxis.Thesemi-majorandsemi-minoraxesoftheclo ud projectedontotheplaneoftheskyaredenedbyR maxandR min.WedenedyZ=Rastheaspectratioofthelamentarycloud.IRDCHhasarelat ivelythin,lamentary morphologyasseeninFigure 4-1 .Usingtheregiondenedbytheredrectangular regiontodenethelament,wesetR max=R min = 2.18.Giventhismorphology,we assumethatthesymmetryaxisofthecloudisneartobeingint heplaneoftheskyand adoptaducialvalueoftheinclinationanglebetweenthisa xisandthelineofsightto be = 60 .Therefore,weassumeR = R minandZ = R max=sin sothaty = 2.52.The uncertaintyofyinthisassumptionissuchthata15 changeininclinationwouldcause a 15%uncertaintiesiny.AsinPaperI,weuseageometricmeanobservedradius ofR obs( R max R min ) 1=2,whichisalsorelatedtoRvia,R obs = R cos 1=2[1 + ( y tan) 2 ] 1=4. BM92denedR masthemeanvalueofR obsaveragedoverallviewingangles,however weexpressedthequantitieshereintermsofRandR obs.Thisapproachtoavirial analysisisapproximateandweconsideramoreappropriate lamentaryanalysisof IRDCHinthefollowingsection. Asstatedby McKee&Zweibel ( 1992 ),aclumpshouldbeinvirialequilibriumifit isembeddedinanenvironmentthatisevolvingonalargertim escalethantheclump's dynamicaltimescale:t s2 R= .Thevirialequationgivenby McKee&Zweibel ( 1992 ) 77

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is:0 = 2(TT0 ) +M+ W .(4–4) Here, T istheclumpkineticenergy, T0isthekineticenergyresultingfromthesurface pressureontheclump, M isthemagneticenergyassociatedwiththecloud,andWis thegravitationalbindingenergy,whichforanellipsoidal cloudis(BM92)W =3 5 a 1 a 2 GM 2 R ,(4–5) whereforapower-lawdensitydistribution /rk ,a 1 = (1k =3)=(12 k =5)anda 2 = a rcsinh( y 21) 1=2 ( y 21) 1=2(4–6) forprolateclouds.Basedontheastudyofthedensityprole sinIRDCsby Butler& Tan ( 2011 ),weadoptk= 1sothata 1 = 10=9.Wefoundthata 2is0.681giventhatyismeasuredtobe2.52.Thisdenitionofa 2isslightlydifferentfromtheformstated inBM92sincewedonotconsiderR m.Themassofthelamentwasestimatedby takingtheaveragevaluesofthosemeasuredbytheMIRdustex tinctionandtheC 18 Olineemission(seeprevioussection).Weestimatedagravit ationalbindingenergyofW =4.510 46 erg.WeexpectedthattheuncertaintiesinWarelargeduetothe measurementserrorsinandR. Weestimatetheclumpkineticenergy, T= (3=2) M2,whereMisthemassof thelamentestimatedthroughMIRextinction,M SMF.Weonlyusetheextinctionmass asthemassestimatedbyC 18 Osuffersfromdepletion(PaperI).Theaveragetotal 1Dvelocitydispersion, ,wasderivedfromtheC 18 Olineemissionbycountingonly thosepartsoftheenvelope-subtractedspectrawithpositi vesignalgreaterthanor equalto1 oftheRMSnoise.Weestimatedthat isaccuratetowithin10%.Wend T= 5.110 46 ergwithuncertaintiesataboutthe40%level. Weusedtwomethodstoestimatethesurfacetermforthekinet icenergyis T0 = (3=2) P 0 V.Fortherstmethod,MethodA,wemeasuredthemasssurfaced ensity 78

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ofthesurroundingmolecularcloudfromtheC 18 Oemissionoftheenveloperegions. Duetothelowcolumndensityoftheenveloperegionswithres pecttothelament, theyshouldnotsufferfromdepletion.Wefound 13CO (env) = 0.00892 g cm2.From McKee&Tan ( 2003 ),iftheenvelopeisself-gravitating,ithasameaninterna lpressure givenbyP (env) = 1.85 G 2 (env)withparametersf g = 1(i.e.fullygasdominated), geomR 3 obs=( R 2 Z ) = 1.3, B = 2.8(theducialvalueof McKee&Tan ,measuringthe ratioofthetotalpressureincludingmagneticeldstothat assumingtheywereabsent) and vir = 1.Therefore,weestimatedaP 0 = P (env) = 9.821012cgswithacloud volumeofV = 4R 2 Z=3,nding T0 ( A ) = 0.3010 46 erg. Inthesecondmethod,MethodB,weassumedtheenveloperegio nhada cylindrical,annularvolumewithanouterradiusof2 RandinnerradiusR.Therefore, thedensityoftheenveloperegionwas = 4(env)=(3R ) = 1.421021 g cm3. Thiswasequivalenttoavolumedensityofn H (env) = 850 cm3.Finally,weequatedP 0 =(env)2 (env),where (env)isthevelocitydispersionoftheenvelopegas (1.52 km s1)andestimated T0 ( B ) = (3=2) VP 0!0.9910 46 erg,withV = (4=3)R 2 Z. Ourresultsindicatedthatthesurfacepressuretermofthev irialequationissmaller thantheinternalkineticenergyterm,suggestingthatthe lamentisself-gravitating ratherthanbeingpressureconned.Onthecontrary,theana lysisfromHT11found largesurfacepressuretermswhichdominatedtheinternalk ineticenergy.This discrepancyismostlikelyduetotworeasons.First,inthis studyweevaluated appropriateexcitationtemperaturesthroughthelament( 7K). Hernandez&Tan assumedaconstantT exof15K,causinganunderestimationinthecolumndensities. Secondly,PaperIshowedthattheC 18 Omolecularlineemissionalongthelament suffersfromdepletion.Depletioneffectswerealsoseenin Hernandez&Tan 's13 COstudy,wherethelament'skineticenergyfactoredintheun derestimatedmass.Inthis study,onlytheM SMFwasusedinthelament'skineticenergytoavoidtheeffects of depletion. 79

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Table4-1.IRDCellipsoidalvirialanalysis Cloudproperty d(kpc)2.90.5R(pc)0.870.15 R obs(pc)1.280.16 yZ=R 2.520.38 SMF(g cm2)0.02780.0056 C18O (env)(g cm2)0.008920.00178 M SMF(M )872230 a 110/9a 20.681W(10 46erg) 4.51.8 (km/s)1.390.2 t s = 2 R= (Myr)1.20.2T (10 46erg)5.11.3T0 ( A )(10 46erg)0.300.12T0 ( B )(10 46erg)0.990.26 52 R=( GM ) 2.240.39 Wealsoevaluatedthedimensionlessvirialparameterasde nedbyBertoldi& McKee(1992)as 52 R m=( GM ),todescribethedynamicalstateofclouds.We foundthat = 2.24.Thisestimateisontheorderofunity,suggestingthatself -gravityis important.Thisresultisinagreementwiththeclumpkineti cenergyanalysisabove.To summarizeouranalysis,theellipsoidalvirialparameters arelistedinTable 4-1 4.6.2FilamentaryCloudVirialAnalysisofIRDCH IRDCHhasastronglamentarystructure.Therefore,weperf ormalamentary virialanalysisfollowingthemethodof Fiege&Pudritz ( 2000 ,hereafterFP00).For pressure-conned,non-rotating,self-gravitating,lam entary(i.e.lengths widths) cloudstreadedbyhelicalmagneticelds,FP00showedthatt heyareinvirialequilibrium givenby:P 0 P = 1m m vir1 Ml jW lj .(4–7) HereP 0istheexternalpressureatthesurfaceofthelament,P =2istheaverage totalpressureinthelament,misthemassperunitlength,m vir22=Gisthevirial 80

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massperunitlength, Mlisthemagneticenergyperunitlength,andW l =m 2 Gisthe gravitationalenergyperunitlength. AsdoneinHT11andPaperI,wedividedthelamentinto4ortho gonalstrips (seeFig. 4-1 ).Eachstriphasanangularwidthof1.12 0 alongthelament.Assuminga ducialvalueoftheinclinationanglebetweenthecloudsym metryaxisandthelineof sightof = 60 ,thephysicalwidthofeachlamentstripis1.09 0 .Welisttheestimated physicalparametersinTable 4-1 .Theseincludevaluesof 13CO, SMF,M(calculated fromthemeanvalueof),m, v, ,m vir,P, 13CO (env), (env), v (env), (env)andP O = P (env) (env)2 (env). Forcomparison,weplotP 0=Pversusm=m viralongwiththetheoreticalmodels ofFP00inFigure 4-2 .Theirmodelsallowedforpositivevaluesof Ml= jW lj (i.e. poloidally-dominatedB-eldsthatprovidenetsupporttot helamentagainstgravitational collapse)andnegativevalues(i.e.toroidally-dominated B-eldsthatprovidenet connementofthelament).Intheircomparisonofthesemod elswithobservations, includingRhoOphiuchus,Taurus,andOrion,theyfoundthatP 0=P1.Ourresultsalso indicatethatP 0=P<1,suggestingthatthesurfacepressureofthelamentisgrea ter thanintheenveloperegion.However,themeanP 0=Pis 0.5,alsoindicatingthatthe surfacepressuretermsarestillsignicant. Thelamentaryanalysisof Hernandez&Tan ( 2011 )foundtheoppositeresultof allfourregionswithP 0=P1,whichechoedtheirellipsoidalvirialanalysiswherethe surfacepressuretermswerefoundtobedynamicallyimporta ntandthatthelament hadnotyetreachedvirialequilibrium.Thisdiscrepancyis againmostlikelyduetoboth theassumedlargeT exof15Kthroughoutthelamentandtheeffectsofdepletionin the13 CObasedestimates.Thesefactorswouldhavecausedthepressu reinthelamentto beunderestimated,forcingthesurfacepressuretermstose emtodominate. ThestudybyFP00foundthattheirsourceslaywithintherang e0.11
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lamentisconnedwithahelicalandtoroidallydominatedm agneticeld.Wetherefore concludethatself-gravityandsurfacepressurealonearei nsufcientatfullysupporting thecloudagainstcollapsesincemislessthanm vir. StripsH2andH4havethesmallestP 0=Pvaluesat 0.3.Fromanexaminationof the8 mSpitzer-GLIMPSEimage(Fig. 4-1 ),wendthatthesetwostripsaresitesof relativelyactivestarformation.Therefore,theseregion sarethemostlikelytobeinvirial equilibriumandperhapsfullyself-gravitating. Wealsoconsideredhowthesevirialresultswouldvaryifdif ferentabundance ratioswereassumedforthe C18Oestimates.Figure 4-3 presentstheresultfromour samelamentaryvirialanalysis,butwiththeC 18 Omasssurfacedensitiescalculated assumingtheabundanceratiosof Fontanietal. ( 2006 ).TheirstudyusedaC 18 OtoH 2abundanceratioof3.48107(n 16O=n 18O = 383from Wilson&Rood ( 1994 )andn 12CO=n H2 = 1.33104from Frerkingetal. ( 1982 )and Wilson&Rood ( 1994 ).These abundanceratioincreaseP 0=Pby75%.Them=m virvaluesremainthesameasthey arebasedononlythe SMFestimates.Althoughtheseresultsaresimilartothose above(withtheexceptionofH1withP 0=P = 1.04,theysuggestthatthelamentary virialanalysisishighlysensitivetotheassumedabundanc eratios,whichcanvary considerablythroughouttheGalaxy. 4.7ConclusionsoftheIRDCHDynamicalState Wehavestudiedthedynamicalstateofthehighlylamentary IRDCHusing masssurfacedensitiesandkinematicinformationderivedf romC 18 Omolecularline emissionfromtheIRAM30mtelescope.Forbothellipsoidala ndlamentarygeometries, weevaluatedthetermsofthesteady-statevirialequation ndingthatthelamentis consistentwithbeinginvirialequilibrium.Thesurfacepr essureisestimatedtobe lessthantheinternalpressure,howevervaluesof


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Table4-2.IRDClamentaryvirialanalysis CloudpropertyH1H2H3H4H tot SMF(102 g cm2)1.682.071.433.732.23M(M )1902341624211010m(Mpc1)174214148386131 (1022 g cm3)50.161.542.611166.3 v(km s1)45.545.445.445.145.3 (km s1)1.741.501.431.301.39m vir(Mpc1)14101050944782903P(1012 cgs)15213986.5187129 13CO (env)(102 g cm2)0.01430.007280.006110.007970.00892 (env)(1022 g cm3)34.217.314.619.021.3 v (env)(km s1)45.544.845.044.745.1 ( env )(km s1)1.621.591.511.671.52P (env)(1012 cgs)90.243.833.352.848.9 issupportedbyaconningtoroidallymagneticeld,andnot self-gravityorsurface pressurealone.Thetworegionswhichappeartobeclosestto virialequilibriumalso appeartobesiteswithactivestarformation. 83

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Figure4-1.MorphologyofthelamentaryIRDCH.(a): Spitzer GLIMPSEIRAC8 m image,withlinearintensityscaleinMJySr1.Theimagehas1.2 00 pixelsand thePSFhasaFWHMof2 00 .(b)Masssurfacedensity, SMF,withlinear intensityscaleing cm2,derivedfromtheimageinpanel(a)usingthesmall medianlterMIRextinctionmappingmethodof Butler&Tan ( 2009 ; 2011 ). MappingtotheC 18 O(J = 1!0)gridforthedepletionanalysis,weonly utilizethosepixelswith SMF>0.01 g cm2,butweadditionallyexclude11 pixels >30%affectedbyvaluesof SMF0,e.g.duetoMIR-brightsources orpoorbackgroundmodeling.Theseareindicatedbyan“X”.( c)Integrated intensitymapofC 18 O(J = 2!1)emissionoverthevelocityrangeof4050 km s1,theemissionbelievedtobeassociatedwiththeIRDC (HT11),inlinearunitsofK km s1andapixelscaleof5 00 .(d)Integrated intensitymapof13 CO(J = 2!1)emissionoverthevelocityrangeof4050 km s1,theemissionbelievedtobeassociatedwiththeIRDC (HT11),inlinearunitsofK km s1andapixelscaleof5 00 84

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Figure4-2.P 0=Pversusm=m virforstripsinIRDCH(opensquaresjoinedbydottedline forF1toF7).Thesmoothcurvesshowtheconditionssatised by equation( 4–7 )for Ml= jW lj <0(solidlines), Ml= jW lj= 0(dottedline),and Ml= jW lj >0(dashedlines).TheobservedvaluesofP 0=P<1suggestthat thelamentisconsistentwithbeinginvirialequilibrium. 85

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Figure4-3.P 0=Pversusm=m virforstripsinIRDCH.Theanalysishereisthesameasin Figure 4-2 ,butassumestheabundanceratiousedinFontanietal.(2006 ). ThesenewabundancesleadtoanincreaseinP 0=Pof75%. 86

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CHAPTER5 IRDCFORMATIONANDGLOBALGMCPROPERTIES Inthischapter,werevisitthe13 COdatasetprovidedbytheGRStoinvestigate theformationandevolutionofthelargescaleGMCs.Usingdi fferentmethodsof derivingGMCmorphology,weinvestigateGMCmass,position angleoftherotationaxis projectedontheplaneofthesky,andthevirialparameter.T heworkhasnotyetbeen submittedforpublication. 5.1MotivationforaStudyonIRDCFormationandGlobalGMCPr operties InthediskoftheMilkyWayweobservethatmoststarsareborn fromthedensest, coldest,parsec-scalegasclumpswithin 10100parsec-scalegiantmolecular clouds(GMCs).Starformationefcienciesintheclumpsare about10-30%( Lada& Lada 2003 ),butverylowintherestoftheGMCmaterial(e.g. Ladaetal.2010 ).Intheir earlieststages,manyoftheseclumpsappearasInfraredDar kClouds(IRDCs)and areeasilyidentiedthroughhighextinctionat8 m.Tounderstandtheprocessesthat initiatestarformationbycreatingIRDCs,weneedtounders tandthekinematicsofthe lower-densitygasthroughouttheentireGMCstructure. Thiskinematicinformationmayalsoshedlightontheglobal evolutionofGMCs, aboutwhichtherearemanyopenquestions.Itiscurrentlyun decidedwhetherthey liveshortlives(e.g. Clark&Bonnell2005 )byformingrapidlyfromconvergingows ofatomicgas,remaininggloballygravitationallyunbound ,andthenbeingdestroyed quicklybycontinuationoftheowsthatcreatedthecloudan d/orfeedbackfromnewborn stars.Alternatively,someauthorshavesuggestedGMCsliv elonger,foratleasta fewdynamicaltimescales,andaregravitationallybound(e .g. Tan2000 ; Tassis& Mouschovias2004 ; Matzner2007 ,see McKee&Ostriker ( 2007 )forareview).In additiontoGMCvirialparameterswhichdirectlymeasureth edegreeofgravitational boundedness,webelieveakeyobservationalaspectofthisd ebateisthedistributionof GMCangularmomenta. 87

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IntheMilkyWay, Phillips ( 1999 )showedthatforclumps,therewasarandom distributionoftheanglebetweenthecloud'sangularveloc ityandtheGalacticplane. Ontheotherhand,isolatedcloudshadorientationstowards theGalacticpoles.They concludedthattherotationoflarge-scalestructureswasd uetogalacticshear,while therandomizedorientationoftheclumppositionangleswas duetodynamicaland/or magneticinteractions. Kodaetal. ( 2006 )foundthatformorethan500molecularclouds, therewasnopreferreddirectionofspin.Morerecently, Imara&Blitz ( 2011 )foundthat althoughthereweresignicantvelocitygradientswithin vemolecularcloudsandtheir surroundingatomicgas,thevelocitygradientpositionang leswerewidelydistributed, indicatingthatthemolecularcloudsdidnotformfromtheco llapseofatomicgas. GMCrotationhasalsobeenstudiedinthenearbygalaxyM33. Rosolowskyetal. ( 2003 )reportedthatGMCsinM33showbothpro-andretrograderota tionwithrespect totherotationofthegalaxy,with40%retrograde.Morerece ntly, Imaraetal. ( 2011 ) found,throughhigherresolutiondataforthesameGMCsinM3 3,that53%ofthemhave retro-graderotationwithrespecttotheirsurroundingHI, furtherindicatingthattheydid notformfromcollapseofatomicgas.Furthermore,theyfoun dthat62%oftheGMCs inM33haverotationalpositionanglesthatareinaretro-gr adesensewithrespectto galacticrotation. OneexpectsthatifGMCsformrapidlyfrommorewidelydisper sedatomicgas, thentheGMCrotationshouldalwaysbeprograde,followingt hedirectionofthegeneral galacticrotation.Thiswasseeninthenumericalsimulatio nsof Ostriker&Kim ( 2004 ) and Tasker&Tan ( 2009 ).IfGMCsliveforlongerandaregravitationallybound,the y havegreateropportunitytosufferstronginteractionswit hotherGMCs,whichcanlead torandomizationofrotationdirections,thereforecreati ngbothapro-andretrograde population. Weuse13 COdatafromtheBU-FCRAOMilkyWayGalacticRingSurvey(GRS) tomeasurethepropertiesofGMCssurroundingIRDCs.First, forasampleofnine 88

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relativelynearbyIRDCs/GMCs,weusethreedifferentmetho dsfordeningGMC morphology.Foreachmethod,weestimatetheGMCmass,thero tationaxisorientation (projectedontheplaneofthesky)withrespecttothedirect ionofGalacticrotation,and thevirialparameter(theratioofkinetictogravitational energy).Thesimplestmethod ofdeningthesurroundingmoleculargasinvolvessummingt hemolecularemission withinacircularapertureofagivenradius(weconsider10, 20and30parsecs)and withinagivenvelocityrange,dv =15 km s1,abouttheIRDCmeanvelocity.This simplemethodallowsustoexaminephysicalpropertiesasaf unctionofscalearound theIRDC,whiletheothermethodsinvolvedeningGMCsastop ologicallyconnected structures,andaredescribedinmoredetailbelow.Onceweh aveunderstoodthe variationinresultsduetoGMCdenition,wethengoontoapp lythesimplestmethodto amuchlargersampleofseveralhundredGalacticIRDCs/GMCs WediscusstheresultsofGMCproperties,especiallythevir ialparameter,asa functionofscalearoundtheirIRDCs.Howthesephysicalpro pertiesvarydepending onthemethodofidentifyingtheGMCisalsodiscussed.Weals opresenttheresultsof measuringGMCrotation.Consistentwithpreviousstudies, wendclearevidencefora substantialretrogradepopulation,anddiscusstheimplic ationsforGMCevolutionand lifetimes. 5.2TheGRSSurvey ToinvestigatethekinematicsofGMCs,weusethe13 CO(J= 1!0)lineemission datafromtheBU-FCRAOMilkyWayGalacticRingSurvey(GRS; Jacksonetal.2006 ). TheGRScoverspartoftherstquadrantofthegalaxywithaGa lacticlongituderanging froml18 to55 andGalacticlatitudecoveringb1 .Comparedwithprevious largescalemolecularlinesurveys,suchastheUniversityo fMassachusetts-StonyBrook (UMSB)12 CO J = 10GalacticPlaneSurvey( Sandersetal.1986 ; Clemensetal. 1986 )whichwasundersampledwithresolutionof48 00 andagridspacingof3 0 ,theGRS 89

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providesabetterangularresolutionof46 00 with22 00 sampling,aswellasaspectral resolutionof0.2 km s1.Thetypical1 RMSnoiseisTA = 0.13Kperchanel. 5.3GMCpropertiesAroundaSmallSampleofLocalIRDCs 5.3.1TheNineCloudIRDCSample OursampleofnineIRDCsisbasedontheIRDCsampleof Butler&Tan ( 2009 2011 )tocreateamid-infraredextinctionmappingtechnique.On lynineoftheirten cloudswereusedasCloudJliesoutsidetheGRS.Thecloudswe rechosenfromthe sampleof Rathborneetal. ( 2006 )basedontheirrelativelynearbylocation,theirhigh contrastcomparedtothesurroundingdiffuseemission,and becauseoftheirrelatively simplesurroundingdiffuseemission. Simonetal. ( 2006b )estimatedkinematicdistances totheIRDCsassumingthe Clemens ( 1985 )rotationcurve.Theuncertaintiesareon theorderof0.5 kpcandaremostlikelytheresultoflineofsightnoncircularmo tionsof 8 km s1. 5.3.2DeningGMCmorphology EachIRDCisassumedtobeembeddedinaGMC.Toextractthe13 COemission ofeachGMC,werstusethe( l b )centerofmassofeachIRDC,derivedusing thepositionandsizeparametersfrom Simonetal. ( 2006a ),asthecenteroftheir correspondingGMC.Next,theextentoftheGMCisdenedbyth esurroundingmaterial outtoaspeciedcircularradiusandvelocitywidth.Thel b vshapeoftheGMCis exploredusingthreecases.Method1denestheGMCasbeingr epresentedbyall the13 COemissionfromacircularregionoftheskywithextractionra diiof10,20,30pc andavelocitywidthof 15 km s1(centeredontheline-of-sightvelocityoftheIRDC), i.e.acylinderinl b vspace.Method2useanearest-neighborroutinetodetermine ifanl b vpositionqualiesaspartoftheGMCbasedonitsintensity.F irst,wesetan intensitythresholdof5 (T A = 0.65K).Then,beginningatthecenteroftheGMC,the intensityateachneighboringlocationischeckedtoseeifi tfulllstheintensitythreshold. Ifaneighboringpositionisfoundtobeequalorabovethethr eshold,itisconsideredpart 90

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ofthecloud.Ifaneighboringpositionisbelowthethreshol d,itisomittedfromtherest ofthecloudanalysis.Next,thissameprocedureisappliedt othequaliedneighboringl b vpositionsandtheirneighbors.Thisroutineisrepeatedunt ilallneighboring positionsfallbelowthethreshold,signifyingtheedgeoft hecloud,oruntiltheroutine hitstheextractionradiusandvelocityboundary.LikeMeth od1,Method2isusedat theextractionradiiof10,20,30pcandavelocitywidthof 15 km s1centeredonthe IRDCcenterofmass.Method3isanextendedversionofMethod 2wherethecloud extractionradiiissettothemaximumallowedfortheGMCpos itioninasingleGRS cube(l b =1 datacubes). Foreachmethod,thetopandmiddlepanelsofgures 5-1 to 5-9 presentimages oftheintegratedintensityandthelinearmomentum,thetot alintensitymultipliedby thevelocitywithrespecttothecenterofmassateachpositi on,forthecloudswithan extractionradiusof30pc.Thebottompanelspresentthesam eimagesbutforMethod 3.Ingeneral,Method3performedthebestatdeningtheshap eoftheGMC,however manyofthemaretruncatedonvarioussides.Thistruncation issuecouldbesolved forlongcloudsinlongitudewiththeconnectionofmultiple GRSdatacubes.However, theGRSislimitedinlatitudeat 1 .Asexpected,Method1allowedforexcess,noisy emissiontobeconsideredpartoftheGMC.Thisismosteviden tinCloudsB,D,F,G,H, andI.WhileMethod2eliminatedmuchofthisexcessemission ,withtheexceptionsof CloudsBandI,aradiusof30pctruncatedmuchoftheGMCincom parisontoMethod 3.5.3.3MassEstimationFrom13 COToevaluatethemassateachl b vlocation,werstevaluatethecolumndensityof13 COmolecules,N 13CO,inavelocityintervald vfromtheirJ = 1!0emissionassuming LTEandopticallythinconditionsvia:N 13CO = 8Q rot A3 0 g l g u T B ,d v 1exp h kT ex (5–1) 91

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whereQ rotisthepartitionfunction,A = 6.3355108 s1istheEinsteincoefcient, 0 = 0.27204cm,g l = 1andg u = 3arethestatisticalweightsofthelowerand upperlevels, istheopticaldepthofthelineatfrequency ,i.e.atvelocityv,T existheexcitationtemperature(assumedtobethesameforall rotationallevels).For linearmolecules,thepartitionfunctionisQ rot =P 1J =0 (2 J + 1)exp(E J=kT ex )withE J = J ( J + 1) hBwhereJistherotationalquantumnumberandB = 5.510110 10 s1istherotationalconstant.Thusfor13 CO(1-0)wehaveE J=k = 5.289K.ForJ = 1,Q rot = 4.134forT ex = 10K.T B isthebrightnesstemperatureatfrequency ,f ( T )[exp( h=[ kT ])1]1,andT bg = 2.725Kisthebackgroundtemperature.T B isderivedfromtheantennatemperature,T A,viaT A f clump T B ,where isthemain beamefciency( = 0.48fortheGRS)andf clumpisthebeamdilutionfactorofthe13 COemittinggas,whichweassumetobe1duetothelargescaleext entofGMCs.dvis widthofeachGRSchanel,0.2 km s1. Previousstudieshaveshownthatthetypicalexcitationtem peratureofanIRDC isabout20K( Careyetal. 2000 ).However,thestudyby Hernandezetal. ( 2011 ) foundthatthemeanexcitationtemperatureforthehighlyl amentaryIRDCHwas 7K(estimatedfromC 18 O(J = 21)and(J = 10)columndensityratios). Thepeaktemperatures( 15K)residedwithinthehighestdensitycores,whileT exdecreasedto 4Kalongthesurroundingenvelope(seeChapter3,Figure1).B ecause GMCsarelargestructuresofdiffusegassurroundingIRDCs, weadoptaconstantT exof5KforalltheGMCsinthisstudy.Thisexcitationtemperat uresislowerthan thoseusedinpreviousstudies(e.g. Simonetal.2001 2006b )whoassumedaxed excitationtemperatureof10K).However,resultsfrom Hernandezetal. ( 2011 ),along withthosefrom Heyeretal. ( 2009 )whichindicatedthatthe13 COdetectedbytheGRSis sub-thermallyexcited,suggeststhattheexcitationtempe raturesiswellbelow10K.We alsonotethatincreasingT exto10Kdecreasesthecolumndensityby20%. 92

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Inourpreviousstudies( Hernandez&Tan2011 ,Chapter2; Hernandezetal.2011 Chapter3;Hernandezetal.inprep,Chapter4),opticaldept hcorrectionswereapplied tothecolumndensityestimates.Forthe13 COin Hernandez&Tan ( 2011 )itwasfound thatthesecorrectionsleadtoanincreaseincolumndensity byfactors <2inthehighest densityregionsoflamentaryIRDCs.However,thehighestd ensityregionsareonthe sub-parsecscale.Theopticallythinassumptionshouldbes ufcienttomeasurethe columndensitiesofthediffuseGMCsinthisstudy. Columndensitiesareconvertedtoatotalmasssurfacedensi tybyassumingan 12 CO=n 13 CO = 54( Milametal. 2005 )andan 12 CO=n H 2 = 2.0104( Lacyetal. 1994 ). Therefore,theassumedabundanceof13 COtoH 2is3.70106and 13CO = 1.26102 N 13CO 10 16 cm2 g cm2 ,(5–2) assumingamassperHnucleusof H = 2.341024 g.Weestimatea35%errorin 13COtoaccountforuncertaintiesinT exasassumedtobe2KfortheT exof5Kusedin thecolumndensityestimates. Amassforeachl b vlocationwascalculatedbyestimatingthephysicalsizefor theGRSpixelscale(22 00 )byassumingakinematicdistance.BecausetheseGMCsare locatedaroundIRDCs,whichwereseeninabsorptionagainst thebrightMIRemission oftheGalaxy,weadoptedthenearkinematicdistancesof Simonetal. ( 2006b ),who assumeda Clemens ( 1985 )rotationcurve.ThesedistancesaresummarizedinTable 5-1 .Weestimateuncertaintiesof0.5kpcforeachkinematicdis tancetoaccountfor noncircularmotionsof 8 km s1.ThetotalmassoftheGMCisderivedbysimply summingthemassinallbelongingl b vpositionsasdeterminedbyeachmorphology method. ThemassesforallthreemethodsaresummarizedinTables 5-1 and 5-2 .As expected,themassesgenerallyincreasedforMethods1and2 astheradiusincreased. Theaveragemassesforwere0.4690.205, 1.510.65, 2.881.2410 5 M forMethod 93

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1,and0.2650.116, 0.7590.325, 1.440.61010 5 M forMethod2at10,20,and30 pcrespectively.ForMethod3,aradialsizewasestimatedby thetotalareaprojectedon theplaneoftheskybyR 3 =p A= andvariedbetween11and63pc.Themeanmass fromMethod3was4.121.7110 5 M .Thesemassesarecomparabletothemasses estimatedby Roman-Duvaletal. ( 2010 )basedon580molecularcloudsidentiedwith CLUMPFINDinthe13 COGRSdata. TocomparethedifferencesbetweenthecloudstracedbyMeth ods1and2,we comparetheRMSdeviationthemassesfromeachmethod.Atane xtractionradiusof10 pc,theRMSdeviationofMethod1is0.18010 5 M and0.14010 5 M forMethod2. Atanextractionradiusof20pc,theRMSdeviationofMethod1 is0.66110 5 M and0.47510 5 M forMethod2.Finally,atanextractionradiusof30pc,theRM Sdeviation ofMethod1is1.3510 5 M and3.6110 5 M forMethod2.Thus,Method2extracts GMCswhicharemoreconsistentinmassforagivenxedscale. However,themasses estimatedbyMethod2aresensitivetotheassumedintensity thresholdandthemasses wouldconvergetothoseestimatedbyMethod1ifthethreshol dwasdecreased. ThecloudtracingMethod3isanextendedversionofMethod2w hereanentire GRSdatacubeisusedinsteadofxedscale.Thus,thismethod providesthelargest RMSdeviationofmasses,4.123.6110 5 M ,andclearlyidentiesthedifcultyof identifyingGMCs.Forinstance,thecloudstracedbyIRDCsB andIarewellbounded clouds,howeverthecloudstracedbytheremainingIRDCsare truncatedbythespatial limitationsoftheGRSdatacubes.Furthermore,duetothecl oseproximityofIRDCsG andH,theirsurroundingGMCcloudsarenearlyidenticalinm orphologyasshownin Figures 5-7 and 5-8 5.3.4EstimatesofGMCRotation TocalculateaqualitativeestimateoftheGMCageswecomput ethepositionangle, ,betweeneachGMCsangularmomentumvectorandthegalactic rotationaxis.Ideally, itisexpectedthatifGMCsformrapidlyfromtheatomicgasin theGalacticplane,the 94

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directionoftheirrotationshouldbepro-grade.IfGMCsdon otdissipaterapidly,butlive longerthanonesignalcrossingtime,theywouldhavetheopp ortunitytointeractwith neighboringGMCs.Suchinteractionwouldleadtoarandomiz ationofcloudrotation direction,includingbothpro-andretrograderotatingclo uds.Usingtheestimatedmass ateachl b vlocation,alongwiththecorrespondingnearkinematicdist ancesand velocity(withrespecttothecenterofmass),thevectors ~r i j kand ~v i j k,werecalculated foreachpositionwithinthecloud.Therefore,theangularm omentumthroughoutthe cloudwasdirectlyestimatedvia: ~j i j k = m i j k (~r i j k ~v i j k ).(5–3) Then,throughavectorsum,thetotalangularmomentuminthelandbdirections,J landJ b,wascalculated.Thepositionangleofaclouds'angularmom entumvectorswith respecttotheGalacticrotationaxiswasthendenedas: = tan1 J l J b(5–4) Here,(0 << 90 )representspro-gradecloudrotation,i.e.rotationinthe same senseasthegalacticrotation,and( 90 << 180 and90 <<180 )represents retro-gradecloudrotation.Fromabasicerrorpropagation calculationweestimatethat theuncertaintiesin are 10 ForeachIRDCtracer,twoGMCsaretracedbyMethods1and2.Th eposition anglesofthecloudstracedbyMethod1aredenotedby 1inTable 5-1 .Likewise,the cloudstracedbyMethod2aredenotedby 2.Ifthepositionanglesarecomparedon thesameextractionscales,the10pccasehadameandifferen cebetween 1and 2of3630 .Alsoat10pc,ThecloudstracedbyIRDCsDandIhavethelarge st discrepancybetweenthetwomethodswithadifference >70 .The20pccasehasthe largestmeandifferencebetween 1and 2of5570 .Atthisextractionscale,the cloudstracedbyIRDCsEandIhaddifferencesin 1and 2ofover160 .TheGMCsat 95

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theextractionscaleof30pchavethesmallestdiscrepancyb etweenthetwomethods withadifferenceof3335 .Forallthreeextractionscales,thecloudstracedbyIRDC Iconsistentlyhadthelargestdifferencebetween 1and 2.Thisdiscrepancywasmost likelyduetothehighlevelofnoisewithintheIRDCIregiono ftheGRS(Pleaseseethe imagesofFig. 5-9 ). Figure 5-10 presentsthepositionangleestimatesasafunctionofthema ss weightedradiusforMethods1and2.ForMethod1,theupperpa nel,thereisa bi-normaldistributionofthepositionangleswithpeaksat 25 (pro-graderotation) and 130 (retro-graderotation).Thisdistinctionbeginstodissol veat20pc,andthe distributionbecomecompletelyrandomat30pc.Ontheother hand,thepositionangles estimatedfromMethod2arecompletelyrandomizedatallthr eeradii. 5.3.5EstimatesoftheVirialParameter Thedimensionlessvirialparameter,asdenedby Bertoldi&McKee ( 1992 ), isgenerallyusedtodescribethedynamicalstateofGMCs.Th isparameter,which measurestheratioofkinetictogravitationalenergyofasp hericalanduniformcloud,is givenby: 52 R mw GM(5–5) where istheaverage1Dvelocitydispersioninthecloud(asmeasur edfromtheclouds average13 COlineemissionspectra),R mwisthe3DmassweightedGMCradius,andM isthetotal13 COmassofthecloud.Weassumethat isaccuratetowithin10%.The3D massweightedradiusisgivenby p 3=2 R,whereRisthemassweightedradiusofthe GMC.Risscaledbythe p 3=2factortoestimateatruethree-dimensionalcloudradius fromthemeasured2Dprojectedmass.Onaverage,the3Dmassw eightedradiusis 80%oftheextractionradiiused. Thevirialparameterdirectlymeasuresthedegreeofgravit ationalboundnessof thecloud.SincetheseGMCsaretracedbyIRDCs,thevirialpa rameter, ,provides informationconcerningtheIRDCformation. asmeasuredfromallthreemethodsare 96

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>1,suggestingthattheymaynotbegravitationallybound.Fig ure 5-11 presentsthe estimatedvirialparameterfrommethod1, 1,forallnineGMCsasafunctionofradius. Thereisnoclearsystematicchangeof 1withphysicalscale. 5.4GMCRotationandVirialization TobetterunderstandtheGalacticpropertiesofGMCs,weext endourstudyto twomuchlargersamplesofIRDCs.TodothisweappliedourMet hod1technique fordeningtheGMCmorphologyoftwolarge( >100)IRDCcatalogstoinvestigate thedynamicalpropertiesofGMCs.OurmotivationforusingM ethod1isbasedonit's computationalefciencyandthesensitivityMethod2hason it'sassumedintensity thresholdcutoff.Astheintensitythresholdisreduced,th eresultsofMethod2will convergewiththoseofMethod1,whichincludesall13 COemissionaspartoftheGMC. Weexaminedthedistributionsofpositionanglesbetweenth etracedGMC'sangular momentumvectorsprojectedontotheplaneoftheskywithres pecttothegalactic rotationaxis.Wecomparedthesedistributionswiththosef oundintheGMCrotation studyof Kodaetal. ( 2006 ),aswellasthesimulatedGMCstudyof Tasker&Tan ( 2009 ). Thevelocitydispersiontosizerelationisalsocomparedto thesimulationsof Tasker& Tan ( 2009 ).Thedistributionofthevirialparameterforeachcatalog atdifferentradiiwas alsoexamined.5.4.1LargeSampleSelection Weusetwodifferentcatalogsofsourcesforthisstudy.The rstistheIRDCcatalog from Simonetal. ( 2006b ).Inthestudyof Simonetal. ( 2006a ),nearly10,000IRDCs wereidentiedasregionsofhighcontrastin8 mMSXimages.OftheseIRDCs, Simon etal. ( 2006b )identied2468ofthemthatoverlappedwiththeGRS13 COmolecular emissionlinedata.FortheirstudyofIRDCproperties,they reducedtheirsampleto313 byselectingthosewitha8 mcontrastofatleast0.25(anextinctionof25%)andwith amajor-axisgreaterthan1.530 .ThesecondcatalogistakenfromtheGMCelongation andsupersonicmotionstudyof Kodaetal. ( 2006 ).Here,theyidentiedmolecular 97

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cloudsthroughpeaksof13 COlineemissionfromtheGRSsurvey. Kodaetal. ( 2006 ) denedeachmolecularcloudasatopologicallyclosedsurfa ceswithapeakmain-beam brightnesstemperatureabove4Kandaboundarytemperature of2Kwithinthe13 COdatacubes.However,manyoftheirsourceshadclouddiamete rslessthan5pc.Thus, theyeliminateanymolecularcloudsourcesbelow5pc,leavi ngacloudsampleof556 molecularclouds.Thesetwocatalogsallowustoassesswhet herthereisanystatistical differencebetweenmolecularcloudsidentiedthroughext inctionandthoseidentied throughmolecularlineemission. Foreachcatalog,weusedMethod1todenethemorphologyoft heGMC surroundingeachIRDCsource.Estimatesofthemass,thevel ocitygradient,position angleoftheprojectedrotationaxis,andthevirialparamet erweretakenatextraction radiiof10,20,and30pc.Foreachextractionradius,thevel ocitywidthwasset 15 km s1withrespecttothecorrespondingIRDCscenterofmass. 5.4.2Results Theresultsofthepositionangleofprojectedrotationaxis ,distributionsareshown inFigure 5-12 .ForbothGMCcatalogswendnopreferreddirectionofcloud rotation. Forthe Simonetal. catalogwefoundpercentagesofpro-andretrogradepositio n anglesof47%and53%foranextractionradiusof10pc,53%and 47%foranextraction radiusof20pc,and48%and52%foranextractionradiusof30p c.Forthe Kodaetal. catalogthefractionofpro-andretrogradepositionangles were49%and51%foran extractionradiusof10pc,51%and49%foranextractionradi usof20pc,and52%and 48%foranextractionradiusof30pc.Theseresultswereinag reementwiththosefound from Kodaetal. ( 2006 ),whoseanalysisfoundthat52%oftheGMCsareprogradeand 48%areretrograde.TheseresultsalsoagreedwiththeGMCsi mulationsperformedby Tasker&Tan (Fig. 5-13 ),whofoundpercentagesofpro-andretrogradepositionang les of49%and51%.ThroughaKilmogorov-Smirnov(K-S)test,wef oundthattherewasa 98

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smallstatisticaldifferencebetweenthepositionanglesd erivedfromthetwocatalogs,as indicatedbyaKSprobabilityof 0.30. Fromouranalysis,wendtheretherewasanearlyuniformdis tributionofposition anglesbetween 180
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whereM 13 COisthe13 COmass,and isthepower-lawindex.Theselinearts doaccountforthemeasurementuncertainties(asnotedinth e9GMCstudy,the uncertaintiesincludea35%errorinthemasssurfacedensit y(),a0.5kpcerrorin eachnearkinematicdistance,anda10%errorinthemean1Dve locitydispersion( )). Forthe Simonetal. catalog,wefoundlog( M o ) = 6.030.35, 5.250.24, 5.300.23and = 1.1370.080, 0.8910.050, 0.8670.044forthe10,20,and30pccasesrespectively. Forthe Kodaetal. catalogwefoundlog( M o ) = 7.100.35, 6.340.27, 6.200.25and = 1.400.08, 1.120.06, 1.050.05fortheextractionradiiof10,20,and30pc respectively.Wegaugethesignicanceofthesetrendsbyno tingthattheabovevalues of differfromunityby1.6,2.2,and3.0standarddeviationsfo rthe Simonetal. catalog, and4.8,2.2,and0.94standarddeviationsforthe Kodaetal. .catalog,assumingthatthe errorsaredistributednormally. Thestudyby Bertoldi&McKee ( 1992 )exploredthevirialparameterofclumpsfrom fourmolecularclouds.Amajorityoftheirclumpswerelocat edwithinknownGMCs, includingOphiucus,OrionB,Rosette,andCepheusOB3.Usin gobservationsof13 CO, theyfoundthatthevirialparameterwaswellcorrelatedwit hthemassoftheclumps,but withalowerpowerlawindexof = 0.590.11.However,theirresultsreectthevirial parametersofclumpswithinGMCs,andarethereforelowerin mass(log( M o ) = 3.32). Also,theirestimatesoflog( )rangebetween0.5and2,whileouranalysisindicates virialparametersaslargeaslog( )= 3forlargerscaleGMCs.Thus,ourndings suggestthatthevirialparameterincreasesfromtheclumps caletoGMCscale. Incomparisontothetheoreticalpredictionsof Tasker&Tan ( 2009 ),ourestimates of werehigher,byafactorof 8,thantheircloudsatasimulationtimeoft = 250Myr.FortheSimonetalcatalog,wefoundmeanvirialparamet ersoflog = 1.290.21, 1.180.21, 1.130.20forradiiof10,20,and30pc.FortheKodaetal.catalog, wefoundmeanvirialparametersoflog = 1.180.18, 1.050.18, 0.9590.142forradii of10,20,and30pc.Thevirialparametersestimatedby Tasker&Tan werefoundtobe 100

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lowerwithameanoflog = 0.15,howeverwithlowermassesrangingfromlogM = 3.52to7.74 M ,withameanlogarithmicmassof5.71M .Themeantotalmassesestimated inthisstudywerelogM = 4.490.19 M ,4.480.19 M ,5.260.35 M atextractionradii of10,20,and30pcrespectivelyforthe Simonetal. catalogandlogM = 4.380.16 M ,4.910.166 M ,5.220.33 M atextractionradiiof10,20,and30pcrespectivelyforthe Kodaetal. catalog.Consideringthatthevelocitydispersionsfoundh erewereinnear agreementwiththeirsimulations,ourlowercloudmassesti mateswereconsideredtobe themainreasonforthediscrepancybetweenthevirialparam eters. 5.5ConcludingRemarksonIRDCFormationandGlobalGMCProp erties Inthisstudyweused13 COdatafromtheBU-FCRAOGRSsurveytomeasurethe physicalpropertiesofGMCssurroundingIRDCs.Beginningw ithasampleof9relatively nearbyIRDCs/GMCs,weusedthreedifferentmethodsforden ingGMCmorphology. WeestimatedtheGMCmass,thedirectionoftherotationaxis projectedontheplane ofthesky,andthedegreeofvirialization.Wefoundnoindic ationofasystematictrend betweenthevirialparameter, ,andincreasingradius.ForMethod1,wealsofound thatthepositionangledistributionwasbinormalat10pcan dbecamerandomized astheextractionradiuswasincreased.However,forMethod 2,thepositionangle distributionwasrandomatallradii.Next,weappliedMetho d1totwolargesamples ofseveralhundredGalacticIRDCs/GMCs.Wepresentedresul tsofGMCrotation, ndingclearevidenceforasubstantialretrogradepopulat ion,indicatingthattheyhave livedlongenoughtoundergomergersand/orcollisionswith neighboringGMCs.This resultsupportstheoreticalmodelsofstarformationindis kgalaxieswhereformationis triggeredbycloud-cloudcollisions Tan ( 2000 ). 101

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Table5-1.GMCphysicalparametersfromMethods1and2 IDl b R 1 ( pc ) R 2 ( pc ) d ( kpc) M 1 (10 5 M) M 2 (10 5 M)1 () a2 () a log (1 ) log (2 ) A18.822 0.2858.047.804.80.569 0.2320.399 0.1621251650.634 0.1810.774 0.181 .........15.414.1...1.98 0.8081.18 0.4821291400.489 0.1810.677 0.181 .........22.821.5...3.89 1.602.24 0.91196.286.20.479 0.1810.693 0.181 B19.271+0.0746.925.182.40.269 0.1470.141 0.07681091100.997 0.1971.15 0.20 .........13.18.58...0.669 0.3640.241 0.13185.390.30.983 0.1971.24 0.20 .........19.19.38...1.02 0.5550.256 0.13983.895.21.02 0.1971.31 0.20 C28.373+0.0767.817.585.00.719 0.2900.564 0.227-53.4-86.20.515 0.1800.607 0.180 .........15.715.0...2.49 1.001.68 0.678-127-1070.426 0.1800.574 0.180 .........22.520.7...4.66 1.882.79 1.13-123-1030.356 0.1800.542 0.180 D28.531 0.2517.427.905.70.633 0.2480.237 0.092917498.60.834 0.1791.29 0.18 .........14.813.9...1.84 0.7221.07 0.41891.371.70.535 0.1790.744 0.179 .........22.420.6...3.64 1.432.04 0.79984.423.00.363 0.1790.577 0.179 E28.677+0.1327.957.125.10.672 0.2700.300 0.1201241041.14 0.181.45 0.18 .........15.313.1...2.19 0.8780.757 0.30479.4-83.70.902 0.1801.30 0.18 .........22.621.3...4.23 1.702.39 0.95748.938.90.737 0.1800.961 0.180 F34.437+0.2457.546.463.70.330 0.1460.153 0.067411580.90.822 0.1851.09 0.19 .........15.714.3...1.25 0.5540.556 0.2461601370.656 0.1850.969 0.185 .........23.223.1...2.51 1.111.17 0.5191581700.580 0.1850.908 0.185 G34.771 0.5577.436.572.90.388 0.1910.244 0.1201.734.50.651 0.1900.800 0.190 .........15.012.5...1.36 0.6700.657 0.323-159-1040.726 0.1900.963 0.190 .........22.317.4...2.62 1.291.07 0.527-159-1360.705 0.1900.984 0.190 H35.395 0.3367.637.412.90.390 0.1920.211 0.104-62.1-61.31.03 0.191.28 0.19 .........14.713.5...1.20 0.5910.522 0.256-46.6-33.70.859 0.1901.18 0.19 .........23.119.5...2.52 1.240.852 0.419-57.0-21.70.816 0.1901.21 0.19 I38.952 0.4757.246.442.70.252 0.1280.140 0.0712-0.65388.00.979 0.1931.18 0.19 .........12.78.10...0.583 0.2970.174 0.0888-52.01370.953 0.1931.28 0.19 .........17.78.10...0.825 0.4200.174 0.088822.01371.03 0.191.37 0.19 a 10102

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Table5-2.GMCphysicalparametersfromMethod3 IDR mw ,3 ( pc ) M 3 (10 5 M)3 ()10log (3 ) A38.74.94 2.0136.31.41 0.18 B9.390.256 0.13995.11.50 0.20 C35.95.47 2.2014.71.51 0.18 D56.68.02 3.140.03201.63 0.18 E60.811.0 4.391.131.98 0.18 F29.01.67 0.7411651.98 0.18 G36.62.74 1.35-1101.79 0.19 H37.32.84 1.40-1101.18 0.19 I8.100.174 0.08881371.72 0.19 103

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Figure5-1.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudAat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween96.2 to129 and86.2 to165 asthe radiuschangesfrom10to30pcformethods1and2,respective ly,and = 36.3 inmethod3. 104

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Figure5-2.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudBat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween83.8 to109 and90.3 to110 asthe radiuschangesfrom10to30pcformethods1and2,respective ly,and = 95.1 inmethod3. 105

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Figure5-3.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudCat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween 53 to 127 and 86.2 to 107 asthe radiuschangesfrom10to30pcformethods1and2,respective ly,and = 14.7 inmethod3. 106

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Figure5-4.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudDat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween84.4 to174 and 83.7 to104 asthe radiuschangesfrom10to30pcformethods1and2,respective ly,and = 180 inmethod3. 107

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Figure5-5.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudEat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween48.9 to124 and 83.7 to104 asthe radiuschangesfrom10to30pcformethods1and2,respective ly,and = 1.13 inmethod3. 108

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Figure5-6.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudFat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween115 to160 and80.9 to170 asthe radiuschangesfrom10to30pcformethods1and2,respective ly,and = 165 inmethod3. 109

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Figure5-7.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudGat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween1.71 to 159 and 136 to34.5 asthe radiuschangesfrom10to30pcformethods1and2,respective ly,and =110 inmethod3. 110

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Figure5-8.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudHat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween 62.1 to 46.6 and 61.3 to 21.7 as theradiuschangesfrom10to30pcformethods1and2,respect ively,and =110 inmethod3. 111

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Figure5-9.Mapsoftotalintegratedintensity(left)andto tallinearmomentum(right)for cloudIat30pc.Theresultsofmethod1arepresentedintheto ppanels, method2inthemiddlepanels,andmethod3inthebottompanel s.The positionangles, ,rangebetween 52.0 to22.0 and88.0 to137 asthe radiuschangesfrom10to30pcformethods1and2,respective ly,and = 137 inmethod3. 112

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A B Figure5-10. asafunctionofextractionradiusforallnineGMCs.(A) estimatesfrom Method1.Thereisabinormaldistributionataextractionra diusof10pc withpeaksat 25 and 130 .(B)Sameas(A)butforMehtod2.These resultsindicatearandomdistributionof atallextractionradii. 113

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Figure5-11.Thevirialparameter,asestimatedthroughMet hod1,forallnineGMCsas afunctionofradius.Thereisnoclearsystematicchangeof 1withphysical scale. 114

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Figure5-12.Thedistributionofthepositionangle, ,ofcloudangularmomentum vectorswithrespecttothegalacticrotationalaxis.Thele ftcolumnpresents theGMCsfromthe Simonetal. ( 2006a )catalog,whiletherightcolumn presentstheGMCsfromthe Kodaetal. ( 2006 )catalog.Ineach30 binthe numberofGMCs,N carenormalizedtothetotalnumberofGMCs,N TOT. TheerrorbarsrepresentthePoissonerrors. 115

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Figure5-13.Thedistributionofthepositionangle, ,ofcloudangularmomentum vectorswithrespecttothegalacticrotationalaxis.Theto ppanelpresents theGMCsfromthe Simonetal. ( 2006b )catalog,whilethebottompanel presentstheGMCsfromthe Kodaetal. ( 2006 )catalog.Ineach30 binthe numberofGMCs,N carenormalizedtothetotalnumberofGMCs,N TOT.In eachdistribution,the10,20,and30pcradiiareindicatedb ydash,long dash,anddot-dashlines.TheerrorbarsrepresentthePoiss onerrors.The reddistributionpresentstheresultsfromthe ? simulations. 116

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A B Figure5-14.Acomparisonofvelocitydispersionandclouds ize.Theblackpoints representthesimulatedGMCsatt = 250Myrfrom Tasker&Tan ( 2009 ). (A)Themeanvelocitydispersion,witherrorbarsof1 ,forGMCsinthe Simonetal. ( 2006b )catalogwithradiiof10pc(blue),20pc(red),and30 pc(green).(B)Sameas(A),butforthe Kodaetal. ( 2006 )catalog. 117

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Figure5-15.Acomparisonoflog ()withlog ( M 13 CO=M)forradiiof10(top),20 (middle),and30pc(bottom)fortheSimonetal.(2006b)cata log.A comparisonoflog ()withlog ( M 13 CO=M)forradiiof10(top),20(middle), and30pc(bottom)forthe Kodaetal. ( 2006 )catalog. 118

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CHAPTER6 ASEARCHFORASTROCHEMICALTRENDSINSTAR-FORMINGCLOUDS InthisChapter,wepresentachemicalevolutionpilotstudy on16clumpsfromthe CensusofHighandMedium-massProtostars(CHaMP).Weaimto understandthe chemicalevolutionbetweenquiescentandactivestar-form ingregions.Thisworkhasyet tobesubmittedforpublication. 6.1MotivationtoSearchforAstrochemicalTrendsinStar-F ormingClouds IntheMilkyWayGalaxy,mostofthestarsformwithinthedens estandcoldest regionsofgiantmolecularclouds(GMCs)whicharelocateda longtheGalacticplane. Weaimtounderstandthechemicalevolutionbetweenactivea ndquiescentstar-forming cloudswithintheGalacticplane.Wehaveidentiedaregion oftheCHaMPsurvey whichcontainsbothalamentarydarkcloudandabrightanda ctivestar-formingregion, asidentiedthrough8 mimaging(GLIMPSE; Benjaminetal.2003 ).Usingboth90 and115GHzmolecularlinedata,welookforvariousabundanc epatternsbetweenthe thoseclumpswithinthelamentarydarkcloudandthosewith intheactivestar-forming region. 6.2TheCHaMPSurvey TheCensusofHigh-andMedium-massProtostars(CHaMP; Barnesetal. 2011 )isanongoinglarge-scalesurveyofthesouthernGalacticp lanewiththe Mopra22m-diametertelescopeoftheAustraliaTelescopeNa tionalFacility(ATNF) inNSW,Australia.ThissurveyisnowbasedattheUniversity ofFloridaunder thePI,Dr.PeterJ.Barnes.CHaMPistherstcomplete,unbia sed,sensitive,and multi-wavelength,uniform-mappingsurveyatsub-parsecs caleresolutionof90and 115GHzlineemissionfrommassivemolecularclumpsintheMi lkyWay(Figure 6-1 Barnesetal.2006 ).Thesurveycoversa20 6 regionofthesouthernMilkyWay (280
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denseranddensergasbyutilizingunder-sampledmolecular linemapsofthesame region.Thesurveystrategyisdiscussedinmoredetailinth efollowingsub-section.The overallobjectiveoftheCHaMPsurveyare(1)tosystematica llyobservethephysical propertiesofthemassivedensegasclumpswhicharebelieve dtoformmassivestars, (2)characterizethephysicalpropertiesofthestarsandst arclustersformedoutofthese clumps,and(3)toidentifytheimportantevolutionarystag esoftheseclumps.Itisthis lastobjectiveinwhichthisstudyarises.6.2.1Strategy TheinitialstageoftheCHaMPsurveybeganwithunder-sampl edobservationsof fourmolecularspecies:J = 1!0transitionsof12 COat115.271GHz,13 COat110.201 GHz,C 18 Oat109.781GHz,andHCO +at89.189GHz.Theseobservations,takenwith the4mNantentelescopeinLasCampanas,Chile,mappedthecu rrentCHaMPregion, whichencompassespartofVela,Carina,andCentaurus.Them ainobjectiveofthese observationswastomapallofthedensegasintheregionefc ientlywhile“skipping over”lowdensityregionswheremolecularlineemissionisw eak.Todothis,theentire regionwascompletelymappedin12 COwitha30 beam.Then,allregionswhichhad anintegratedintensityof >5 K km s1weremappedin13 CO.Next,regionswhich hada13 COintegratedintensityof >2 K km s1weremappedwiththehighestdensity molecularlinetracers,C 18 OandHCO +.ResultsfromsomeoftheseNantenmapswere presentedby Yonekuraetal. ( 2005 ). 6.2.2MopraObservation WiththenalNantenC 18 Oobservations,aCLUMPFINDanalysis,supplemented byvisualinspectionofthedata,wasperformedinordertobu ildauniformlyselected sampleofcloudsknownastheNantenMasterCatalog(NMC).Th eNMCconsistsof 209clouds,ofwhich4arelocatedwithin“Region26”usedint herestofthisstudy.Over 120oftheseclumps,in27regions,withbrightnessesgreate rthan0.25 K km s1were thenobservedathigherresolutionwiththeMopratelescope 120

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ObservationswiththeMopratelescopebeganin2004.Curren tly,over800hours oftelescopetimehavebeenawardedtotheprojectoverthepa stveyears.90GHz observations,includingthemoleculartracersHCO +,HCN,HNC,andN 2 H +,were mappedusingtheOn-The-Fly(OTF)methodfromJuly2004toSe ptember2007.The 115GHzobservations,includingthemoleculartracers12 CO,13 CO,andC 18 O,were takenduringtheaustralwintersof2009and2010.OTFobserv ationsweretakenina rasterpatternacrosstheskyingalacticl bcoordinategrids.Datawasdumpedfromthe spectrometeratatimeintervalof2seconds.Thus,thedatai sconsistentwithNyquist samplingofthesky,giventhetelescopebeam,observingfre quency,andtelescopedrive rate.ThemapsofRegion26,liketheothersinthesurvey,wer eproducedbymultiple OTFeldswhichweretiledtocoverthemostactivepartsofth eregion.Theaverage sizeofthesemapswere50 50 .Fortimepermitted,eachOTFeldwasmappedatleast onceineachlandbdirectionstominimizerasteringartifactsandnoise. In2006,theMOPSwidebanddigitallterbandwasinstalledo ntheMopra telescope.MOPSallowsfor8(in2006)and16(beginningin20 07)138-MHz-wide zoommodestobeobservedsimultaneouslyfromwithinthe8.2 GHzlterbank.For eachzoommode,thereare4096channelsineachpolarization .Theresultingspectral resolutionis0.11 km s1at90GHzand0.09 km s1at110GHz.Thehalf-powerbeam sizesare3600 at90GHzand3300 at115GHz. 6.2.3DataReduction Allofthedata,16IFzoommodesforeach90and110GHzrun,was reducedusing theLivedata-Gridzillapackage( Barnesetal. 2011 ).TherawOTFdatawasprocessed bybandpassdivisionandbaselinesubtraction.Then,the2secondlongOTFsamples wereregriddedintoaregulargridof1200 pixelswithaT2 sysweighting.Inordertoimprove theS/N,atthegriddingstage,theintrinsicbeamwassmooth edto4000 from3600 inthe 90GHzdataandto3700 from3300 inthe115GHzdata.Thenall b vdatacubeshave 121

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RMSnoiselevelsof 0.3Kper0.1 km s1channelat90GHzandarangeof0.30.8K per0.09 km s1channelat115GHz. 6.3TheAnalysisofRegion26 Toinvestigatevariousabundancepatternsbetweenstar-fo rmingclumpsatdifferent evolutionarystages,wefocusononeregionoftheCHaMPsurv ey,Region26.This regionspans0.6 0.3 andislocatedatl = 299.3, b =0.35 .Thisregionis presentedinFigure 6-2 asitappearsat8 m(Spitzer-GLIMPSE).Thegreenoutline representtheareacoveredbytheMopraOTFmapstakenat115G Hz.Inthelower halfoftheregion,centeredatl = 299.25, b =0.38 ,isthelamentarydarkcloud believedtorepresenttheinitialconditionsofstarformat ion.Tothenorth,centeredatl = 299.36, b =0.26 liestheactivestar-formingregionidentiedbybrightemi ssion at8 m.Bothoftheseregions,quiescentandactive,arebelieved tobepartofthesame GMCastheyareseparatedbyonly 60 andhavenearlythesameradialvelocities ( v2 km s1).Allclumpsarethereforeassumedtolieatthesamedistanc eof4.7 kpc, takenfrom Grabelskyetal. ( 1988 ).Foracloserlookatthesetwodistinctregions,Figure 6-3 presentstheHCO +(J = 1!0)integratedintensitymapofthequiescentandactive regionsalongwiththeirappearanceat8 m. Wealsoexaminethe17clumpsfoundwithintheregion(showna sblackellipses inFig. 6-2 ).Theseclumpswereoriginallyidentiedaspartofonlyfou rclumpsofthe NMC.However,thehigherresolutionoftheMopraHCO +mapsindicatedthattheregion wasmorecomplex,containing17clumps(ClumpID:201a-208b Barnesetal.2011 ). Theseclumpswereidentiedbyrequiringanintegratedinte nsityofatleast5 ,aswell asapeaktemperatureofatleast3 inthel b vdatacube.Theclumpcenterwas denedbythecoordinatesofthepeakintegratedintensity. Themajorandminoraxes ofeachclumpwasfoundbyttinga2Dellipticalgaussiantot heemissionpeak.The line-of-sightvelocityasmeasuredfromHCO +isalsostatednexttoeachclump.A summaryoftheseclumpphysicalparametersareinTable 6.3 122

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Table6-1.CHaMPclumpphysicalparameters IDl bmajmin P A d L Bol M HCO + L bol=M HCO +degdeg( 00 )( 00 )degkpc LM (L =M ) 201a298.996-0.32513475494.71160051122.7201b299.033-0.361179851174.72570081231.7202a299.159-0.39570764884.7938033502.80202b299.256-0.431282701004.725506174.13202c299.333-0.315107871004.716170105015.5202d299.283-0.33814351734.738507585.07202e299.369-0.3318751984.715504633.34202f299.393-0.34514664704.712205122.38202g299.443-0.321144104504.721105353.94202h299.383-0.43515174904.795110100.943202i299.429-0.4312123604.78118360.970203a299.386-0.2311006004.775708309.131203b299.376-0.25191461034.734606185.60203c299.343-0.248166771404.719400163011.9203d299.359-0.27111378734.71450080118.1208a299.543-0.34821277484.7371015202.45208b299.533-0.31810336134.710203213.16 123

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6.3.1IntegratedIntensityMaps AfterareductionofalloftheOTFdataobservedinthisregio n,wenddetections abovethe1 RMSnoiselimitoftheJ = 1!0transitionsmolecularspecies:12 CO,13 CO,C 18 O,HCO +,HCN,andN 2 H +.Herewepresenttheintegratedintensitymaps ofeachspeciesovertheentireobservedregion.Alloftheda taweregriddedtoapixel scaleof1200 (fora3600 beamat90GHzanda3300 beamat115GHz).Theintensities,T AinunitsofK,weretransformedintobrightnesstemperature s,T B,v = T A= ,using themainbeamefcienciesfrom Laddetal. ( 2005 ).Theystatedan = 0.65at86GHz and = 0.55at115GHz.Toobtaintheappropriate foracertainfrequency,asimple linearinterpolationwasperformed,i.e.for13 COatafrequencyof110.201GHz,weuse = 0.57.Overlayedoneachintegratedintensitymaparethe17clump sidentiedby Barnesetal. ( 2011 ). Figure 6-4 presentstheintegratedintensitymapof12 CO.Theemissionwas integratedoverthevelocityrangeof 44to 36 km s1.Over90velocitychannelsof width0.088 km s1,the1 RMSnoisewas0.71 K km s1.Thebrightestemissionwas seentowardstheupperleftoftheregion,correspondingtot hoseregionswhichwere believedtobeactivelyformingstars. Figure 6-5 presentstheintegratedintensitymapof13 CO.Theemissionwas integratedoverthevelocityrangeof 42to 36 km s1.Over64velocitychannelsof width0.092 km s1,the1 RMSnoisewas0.36 K km s1.Brightemissionwasseenover amajorityoftheclumps.Thedarklamentarycloudlocatedw ithinourquiescentregion wasclearlyseen,beginninginclump202aandextendingtoth eeast. Figure 6-6 presentstheintegratedintensitymapofC 18 O.Theemissionwas integratedoverthevelocityrangeof 42to 38 km s1.Over44velocitychannelsof width0.092 km s1,the1 RMSnoisewas0.30 K km s1.Thebrightestemissionwas seenwithinthedarklamentarycloudlocatedwithinourqui escentregion,howevernot asclearlyasin13 CO.Onebrightcorewasseenneartheeasternedgeofclump202a 124

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andemissionextendstotheeast.Thisindicatesthatthela mentarycloudcontains regionsofcold,densegascapableofeventuallyundergoing starformation. Figure 6-7 presentstheintegratedintensitymapofHCO +.Theemissionwas integratedoverthevelocityrangeof 42to 37 km s1.Over45velocitychannelsof width0.11 km s1,the1 RMSnoisewas0.22 K km s1.Thebrightestemission,tracing thedensestgas,wasclearlyseeninbothquiescentandactiv eregions. Figure 6-8 presentstheintegratedintensitymapofHCN.TheJ = 1!0transition containsthreehypernelines.Theemissionwasintegrated onlyoverthebrightest hyperneline(88.632GHz)usingthevelocityrangeof 41to 37 km s1.Over44 velocitychannelsofwidth0.11 km s1,the1 RMSnoisewas0.25 K km s1.The brightestemission,tracingthedensestgas,wasclearlyse eninbothquiescentand activeregions,butwithoveralllowerintensitiesoftheHCO +. Figure 6-9 presentstheintegratedintensitymapofN 2 H +.TheJ = 1!0transitioncontainssevenhypernelines.Theemissionwas integratedonlyoverthe brightesthyperneline(93.174GHz)usingthevelocityran geof 42to 36 km s1. Over54velocitychannelsofwidth0.11 km s1,the1 RMSnoisewas0.28 K km s1. Arelativelysmallamountofemissionwasseeninthenorther nactiveregion.The brightestemissionisseenwithinthequiescentlamentalo ngclump202a. 6.4AstrochemistryofStar-FormingClouds Wenowinvestigatehowabundancesofvariousspeciesvaryin thedenseclumps andsearchfortrendswithclumpevolution.Tomakeabasicas sessmentofhowfar evolvedeachclumpis,weevaluatedthequantityL bol=M HCO +.Herethebolometric luminosity,L bol,wasprovidedbyMaetal.(inprep).TocalculateL bol,Maetal.gathered arangeofuxesfrom2MASS,Spitzer-IRAC-GLIMPSEimages,M SX,andIRAS-HIRES. Usingaspectralenergydistribution(SED),withuxesmeas uredwithinthe2Dgaussian ellipsetsof Barnesetal. ( 2011 ),twotemperaturegreybodymodelsarettothedata. Theirmethodincludedabackgroundemissioncorrectiontot heuxandallowedfor 125

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thedustemissivityindextovaryfrom1.5to2.5.Theyfoundt hattheirresultswere accuratetowithin15%forsourceswithpreviouslypublishe dluminosities( Hilletal. 2005 ).TheHCO +massesweretakenfrom Barnesetal. ( 2011 ),whereM HCO +was calculatedassumingLTEconditions,aconstantexcitation temperatureofT ex = 10K, andaccountingforopticaldepth.Figure 6-10 presentstheluminosityfunctionofRegion 26.TheseparametersarealsosummarizedinTable 6.3 Thedivisionofsourcesinto“quiescent”and“active”group swaspurelybasedon thedistributionofL bol=M HCO +,wherethemedianis 4 L =M (themedianisused insteadofthemeanduetolownumberstatistics,i.e.17clum ps).Weconsideredthe semi-interquartilerangetoestimatethedispersionaroun dthemedian,whereQ 1 = 2.62andQ 3 = 13.67.Hence,theL bol=M HCO +distributionhasamedianof4.135.5and allclumpswithL bol=M HCO +<9.63 L =M arelargerthanonedeviation.Usingthis analysis,alongwiththenoticeablebinomialdistribution (seeFigure 6-10 ),wesetthe divisionbetween“active”andand“quiescent”clumpstobea t8 L =M .Anyclumpswith aL bol=M HCO +lessthan8 L =M wereconsideredbea“quiescent”clump.Conversely, thoseclumpswithaL bol=M HCO +greaterthan8 L =M wereconsideredtobe“active” clumps.Intotal,therewere11clumpsinthe“quiescent”gro upand6inthe“active” group(clump202iwaseliminatedfromfurtherstudyasitwas notobservedat115 GHz).InFigure 6-11 wepresenttheaveragespectrainthequiescent(top)andact ive (bottom)clumpsforthevariousspeciesdiscussedinthepre vioussection.Toderive anaveragespectra,themeanline-of-sightvelocityofeach clumpwasrstestimated throughtheopticallythintracerC 18 O.Next,thismeanline-ofsightvelocitywasusedto centerallothermolecularspeciesspectratotheclump'sre ferenceframe.Finally,for eachmolecularspecies,theaverage“quiescent”spectrawa sgeneratedbyco-adding allthecenteredspectraofall“quiescent”clumps,andlike wisefortheaverage“active” spectra.Bothsetsofclumpsshowedbrightemissionin12 CO,13 CO,andC 18 O.This ndingwastobeexpectedsinceCOgenerallytracesthelarge scalestructure.One 126

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trendwedidseewasalackofN 2 H +intheactivespectra.However,thistrendwassmall consideringthattheN 2 H +emissioninthequiescentspectraisjustgreaterthanthe RMSnoiselimit. Tofurthersearchforchemicaltrendsbetweenthetwosetsof clumps,wecompared theintegratedintensitiesofHCO +withthoseoftheN 2 H +.Bothintegratedintensities werenormalizedtotheintegratedintensityofC 18 Oinordertoassesstheabundances relativetothegascontentoftheclump.Ofallthemolecular speciesobserved, theCOisotopologuesarereasonabletracersofthediffusem oleculargasofthe clumps.However,theC 18 Oistheleastlikelytobeopticallythickandshouldprovide areasonableestimateofthegascontentineachclump.Inall cases,theC 18 OandHCO +wereintegratedoverthevelocityrangeof 4 km s1forallclumps.FortheN 2 H +, toincludeallhypernelineemission,avelocityrangeof 9 km s1wasused.Figure 6-12 presentsthecomparisonoftheseintegratedintensityrati os.Foreachclump, the3 RMSuncertaintiesintheintegratedintensitywereestimat edfromthetypical noiseofeachspecies.Fromavisualinspectionofthiscompa rison,weseenotrendof decreasingN 2 H +withinthe“active”clumpswithrespecttothe“quiescent”c lumps.This trendwasexpectedasN 2 H +isknowntodecreaseasstar-formationactivityincreases. ThisisduetothechemicalreactionofN 2 H +withH 2 O,whichbecomesmoreabundant asicemantelssublimate( Casellietal.1993 ; Pirogovetal.2007 ).Furthermore,we comparedtheintegratedintensitiesofHCO +,N 2 H +,andHCN,allnormalizedtoC 18 O, withL bol=M HCO +(Figure 6-13 ).Alsofromavisualinspection,weconcludedthatthere arenoimmediatetrendsbetweenthemeasuredabundancesandL bol=M HCO +AlthoughwefoundnoimmediateabundancetrendswithL bol=M HCO +,thereare furtheravenuestotakeinattemptingtofollowthechemical evolutionofstarforming clumps.Onemethodcouldbetoinvestigateabundancetrends withrespecttoanother evolutionaryparameter,suchasincreasingbolometriclum inosity(T bol),and/orthe linewidth( v).Futureresearchforup-comingpublicationscouldinclud esuchstudies 127

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as:comparisonsbetweentheintensitiesandlinewidthsoft hedifferentspecies,velocity offsetsbetweenthedifferentspecies,andpositionaloffs etsbetweenspecies'peak emission.Wealsohaveplanstoextendourclumpsamplebyusi ngalltheCHaMP clumpsof Barnesetal. ( 2011 ),insteadofonlythosewithinRegion26.Wecanimprove theprobabilityofdetectingweakmolecularlineemission, suchasN 2 H +,byincreasing theclumpsample. 6.5SummaryofFindingsinAstrochemicalTrends Wepresentedapilotstudyaimedatunderstandingthechemic alevolutionbetween quiescentandactivestarformingclouds.WithintheCHaMPs urvey,weidentieda20 6 regionwhichincludedalamentarydarkcloud,abrightacti vestarforming region,andincluded16clumpsidentiedbyHCO +from Barnesetal. ( 2011 ).These clumpsweredividedinto“quiescent”and“active”groupsth roughabolometricluminosity function.Throughancomparisonbetweentheintegratedint ensitiesofHCO +andN 2 H +ineachclump,wefoundnotrendofN 2 H +abundancedecreasingduringtheevolutionof star-formationactivity.Wewillcontinuethischemicalab undancestudybyincreasingthe sizeofourclumpsampleinordertoincreasetheprobability ofdetectingweakmolecular lineemissionfromvariousspecies. 128

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Figure6-1.TheextentoftheCHaMPsurveyasshownby Barnesetal. ( 2011 ).The surveyconcentratestherectangularregionof280 to300 inlongitudeand 4 to2 inlatitude.Hereeachcoloredboxrepresentsaregionobser ved andeachblackdotrepresentsasourcefoundintheNantenMas ter Catalogue(see Barnesetal.2011 formoreinformation).Forthisstudy,we focusonregion26(tealbox),whichislocatedneartheupper lefthand corner. 129

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Figure6-2.Region26presentedin8 m(Spitzer-GLIMPSE).Theregionspans0.6 0.3 aniscenteredatl = 299.25, b =0.38 .Thegreenoutline representstheregionsmappedbytheMopra22mtelescopeat1 15GHz. The90GHzrunwasnearlyaslarge.Theblackellipsesreprese ntthe17 clumpsidentiedbytheirHCO +emission( Barnesetal. 2011 ).Alongwith thecatalogID,theline-of-sightvelocityasmeasuredbyHCO +isalsolisted. Thequiescentandactiveregionsareshownwithredboxesand areshown incloserdetailinFigure 6-3 130

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Figure6-3.ThemainquiescentandactiveregionsofRegion2 6.Top:MopraHCO +integratedintensitymapsat12 00 gridding.Bottom:8 mSpitzer-GLIMPSE images.Lefthandside:Thequiescentregioncontainingal amentarydense gasstructure.Righthandside:Theactiveregioncontainin gseveralmid-IR brightclumps. 131

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Figure6-4.Mopra12 COintegratedintensitymap.Theemissionwasintegratedover the velocityrangeof 44to 36 km s1.Over90velocitychannelsofwidth0.088 km s1,the1 RMSnoiseis0.71 K km s1132

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Figure6-5.Mopra13 COintegratedintensitymap.Theemissionwasintegratedover the velocityrangeof 42to 36 km s1.Over64velocitychannelsofwidth0.092 km s1,the1 RMSnoiseis0.36 K km s1. 133

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Figure6-6.MopraC 18 Ointegratedintensitymap.Theemissionwasintegratedover the velocityrangeof 42to 38 km s1.Over44velocitychannelsofwidth0.092 km s1,the1 RMSnoiseis0.30 K km s1. 134

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Figure6-7.MopraHCO +integratedintensitymap.Theemissionwasintegratedover the velocityrangeof 42to 37 km s1.Over45velocitychannelsofwidth0.11 km s1,the1 RMSnoiseis0.22 K km s1135

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Figure6-8.MopraHCNintegratedintensitymap.Theemissio nwasintegratedoverthe velocityrangeof 41to 37 km s1.Over44velocitychannelsofwidth0.11 km s1,the1 RMSnoiseis0.25 K km s1. 136

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Figure6-9.MopraN 2 H +integratedintensitymap.Theemissionwasintegratedover the velocityrangeof 42to 36 km s1.Over54velocitychannelsofwidth0.11 km s1,the1 RMSnoiseis0.28 K km s1. 137

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Figure6-10.LuminosityfunctionofRegion26.Thebolometr icluminositiesL bolwere takenfromMaetal.(inprep).TheHCO +masses,M HCO +weretakenfrom Barnesetal. ( 2011 ).SourceswithL bol=M HCO +lessthan8 L =M were consideredtobe“quiescent”,whilethoseabove8 L =M wereconsidered “active”. 138

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0 5 10 0 2 4 0 0.5 1 0 0.5 1 0 0.5 1 -100102030 -0.2 0 0.2 0.4 A 0 5 10 0 2 4 0 0.5 1 0 0.5 1 0 0.5 1 -100102030 -0.2 0 0.2 0.4 B Figure6-11.Thespectraofvariousmolecularspecies.Toin creasethesignaltonoise, theemissionhasbeenco-addedoverthetwoclumpsets,which havevery simularvelocities.(A)Thequiescentclumpspectra.(B)Th eactiveclumps spectra. 139

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Figure6-12.AcomparisonofHCO +andN 2 H +integratedintensities,normalizedtoC 18 OofalltheclumpsinRegion26.Thebluepointsrepresentquie scent clumps,whiletheredpointsrepresentactiveclumps.Theyerrorbars representtheratioofthe3 RMSuncertaintyinI(HCO +)toI(C 18 O),while thex-errorbarsrepresentthesamelevelofuncertaintyfor theratioof I(N 2 H +)toI(C 18 O).TheboxedpointsrepresentthemeanC 18 Onormalized integratedintensitiesofthequiescent(blue)andactive( red)clumps.We seenotrendofN 2 H +abundancedecreasingduringtheevolutionof star-formationactivity. 140

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Figure6-13.TheintegratedintensitiesofHCO +,N 2 H +,andHCN(allnormalizedtoC 18 O)havebeencompareddirectlytoL bol=M HCO +fromMaetal.(inprep). Ally-errorbarsrepresentthe3 RMSuncertaintiesforthecorresponding integratedintensityratios.Thequiescentclumpsareshow ninblue,while theactiveclumpsareshowninred. 141

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CHAPTER7 SUMMARYANDCONCLUSIONS OneofthefundamentalprocessintheevolutionoftheMilkyW ayistheformation ofstarclustersfromgiantmolecularclouds(GMCs).Inthis dissertationIaddressed someofthequestionconcerningstarclusterformation.The focusofmystudieswere onthekinematicsandphysicalpropertiesofInfraredDarkC louds(IRDCs),including theirsurroundingGMCs,astheyarebelievedtorepresentth einitialconditionsofstar andstarclusterformation.InChapter2( Hernandez&Tan 2011 )Ianalyzedtwohighly lamentaryIRDCsusing13 CO J = 10lineemissiondatafromtheGalacticRing Survey(GRS; Jacksonetal.2006 ).Whilepayingcarefulattentiontothemolecular envelopessurroundingthelaments,themasssurfacedensi tieswerederivedfrom13 CO, 13CO,andcomparedwiththosederivedfromthesmall-median-lt er(SMF) mid-infrareddustextinctionmappingof Butler&Tan ( 2009 ), SMF.Ifoundthattherewas anapproximatelylinearrelationshipbetweenthetwometho dsofmeasuringthemass surfacedensity.Furthermore,therewasevidencethatther atio 13CO= SMFdecreased withincreasing SMF.Thisdecreasingtrendmaybeduetoasystematicdecreasein excitationtemperature,increaseindustopacity,ordecre aseofthe13 COabundance duetoCOdepletionontodustgrainsinregionsofhighcolumn density.Tostudythe dynamicalstateofthelamentaryIRDCs,Iperformedanelli psoidalandlamentary virialanalysisoneachcloud.Ifoundthatthesurfacepress uretermsaredynamically importanttothestructureofthelamentandtherefore,the selamentsmaynotyetbe invirialequilibrium.Also,thereistentativeevidenceth attheregionsofthelamentwith themoststarformationactivityareclosertovirialequili brium. InChapter3( Hernandezetal. 2011 ),Ifurtheranalyzedthehighlylamentary IRDCknownasFilamentH(G035.39 00.33)usingmoresensitive,higherresolution molecularlineemissiondatatakenwiththeIRAM30mtelesco pe.TheIRAMdataset containedC 18 OemissionlinedatafromtheJ = 10andJ = 21transitions.First, 142

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usingratiosofcolumndensityestimatesfromeachtransiti on,Iderivedtheexcitation temperaturesasafunctionofpositionandvelocityinthecl oud.Ifoundthatthetypical excitationtemperaturewithinthecloudis 7K.Next,Iderivedthemasssurface densities, C18O,whileassumingstandardgasphaseabundancesandaccounti ng foropticaldepthintheline.Theseresultswerethencompar edtothemasssurface densitiesderivedfrommid-infrared(MIR)extinctionmapp ing, SMF,from Butler&Tan ( 2009 ).Withasignicanceof10 ,Ifoundthat C18O= SMFdecreasesbyaboutafactor of5as SMFincreasesfrom 0.02to0.2gcm2,whichwasinterpretedasevidence forCOdepletion.Thislevelofdepletionsuggeststhatseve ralhundredsolarmasses ofcloudmaterialarebeingaffected.Ipresentedamapofthe depletionfactorinthe lament,whichisonetherstcompletemappingsofamassive cloudinwhichCO depletionhasbeenobserveddirectly. InChapter4(Hernandezetal.inprep),Icontinuedworkingw iththe30mIRAM dataofFilamentHtoreassessthevirialstateofthelament .IusedtheC 18 O,J = 10andJ = 21transitions,molecularlineemissiontoderiveinformatio nonthelament's kinematics.Withthemoreaccurateexcitationtemperature sestimatesandevidenceof COdepletionfoundinthepreviousChapter,Iperformedanel lipsoidalandlamentary analysis.Myresultsindicatedthatthelamentisinastate moreconsistentwiththe virialequilibriummodelsof Fiege&Pudritz ( 2000 ),althoughthesurfacepressureterms arestillquiteimportant.Thecomparisontothevirialequi libriummodelsalsoindicate thatthelamentissupportedbyaconningtoroidallymagne ticeld,andnotself-gravity orsurfacepressurealone.Thereisalsoevidencethatthetw oregionsclosesttovirial equilibriumalsoincludeproto-stellaractivity. Chapter5embarksuponastudyofthelargerscalesofGMCenvi ronmentsaround IRDCs.BeginningwithasmallsampleofnineIRDCs,Imeasure dtheGMCmass, positionangleoftherotationalaxisprojectedontheplane oftheskyandthevirial parameteroftheirassociatedGMCs.Idiscussedhowthesere sultsdependedonthe 143

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scaleandmethodusedtodenetheGMCmorphology.UsingtheG RS13 COemission data,Ifoundmasses 10 5 M ,abroadrangeofprojectedrotationaxispositionangles, andlog 1,suggestingthatthemoleculargasisperturbedonthesesca les.Ialso foundthattherewasnotrendsbetween andthesizescaleorwiththemethodusedto extracttheGMC. Next,IperformedasimularstudyusingtwolargesamplesofI RDCs/GMCs:one basedontheassociationof285IRDCs,andonewith556clouds basedon13 COemissionfromtheGRS.Byinvestigatingthedistributionof positionanglesofcloud rotationaxesprojectedontheplaneofthesky,wefoundthat thereisnostatistical differencebetweenthetwocloudsamples,veriedbyaKSpro babilityof 0.30.I alsoconcludedthatasubstantialfractionofthecloudsrot ateinaretro-gradesense comparedtotheGalacticrotation.Thisconclusionmayhave implicationsforthe formationandevolutionofGMCsbysuggestingthatsomeclou dshavehadtimeto interactwithneighboringclouds.Thisconclusionalsosup portstheoreticalmodelsof cloudformationandevolutionthroughcloud-cloudcollisi ons. Inthelaststudyofmydissertation,Chapter6,Ipresenteda pilotstudyon16 clumpsfromtheCensusofHighandMedium-massProto-stars( CHaMP)team.The CHaMPSurveyistherstlarge-scale,unbiaseduniformmapp ingsurveyatsub-parsec resolutionofmassiveclumpsintheSouthernMilkyWay(280
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BIOGRAPHICALSKETCH AudraHernandezwasborninPortsmouth,VA,USA.InDecember of1984,she movedwithherfamilytoColorado.SheattendedElizabethHi ghSchoolandgraduated inMayof1998.SheattendedtheUniversityofColoradoinBou lder,CO,USAand graduatedcumLaudewithaBachelorofArtsdegreeinphysics andmathematicswith anemphasisinastrophysicsinMayof2003.Audrathenattend edtheUniversityof FloridainGainesville,FL,USAandrecievedherMasterofSc iencedegreeinastronomy in2006.SherecievedherPh.D.inastronomyintheAugustof2 011. 150