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Shapes of Stellar Birth

Permanent Link: http://ufdc.ufl.edu/UFE0024324/00001

Material Information

Title: Shapes of Stellar Birth A Statistical Analysis of the Internal Structure of Young Embedded Clusters
Physical Description: 1 online resource (297 p.)
Language: english
Creator: Ferreira, Bruno
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: clusters, embedded, star
Astronomy -- Dissertations, Academic -- UF
Genre: Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We now know that the majority of stars form in clusters deeply embedded in molecular gas. Young embedded clusters are seen as being one of the best sites for studying the formation and early evolution of stars because of the large number of stars located in a small spatial volume; as such, the study of clusters is an extremely active field. However, many of these studies have been independent of each other, which has often made it challenging to compare the derived cluster properties; this has been accentuated by the lack of coherent statistical methods for measuring the cluster properties. Furthermore, we know now that, in addition to forming in a clustered mode, stars also form through a distributed mode, characterized by lower surface densities; the physical processes which govern these modes are still not understood. My goal was to further our understanding of how clusters form and evolve, through a comprehensive, uniform and unbiased study and comparison of their properties. In this dissertation I have developed a method which identifies clusters as well as measures some of their fundamental properties such as size, number of members, extinction and infrared excess fraction. My novel approach is based upon a nearest-neighbor method of sampling surface density; clusters are, by definition, surface density enhancements, and we show that the nearest-neighbor is a good tool for evaluating a wide range of density distributions. This method was designed to be applicable to a large variety of cluster fields, and allows us to remove biases incurred by other currently used forms of cluster detection. To arrive at a robust method of cluster identification, I have used Monte Carlo simulations to generate artificial clusters. Using these simulations I recreated a wide range of cluster scenarios to test and optimize the nearest-neighbor method; once tested, I then applied the method to 43 known clusters, constituting a representative sample of nearby young embedded clusters. Studying this sample of clusters has allowed me to obtain a global understanding of clusters by comparing their properties. Upon applying the method to the cluster catalog I find that the average total radius and core radius of a cluster is, respectively, 0.61 pc and 0.28 pc; the clusters have an average number of members of 132, average infrared excess fraction of 22% and average V-band extinction of 16 magnitudes. In addition to the clusters upon which I centered the fields, I also find 13 new clusters; I believe that some of these may, in fact, be substructure of the main cluster but without independent distance estimates to these new clusters it is not possible to be sure of this or of the measured values for the parameters. In addition to quantifying some of the more well-known cluster properties, I also studied a cluster's internal density structure; this was accomplished by using the distribution of its nearest-neighbor separations and by developing a new parameter which quantifies a cluster's degree of central condensation. In analyzing a cluster's internal structure I find that clusters can be categorized as either centrally condensed or flat; centrally condensed clusters can be fit by power-law functions and are thought to be the product of a gravitationally-driven formation scenario, whereas flat clusters are thought to be formed through a turbulence-dominated formation. I find that 64% of the known, nearby, young clusters fall in the centrally condensed category. I also find evidence indicating the presence of a halo population; a halo component has been previously suggested for a couple of clusters and I show that, by using the distribution of nearest-neighbour separations to evaluate the internal density structure, there is strong evidence for the presence of a halo in many of our clusters. Furthermore, I have applied the methods of cluster identification and analysis to a giant molecular cloud; this was done with the intent of both applying the cluster identification method to a large area and to study the clusters in the context of their environment. To perform this study I have used data from the FLAMINGOS near-infrared survey which, by using infrared excess as an indicator of youth, allowed me to trace the cloud's young stellar population. Results show that the molecular cloud's young stellar population can be divided into 4 categories: i) core, ii) halo, iii) aggregate and iv) field, according to its nearest neighbour distribution. Using this method I have estimated that, for Monoceros OB1 giant molecular cloud, the number of stars born in clusters is 68%. Finally, I have taken a closer look at the region surrounding the well-studied NGC 2264 cluster. I find the existence of a large halo component connecting the three known star forming regions (IRS1, IRS2 and S Mon) in NGC 2264, and I have compared the distribution of young sources, as identified using FLAMINGOS, to the distribution of Class I, thick disk Class II, and anemic disk Class II sources, as identified using SPITZER, for cluster NGC 2264. I find that the FLAMINGOS young sources and the thick disk Class II sources share very similar spatial distributions which coincide with the known regions of star formation.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Bruno Ferreira.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Lada, Elizabeth A.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-04-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0024324:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024324/00001

Material Information

Title: Shapes of Stellar Birth A Statistical Analysis of the Internal Structure of Young Embedded Clusters
Physical Description: 1 online resource (297 p.)
Language: english
Creator: Ferreira, Bruno
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: clusters, embedded, star
Astronomy -- Dissertations, Academic -- UF
Genre: Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We now know that the majority of stars form in clusters deeply embedded in molecular gas. Young embedded clusters are seen as being one of the best sites for studying the formation and early evolution of stars because of the large number of stars located in a small spatial volume; as such, the study of clusters is an extremely active field. However, many of these studies have been independent of each other, which has often made it challenging to compare the derived cluster properties; this has been accentuated by the lack of coherent statistical methods for measuring the cluster properties. Furthermore, we know now that, in addition to forming in a clustered mode, stars also form through a distributed mode, characterized by lower surface densities; the physical processes which govern these modes are still not understood. My goal was to further our understanding of how clusters form and evolve, through a comprehensive, uniform and unbiased study and comparison of their properties. In this dissertation I have developed a method which identifies clusters as well as measures some of their fundamental properties such as size, number of members, extinction and infrared excess fraction. My novel approach is based upon a nearest-neighbor method of sampling surface density; clusters are, by definition, surface density enhancements, and we show that the nearest-neighbor is a good tool for evaluating a wide range of density distributions. This method was designed to be applicable to a large variety of cluster fields, and allows us to remove biases incurred by other currently used forms of cluster detection. To arrive at a robust method of cluster identification, I have used Monte Carlo simulations to generate artificial clusters. Using these simulations I recreated a wide range of cluster scenarios to test and optimize the nearest-neighbor method; once tested, I then applied the method to 43 known clusters, constituting a representative sample of nearby young embedded clusters. Studying this sample of clusters has allowed me to obtain a global understanding of clusters by comparing their properties. Upon applying the method to the cluster catalog I find that the average total radius and core radius of a cluster is, respectively, 0.61 pc and 0.28 pc; the clusters have an average number of members of 132, average infrared excess fraction of 22% and average V-band extinction of 16 magnitudes. In addition to the clusters upon which I centered the fields, I also find 13 new clusters; I believe that some of these may, in fact, be substructure of the main cluster but without independent distance estimates to these new clusters it is not possible to be sure of this or of the measured values for the parameters. In addition to quantifying some of the more well-known cluster properties, I also studied a cluster's internal density structure; this was accomplished by using the distribution of its nearest-neighbor separations and by developing a new parameter which quantifies a cluster's degree of central condensation. In analyzing a cluster's internal structure I find that clusters can be categorized as either centrally condensed or flat; centrally condensed clusters can be fit by power-law functions and are thought to be the product of a gravitationally-driven formation scenario, whereas flat clusters are thought to be formed through a turbulence-dominated formation. I find that 64% of the known, nearby, young clusters fall in the centrally condensed category. I also find evidence indicating the presence of a halo population; a halo component has been previously suggested for a couple of clusters and I show that, by using the distribution of nearest-neighbour separations to evaluate the internal density structure, there is strong evidence for the presence of a halo in many of our clusters. Furthermore, I have applied the methods of cluster identification and analysis to a giant molecular cloud; this was done with the intent of both applying the cluster identification method to a large area and to study the clusters in the context of their environment. To perform this study I have used data from the FLAMINGOS near-infrared survey which, by using infrared excess as an indicator of youth, allowed me to trace the cloud's young stellar population. Results show that the molecular cloud's young stellar population can be divided into 4 categories: i) core, ii) halo, iii) aggregate and iv) field, according to its nearest neighbour distribution. Using this method I have estimated that, for Monoceros OB1 giant molecular cloud, the number of stars born in clusters is 68%. Finally, I have taken a closer look at the region surrounding the well-studied NGC 2264 cluster. I find the existence of a large halo component connecting the three known star forming regions (IRS1, IRS2 and S Mon) in NGC 2264, and I have compared the distribution of young sources, as identified using FLAMINGOS, to the distribution of Class I, thick disk Class II, and anemic disk Class II sources, as identified using SPITZER, for cluster NGC 2264. I find that the FLAMINGOS young sources and the thick disk Class II sources share very similar spatial distributions which coincide with the known regions of star formation.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Bruno Ferreira.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Lada, Elizabeth A.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-04-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0024324:00001


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SHAPESOFSTELLARBIRTH: ASTATISTICALANALYSISOFTHEINTERNALSTRUCTURE OFYOUNGEMBEDDEDCLUSTERS By BRUNORICARDOMALTAFERREIRA ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2010 1

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c r 2010BrunoRicardoMaltaFerreira 2

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" Eprecisomuitocaosinteriorparaparirumaestrelaquedan ca" "Oneneedsmuchinnerchaostogivebirthtoastarthatdances Nietzche Thisworkisdedicatedtomyfamilyandfriends 3

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ACKNOWLEDGMENTS Manypeoplehavebothknowinglyandunknowinglyhelpedmeon thisjourney.How eachofthoseinteractionsandrelationshipshaveencourag edmetoreachthisgoalisa websoentangledthatonlyoccasionallydoIcatchaglimpseo fitsinterconnectedness. Itisacuriousfactthatsomanyeventsthatatthetimeseemed eitherinsignicant,or evenblatantlydetrimental,tomenishingthePhDhavereve aledthemselvestobe key moments. I'drstliketoacknowledgetheUniversityofFloridaandth eDepartmentof Astronomyforinvestingininternationalstudents;theyha vefullyfundedmystudies andmylivingthroughoutthepast6years,allowingmetolive mydreamofperforming cuttingedgescienticresearch.I'dliketoespeciallyack nowledgeDebraAndersonatthe UniversityofFlorida'sInternationalCenterforthehelps hegavemeandforthecareshe showsinmakingsureallinternationalstudentsarelookeda fter. SevenyearsagoIappliedtotheUniversityofFloridatowork directlywithDr. ElizabethLada.Iamveryappreciativeofheracceptingmeas herstudentandforguiding methroughouttheseyears.IfeelveryfortunatethatDr.Lad ahasalwaysbeensupportive ofmyneedsanddecisions;shehasshownendlesspatienceand ,mostimportantly,trustin mychoices.IalsowanttosingleoutandacknowledgeDr.Lada 'simpressiveabilitytolist endlessinterestingprojectseverytimewehadameeting;th eseoftenprovidedfuelforme whenmyownmotivationwaslow. Theonlyotherscience-relatedacknowledgmentistomyhigh schoolphysicsprofessor, DrKeithOrd.Dr.Ordstandsoutinmylifeasbeingtherstper sontochallengeand encouragemetolivelifemorefullyandwithgreaterpresenc e. IthasbecomecleartomethatthosepeopleIwanttothankmost arealsotheones withwhomIhavesharedmanyofmymeals.Forthisreason,Iamd eeplygratefulforthe lunchesservedbytheHareKrishnacommunityatthePlazaoft heAmericas;Ihavebeen 4

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eatingthereoverthecourseofthepast7yearsandIhaveyett otireoftheirfood.Iam particularlyappreciativeofHananwhohasbecomeagoodfri end;todahveShalomHanan. SomeofthetastiestbitesIhaveexperiencedhavebeeninsom eofthemost uncommonofplaces;forthisIhavetothankallthosewhoshar emypassionforrock climbing.MaximZolotukhin,GavinHeverly,RandallHill,J eremyRush,ChrisHale, MatthewMiller,JohnReger,AlisonTudor,MikePalmer,Mike Johnson,Margarita Torres,JasonCandler,BenJames,LeeFriedlanderand,ofco urse,mymostfrequent "partner-in-climb"JoeLewis;Idon'tknowwhatcheesethat waswehadwhilesittingin theparkinglotofWal-Martrightbythehighwaybutitwasgoo d!JoeandhiswifeNicole havewelcomedmeintotheirfamilyandhavesupportedmeemot ionallyandphysically throughoutmyyearsinGainesville,Isimplycannotthankth emenough. Arecentandmostpreciousyearofmylifewasspentsharingme alswiththepeople attheFloridaSchoolofMassage,whereIexperiencedsomeof themostheartfelt conversations.BlueandOriaconsistentlyamazedmewithth eirsimple,organicvegetarian meals.IwanttothankMichaelandValerieBroas,PaulLinn,P eteWhithridge,Pauland JosieDavenport,FrankMerillat,DougLoeb,AnneMarshall, CateMiller,MeganRood, AdamSilverberg,Kathleen(Gift)Fox,CristianArroyo,Kar enBall,DarrenBurgess, MauraBrady,VincentCambrea,JosephCosenza,JenniferDow ney,JenniferGreenwood, BobLee,LauraTehennepe,JohnaBurgess,MichelleFossler, CoreyLaFave,KippKipp, ShazaDavis,JustinChang,WeberWu,AshleyBlincow,JJBuch olz,MarshallBrunson, AnneBrown,ShannonSatiChmelar,MarcelaMartinez,andman yotherswhogavemethe giftoftheirhonestpresence.Ialsowanttogiveaspecialhu gofappreciationtoHuxley Coulterwhounderstandsthevalueofsilenceandheartfeltl istening. Thecommunityofyogisandyoginis,inbothLisbonandGaines ville,havetaughtme twoimportantlessonsaboutfood:1)thatafeastistheresul tofeachpersoncontributing justonesmallingredientand2)thateatingandenjoyingfoo daretakentoacompletely newdimensionwhenwetakethetimetofast.IwanttothankTil akapash,Dada,Antonio 5

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(Toni)Saraiva,thoseattheAnandamargacenterinSintra,Y ogaJim,YogiBear, NobelAng,KieranandSeanMcGrail,VincentandMariaHerzog ,Rona,VijayReddy, RohitBadal,ArielHicks,JanelleSununtnasuk,ErynJohnso n,KathrynWallster,Priel Schmalbach,IlonayGoncalo,andGabilu. Ihavealwaysappreciatedsharingamealwiththosewhoaremo reexperiencedinlife andhavecomeoutofthoseexperiencesyounger,forthisreas onIamgratefulforallthe mealsinRafaelGuzman'scompany,withandwithoutlafamosa "botelladevino".Vivala compa~niadelpa~nuelo. IstillfeelstrangewhenThursdayeveningrollsaroundandI 'mnotbikingtothe Gayaut-Kempkahousetoimprovisearichsaladinthecompany of"thegirls";thankyou JenniferGayaut,KathrynTancig,AimeeGayaut,BettyKempk aandAutumnThompson. YoubecamesuchabeautifulpartofmylifesoquicklyandIloo kforwardtothedays whenwewillagainshareanicebottleofredwineorawinterdi pintheItchetucknee. DuringmylastvisittoGainesville,alreadywithoutahomet here,Irelieduponthe hospitalityoffriends.Jenny,Rob,andtheirpreciousIsai ahnotonlyallowedmetosleep andeatintheirhomebuthelpedmetofeellikeIwaspartofthe irfamily.Imissyouand can'twaittovisitoncemore. Portugalhasalwaysbeenmyhome,anditspeoplemypeople,de spiteallofmy absences.Iwanttoespeciallyexpressmyappreciationfort hesupportIreceivedfrom CatarinaMoreira,whowassuchabigpartofmylifeduringmyt ransitiontoGainesville, aswellasSoniaArroz,AlbertoNegr~ao,PaulaTeixeira,Jo anaPereira,JoanaSantos,Luisa Arruda,SambingoCardosoandSilviaVicente. Despitethe7yearsintheDepartmentofAstronomyIhaveshar edveryfewmeals withthoseIcrossinthehalls,generallypreferringtoeate itheroutsideor,whenthe deadlineswerenear,infrontofthecomputer.However,Noah Rashkind,JorgeGallego, Soung-Chul,CarlosRoman-Zu~nigaandJoannaLevineare veastronomerswhohave alsobecomegoodfriends.IwanttothankCarlosandJoannafo rthepizzanightsatthe 6

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oceaswellasthebanana-breadAir-IndianightsatCarlosa ndFabiola'shouse.Jorge GallegoisprobablythefriendIhavesharedmealswithinthe largestrangeofplaces. Hehasbeenavictimofmygoodmoodsandmybadmoodsandknowin gmyselfIhonor hiscommitmenttobeingmyfriend.ToJorgeandSoung-Chul,t heTempleofLovewill foreverliveinus. IamespeciallyappreciativeofthesupportIhavereceivedf rommyparents,Jorge andTeresa,andmybrother,Nelson,whomIhadtoleaveinorde rtosetuponthispath; thelongerIfermentinthisworldthemoremyloveforthemgro ws.Intimeswhenmy astrophysicalmotivationwaslowestIwouldrecallhowmy"a mateurastronomer"dad single-handedlybuiltanobservatory,witharotatingdome ,inthebackyard;hehasalways beenproofofwhatdetermination(andstubbornness)canach ieve.Mymotherkeptme intouchwithmyPortugueserootsbysendingmetraditionalf ood;Iwillalwayswonder whatthoughtsranthroughthemailman'smindashedelivered thosepackagesofstinky Portuguesecheese. FinallyIwanttothankmywifeUrsula.Gettingtoreallyknow somebodyinevitably meansyoumeettheirless-gloriousside;Ursulahascomeint omylifeinthepasttwo yearsandhashadtoenduresomeofmymostburdensomestateso fbeing(suchassitting catatonicallyinfrontofacomputerformonthsonend).Onth egooddaysshewasmy cookandmymuse.Shewasmyeditor,havingreadmydissertati onmorethananyone elseandpatientlyguidingmetounderstandthepowerofthes emicolon,andmycondant whenthingswerenotexactlypanningoutasIwantedthemto.T hankyouforyour presence,IloveyouandIpromisetonotstartanotherPhDany timesoon. 7

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................4 LISTOFTABLES .....................................12 LISTOFFIGURES ....................................13 ABSTRACT ........................................20 CHAPTER 1INTRODUCTION ..................................23 1.1GiantMolecularClouds ............................24 1.2EvolutionarySequenceofStarFormation ...................26 1.2.1OverviewofStellarBirth ........................26 1.2.2TheFour-ClassSystem .........................28 1.3StellarClusters .................................29 1.3.1BirthandEvolution ...........................30 1.3.2FinalStages ...............................31 1.4ScopeofthisWorkandOurGoals .......................32 1.5OutlineofDissertation .............................33 2DETECTION,ANALYSIS,ANDMODELINGOFCLUSTERS .........34 2.1MethodsofClusterDetectionandAnalysis ..................34 2.1.1Introduction ...............................34 2.1.2ATypicalClusterField .........................35 2.2MethodsforMappingSurfaceDensity ....................35 2.2.1NyquistBinning .............................35 2.2.2MinimumSpanningTree ........................38 2.2.3Two-PointCorrelationFunction ....................39 2.2.4NearestNeighbor ............................40 2.2.4.1MeasuringClusterPropertieswiththeNNM ........42 2.2.4.2ChoosingtheJ-Value .....................43 3MONTECARLOSIMULATIONSOFCLUSTERS ................45 3.1MotivationforDevelopingClusterSimulations ................45 3.2MonteCarloSimulations ............................45 3.3FundamentalClusterParameters .......................45 3.3.1SyntheticLuminosityFunctions ....................46 3.3.2RadialDensityProles .........................46 3.4ClusterIdentication ..............................49 3.4.1StudyingtheDistributionofNNSeparations .............50 3.4.2ChoosingtheOptimalCutoValue ..................56 8

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3.5SimulationsofInternalDensityStructure ...................61 3.5.1SimulationsofClusterHalos ......................61 3.5.2SimulationsofMultipleClusters ....................68 3.5.3AccountingfortheEectsofExtinction ................75 4AUNIFORMSTUDYOFEMBEDDEDCLUSTERSWITHTHENNM ....80 4.1EmbeddedClusterCatalog ...........................80 4.1.1Usingthe2MASSSurvey ........................83 4.1.2ChoiceofFieldSizeandDataQuality .................83 4.2ResultsofApplyingtheNearestNeighborClusterDetect ionMethod ...84 4.2.1ClusterDetections ............................86 4.2.2DistributionsofClusterProperties ...................86 4.2.2.1EquivalentRadius ......................87 4.2.2.2CoreRadius ..........................88 4.2.2.3Density-Proles ........................89 4.2.2.4Circularity ...........................93 4.2.2.5NumberofMembers .....................95 4.2.2.6FractionofInfraredExcessSources .............99 4.2.2.7AverageExtinction ......................101 4.2.2.8CorrelatingEquivalentRadiusandNumberofMember s .102 4.3AnalysisofDensityStructureinIndividualClusters .............105 4.3.1ClusterNGC1333 ............................106 4.3.2ClusterNGC2264 ............................108 4.3.3ClusterNGC2264SouthRegion ....................108 4.3.4TrapeziumCluster ...........................108 4.3.5ClusterIC348 ..............................111 4.3.6ClusterNGC2024 ............................114 4.3.7ClusterNGC2071 ............................114 4.3.8ClusterS106 ...............................117 4.3.9ClusterLKH 101 ............................117 4.3.10ClusterGGD12-15 ...........................117 4.4Discussion/Conclusion .............................117 4.5TablesofResults ................................125 4.5.1ClusterProperties ............................125 4.5.2ComparingResults ...........................128 4.5.3CutoValues ..............................128 5APPLYINGTHENNMTOMONOCEROSOB1 .................131 5.1MotivationandIntroductiontoMonOB1 ..................131 5.2FLAMINGOS ..................................132 5.2.1Specications ..............................132 5.2.2GoalofFLAMINGOS ..........................133 5.2.3Observations ...............................133 5.2.4ReductionofData ............................135 9

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5.2.5PhotometricSelectionCriteria .....................136 5.2.6SpatialCoverageofMonOB1 .....................140 5.3ANearestNeighborNear-InfraredAnalysisofMonOB1 ..........143 5.3.1SpatialStructureofMonOB1 .....................143 5.3.2EstablishingOurCatalogofIRxSources ...............145 5.3.2.1Color-ColorDiagrams ....................145 5.3.2.2DepthofEachCut ......................152 5.3.2.3DistributionofIRxSources .................152 5.3.3AdaptingtheNNMtoIRxStudies ...................154 5.4Results ......................................157 5.4.1DistributionofNNSeparations ....................158 5.4.2PropertiesofClustersIdentiedinMonOB1 .............163 5.4.3AStudyoftheClusteredvsDistributedStarFormation .......171 5.4.4MeasuringtheFractionofStarsinClusters ..............178 5.5DiscussionofBackgroundContamination ...................179 5.6Discussion ....................................181 6ACOMPARISONOFRESULTSFORNGC2264 .................184 6.1IntroductionandMotivation ..........................184 6.2MappingtheMolecularStructure .......................185 6.3Conclusion ....................................194 7SUMMARYANDFUTUREWORK ........................196 APPENDIX AFURTHERRESULTSOFCLUSTERSOBSERVEDWITHNNM ........198 A.1ContoursandSourceDistributionsofClustersobserved with2MASS ...198 A.2SurfaceDensityRadialProles ........................217 A.3CorrelationsbetweenClusterParameters ...................232 A.3.1CorrelationsBetweenClusterParameters ...............232 A.3.2CentralCondensationvsExtinction ..................232 A.3.3ExtinctionvsInfraredExcessFraction ................237 A.3.4EquivalentRadiusvsMass .......................238 A.3.5MaximumDensityvsMass .......................238 A.3.6CorrelationBetweenMaximumDensityandNumberofMem bers ..241 A.3.7FractionofIRxSourcesvsCircularity .................241 A.3.8CircularityvsExtinction ........................241 A.3.9CentralCondensationvsCoreRadius .................245 A.4AnalysisofStatisticalErrorsinCoreandEquivalentRa dii .........248 BDETAILSOFFLAMINGOSOBSERVATIONSOFMONOCEROS .......252 B.1MonAObservations ...............................252 B.2MonBObservations ...............................257 10

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B.3AreasofMonOB1Fields ...........................268 B.4ControlFields ..................................268 CDETECTIONOFSMALLCLUSTERSUSINGJ=10 ...............278 REFERENCES .......................................282 BIOGRAPHICALSKETCH ................................294 11

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LISTOFTABLES Table page 3-1Simulatingclusterswithradius=0.1units .....................57 3-2Simulatingclusterswithradius=0.2units .....................58 3-3Simulatingclusterswithradius=0.3units .....................59 3-4Simulatingclusterswithradius=0.5units .....................60 4-1CatalogofClusterFields ...............................81 4-2DetectedClusters ...................................126 4-3ComparisonwithValuesinLiterature ........................128 4-4CutoValues .....................................129 5-1PhotometricLimits ..................................153 5-2NumberofSourcesExhibitingInfraredExcess ...................154 5-3ClusterDetectionsforConservativeCut ......................168 5-4NumberofSourcesinEachPopulation .......................179 A-1BootstrapAnalysisofStatisticalErrors .......................249 B-1DetailsofMonAObservations ............................253 B-2DetailsofMonBObservations ............................258 B-3RawandFinalAreasforMonocerosFields .....................269 B-4AveragesandSTDevforMonocerosControlFields ................271 C-1SimulatingClusters.Radius=0.1,j-value=10 ..................279 C-2SimulatingClusters.Radius=0.2,j-value=10 ..................280 C-3SimulatingClusters.Radius=0.3,j-value=10 ..................281 12

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LISTOFFIGURES Figure page 2-12MASS K s -bandimageofIC348 ..........................36 2-22MASS K s -bandimageofTrapezium ........................36 2-32MASS K s -bandimageofNGC1333 ........................37 2-4Exampleofbinning. .................................37 2-5FiguredemonstratingtheapplicationoftheNNM .................41 3-1SchematicrepresentationofsetupforMonteCarloSimul ations ..........46 3-2Flowchartshowingprocessofgeneratingclusterandel dpopulations ......47 3-3SyntheticK-bandluminosityfunctionsforacontrolel dandaclustereld. ..48 3-4Radialprolessampledtocreatedistributionsofclust ersources .........49 3-5Distributionsofsourcesforthesimulatedproles .................50 3-6DistributionofNNseparationsforj=20,10,5,3,2 ................51 3-7NNseparationsforthesimulatedproles ......................54 3-8Typicalsourceseparationsandcontourplots ....................55 3-9Schematicrepresentationofasimulatedeldincluding ahalo ..........62 3-10Distributionsofsourcesforthesimulatedprolesinc ludingahalo ........63 3-11NNseparationsofhalosimulationsfora 1 r 2 prole .................64 3-12NNseparationsofhalosimulationsfora 1 r prole .................65 3-13NNseparationsofhalosimulationsforaCteprole ................66 3-14Evaluatingthechoiceofthecutovalueforclusterswi thhalo ..........68 3-15Simulatingtwo 1 r 2 proleclusterssignicantlyseparated .............71 3-16Simulatingtwo 1 r 2 proleclustersneartoeachother ................72 3-17Simulatingtwo 1 r proleclusterssignicantlyseparated .............73 3-18Simulatingtwo 1 r proleclustersneartoeachother ................74 3-19Simulatingtwo,signicantlyseparated,dierentpro leclusters .........76 3-20Simulatingtwoproximalclusterswithdierentprole s ..............77 13

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3-21Simulatingtheeectsofextinction .........................79 4-1Imageofatypical2MASSdataqueryoutput ...................85 4-2Distributionsofequivalentradii ...........................88 4-3Distributionofcoreradii ...............................89 4-4Distributionsofstructureparameter forthreedistinctproles .........90 4-5SameasFigure4-4butincludingextinction ....................91 4-6Distributionsof forsimulatedandrealclusters ..................92 4-7Contourplotsfortwoclusterswithdierentisoperimet ricquotients .......93 4-8Distributionsofcircularity ..............................94 4-9Numberofclustermembers .............................96 4-10Figurecorrelatingmassandnumberofmembers ..................98 4-11ECMDFfortheclustercatalog ...........................99 4-12Distributionsoffractionofinfraredexcesssources .................100 4-13Correlationbetweenfractionof IRx frac sourcesand ...............101 4-14Distributionofaverageextinction ..........................102 4-15Figurecorrelatingsizeandmembership .......................103 4-16DensitycontoursanddistributionofNNseparationsfo rNGC1333 .......107 4-17DensitycontoursanddistributionofNNseparationsfo rNGC2264 .......109 4-18DensitycontoursanddistributionofNNseparationsfo rNGC2264South ....110 4-19DensitycontoursanddistributionofNNseparationsfo rTrapezium .......112 4-20DensitycontoursanddistributionofNNseparationsfo rIC348 ..........113 4-21DensitycontoursanddistributionofNNseparationsfo rNGC2024 .......115 4-22DensitycontoursanddistributionofNNseparationsfo rNGC2071 .......116 4-23DensitycontoursanddistributionofNNseparationsfo rS106 ..........118 4-24DensitycontoursanddistributionofNNseparationsfo rLKH 101 .......119 4-25DensitycontoursanddistributionofNNseparationsfo rGGD12-15 .......120 5-1DivisionofMonocerosintoFLAMINGOSelds ..................134 14

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5-2J,H,KFLAMINGOSphotometryerrorsforMonA,MonBcatalo gs .......137 5-3FLAMINGOScompletenesslimitestimate .....................138 5-4ComparisonofFLAMINGOSphotometrywith2MASSphotomet ry .......139 5-5LocationofFLAMINGOSeldsfortheMonOB1region .............141 5-6Eectsofimposingboundaryconditions ......................142 5-7FinaldistributionofsourcescoveringMonoceros ..................142 5-8DustextinctionmapofMonOB1 ..........................144 5-9Comparisonofextinctionmeasurements ......................145 5-10JHKcolor-colordiagramshowinglocationofIRxregion .............146 5-11ContourplotoftheCCDforsourceshavingK < 17.25 ...............148 5-12Color-colordiagramsformagnitudecutsat14.5and15. 25 ............150 5-13Color-colordiagramsformagnitudecutsat15.75and16 .5 ............151 5-14DistributionofIRxsourcesforK < 14.5andforK < 15.25 .............155 5-15DistributionofIRxsourcesforK < 15.75andforK < 16.5 .............156 5-16Distributionof10thNNdistances ..........................159 5-17ClusteringofIRxsourcesforK < 14.5andforK < 15.25 ..............161 5-18ClusteringofIRxsourcesforK < 15.75andforK < 16.5 ..............162 5-19Cluster1-withK < 15.25 ..............................164 5-20Propertiesofcluster1-withK < 15.25 .......................164 5-21Cluster2-withK < 15.25 ..............................165 5-22Propertiesofcluster2-withK < 15.25 .......................165 5-23Cluster3-withK < 15.25 ..............................166 5-24Propertiesofcluster3-withK < 15.25 .......................166 5-25Locationofclustercentersusingtheoptimalmagnitud ecut ...........169 5-26Locationofdetections ................................170 5-27DistributionofNNseparationsfordierentpopulatio nsinMonOB1 ......172 5-28SameasFigure5-27butforK < 15.75andK < 16.5 .................174 15

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5-29Color-colordiagramsforIRxpopulationsintheconser vativecut .........175 5-30J-Hdistributionsforpopulationsintheconservative cut .............178 5-31J-HdistributionsforIRxpopulationsintheconservat ivecut ...........178 5-32ComparisonofIRxnumberdensities ........................180 6-1ExtinctionmapoftheNGC2264region .......................186 6-2TheNGC2264regionwithIRxsources,K < 15.25 .................187 6-3SameasFigure6-2butforK < 15.75 ........................188 6-4SameasFigure6-2butforK < 16.5 .........................188 6-5Comparisonof2MASScontoursandIRxsources .................190 6-6LocationofCIIAnemic/ThickDisk,CISources,K < 15.25 ............191 6-7SameasFigure6-6butforK < 16.5 .........................192 A-1NGC1333. .......................................199 A-2IC348. .........................................199 A-3NGC2024. .......................................200 A-4NGC2068. .......................................200 A-5NGC2071. .......................................201 A-6Trapezium. ......................................201 A-7L1641N. ........................................202 A-8S106. ..........................................202 A-9RCrA. .........................................203 A-10L988e. .........................................203 A-11CepA. .........................................204 A-12MonR2. ........................................204 A-13GGD12-15. ......................................205 A-14NGC2264. .......................................205 A-15NGC2264South. ...................................206 A-16LKH 101. ......................................206 16

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A-17AFGL490. ......................................207 A-18ChameleonI. .....................................207 A-19KMS35. ........................................208 A-20CKGroup. .......................................208 A-21NGC2023. .......................................209 A-22V380OrimeleonI. ...................................209 A-23IRAS05401-1002. ...................................210 A-24IRAS243,245. .....................................210 A-25CB34. .........................................211 A-26IRAS08375-4109. ...................................211 A-27IRAS08404-4033. ...................................212 A-28IRAS08448-4343. ...................................212 A-29IRAS08470-4243. ...................................213 A-30IRAS08470-4321. ...................................213 A-31IRAS08476-4306. ...................................214 A-32IRAS08477-4359. ...................................214 A-33BBW192E. ......................................215 A-34IRAS20050+2720. ..................................215 A-35HD216629. ......................................216 A-36L1211. .........................................216 A-37VYMon. ........................................217 A-38Radialprolesforclusters ..............................218 A-39Radialprolesforclusters ..............................219 A-40Radialprolesforclusters ..............................220 A-41Radialprolesforclusters ..............................221 A-42Radialprolesforclusters ..............................222 A-43Radialprolesforclusters ..............................223 17

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A-44Radialprolesforclusters ..............................224 A-45Radialprolesforclusters ..............................225 A-46Radialprolesforclusters ..............................226 A-47Radialprolesforclusters ..............................227 A-48Radialprolesforclusters ..............................228 A-49Radialprolesforclusters ..............................229 A-50Radialprolesforclusters ..............................230 A-51Radialprolesforallclusters ............................231 A-52Correlationbetweenradialproleandtau .....................233 A-53Correlationbetweenradialproleandmass ....................233 A-54Correlationbetweenradialproleandnumberofsource s .............234 A-55Correlationbetweenradialproleandequivalentradi us ..............234 A-56Correlationbetweenradialproleandcoreradius .................235 A-57Correlationbetweenradialproleandinfraredexcess fraction ..........235 A-58Correlationbetweenradialproleandextinction ..................236 A-59Correlationbetweenradialproleandmaximumdensity .............236 A-60Correlationbetweenextinctionand ........................237 A-61Correlationbetweenextinctionand IRx frac ....................239 A-62Figurecorrelatingclustermassandclustersize ..................240 A-63Figurecorrelatingmassandmaximumdensityformainan dnewclusters ....242 A-64Figurecorrelatingnumberofmembersandmaximumdensi ty ..........243 A-65CorrelationbetweenfractionofIRxsourcesandIQ ................244 A-66CorrelationbetweenextinctionandIQ .......................246 A-67Correlationbetweencoreradiusand .......................247 B-1ComparisonofJ-bandphotometryerrorsforthefourcont rolelds ........272 B-2ComparisonofH-bandphotometryerrorsforthefourcont rolelds .......273 B-3ComparisonofK-bandphotometryerrorsforthefourcont rolelds .......273 18

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B-4Locationsofsourcesforthefourcontrolelds ...................274 B-5DistributionofIRxsourceforthefourcontrolelds ................274 B-6KLFforthefourcontrolelds ............................275 B-7CombinedKLFforcontrolelds2,3and4 .....................275 B-8CCDforthefourcontrolelds ............................276 B-9CMDforthefourcontrolelds ...........................276 B-10CMDforthefourcontrolelds ...........................277 19

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy SHAPESOFSTELLARBIRTH: ASTATISTICALANALYSISOFTHEINTERNALSTRUCTURE OFYOUNGEMBEDDEDCLUSTERS By BrunoRicardoMaltaFerreira May2010 Chair:ElizabethA.LadaMajor:Astronomy Wenowknowthatthemajorityofstarsforminclustersdeeply embeddedin moleculargas.Youngembeddedclustersareseenasbeingone ofthebestsitesfor studyingtheformationandearlyevolutionofstarsbecause ofthelargenumberof starslocatedinasmallspatialvolume;assuch,thestudyof clustersisanextremely activeeld.However,manyofthesestudieshavebeenindepe ndentofeachother, whichhasoftenmadeitchallengingtocomparethederivedcl usterproperties;this hasbeenaccentuatedbythelackofcoherentstatisticalmet hodsformeasuringthecluster properties.Furthermore,weknownowthat,inadditiontofo rminginaclusteredmode, starsalsoformthroughadistributedmode,characterizedb ylowersurfacedensities;the physicalprocesseswhichgovernthesemodesarestillnotun derstood. Mygoalwastofurtherourunderstandingofhowclustersform andevolve,through acomprehensive,uniformandunbiasedstudyandcomparison oftheirproperties.In thisdissertationIhavedevelopedamethodwhichidenties clustersaswellasmeasures someoftheirfundamentalpropertiessuchassize,numberof members,extinctionand infraredexcessfraction.Mynovelapproachisbaseduponan earest-neighbormethodof samplingsurfacedensity;clustersare,bydenition,surf acedensityenhancements,and weshowthatthenearest-neighborisagoodtoolforevaluati ngawiderangeofdensity distributions.Thismethodwasdesignedtobeapplicableto alargevarietyofcluster 20

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elds,andallowsustoremovebiasesincurredbyothercurre ntlyusedformsofcluster detection.Toarriveatarobustmethodofclusteridentica tion,IhaveusedMonteCarlo simulationstogeneratearticialclusters.Usingthesesi mulationsIrecreatedawiderange ofclusterscenariostotestandoptimizethenearest-neigh bormethod;oncetested,Ithen appliedthemethodto43knownclusters,constitutingarepr esentativesampleofnearby youngembeddedclusters.Studyingthissampleofclustersh asallowedmetoobtaina globalunderstandingofclustersbycomparingtheirproper ties.Uponapplyingthemethod totheclustercatalogIndthattheaveragetotalradiusand coreradiusofaclusteris, respectively,0.61pcand0.28pc;theclustershaveanavera genumberofmembersof132, average IRx frac of22%andaverageV-bandextinctionof16magnitudes.Inadd itionto theclustersuponwhichIcenteredtheelds,Ialsond13new clusters;Ibelievethat someofthesemay,infact,besubstructureofthemaincluste rbutwithoutindependent distanceestimatestothesenewclustersitisnotpossiblet obesureofthisorofthe measuredvaluesfortheparameters. Inadditiontoquantifyingsomeofthemorewell-knownclust erproperties,Ialso studiedacluster'sinternaldensitystructure;thiswasac complishedbyusingthe distributionofitsnearest-neighborseparationsandbyde velopinganewparameter whichquantiesacluster'sdegreeofcentralcondensation .Inanalyzingacluster's internalstructureIndthatclusterscanbecategorizedas eithercentrallycondensed orrat;centrallycondensedclusterscanbetbypower-lawf unctionsandarethought tobetheproductofagravitationally-drivenformationsce nario,whereasratclusters arethoughttobeformedthroughaturbulence-dominatedfor mation.Indthat64% oftheknown,nearby,youngclustersfallinthecentrallyco ndensedcategory.Ialso ndevidenceindicatingthepresenceofahalopopulation;a halocomponenthasbeen previouslysuggestedforacoupleofclustersandIshowthat ,byusingthedistributionof nearest-neighbourseparationstoevaluatetheinternalde nsitystructure,thereisstrong evidenceforthepresenceofahaloinmanyofourclusters. 21

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Furthermore,Ihaveappliedthemethodsofclusteridentic ationandanalysisto agiantmolecularcloud;thiswasdonewiththeintentofboth applyingthecluster identicationmethodtoalargeareaandtostudythecluster sinthecontextoftheir environment.ToperformthisstudyIhaveuseddatafromtheF LAMINGOSnear-infrared surveywhich,byusinginfraredexcessasanindicatorofyou th,allowedmetotracethe cloud'syoungstellarpopulation.Resultsshowthatthemol ecularcloud'syoungstellar populationcanbedividedinto4categories:i)core,ii)hal o,iii)aggregateandiv)eld, accordingtoitsnearestneighbourdistribution.Usingthi smethodIhaveestimatedthat, forMonocerosOB1giantmolecularcloud,thenumberofstars borninclustersis68%. Finally,Ihavetakenacloserlookattheregionsurrounding thewell-studiedNGC 2264cluster.Indtheexistenceofalargehalocomponentco nnectingthethreeknown starformingregions(IRS1,IRS2andSMon)inNGC2264,andIh avecomparedthe distributionofyoungsources,asidentiedusingFLAMINGO S,tothedistributionof ClassI,thickdiskClassII,andanemicdiskClassIIsources ,asidentiedusingSPITZER, forclusterNGC2264.IndthattheFLAMINGOSyoungsourcesa ndthethickdisk ClassIIsourcesshareverysimilarspatialdistributionsw hichcoincidewiththeknown regionsofstarformation. 22

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CHAPTER1 INTRODUCTION Understandingtheformationofstarshasbeenoneofthemajo rchallengesin astrophysicsformanydecades;wenowcomprehendtheproces sesoccurringinthe depthsofastaronceithasformed,butitsinitialmomentsre mainamystery.Only recentlyhasitbecomeclearthatstarsprefertoformingrou ps,asopposedtoinisolation; theyoungestofthesegroupsareknownas embeddedclusters (ECs).Duetotheirrole asthebirthplaceofmoststars,ECsarealsoknownas stellarnurseries .Thestudyof thesestellarnurserieshasinmanywaysprovenitselfessen tialtotheunderstandingof stellarphysicsandtheuniverse.Forexample,theseentiti esareexcellenttestbedsforstar formingtheoriesbecausetheycontainalargenumberofstar s,spanningawiderangeof masses,alllocatedinasmallvolume.Ourresearchhasbeenf ocusedonfurtheringour understandingoftheformationandevolutionoftheseECs. ThoughtheformationofanECisaverycomplexprocessnotyet fullyunderstood, itisknownthattheseentitiesaresensitivetoboththeinit ialconditionsimposedby theirenvironmentandthedierentgoverningmechanismspr esentinthatenvironment; examplesofsuchmechanismsaregravity,magneticelds,th ermalpressure,and turbulence.Inevitably,theinruenceofthesefactorsmust bererectedintheresultant propertiesoftheECs;therefore,astatisticalstudyofthe sepropertiesshouldrevealthis connection.Inthisdissertationwedevelopamethodforide ntifyingECsanduniformly measuringtheirpropertiesinordertoanalyzesuchaconnec tion.Inthisworkwealso developanewmeasureofacluster'sdensitystructure;thed ensitystructurehasnotbeen studiedforacomprehensivesampleofECs,andwesetouttose ewhatinformationit couldprovideforfurtheringourunderstandingofECs. InSection 1.1 wediscussgiantmolecularclouds,whicharethehostsofECs ;in Section 1.2 ,wediscussthepresentlyacceptedevolutionarysequenceo fisolatedstar formation;inSection 1.3 wediscussthebirth,evolutionandnalstagesofstarclust ers; 23

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andnally,inSection 1.4 wepresentthescopeofthisdissertation,ourgoals,andthe outline. 1.1GiantMolecularClouds Studiesinstarformationreceivedasignicantboostwhen, inthe1940s,starswere discoveredindarkclouds.ThesestarswereT-Tauritypesta rs,whichareknowntobe young,andthisdiscoveryindicatedthatitwasinmolecular clouds(MCs),someofthe darkest,coldest,densestplacesintheUniverse,thatstar formationtookplace( Joy1942 BokandReilly1947 ZuckermanandPalmer1974 Bok1978 ).SincetheseMCsarethe hostsforstarformationitislogicalthatthephysicalcond itionsoftheMCdictatethe propertiesofthestarformationthatoccurswithin( Evans1999 ),andassuchwebegin withadescriptionoftheseregions. GMCsarethelargestcohesiveentitiesinagalaxy,capableo fbeingaslargeasthe thicknessofagalaxy.Primarilycomposedofmolecularhydr ogen, H 2 ,GMCshaveaverage densitiesof10 2 10 3 particles cm 3 ,totalmassesoftheorder10 4 10 6 M ( StarkandBlitz 1978 ),andcanreachtensofparsecsindiameter( BlitzandShu1980 StarkandBlitz 1978 ).CurrenttheoriessupportGMCsbeingformedthroughtheco ndensationofHI, howeverhowthishappensisstillunknown(severaltheories arebeingentertained;this fallsbeyondthescopeofthiswork);intermsoftheirlifesp anhowever,anstrictupper limitof2 5 10 8 yrissetbythedepletionofthemoleculargasduetostarform ationin theentireGalaxy( BlitzandWilliams1999 ). IthasbeenestimatedthationizationfromO-typestarsshou ldcompletelyevaporate themoleculargasin2 4 10 7 yr.GMCageshavebeenmeasuredat 3 10 7 yrby BlitzandShu ( 1980 )andevidenceoftheirdispersalby10Myrhasbeenpresented by Leisawitzetal. ( 1989 )intheirCOsurveyof34openclusters. GMCsareverycoldregions,havingtemperaturesintherange of7-15degrees Kelvin.Suchlowtemperaturesarecausedbythepresenceofd ustgrainswhicheciently absorbopticalstarlightandreduceheatingfromexternalr adiation( BerginandTafalla 24

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2007 ).Thiseectmakesthesecloudstoocoldtoproduceradiatio ninvisiblewavelengths and,assuch,thesegiantsappearintheskyasdarkpatchesor clouds.Inordertotrace coldGMCsitisnecessarytoperformobservationsatradio/m illimeterwavelengths,where emissionsfromtracemoleculessuchasCOaredetectable.Th eMilkyWayGalaxyhas beenmappedusingsuchtracemolecules( Dameetal.2001 )andresultsshowthatGMCs withactivestarformationarepreferentiallylocatednear theGalaxy'sspiralarms. Studyingthedistributionoftheinterstellarmolecularga shasalsoshownthatthis gasisstructuredintocloudsandclumpsonaverywiderangeo fscales.GMCslieatthe largeendofthisrange;thesamestructureisobservedinthe sub-stellarmasseswhich arehundredthsofaparsecinsize( BlitzandShu1980 Elmegreenetal.2000 ).Thisis signicantbothbecausethedistributionofthisgasisanin dicatorofthemechanisms governingtheGMCandbecausethegassetssomeoftheinitial conditionsforstar formation. Inordertostudythelightemittedbythoseyoungstars,wene edtoalsostudy howthatlighthasbeenaectedalongthepathseparatingthe starandtheobserver. Occupyingthispathwendcolddust,whichmakesuptheGMCs, andinterstellardust grains,bothecientabsorbersoflight.Howmuchabsorptio nactuallyoccurswilldepend onthewavelengthofthelight,withwavelengthssmallertha n0.1 m,thesamediameter asthegrains,beingtheonesmoststronglyaected.Forthis reason,optical(V-band) photons,whichhaveawavelengthof0.5 mwillencounter10timesmoreextinction ontheirpathtoEarththananinfraredK-bandphoton(2.22 m)travelingthesame path.Thisselectiveabsorptionofcertainwavelengthsmak esitsuchthatstarsborn withinGMCswillbemoreeasilyobservedintheinfraredthan atshorterwavelengths. Therangeoftheinfraredisconsideredtospan0.75 mto1000 mbut,forembedded clusterastronomy,themostcommonregionofobservationha sbeenthenear-infraredJ(1.25 m),H(1.65 m)and K (2.2 m). 25

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Themathematicalrelationshipbetweenastar'semittedlig ht,thelightthatreaches anobserveronEarth,andthedustencounteredinthelight's journeyisshownin Equation 1{1 ,where m referstothestar'sapparentmagnitude, M isitsabsolute magnitude, A istheextinctioncoecient,and isthewavelength.Thegeneraltrendis oneofsteadilyincreasingaverageextinctionwithdecreas ingwavelength. m = M +5 log ( r= 10 pc )+ A (1{1) 1.2EvolutionarySequenceofStarFormation 1.2.1OverviewofStellarBirth Thelightwhichwereceiveisnotonlyafunctionofthemateri alitencountersalong itspathbutalsooftheevolutionarystateofthestaritself ,sowenextdescribeour knowledgeofastar'sevolution.Throughoutthisworkwewil loftenusethetermYSO, denotingYoungStellarObject,whichingeneralreferstoan ystarinitsearlystagesof evolutionand,morespecically,referstoprotostarsandp re-mainsequencestars. Theformationofanisolatedstarhasbeenextensivelystudi edandaworking paradigmseemstohavebeenreached(e.g.see Shuetal.1987 McKeeandOstriker 2007 ).Figure1in TassisandMouschovias ( 2004 ),showsagraphicalrepresentationof theacceptedstarformation(SF)timeline,fromtheprenata lmolecularmaterialtothe formationofamainsequencestar.Individualstagesinthet imelinearenottoscaleand aresubjecttovariabilitydependingonthestar'smass( Strom1995 ). Formain-sequencestars,therelationshipthatexistsbetw eenastar'sluminosity anditseectivetemperaturehasbeenwellstudied;thisrel ationshipisseeninthe Hertzsprung-Russell(HR)diagramwhichgraphicallyshows thedierentstagesofa star'sevolution.YSOs,however,cannotbeclassiedthrou ghtheirplacementonan HRdiagram.Astar'splacementonanHRdiagramrequiresthek nowledgeofbothits luminosityandeectivetemperature,whereluminositycan bemeasuredbyknowingthe observedruxandthedistance,andtheeectivetemperature ismeasuredeitherthrough 26

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colorsorobservationsoftemperature-sensitivespectral features.Thismethodworks wellaslongasthestarcanbecharacterizedbyasingleeect ivetemperatureandits spectrumresemblesthatofablack-body.YSOs,however,are stillenvelopedwithinthe densemolecularcloudcoreinwhichtheywereborn,sotheirl ightisstronglyinruencedby absorptionandreprocessingbythedust.Emissionsfromthe circumstellardustexhibita widerangeofeectivetemperaturesandtheirspectraldist ributiondoesnotresemblethat ofablackbody. LadaandWilking ( 1984 )discoveredthattheshapeofaYSO'sspectralenergy distribution(SED)intheinfrareddependsonthenatureand distributionofthe surroundingmaterialandthatitisafunctionoftheYSOssta teofevolution.Together withatheoreticalpictureofSFthroughthecollapseofanis olatedrotatingdensecore ( Terebeyetal.1984 ),thisdiscoverygaverisetoamodelinvolvingthreemainst ages ofSF.Thesestagesare:i)thecollapseoftheenvelopeleadi ngtotheformationof theprotostarandthedisk;ii)accretionofthediskontothe formingstar;andiii)the dissipationofthediskbyplanetformationandevaporation .Eachofthesestagesbecame associatedwithaYSOclassandacorrelationbetweenthecla ssandthespectralindex (a)oftheSEDwasestablished( Lada1987 ).Theboundariesfortheindex,a,which denedeachclasswere:i)classI:0
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1.2.2TheFour-ClassSystem Figure7in Shuetal. ( 1987 ),illustratestheseinitialstagesofSF.Thetimelinephas es ofFigure1in TassisandMouschovias ( 2004 )(denotedwithcapitalletters)correlate wellwiththestagesinFigure7in Shuetal. ( 1987 )(lowercaseletters),wherephaseA correspondstostagea,phaseBtostagesbandc,andphaseCto staged. TheinitialcongurationforthismodelofisolatedSFistha tofamolecularcloud inequilibriumsupportedbybothmagneticandturbulentene rgies. A thuscorresponds totherststageofSF,believedtobeonsetbythepartiallos softhissupportthrough ambipolardiusionorthroughleakingofturbulentenergy. Lowangular-momentum moleculargaswillcollapserst,formingslowlyrotating, cold,gravitationally-bound cloudcores;surroundingthiscorewillbethelower-densit ymoleculargaswhichhas higherangular-momentum.Magneticeldlineswillbepulle din,closetogether,asthey followthegasmotionduringthecorecollapse,causingabui ldupinmagneticpressure whichactsasanimpedimenttofurthercollapse.Assuch,the senewlyformedcores arealsosupportedagainstgravitybythermal,magnetic,an dturbulentpressures.Itis expectedthatthemagneticforcesaresignicantindenseco resbutfewcoreshavehad themagnitudeoftheirmagneticeldmeasured.Thedirectio nofthemagneticeldhas beenmeasuredthroughbothopticalandnear-infraredpolar izationmapsbutnottheir magnitude.Anotherforcewhichisthoughttoneutralizecol lapseisbelievedtocomefrom thebuild-upofacentrifugalbarrier;thisoccursbecaused uetoconservationofangular momentumtheinitialrotationalmotioninthecoremustincr easeduringcollapse. ThenextphaseofSFisphaseB,andfromthisphaseonwardsthe YSOcanbe classiedsowewillusethesystemofclassestodescribethe evolutionoftheYSO.Phase Bencompassestwoclassesofsources: class0sources and classIsources Class0 sourcescorrespondtoveryyoungprotostarshavingacorewh ichhasnotyet accretedthebulkofitsnalstellarmass( Andre1996 ).ThecentralYSO(orprotostar)is deeplyembeddedinthecoresoitcannotbeobserveddirectly withwithvisibleorinfrared 28

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observations;itdoesexhibitbipolarmolecularoutrowsan dcompactcentimeteremissiontypicalofaccretion-anditcanbedetectedinsub-millimet ercontinuumsurveys. ClassI sourcesdisplaysignicantnear-infraredemissionfromth ecoreand far-infraredemissionfromtheenvelope.Thesesourcesare atalatestageofaccretion, andattheendofphaseBthestarhasalmostreacheditsnalma ss.However,thecentral YSOstilltendstobetooembeddedtobeobservedintheoptica l. ClassII sourcesareYSOsforwhichthecircumstellarenvelopehasth innedthus revealingthecentralobject;classicalT-Tauri(CTT)star sareClassIIsources.Theystill haveanopticallythickdisksurroundingtheprotostar,whi chisresponsiblefortherat SEDproleintheinfraredprovidingemissioninexcessofth atexpectedfromablackbody, andaccretioncontinuesbutatalowerrate.ClassIIsources aresomewhereinbetween phaseBandphaseC,inFigure1in TassisandMouschovias ( 2004 ),andthisstageis thoughttolastabout10 6 years. ClassIII objectsarealsoknownasweak-lineT-Tauristars,thesesta rshavelostthe vastmajorityoftheirgaseousdiskduetoplanetaryformati onand/oraccretion.Initially consideredasclearlydistinctfromCTTS,andhavingSEDsde voidofinfraredexcess,it isnowbelieved( Gras-VelazquezandRay2005 )thatacontinuumexistsintermsofthe infraredexcesspropertiesfromCTTStoWTTS.Atthispointi naYSO'sevolutionan estimated10 7 yearshavepassedsincethebeginningofthecollapse. 1.3StellarClusters Intheprevioussectionwepresentedasmalloverviewofouru nderstandingofisolated SF.Astronomersnowknowthatstarspreferentiallyforminc lusters,notinisolation.This hasbecomeapparentthroughlarge-scalesurveysofbothYSO s( LadaandLada2003 )and densecores( Enochetal.2007 )and,assuch,acompletepictureofSFmustincludean understandingofclusteredSF. 29

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1.3.1BirthandEvolution Embeddedclusters(ECs)are,asthenamesuggests,stellarc lusterseitherpartiallyor fullyembeddedintheirdustyparentalGMCsandassucharere nderedpartiallyortotally invisibleatopticalwavelengthsbutarebestobservedinth einfrared.Beingstillembedded bythemolecularcloudfromwhichtheyformed,ECsaretheyou ngesttypestellarcluster andthetypeinwhichtheconnectiontothecloudismostwellp reserved.Theprocess ofclusterbirthoccursonatimescaleoftheorderof10 6 years( Carpenteretal.1997 ), whichisthesametimescaleasthedynamicalprocessesinthe clouditselfandoneorderof magnitudeshorterthanthecloudlifetime( BlitzandShu1980 ). Theseentitieshaveonlybeenobservedindetailfromthelat e1980sonwards, withtheadventofnear-infraredarraydetectors.Near-inf raredarrayshaveprovided atremendousincreaseinbothsensitivityandcoverageinco mparisontoinfrared detectors.Thisdevelopmentgavewaytosomeoftherstinfr aredsurveysofstar-forming regions( Ladaetal.1991b performinganinfraredsurveyofL1630, Strometal.1989 studyingstellarpopulationsinLYNDS1641darkcloud, Ladaetal.1991a performing infraredimagingofM17, Barsonyetal.1991 studyingLkH-alpha101infraredcluster, HodappandRayner1991 studyingtheS106cluster, Tapia1991 studyingtheembedded clusterIRAS17136-3617and Postmanetal.1996 performingthePalomardistantcluster survey). IntheirseminalsurveyofECsinOrionB(L1630),aregionoft heOrionmolecular cloud, Ladaetal. ( 1991b )foundthatbetween58%and96%ofalltheembeddedstars werecontainedinjustfourclusters.Thisresultindicated thatSFisaverylocalized eventasopposedtooccuringhomogeneouslythroughoutthew holecloud.Presently,itis thoughtthatover90%ofallstarsoriginatedinECs,andthat ECscanberegardedasthe fundamentalunitsofSF,thebuildingblocksofagalaxy'sst ellarpopulation. Manynonlinearprocessesareinvolvedwhenwelookatattheq uestionsofcluster formationandofSFinclusters.Theseprocessesincludetur bulentmotions,gravity, 30

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collisions,N-bodyinteractions,radiationandwindsfrom youngstars,andshocks; simulatingalloftheseis,currently,atasktoocomplicate dandunrealisticfortheoretical computations.Today'semergingparadigmconsiderslargescalesupersonicturbulenceas theprocesswhichmostdictatesthemacrophysicsofSF( McKeeandOstriker2007 );as such,modelssimulatingthefragmentationofaspherically symmetricmolecularcloudand withturbulenceastheircenterpiecehavebeenconstructed ( Bonnelletal.2003 Bateetal. 2003 ).Inthesesimulations,fragmentationisgenerallytrigge redbythelossofthecloud's turbulentsupport,givingwaytogravitationalcontractio nfollowedbytheformationof lamentsandclumps.Astheselamentsandclumpshaphazard lycollidetheyactasthe buildingblocksforclusters.Othermodelshavealsobeenge neratedwhichattemptedto recreatetheformationofstellarclustersthroughthefrag mentationofregionsofacloud ( KlessenandBurkert2000 KlessenandBurkert2001 ). Eventhoughsimulationshavemanagedtorecreatesomeofthe simplersequences bywhichmolecularcloudsmayevolveandformclusters,itis inevitablethat,in reality,thesituationismuchmorecomplex.Observational evidencesuggeststhe existenceofothermechanismsforSF,suchasfromtriggered SF(duetoionizationfronts poweredbyproximalHIIregions( EfremovandElmegreen1998 PhelpsandLada1997 ElmegreenandLada1977 )).Furthermore,SFmechanismsaremademorecomplexby processessuchasmergers( MurrayandLin1996 )andintenseUVradiationfrommassive stars( StorzerandHollenbach1999 )(see AdamsandMyers2001 foramorecomplete discussion).Infact,itislikelythatthemostfamousstarf ormingregion,Orion,andthe molecularcomplexitisapartof(theOrion-Monoceroscompl ex)wereformedthrough theinteractionoftwoexpandingsupershellsandtheireec tontheinter-stellarmedium (ISM).1.3.2FinalStages Thenalphaseofacluster'sevolutionisitsemergencefrom themolecularcloud. Thisphasehasbeenwellstudiedbothnumerically,throughN -bodysimulations 31

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( Ladaetal.1984 ),andanalytically( Hills1980 Saiyadpouretal.1997 ).Thesestudies haveshownthatnewlyformedclusterswillndthemselvesin atenuousbalance,being verysusceptibletothesurroundingprocesses,andgeneral lyendupdispersing.Ithas beenestimated( LadaandLada2003 )thatonly4-7%ofECssurvive(remainbound)their emergencefromthemolecularcloud.Whethertheclustersur vivesthisphaseasabound entityornotcan,toalargeextent,beinferredbyevaluatin gtheeciencywithwhich moleculargasisconvertedintostars. Embeddedclustersaresurroundedbymolecularmaterialtha thasnotbeenconverted intostars,materialwhichisactuallyprovidingmuchofthe system'sbindingenergy.The dispersalofthismaterialismainlyfueledbythepresenceo fstellarwindsandoutrows originatingfrommassivestars,aprocesswhichoccursonat imescaleof10 6 yr.Weighing therateatwhichgasremovaloccursagainstthestarformati oneciency,SFE,(the fractionofgasthathasbeenconvertedintostars, SFE = M stars = ( M gas + M stars ))cantell uswhethertheclusterwillornotremainbound(seeLL03). 1.4ScopeofthisWorkandOurGoals Starformationtakesplaceinmanydierentenvironments,u ndermanydierent initialconditions,andundertheinruenceofmanydierent processes;allofthesefactors inevitablyhaveimportantrolesindeterminingthecluster thatisformed.Thecluster isaproductoftheconditionsitissubjectto,anditisonlyl ogicaltoassumethatthe youngeststellarclusters,theembeddedclusters,stillpr eservestrongconnectionsto thoseconditionsandcarrytheirsignatureinthedistribut ionoftheirproperties.As such,measurementsoftheclustersize(radius),thenumber ofmembers,thestructure, thedistributionofstellarmasses,andotherproperties,c anbeusedtofurtherour understandingoftheconnectionbetweentheclusterandthe conditionsthatgaverise toit.Asystematicandunbiasedmeasurementoftheseproper tieshasbeenlacking,and thisworksetsouttollthatgap. Welisthereourmaingoals: 32

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1.Todevelopaautomated(orsemi-automated)methodtosear chfor,identify,and analyzeyoungclusters; 2.Tomeasurethephysicalproperties(suchassize,mass,de nsity,evolutionarystate, andstructure)andtocharacterizethespatialstructureof ECsinastatistically completesampleofyoungclusters; 3.Toinvestigatetherelationsbetweenthesepropertiesan dhowtheserelationships varywithclusterevolution; 4.Toinvestigatewhichstarformationtheoriesareinalign mentwithourresultsin ordertoseeiftheseresultssupportadominantmechanismof clusterformation(e.g. turbulenceorgravitationcollapse); 1.5OutlineofDissertation Wehaveorganizedthedissertationasfollows:InChapter 2 wedescribesomeofthemethodswhichhavebeenusedfordetec ting andstudyingthepropertiesofclustersandwediscussadvan tagesanddisadvantagesof eachwithregardstoourobjectives.Wethengointomoredept hdescribingthemethod mostadequateforourobjectives.Chapter 3 thenpresentsadescriptionofthecluster simulationswhichweredevelopedandperformedtotestthis method.InChapter 4 we presentourclustercataloguponwhichthemethodsofdetect ingandanalyzingclusters wereused,andwethenpresenttheresultsofthatstudy.InCh apter 5 weintroducethe FLAMINGOSnear-infraredsurveyofmolecularcloudsandpre senttheresultsofusing themethodoutlinedinChapter 2 todetectandanalyzeclustersinthenearbymolecular cloud,theMonocerosOBAssociation(MonOB1);wealsocompa retheseresultstoour previousworkintheRosette.InChapter 6 wediscusswhatourresultscontributeto theunderstandingoftheNGC2264region,themostprominent star-formingregionin MonOB1.InChapter 7 wediscusstheimplicationsofourresultsoncurrenttheori esof clusteredstarformation,andnalizebypresentingfuture directionsofresearchwhich wouldcomplementourwork. 33

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CHAPTER2 DETECTION,ANALYSIS,ANDMODELINGOFCLUSTERS 2.1MethodsofClusterDetectionandAnalysis 2.1.1Introduction Avarietyofmethodshavebeenusedtosearchfor,identifyan dcharacterize embeddedclusters(ECs).Inthischapterwepresentsomeoft hemorecommonmethods usedinclustersearches,discusstheiradvantagesanddisa dvantageswithrespecttoour objectives,anddescribeindepththemethodweadoptedfort hisdissertation. Ourobjectivewastodevelopanautomatedclusterrecogniti onprogram(CRP) whichcouldbeappliedtobothsmall( < 10pc)andlarge( > 10-20pc)regionsofthe sky,unbiasedlyidentifyingyoungclusters;inaddition,w eneededthismethodtorequire minimaluserinterface,inordertobothreducetheintroduc tionofhumanbiasesandto makeitastime-ecientaspossible.Finally,whenapplying themethodtodistinctregions ofthesky,werequiredthatourmethodtreateachregioninal ikemanner,toallowfora reliablecomparisonofdata. WecancategorizethemainmethodsofsearchingforECs,from thelargesttothe morelocalized,asfollows:1)systematicsurveyscovering aGMC;2)systematicsurveys carriedoutinthevicinityofstarformingsignpostssuchas outrows,IRASsources,and HerbigAe/Bestars;and3)studiesofknownstarformingregi ons. Thesimplestsearchmethodsarebasedonevaluatingthestel larnumberdensity throughstarcounting;star-countmethodshavetheadvanta geofonlyrequiring single-lterobservations,signicantlyminimizingboth telescopeandanalysistime. Star-countmethodsworkbyevaluatingthesurfacenumberde nsityofstarsacrossaeld; potentialclustersareidentiedbythepresenceofanexces sinthestellarsurfacedensity withrespecttothesurroundingstellardensity.Historica lly,starcountmethodshavebeen usedforavarietyofobjectives,someofwhichhavebeen:the studyofgalacticstructure (lookingforstellarclusteringneartheNorthGalacticPol eby BahcallandSoneira ( 1981 )), 34

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identifyingandcharacterizingclusterpopulations(inth eOrionBcloudby Ladaetal. 1991b ),andcharacterizingclusterproperties( Gutermuthetal.2005 ).Infact,useof numberdensityforidentifyingthepresenceofclustersisc ommoninmostoftoday'smajor eldsofresearch.Forexample,inmathematicsthismethodi susedforndingclustersin numberseries,andinbiologyforstudyingthedistribution softrees,andanimals. 2.1.2ATypicalClusterField InFigures 2-1 2-2 ,and 2-3 ,weshow K s -lterimagesofclustereldsobservedwith the2-MicronAll-SkySurvey(2MASS)astypicalexamplesofc lusterelds.Ascanbe observedinthesegures,clustersvarygreatlyinsize,sha peandspatialnumberdensityof stars;infact,thenumberdensitycanvaryalotforthesamec lusteraswelookatdierent regions.Assuch,anotherimportantfeaturethatthismetho dmusthaveisthatitmust beversatileenoughinordertobeapplicabletoalargerange ofspatialdensities.With methodsthatonlyusethesurfacedensityofstars,theaccur acyofmeasuringthecluster propertiesisintimatelytiedtohowwellthismethodtraces thevariationsofthelocal density. 2.2MethodsforMappingSurfaceDensity 2.2.1NyquistBinning Possiblythesimplestandmoststraightforwardwayofmappi ngthelocalstellar densityisthatofbinning.Binningisperformedbysimplydi vidingtheeldintosquares, orbins,ofevenlengthl,andcalculatingthenumberdensity ,ofeachbinaccordingto Equation 2{1 whereNisthenumberofsourcesineachbin,andAisthebinare a.This processisschematicallyshowninFigure 2-4 = N A (2{1) Inthisway,thebinssamplethedensityoftheeldandaconto urmapcanbe constructed.Theaccuracywithwhichthedensityructuatio nsarereproducedbybinning isdirectlydependentupontheresolutionwithwhichtheyar esampled.Inthiscase,the 35

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Figure2-1.2MASS K s -bandimageofIC348,thecircleindicatesthe2MASScenterf or thiscluster.Imagefrom2MASSdata, Skrutskieetal. ( 2006 ). Figure2-2.2MASS K s -bandimageofTrapezium,thecircleindicatesthe2MASScen ter forthiscluster.Imagefrom2MASSdata, Skrutskieetal. ( 2006 ). 36

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Figure2-3.2MASS K s -bandimageofNGC1333,thecircleindicatesthe2MASScente r forthiscluster.Imagefrom2MASSdata, Skrutskieetal. ( 2006 ). A B Figure2-4.Exampleofbinning.PanelAshowsanexampleofas tareldwhilepanelBis ofaeldthathasbeenbinned. 37

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choiceofl,thebinlength,denestheresolutionelementof theresultantmap.Ifalarger valueof"l"weretobechosenthentheresolutionwouldbered uced;thiswouldmakethe mappinglesssensitivetosmallvariationsindensityand,t hus,coarser.Likewise,using asmallervalueoflwouldincreasetheresolution;therisko fhigherresolutionmapping isthatonecanoversamplethepopulation.Thesamplingbint hatneitherundersamples noroversamplestheeldistermedtheNyquistbin-sizeandc anbefoundbyfollowing theNyquist-Shannonsamplingtheorem(adescriptionofthi stheoremisbeyondthescope ofthisworkandweassurethereaderthatitinnowayhinderst heunderstandingofthe conceptsthatfollow). Figure3from Kumaretal.2004 showsanexampleinliteraturewherebinninghas beenusedtocreatecontourmapsofthestellarsurfacedensi ty. Therearetwodisadvantagesofthismethod: 1.Nyquistbinningrequirestheapriorichoiceoftheidealb insize.Theprocessof ndingthisidealbinsizewouldrequiretheeldtobeanalyz edwithdierentbin sizes;thisgoesagainstourgoalofcreatinganautomaticpr ocesswithminimaluser interface. 2.ThereisnosinglebinsizethatcanNyquistsamplethedie rentregionsofacluster eld.Eachclustereldfrequentlyhasaverylargerangeofd ensityvalues,often rangingmorethan3ordersofmagnitude.InFigure3from Kumaretal.2004 the largerresolutionelementserveswelltomeasurethedensit yructuationsofthe low-densityregionbutnotthestructureofthecluster. TheNyquistbinningmethodistermeda parametricmethod sinceitrequiresthe apriorichoiceofavalueforaparameter(thesamplinglengt h);thenexttwomethods discussedare non-parametric 2.2.2MinimumSpanningTree TheMinimumSpanningTree(MST)methodhasrecentlyseenasu rgeinits applicationtothestudyofembeddedclusters( SchmejaandKlessen2006 Gutermuthetal. 2008 ).Asiscommonwithseveralmethodsofstudyingdistributio ns,theMSThas itsoriginsingraphtheory,beinglateradaptedtostudyord eranddisorderamongst setsofparticlesinphysics( Dussertetal.1986 Dussert1988 ).Sincethenithasoften 38

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beenusedingalacticastronomytoanalyzelarge-scalestru ctures( Bhavsaretal.1996 ), forexampleamongstgalaxyclusters( Barrowetal.1985 KrzewinaandSaslaw1996 AdamiandMazure1999 ),andquasars( Grahametal.1995 ). Theminimumspanningtreeofagroupofpointsiscreatedbyjo iningallofthepoints inthegroupwhilefollowingtherulesthatthistreemustnot haveanyloops,eachpoint canonlybevisitedonce,andthetreemustbeofminimaltotal length(thusreferred toastheMinimumSpanningTree)withrespecttoallpossible trees.Theprocessof constructingtheMSTisshowninFigure2from Barrowetal. ( 1985 ),inpanel(a)the distributionofpointsisshown;in(b)thosepointsareallc onnected;andin(c)and(d) "noise"isremovedby,respectively,pruning,whichconsis tsofremoving"small"branches, andseparating,whichconsistsinremovingfromtheMSTalle dgeshavinglengthsgreater thanacertaincut-o.Therearenumeroustreesforagivendi stributionbut,fortheMST, thehistogramconstructedfromthelengthsofthesegmentsi sunique.Thishistogramis knownastherankhistogram(RH) Thedisadvantagesofthismethodare: 1.TheMSTmethoddoesnotprovideinformationabouttheloca ldensityofthe distribution,norofthesize(coreradius,totalradius,pe rimeter)ofthecluster. 2.Whenconsideringadistributionofpoints,eachofwhichi sassociatedwitha starinacluster,theneachpointinthesetisconsideredtob eaclustermember. However,inrealobservationstheeldiscomprisedofbothc lustermembersand alsocontaminationfromthebackgroundandforeground.The inruenceofthese extraneoussourceswillbemostpronouncedatthelevelofth enearestneighbour (formingclosebinarysystemsandclosetriplesystems)and becomelesssignicant onmoreglobalscales.TheMSTworksonthenearestneighbour levelsoitismost suitedfordistributionsinwhicheachpointisknowntobeam ember. 3.Thecutovaluesforthepruningandtheseparatingstilln eedtobechosenanditis unclearastowhetherthesewouldvaryforthedierentclust ereldsasthesurface densitiesvaried. 2.2.3Two-PointCorrelationFunction Anothercommonlyusedmethodofanalyzingspatialpointpat ternsisknownasthe two-pointcorrelationfunction.Thisfunctionhas,simila rlytotheMSTmethod,seen 39

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muchapplicationtogalacticastronomy( deLapparentandSlezak2007 )andalsotothe studyoflargescalestructure( Gandhietal.2006 )andyoungstars( Enochetal.2007 KrausandHillenbrand2008 ).Accordingto Peebles ( 1980 ),whenrstdescribingthe applicationofthisfunctiontodistributionsofgalaxies, thetwo-pointcorrelationfunction describestheprobabilitythatanothergalaxywillbefound withinagivendistance.As such,evaluatingthisfunctionacrosstheeldwillyieldav aluethatrepresentsthedensity oftwo-pointdistancesforagivensetofentities;thehighe rthisvalueis,foragiven distance,themorelumpyorclusteredisthedistributionat thatdistance.Usingthis methodtoevaluatethetwo-pointdistancesinaclusterofga laxiesresultsinafunction havingdistinctpeaksassociatedwiththeintra-clusteran dtheinter-clusterseparations ( Fatemi-Ghomietal.1999 ). Itisimportanttonotethat,tobeusedcorrectly,thisfunct ionmustbeevaluated ateachpointandthenaveragedoverallthepointsbecauseon apoint-to-pointbasisit ructuateswildly;furthermore,itisveryimportantthatal lsources,atwhichthefunction ismeasured,belongtothepopulationbeingevaluated. Theconsofthismethodare: 1.Itisveryimportantthateachsourceinthedistributionb eaphysicallysignicant memberoftheset,extraneoussourcestendtostronglyinrue ncethefunction;this mayposeaproblembecausewhenevaluatingthestructureofa stellarclusterwe mustexpectthepresenceofsourcecontamination. 2.Thetwo-pointcorrelationfunctionisnotunique,diere ntstellardistributionsmay leadtothesamefunction,andtheadditionalanalysisofthe spatialdistributionby eyeisessential,whichwewanttoavoid. 2.2.4NearestNeighbor Wewillnowdescribethenearestneighbormethod(NNM).Asth enamewould suggest,theNNMreliesuponmeasuringthedistancetoasour ce'snearestneighbor (NN)inordertoevaluatethelocalstellarnumberdensity.T hismethodwasrst developedthroughstudiesinwildlifeecology(specicall ypopulationecology)with theworksof Thompson ( 1956 )and Sinclair ( 1985 )asatoolforquantifyingclustering(or 40

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Figure2-5.FiguredemonstratingtheapplicationoftheNNM formeasuringthelocal stellardensity.Eachstarinsidethecircleisnumberedacc ordingtoitsdistance fromthecentralstar.Inthiscasewearemeasuringthedista ncetothestar's 5thNN. deviationsfromrandom)oftreesandnests.Ataboutthesame time,itwasrstapplied toastronomy( ClarkandEvans1954 ),butsubsequentapplicationsdidnotcloselyfollow. Themajorityofthegroundworkforitsapplicationtowardst hestudyofstellarclusters waslaidoutmuchlaterby CasertanoandHut ( 1985 )(CH85). AnimportantdierencebetweenbinningmethodsandtheNNMi sthattheNNM isnon-parametricsoitdoesnotrequiretheapriorichoiceo fabinsize,orasampling length.Instead,itusesthedistance, r j ,fromeachstartoitsj th NNinordertoestimate localstellardensity.Figure 2-5 showsthebasicconceptoftheNNM,particularly,howthe distancetoastar's j th NNisusedtoestimatethelocalstellardensity. Thevalueofjneedstobedenedinordertoapplythedensitye stimatoryet, importantly,itdoesnotxtheresolutionelementthrougho uttheeld.Thedistanceto the j th NNwillvarythroughouttheeld,beingcloserfordenserare asandmoredistant forsparserarea,sothesamplingresolutionwillalsovarya ccordingtothedensity.Thisis insomewayscomparabletohavinganon-xedNyquistbinsize samplingtheeld,and allowsforaccuratemeasurementsofthelocaldensity. Incomparisontothetwo-pointcorrelationfunctionandthe MSTmethod,theNNM isnotrestrictedtotheevaluationoftherstNN.Thisisimp ortantbecause,assuch,the 41

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NNMneednotbeassensitivetothepresenceofaeldofextran eoussourcesasarethose methods. Withtherisingimportanceofstudyingthestellarnumberde nsityofyoungclusters, theNNMhas,similarlytotheMSTmethod,seenanincreaseini tsuse( Gutermuthetal. 2008 Teixeiraetal.2006 Gutermuthetal.2005 )yetithasoftenbeenintheformofits rstNN.InouropinionusingtherstNNisamisuseofthemeth odinthatnotonlydoes itmissthemainstrengthsofthisapplicationbutwillincor rectlyestimatethevaluesof thelocaldensity.ThisisexplainedinCH85whereitisshown thatusingtherstNNas atracerofthelocaldensitywillrenderthemeasurementsve rysensitivetotheeld,thus leadingtoinaccurateestimates. WehaveoptedfortheuseoftheNNMforclusteridentication andanalysisandin thefollowingsectionswegointofurtherdetailontheuseof thismethod,includingthe importantchoiceofthej-value.2.2.4.1MeasuringClusterPropertieswiththeNNM Itthusfollowsthat,foraparticularchoiceofj,thedensit y, j ,isrelatedtothe distance, r j ,byEquation 2{2 where"m"istheaveragemassofthesources(sinceweare onlyinterestedinthenumberdensitywecanusem=1),and V ( r j )isthevolumeofa spherewhoseradiusequals r j .Equation 2{2 isequallyvalidifwesubstituteasurfacearea S ( r j )forthevolume,where S ( r j )= r 2 j = j 1 V ( r j ) m (2{2) Havingspeciedadensityestimator,wecanthendenethede nsity-weighted enhancementcenterbyEquation 2{3 andthedensity-weightedaveragedensityby Equation 2{4 .Intheseequations"i"istheindexidentifyingeachsource intheeld. x d;j = P i x i ( i ) j P i ( i ) j (2{3) 42

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d;j = P i ( ( i ) j ) 2 P i ( i ) j (2{4) Furthermore,the density-radius iscalculatedusingEquation 2{5 ;thisradiusisa density-weightedaverageofthedistancefromeachsourcet othedensitycenter.The density-radiusprovidesuswithameasureofthecoresizean dthuswewillfromhereon usethetermsdensity-radiusand coreradius interchangeably. r d;j = P i j x i x d;j j ( i ) j P i ( i ) j (2{5) 2.2.4.2ChoosingtheJ-Value Theconnectionbetweenthechosenj-valueandthesensitivi tytodensityructuations canbestatedasfollows:asmallj-valueincreasesthelocal ityofthedensitymeasurements atthesametimeasincreasingsensitivitytorandomdensity ructuations,whereasalargej valuewillreducethatsensitivityatthecostoflosingsome locality. Allpointdistributions,includingrandomlydistributedp oints,exhibitsomedegree ofclusteringduetostatisticalructuations.Thesestatis ticalructuationsarethesource ofmanyclustersconsistingofasmallnumber( < 5)ofsources,manyofwhicharenot physicallysignicant;asthenumberofmembersincreasess odoesthelikelihoodthat theclusteringisreal.CH85demonstratethatboththej=1an dj=2densityestimators areextremelysensitivetosuchlow-levelructuations,thu shinderingtheirvalueas reliabledensityestimators;infact,CH85goontoshowthat aj-valueofatleast6is recommended. Undertherightcircumstancesj-valueslowerthan6canbeus ed,asfoundinthe worksof BahcallandSoneira ( 1981 ), Nakajimaetal. ( 1998 ),and Larson ( 1995 ).The primarydistinguishingcircumstanceintheseworksisthat themethodwasappliedtoa veryselectsetofstars.Inboth BahcallandSoneira ( 1981 )and Nakajimaetal. ( 1998 )the setwasofpre-mainsequencestars;in Larson ( 1995 )theauthorsusedsolelyT-Tauristars. 43

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Alloftheauthorsconstrainedtheiroriginalsetofstarsto justtheirpopulationsofinterest andsearchedforbinarityandmultiplicity-smallgrouping sofstars-amongstthenew set.Suchconstraintsofthestudysamplelowertheprobabil ityofdetectingfakegroupings intwoways:1)allructuationsbecomephysicallysignican tand2)thecontamination frombackgroundsourcesisreduced.Forthosereasons,theu seofalowj-valueisviable forstudyingthestructureoftheseteventhoughitwillstil lprovideincorrectestimatesof theaveragedensity. Inthecaseofembeddedclusters,weare1)workingwithlarge numbers(N > 3000)of starsineacheldand2)identifyingclustersamidsteldsc ontainingbothbackgroundand clustersources.Forbothofthesereasonsweneededtochoos eaj-valuethattakesinto accountthepossiblepresenceoffalseECs. Inorderto:i)determineouridealj-value;ii)optimizemea surementsofcluster properties;andiii)developandreneamethodforquantify ingtheclusterstructurewe appliedourNNMtovarioussimulatedclusters.Usingcluste rsimulationsallowedusto comparetheinputvaluesofclusterparameterstooutputval uesprovidedbytheNNM, thustestingthelimitationsofourmethod.Wepresentthede velopmentandresultsof thosesimulationsinthenextchapter. 44

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CHAPTER3 MONTECARLOSIMULATIONSOFCLUSTERS 3.1MotivationforDevelopingClusterSimulations Thegroundworkformeasuringclusterdensitiesandsizesus ingtheNNMwas discussedbyCH85,howevernootherstudyexistswhichexhau stivelydiscussesthe applicationofaNNanalysistothestudyofstellarclusters .Assuch,wehavetestedthe capabilitiesandlimitationsofourNNMonsimulatedcontro lclusters,priortoapplying itonrealclusters.InthissectionIpresentthedevelopmen tandresultsofthecluster simulationswhichwereusedtotesttheNNM.Thesesimulatio nsrecreatedthewide varietyofscenarioswhichwetendtondinrealclustereld s.AMonteCarlo(MC) formulationwasusedtogeneratethesimulations. 3.2MonteCarloSimulations MonteCarlomethodsaresonamedfortheirsimilaritytobeha viorpatternsobserved incasinos,theyaremethodsthatrelyonrepeatedandrandom samplingsofpreviously chosendistributionsinordertosimulatephysicalandmath ematicalsystems.UsingaMC formulationpermitsustorunmultiplesimulationsofeachc lusterinordertoprovidea statisticallysignicantsamplingofthedistribution;in ourapplicationofthismethodwe ran20simulationsforeveryeld. Twoimportantdistributionscharacterizeeverystellarcl uster:1)thedistributionof luminosities(luminosityfunction(LF));and2)thecluste r'sradialdensitydistributionof sources.Bygeneratingandthensamplingthesetwodistribu tionswiththeMCmethodwe simulatedboththeeldandtheclusterpopulation;varying thedistributionsthemselves wegeneratedarangeofpropertiesoftenfoundinrealobserv ationsofstellarclusters.In total,662clustereldsweregenerated. 3.3FundamentalClusterParameters Thesimplestclustereldcanbeconstructedasatwocompone ntsystemcomprised of:1)thebackground/foregroundeldpopulation,distrib utedrandomlyandextending 45

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Figure3-1.SchematicrepresentationofsetupforMonteCar loSimulations.Acircular clusterisshown,embeddedinamuchlargersquareeld. overthewholeeld;and2)theclusterpopulation,locatedi nanareaofniteradius, havingfewertotalnumberofmembersthanthosepresentinth ewholeeldarea, andwhosemembersfollowaspeciedradialprole.Oursimul atedclusterswere predominantlycircularwhiletheeldwassquarewitheachs idebeingovertwicethe radiusoftheclusterinordertoavoidboundaryeects;elli pticalclusterswerealso simulatedbutwendthattheydonotchangeourresults.Ours etupisshowninFigure 3-1 andarowchartoftheMonteCarloprogramusedtogeneratesim ulatedclustersis showninFigure 3-2 3.3.1SyntheticLuminosityFunctions ThesyntheticLFsweremodeledupontheKLFoftheTrapeziumc luster,usingLF modelsby Muenchetal. ( 2003b );theTrapeziumclusterispartofalargerclusterknown astheOrionNebulaCluster(ONC)whosestarsare 1-3Myrinage( Hillenbrandetal. 2001 ).Beingverydenselypopulatedandnearby( d 350 500pc( Hillenbrand1997 ))has madethiscluster,arguably,themostextensivelystudieds tarformingregion,thusitsKLF hasbeenaccuratelydetermined.InFigure 3-3 weshowthesyntheticLFsforthecontrol eldandfortheclustersusedinoursimulations.3.3.2RadialDensityProles IthasbeenshownthatsurfacedensityprolesofECscanbet tedbya 1 r prole ( Muenchetal.2003b );inordertoinvestigatethedensitystructureofECs,wesi mulated 46

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Figure3-2.Flowchartshowingtheprocessofgeneratingbot htheclusterandeld populations."k"referstothek-bandmagnitudeattributed toasource."x,y" referstothepositionofthesourcebeinggenerated."N"ist henumberof pointsthatneedtobegenerated.Nisxedat6000fortheeld population. Index"i"referstothenumberofiterations.Whentheprogra misrstcalled thevalueof"i"issetat0.Once"i"reaches20thesimulation iscomplete. EachiterationproducesonegroupcontainingNsetsof(x,y, k).Attheendof eachsimulationwehave20suchgroupswhicharethenaverage dtoproduce onenalgroup. 47

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A B Figure3-3.SyntheticK-bandluminosityfunctionsforacon troleldandaclustereld. ThesyntheticK-bandluminosityfunctionsforthecontrol eldisshownin panelAandthatoftheclustereldinB.Theclustereldpeak s,andismore populatedthanthecontroleld,atsmaller(brighter)magn itudes.Weapply theseprolestothedatapointsbeinggeneratedinoursimul ations. clustershavingthreedensitystructures.Thesewere:(1)r at-proleclusters,havinga constantradialstellardensitydistribution;(2)cluster switha 1 r densityprole;and(3) clusterswitha 1 r 2 densityprole. InFigure 3-4 weshowfourdierentradialproles;thedistinctionbetwe enthefour prolesisbestseeninpanelBwhichhaslog-logaxes.Kingpr oleshavebeenshownto traceradialprolesofdynamicallystableclusters,sucha sglobularandopenclusters, wheretheinternalstructurehasreachedalevelofenergyeq uipartition( Bonattoetal. 2006 ).WedonotexpectyoungECstobedynamicallystableyetwead dtheKingprole, inthisgure,forcomparison;theproleswerethensampled bytheMonteCarlomethod togeneratetheclusters.Thesegeneratedclustershavethe ircenterscoincidentwiththe originofthex-yaxiswhichisalsothemidpointofthesimula tedeld;boththex-and y-axisbisectthegeneratedclustersandinFigure 3-5 weshowthenumberofsourcesat dierentpointsalongthex-axisforthethreemainproles( weexcludetheKingprole inthisanalysis).Eachpanelshowninthisgureisgenerate dfromonlyonerealization; 48

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A B Figure3-4.Radialprolessampledtocreatedistributions ofclustersources.PanelA showstheseprolesplottedonnormal-normalaxeswhereasB showsthese prolesonalog-logscale.Theseproleswerethensampledb yaMonteCarlo methodinordertocreatethedistributionsofclustersourc es. theclustershaveradiiequalto0.5unitsand1200members,t heyaresurroundedbya backgroundwhichissquareinshape,oflength2.5units,and containing6000members. Wecanrecreatethetwomostcommonlyobservedsituationsby varyingthenumber ofclustermembers(inagivenarea)andthedensityprole;t hosesituationsare:(1) clustershavingahighdensity-ratioand(2)clusterswitha lowdensity-ratio.Weusethe termdensity-ratiotorefertotheratioofaveragestellard ensityforclustersourcestothe averagestellardensityofeldsources,andwewillhereaft errefertothisparameteras. = < cluster > : < field > (3{1) 3.4ClusterIdentication Wewereparticularlyinterestedonidentifyingandanalyzi ngclustersthathadlow valuessincetheserevealedthemselvestobethehardesttoi dentifyandaccuratelymeasure theirproperties.Theserepresentthemostchallengingsit uationsfortheCRP.662cluster eldsweresimulated;clustersweresimulatedhavingbetwe en10and1200membersand radiibetween0.1unitsand0.5units,valuesfortheseclus tersrangedfrom1to60. 49

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Figure3-5.Distributionofsourcesforthesimulatedprol es.Fromlefttorightthe distributionscorrespondto 1 r 2 1 r ,andaratprole.Thedashedverticallines indicatetheboundariesofthesimulatedcluster.Eachpane lshowninthis gureisgeneratedfromonlyonerealization;thesecluster shaveradiiequalto 0.5unitsandnumberofsourcesequalto1200sources,thebac kground(eld) isasquareoflength2.5unitsandcontains6000sources. 3.4.1StudyingtheDistributionofNNSeparations Themainchallengeinusingthismethodresidedinclearlydi scerningbetween theeldandtheclusterpopulation;thisispossible(thoug hnotsimple)becauseeach populationpresentsadistinctdistributionofNNseparati ons.Wesawabovehowthe distributionofclusterstarswilldependupontheirdensit yproleanddensity-ratio;in addition,thedistributionofeldstarsalsohasitspartic ulardistribution;anidealeld populationofstarspresentsarandomspatialdistribution andithasbeendemonstrated ( Thompson1956 )thatthedistributionofj th NNseparationsforsuchapopulationfollows achi-squarefunctionhaving2jdegreesoffreedom. Whenaclusterispresent,andsuperimposedupontheeldpop ulation,thedeparture fromrandomnesscanbeclearlyidentiedinthedistributio nofNNseparationsby theappearanceofanoverpopulationlocatedatsmallsepara tions.Theintensityof thisoverpopulationisdirectlycorrelatedtothenumberof membersinthecluster;the separationcorrespondingtothepeakoftheoverpopulation iscorrelatedtothemean densityofclustermembers.Inthisway,studyingtheneares tneighbourdistributions allowedustoidentifythepresenceandpropertiesofcluste rsinaeld. 50

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Figure3-6.DistributionofNNseparationsforj=20,10,5,3 ,2.Thelowerleftandthe upperrightpanelsareforthesamej-value,j=5,butweuseas mallerbin sizefortheupperrightpanelinordertoclearlyshowthedis tribution.The twopeaksareseenforallj-valuesbutthedierenceinthepe akseparations decreases,makinglowerj-valuesmoresensitivetorandomd ensityructuations. 51

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Thedistinctionbetweentheclusterpopulationandthatoft heeldorbackground sourcescanbeseeninthedistributionofNNseparationsfor anychoiceofj-value;this weshowinFigure 3-6 wheretheNNdistributionofoneeldhasbeensampledusing dierentj-values.Whendecidinguponaj-value,itisimpor tanttounderstandthatlarger valueswillguardagainsttheinruenceofstatisticaldensi tyructuations.Figure 3-6 shows that,aswesampletheeldwithaprogressivelysmallerj-va luethetwopeaksinthe distributionmoveclosertogether;forthetopleftpanelth erstpeakislocatedat0.02 andthesecondpeakat 0 : 17whereasforthelowerrightpaneltherstpeakisat0.01 andthesecondat0.04.Randomlydistributedsourcesandste llareldsareexpectedto exhibitasmoothdensitymap,thisisobservedbutonlyonagl obalscale,onalocalscale thereareoftenlargeructuationsinthedensitycausedbycl osepairsandtriplets;these ructuationsareespeciallyevidentwhenweconsidersmalle rseparations,sotheywillbe rstmanifestinthedistributionsoflowj-values.Accordi ngtoCH85,6isthesmallest j-valueforwhichthelocaldensityestimatesareaccurate, notbeingsignicantlyaected bytheinevitablestatisticaldensityructuations;larger j-valuescanbeusedprovidedthey aresignicantlysmallerthanthetotalnumberofsourcesin thesample.Furthermore, wendthat,inordertoaccuratelytracetheboundaryofaclu ster,thej-valueshouldbe similartoorlessthanthenumberofclustermembers;ifthej -valueislargerthenitmay signicantlysmooththisboundaryyieldingininaccurates izemeasurements. Wetestedj-valuesonbothsimulatedandrealclustersinord ertodeterminethe optimalj-value;170clustersweresimulated,therealclus tersarelistedinthecluster catalogofChapter 4 .J-valuesof2,5,10,20,30,50,and100wereusedonsquaree lds withsidesmeasuring2.5unitsoccupiedbyclustershaving1 200,1000,800,600,400 and200members,aradiusof0.5units,6000eldsources,and forthethreeproles: Cte, 1 r and 1 r 2 .Weevaluatedeachj-valueby:1)makingdensitymapsofthe eldsand visuallycomparingthesemapstoseewhichinonesthecluste risbestseen;2)visually 52

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comparingthedistributionsofNNdistancestoseeforwhich j-valuesthecluster-peakis mostpronounced. Wendthattheverylow(2and5)j-valuesareunsuitablebeca usetheygenerate verypatchydensitymaps;thisistobeexpectedsincelowj-v aluesareoverlysensitive torandomdensityructuationsoccurringinthebackground. Wealsondthathigh j-values(50and100)areunsuitablebecausetheysignican tlysmooththedensitymap, thussmoothingtheclusteredges.Oftheremainingthreej-v alues,10,20and30,we chosej=20.J=30wasexcludedbecauseitplacedalowerlimit onthenumberofcluster membersof30,whichweconsideredtoohigh.J=10isbetterth anj=20inmeasuring thepropertiesofsmallclustersbutitismoresensitiveto" fake"clusters{clusters generatedthroughrandomdensityructuations{soweexclud ethisvalue(seeChapter C fordetailsonmeasuringclusterpropertieswithj=10).J=2 0makesusmostaccuratein detectingandmeasuringtheboundariesofclustershaving N 20whileavoidingrandom ructuationsofthedensity;inordertotracethedensityruc tuationsintheinteriorofthe clusterswithincreasedaccuracyweusedalowerj-valueof6 ApplyingaNNanalysistotheprolesshowninFigure 3-5 wendthateachprole resultsinadistinctdistributionof20thNNseparations;t heseareshowninFigure 3-7 .Thedistributionsare,fromlefttoright, 1 r 2 1 r ,andrat.Theseguresshowthat steeperproles(thoseontheleft)willresultinalargerra ngeofseparationsandawide distribution,whereasratterproleswillhaveasmallerra ngeofseparationsandanarrow, peaked,distribution;furthermore, 1 r 2 prolestendtopeakatsmallerseparationsthan 1 r or ratproles.Whileasteepdensityprolemayhaveamuchhigh ercentraldensitythana ratprole,italsohasalowerdensityattheclusterboundar ies.Therangeofseparations andthepeaksinFigure 3-4 rerecttherangeandpeakofthedensitiesseenintheproles ofFigure 3-7 InFigure 3-8 weshowthesurfacedensitycontourplotsandthedistributi onsof20 th NNdistancesfortwosimulatedclusterelds.Thelargerpea kofeachdistributionis 53

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Figure3-7.NNseparationsforthesimulatedproles.Froml efttorightthedistributions correspondto 1 r 2 1 r ,andaratprole.Weobservethatthedierentproles resultindistinctdistributionsof20thNNseparations.Th iswillbecome moreimportant,particularlywhenweconsidertheclusterb lendingintothe distributionoftheeldandthedeterminationofthecluste rboundary.Steeper proles,suchas 1 r 2 ,resultindistributionswithlargerrangesofseparations and arethusmorepronetoblending. generatedbythesparserbutmorepopulouso-eldpopulati on,whichiscomprisedof starsthatdonotbelongtothecluster;thesmallerpeaks,lo catedatcloserseparations,are generatedbytheclusterpopulations.Bothdistributionsa reforclusterswitha 1 r 2 prole, dieringonlyintheirvalueofthedensity-ratio.Thepanel ontheupperleftcorresponds toaeldcontainingahighcluster,itsmean20thNN-densit ybeing60timesgreater thanthatoftheeldpopulation;thepanelontheupperright containsalowcluster, whosemeandensityis7timeslargerthanthatoftheeld.The separationvaluewhich bestdiscernstheclusterpopulationfromtheeldpopulati onisdenedasthe"cuto value";thecutovalueisanindicatorofwheretheclustera ndeldpopulationsbegin toblendtogether.Usingthiscuto,sourceswhose20 th NNseparationissmallerthan thecutoareconsideredpossibleclustermemberswhereast hosewithlargerseparations areconsideredbelongingtotheeld.Throughtheuseofours imulationswerecreated approximately60clustersrepresentingawiderangeofscen ariosandmeasuredthecuto separationforeach;wendthatthevalueofthecutosepara tionisdependentuponboth andtheclusterprole. 54

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Figure3-8.Typicalsourceseparationsandcontourplots.T hetwohistogramsshowNN distributionsfortwotypicalcasesofsourceseparationsf oundinourstudies. Thedashedlineisseparatedfromtheo-eldpeakby1 : 5 ( field ).The upperleftandbottomleftplotsarerepresentativeofaeld containing astronglypopulatedclusterfollowinga 1 r 2 prole;thereisasignicant overdensity,peakingat0.02unitsofseparation,makingth ecluster distributioneasilyidentiable.Theupperrightandbotto mrightplots representafaintcluster,alsowitha 1 r 2 prole;theclusterboundaryhas signicantlylostitscircularityastheclusterpopulatio nstronglyblendswith theeldpopulation.Theextraneoussmallercontoursareno trealclusters, theyarerandomructuationsintheeldhavingdensitiesequ alto,orabove, thechosencutovalue. 55

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3.4.2ChoosingtheOptimalCutoValue ThelargevarietyofNNdistributionswhichwendinourclus tersimulationsandin realclustereldsmadedetermininganoptimalcutovalueo neofourmainchallenges. Theoptimalcutoisonewhich,whenappliedtothesimulated clusters,minimizesthe errorinmeasuringthesizeandthenumberofclustermembers .Despitetheircomplexity, twomainfeaturesstandoutineverydistribution:1)thepea koftheNNdistributionof separationsfortheeldsources;and2)thetroughcreatedb ytheclusterandeldpeaks. Weusedthesefeaturesaspointsofreferenceforchoosingth ecutovalue.Whenusing thepeakwechoseacutovaluewhichwasseparatedfromthepe akby1 : 5 ( field ), towardssmallerseparations,where ( field )isthestandarddeviationoftheelddensity. Wearrivedatthechoiceof1 : 5 ( field )bytheprocessoftestingdierentvalueson approximately80simulatedclusters,comparingtheinputp arameterstothemeasured parameters.Theclusterswereagainsimulatedinasquaree ldofsidesmeasuring2.5 units,witheither1000or6000eldstars,1200,1000,800,6 00,400,200,50,40,30,and 20members,radiiof0.1,0.2,0.3,and0.5units,thethreepr oles:Cte, 1 r and 1 r 2 andof valuesbetweenalowof1:1andahighof1:61.Clusterswithfe werthan20memberscould notbedetectedusingthej=20value.Usingthepeakvalueand using1 : 0 ( field ) providedsizemeasurementsconsistentlylargerthanthein puttedvalues,whereasusing 2 : 0 ( field )oftenprovidedtoosmallasize. InTables 3-1 3-2 3-3 and C-3 weshowtheresultsofmeasuring56simulatedclusters withbothfeatures.Thevaluesinparenthesiswereobtained usingthetrough,whilethe "-"symbolispresentwhennodatawasavailableeitherbecau setheclusterwastoofaint tobedetectedorthetroughwasnotdiscernible;theotherva luesareobtainedwiththe peak-1 : 5 ( field ). Theresultsintable C-3 showusthat: 1.Forlowdensityratios(casesofmoreblending),usingthe peakofthebackground distributionisbetterthanusingthetrough.Infact,atrou ghisoftennotidentiable duetotheblendingand,whenitis,itsuseresultsinlargere rrors. 56

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Table3-1.Simulatingclusterswithradius=0.1units N clus B : C Prole R err N err %% 201:9 1 r 2 200(40)32(9) 301:14 1 r 2 230(70)40(3) 401:23 1 r 2 260(60)13(0) 501:30 1 r 2 270(90)12(2) 201:9 1 r 220(70)36(5) 301:13 1 r 220(70)3(0) 401:27 1 r 250(90)8(8) 501:37 1 r 230(100)14(6) 201:7Cte220(50)14(0)301:15Cte270(50)20(3)401:23Cte240(70)20(3)501:26Cte230(50)14(0) Fieldhas1000membersN clus isthenumberofclustermembers B istheaveragebackgrounddensity C istheaverageclusterdensity R err istheerrorinmeasuringtheradius N err istheerrorinmeasuringthenumberofmembers Cutovaluewas d field 1 : 5 ( field )forallexcept thoseinparenthesisforwhichweusedthetrough 57

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Table3-2.Simulatingclusterswithradius=0.2units N clus B : C Prole R err N err %% 201:3 1 r 2 50(10)23(18) 301:4 1 r 2 75(30)37(23) 401:5 1 r 2 90(55)38(23) 501:6 1 r 2 100(35)22(12) 201:2 1 r 55(10)41(23) 301:3 1 r 55(0)0(13) 401:5 1 r 85(35)10(10) 501:7 1 r 100(35)16(8) 201:2Cte70(20)45(23)301:3Cte75(35)33(13)401:6Cte115(45)43(13)501:8Cte100(40)14(10) Fieldhas1000membersN clus isthenumberofclustermembers B istheaveragebackgrounddensity C istheaverageclusterdensity R err istheerrorinmeasuringtheradius N err istheerrorinmeasuringthenumberofmembers Cutovaluewas d field 1 : 5 ( field )forallexcept thoseinparenthesisforwhichweusedthetrough 58

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Table3-3.Simulatingclusterswithradius=0.3units N clus B : C Prole R err N err %% 20NoDetection--301:2 1 r 2 17(13)23(0) 401:3 1 r 2 40(7)30(15) 501:4 1 r 2 40(7)12(4) 201:1 1 r 33(-)64(-) 301:1 1 r 23(-)27(-) 401:2 1 r 33(20)38(30) 501:3 1 r 47(17)24(14) 20NoDetection--301:2Cte0(-)17(-)401:2Cte40(3)20(8)501:3Cte47(10)18(8) Fieldhas1000membersN clus isthenumberofclustermembers B istheaveragebackgrounddensity C istheaverageclusterdensity R err istheerrorinmeasuringtheradius N err istheerrorinmeasuringthenumberofmembers Cutovaluewas d field 1 : 5 ( field )forallexcept thoseinparenthesisforwhichweusedthetrough 59

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Table3-4.Simulatingclusterswithradius=0.5units N clus B : C Prole R err N err %% 2001:3 1 r 2 42(-)22(-) 4001:7 1 r 2 20(-)0(-) 6001:20 1 r 2 26(-)8(-) 8001:25 1 r 2 10(13)1(2) 10001:40 1 r 2 8(8)0(0) 12001:61 1 r 2 4(6)0(1) 2001:1 1 r 36(-)2(-) 4001:6 1 r 6(-)0(-) 6001:7 1 r 2(10)2(5) 8001:11 1 r 2(4)3(2) 10001:14 1 r 8(0)6(4) 12001:16 1 r 10(2)2(0) 25001:40 1 r 16(6)2(0) 2001:1rat14(-)10(-)4001:2rat2(-)5(-)6001:3rat8(0)7(6)8001:4rat14(6)5(5) 10001:5rat16(6)3(2)12001:6rat16(8)4(3)25001:13rat20(8)2(2) N clus isthenumberofclustermembers B istheaveragebackgrounddensity C istheaverageclusterdensity R err istheerrorinmeasuringtheradius N err istheerrorinmeasuringthenumberofmembers Cutovaluewas d field 1 : 5 ( field )forallexcept thoseinparenthesisforwhichweusedthetrough 60

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2.Forhighdensityratios(littleblending),usingthetrou ghasdeningfeatureresults insmallererrors. 3.Errorsinestimatingthenumberofmembersareconsistent lysmallerthanthose incurredwhenestimatingtheclusterradius. 4.Fortheverylowdensityratiostheerrorsareverylarge(u pto42%for 1 r 2 proles). 5.Forclusterswithverysmallradii(aradiusof0.1unitsco rrespondsto 1 25 ofthe eldsize)wemeasureerrorsinsizeandnumberofmembersupt o270%and40% respectively.Theseerrorsaregreatlyreduced,to100%and 9%,respectively,by usingthetroughasthecuto. Assuch,forminimalblending(highdensityratios)theopti malcutovalueis locatedatthetroughformedbythedistributionofclusterm emberseparationsandthe distributionoftheeld.Whenblendingissignicanttheop timalcutovalueisbest chosenby d field 1 : 5 ( field ),where d field istheseparationcorrespondingtothepeak oftheeldpopulation.Exceptwhenworkingintheregimeofl owdensityratiosandsmall radii,theseguidelinesallowustoreproducethesizeandnu mberofmemberswithless than10%error. 3.5SimulationsofInternalDensityStructure 3.5.1SimulationsofClusterHalos Oneelementofclusterstructurearoundwhichthereissomes peculationisthe presenceofhalos(see Verschuerenetal.1990a Muenchetal.2003b ,).Ahaloisastellar populationsurroundingtheclusterandexhibitingasurfac enumberdensitylowerthan thatofthecluster.Thestarswhichpopulatethehaloaretho ughttobelinkedtothose oftheclustereitherthroughevolution,possiblybeingano lderpopulation,throughmass segregation,orpossiblybeingpartofadistributedmodeof starformation. Wesimulatedahaloasacircularregionwitharadiuseithere qualtoorlargerthan thatofthecluster,havingasimilarLFtotheclusterpopula tion,anddistributedwitha constantdensityprole;assuch,intermsoftheirdensityp roles,thesesimulatedhalos areidenticaltoclusterssimulatedwithaconstantprole. Thehalowasgenerallytwice theradiusandofloweraveragedensitythanthecluster;weg eneratedcluster-to-halo 61

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Figure3-9.Schematicrepresentationofasimulatedeldin cludingahalo.Thehaloisa homogeneouslypopulatedcirclehavingadensitygreaterth anthebackground butsmallerthantheclustercomponent. averagedensityratiosfrom1:4to24:1.Morerigoroussimul ationsshouldtakeintoaccount distinctionsintheLFswhichhavebeenobservedbetweenthe centralclusterpopulation andthehalopopulation(see Muenchetal.2003b );inthiswork,however,wewere interestedinapreliminaryanalysisofhowahalocomponent wouldaltertheobservedNN distributionofseparations.Inordertostudytheinruence ofaddingahalocomponentwe simulated116eldsinwhichclustershadhalos. InFigure 3-10 weshowhowtheadditionofahaloaectsthedistributionofs ources forourthreesimulatedproles;thisgurecanbecomparedt oFigure 3-5 wherethe prolesareshownwithnohalo.Inordertostudytheinruence ofthehalouponclusters ofdierentradialproleswegenerated12simulationsfore achprole;ineachsimulation thenumberofclustermemberswasxedat1200andwevariedth ehalopopulationfrom 1200to200instepsof200aswellasvaryingthehaloradiusfr om0.5(theclusterradius) to1.0.Eachpanelshowninthisgureisgeneratedfromonlyo nerealization;these clustershaveradiiequalto0.5unitsandnumberofsourcese qualto1200sources,thehalo hasaradiusof1.0unitsand1200sources,thebackground(e ld)isasquareoflength2.5 unitsandcontains6000sources.Theverticaldashedlinesa gainindicatethesizeofthe 62

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Figure3-10.Distributionofsourcesforthesimulatedpro lesincludingahalo.From lefttorightthedistributionscorrespondto 1 r 2 1 r 2 ,andarat(Cte)prole. Thedashedverticallinesindicatetheboundariesofthesim ulatedcluster. Eachpanelshowninthisgureisgeneratedfromonlyonereal ization;these clustershaveradiiequalto0.5unitsandnumberofsourcese qualto1200 sources,thehalohasaradiusof1.0unitsand1200sources,t hebackground (eld)isasquareoflength2.5unitsandcontains6000sourc es. clustercomponent,verticaldottedlinesindicatethesize ofthehalopopulation,andthe horizontaldashedlineindicatesthemeanleveloftheeldp opulation. InFigures 3-11 3-12 ,and 3-13 wepresentarepresentativesampleoftheNN distributionsobtainedfromsimulationsinwhichahalopop ulationhasbeenincorporated. Thepanelsinthetoprowcontainthesmallestcluster-to-ha lodensityratio(4:1)whereas thepanelsinthebottomrowcontainthehighestdensityrati osimulated(24:1).In thesethreegures,thepanelsontheleftrepresentthedist ributionsofNNseparations onlyforthecluster-halosystem(i.e.excludingtheeldpo pulation),whereasthepanels ontherightshowthedistributionincludingtheeld.Inthi swaywecanseersthow thepresenceofthehalowillaecttheclustercomponentand thenhowwewouldsee thisdistributioninarealobservation.Thesimulationrep resentedintherstrowof eachgurecontainsahalowiththesamenumberofmembersast heclustercomponent buttwicetheradius,makingitonaverage4timeslessdense. Inthesecondrowthe cluster-to-haloaverage-densityratiois6:1,andintheth irdrowtheratiois24:1.These simulationsshowthatthepresenceofahalo,ifsignicant, willshowupasathirdpeak 63

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Figure3-11.NNseparationsofhalosimulationsfora 1 r 2 prole.Thethreepanelson theleftcolumnrepresentthedistributionsofNNseparatio nsforonlythe cluster-halosystem(i.e.excludingtheeldpopulation), whereasthepanels ontherightshowthedistributionincludingtheeld.Forth etwopanelsin therstrowthehalois4timeslessdensethanthecluster,fo rthetwopanels inthemiddlerowthehalois6timeslessdense,andinthethir drowitis 24timeslessdense.Thisallowsustoseehowahalowillaect thecluster componentand,subsequently,aecttheoverallNNdistribu tion. 64

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Figure3-12.NNseparationsofhalosimulationsfora 1 r prole.Thethreepanelson theleftcolumnrepresentthedistributionsofNNseparatio nsforonlythe cluster-halosystem(i.e.excludingtheeldpopulation), whereasthepanels ontherightshowthedistributionincludingtheeld.Forth etwopanelsin therstrowthehalois4timeslessdensethanthecluster,fo rthetwopanels inthemiddlerowthehalois6timeslessdense,andinthethir drowitis 24timeslessdense.Thisallowsustoseehowahalowillaect thecluster componentand,subsequently,aecttheoverallNNdistribu tion. 65

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Figure3-13.NNseparationsofhalosimulationsforaCtepro le.Thethreepanelson theleftcolumnrepresentthedistributionsofNNseparatio nsforonlythe cluster-halosystem(i.e.excludingtheeldpopulation), whereasthepanels ontherightshowthedistributionincludingtheeld.Forth etwopanelsin therstrowthehalois4timeslessdensethanthecluster,fo rthetwopanels inthemiddlerowthehalois6timeslessdense,andinthethir drowitis 24timeslessdense.Thisallowsustoseehowahalowillaect thecluster componentand,subsequently,aecttheoverallNNdistribu tion. 66

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locatedbetweentheeldandclusterpeaks.Asweconsidersp arserhalopopulationswe noticethatthehalo-peakwillmigratetowards,andeventua llymergewith,theeldpeak. Thepanelsinthethirdrowofeachgurecloselyresembletho seofFigure 3-7 ,asthey shouldsince,atthatpoint,thehalohasanegligiblecontri butionduetoitslownumberof contributingsources. Weaddanotewithregardstothechoiceofthecutovalue,for situationsshownby thepanelsinthethirdrowofeachgure(mostsparsehalo),t hereisnochangetohow wewouldchoosetheoptimalcutosincethepresenceofthetr oughisevident.Inthe othertwosituationsthereisnotroughandthedistribution ismorecomplicated;this, however,stilldoesnotchangehowtheoptimalcutoischose nbecause,inaccordance withtheguidelinesmentionedinSection 3.4.2 ,wethenusethepeakoftheeld.Tostudy thechoiceofthecutovalueinthecasewherenotroughisevi dent,wesimulated6elds foreachofthethreeradialproles;theseeldswereagains quaresofside2.5units,had 6000eldsources,containedaclusterofradius0.5unitsan dwith1200sources,anda haloof0.5unitswhosenumberofmemberswasreducedfrom120 0to200instepsof 200.Foreachofthese18eldswetestedthreecutovalues: d field 1 : 0 ( field ), d field 1 : 5 ( field ),and d field 2 : 0 ( field );theoptimalcutowastheonefor whichtheprogrambestreproducedtheinputvaluesoftheclu ster(i.e.clusterradiusand numberofmembers). Weshowhowthiscutovalueisrelatedtotheidenticationo fthecluster-halo systeminFigure 3-14 ;thesimulatedclusteriscentrallycondensed.Intheupper plotwe showthederiveddistributionofNNseparationsalongwitht hreevaluesofseparations (indicatedbytheverticallines);thedensitiescorrespon dingtotheseseparationsare thenshowninthelowerplot.Thedashedanddottedverticall inesfromtheupperplot correspond,respectively,tothedashedanddottedcontour linesinthelowerplot.We ndthatthepopulationsoftheclusterandhalocomponentsa retightlyintermixed,and itisdiculttoseparatethetwopopulationsusingaclearly identiablefeaturefromthe 67

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Figure3-14.Evaluatingthechoiceofthecutovalueforace ntrallycondensedcluster withahalo.Intheupperplotweshowthedistributionofdist ancesfora simulationwheretheclustercomponentis0.25unitsinradi us,andthehalo componentis0.5unitsinradius.Thedashedanddottedverti callinesinthe upperplotdesignatedistanceswhichcorrespondtothedens itiesshownby dashedanddottedcontourlinesinthelowerplot.Weusethis guretomore clearlydemonstratethatthestructureinthedistribution sofNNseparations rerectsthepresenceofdensitystructuressuchasahalo. NNdistancedistribution.Whatisnowidentiable,usingth epeakoftheeldpopulation asthedeningfeature,isthenewcluster-haloensemble,wh ichshowsupasone cluster Amoredetaileddiscussiononthisdensitystructurewillap pearinChapter 4 whenthe distributionsofNNseparationswillbemeasuredforacatal ogof43embeddedclusters. 3.5.2SimulationsofMultipleClusters Webynomeansintendedonexhaustivelysimulatingallpossi blestellarcongurations observableinclusterelds,therefore,weinitiatethisse ctionwithareminderofour objectives.AtthispointwehaveshownthattheNNMcanbeuse dtoidentifythe 68

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presenceofasimulatedclusterandindicatethepresenceof internaldensitystructure. Wearenowinterestedinusingsimulationstoevaluatewheth erwecan,withtheNNM, discernbetweenaclusterwhichexhibitsacomplexinternal densitystructureandacluster thatisactuallytwoveryproximalclusters.Wehavealready seenhowtheNNMwill observecomplexinternaldensitystructure(bysimulating halos)sonextwesimulatedtwo clustersandvariedtheseparationbetweentheircenters.W esimulatedapproximately50 elds,eachcontainingtwoclusters;wevariedtheproleof theclusters,simulatingclusters withthesameproleandclusterswithdierentproles,wev ariedthenumberofmembers intheclusters,andwevariedthedistancebetweentheclust ers,simulatingclustersfar apartenoughthattheirdensitycontoursdonotblendandsim ulatingclustersthatare veryclosetoeachother.24simulationsweremadeinwhichbo thclustershadthesame prole,8foreachofthethreeproles;eachclusterhadbetw een200and1000sourcesand aradiusof0.5units,theseparationoftheclusterswasbetw eenamaximumof1.6units andaminimumof0.5(asmeasuredfromcentertocenter)inasq uareeldof6000sources measuring2.5unitsinlength.Similarly,24simulationswe remadeinwhichtheclusters haddierentproles,8foreachofthethreeuniquecombinat ions( 1 r 2 and 1 r 1 r 2 andrat, and 1 r andrat).Arepresentativesampleofthesesimulationsissh owninFigures 3-15 through 3-20 Werstpresentresultsofsimulatingtwoclustershavingth esameprole;inFigures 3-15 and 3-16 bothclustershavethesamenumberofmembersanda 1 r 2 prole.The clustersareboth0.5unitsinradius,locatedwithinasquar eeldofsidesequalto2.5 unitsandcontaining6000eldstars,andaredistancedfrom eachotherby1.6units;we seenosignicantinteractionwhenobservingthesurfacede nsitycontourplotshowninthe bottomgure.Theverticaldashedlineintheupperplotindi catesthe d field 1 : 5 ( field ) value;thedarkercontourlineinthelowerplothasadensity correspondingtothatsame value. 69

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InFigure 3-16 webringtheclustersclosertogetheruntiltheircentersar eseparated bythedistanceoftheirradii(0.5units).Thedistribution ofNNseparationsshowsaslight dierencefromwhentheclustersweresignicantlyapart,w ithasecondmaximashowing upclosetotherst.Thesamecontourvalueisplottedandwen oticethatitencompasses bothclusters,creatingoneelongatedcontour;wealsonoti cethathigherdensitycontours canstillidentifytheclustercenters. Thesecondmaximathatisgeneratedbybringingthetwoclust ersclosertogether islocatedathigherseparationsthatwhatwouldbeexpected fromthepresenceofa halo,but,itcouldbeconfusedforahalo.However,plotting higherdensitycontourlevels revealsthepresenceoftwohighdensitypeakswhichallowsu stodistinguishbetweentwo veryproximalclustersoraclusterwithahalo. Inthenextexamplewesimulatetwoclusterseachwitha 1 r prole;theyboth havethesamenumberofmembersandradiiequalto0.5units.F igure 3-17 showsthe distributionofNNseparationsandthecontourplotforwhen theseclustersareseparated by1.6units;theNNdistributionshowstwomaxima,oneforth eclusterpopulationand onefortheeldpopulation,andthecontourplotdoesnotsho wanyinteractionbetween thetwoclusters. InFigure 3-18 thetwoclustershavebeenbroughtclosertogethersuchthat their centersareseparatedbyadistanceof0.5units;wenoticeth attheNNdistribution haschangedbutnotsignicantlyandthatthedarkcontouren compassesbothclusters (similarlytothepreviouscase).Wenotethatbygoingtohig herdensitycontourswe couldstillmakeoutthetwoindividualdensitypeaks,indic atingthepresenceoftwo clusters. Inthislastgurewesimulatethepresenceoftwoclustersha vingdierentdensity proles,onewitha 1 r 2 proleandtheothera 1 r prole.InFigure 3-19 theclustersare againseparatedbyasignicantdistancesuchthattheirpop ulationsdonotinteract;in theupperplotweseethedistributionofNNseparationsandw enoticethatitismadeup 70

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Figure3-15.Simulatingtwo 1 r 2 clusterssignicantlyseparated.Clusterradiiare0.5 units,theirseparationis1.6units.Theverticaldashedli neindicatesthe d field 1 : 5 ( field )value;thedarkercontourinthelowerplothasadensity correspondingtothatvalue. 71

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Figure3-16.Simulatingtwo 1 r 2 proleclustersneartoeachother.Theverticaldashedline indicatesthe d field 1 : 5 ( field )value;thedarkercontourinthelowerplot hasadensitycorrespondingtothatvalue.Bystudyingthedi stributionof NNseparationsinconjunctionwiththedensitycontourswec andistinguish betweenaclusterwithahaloandadoublecluster. 72

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Figure3-17.Simulatingtwo 1 r clusterssignicantlyseparated.Clusterradiiare0.5 units,theirseparationis1.6units.Theverticaldashedli neindicatesthe d field 1 : 5 ( field )value;thedarkercontourinthelowerplothasadensity correspondingtothatvalue. 73

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Figure3-18.Simulatingtwo 1 r proleclustersneartoeachother.Theverticaldashedline indicatesthe d field 1 : 5 ( field )value;thedarkercontourinthelowerplot hasadensitycorrespondingtothatvalue.Bystudyingthedi stributionof NNseparationsinconjunctionwiththedensitycontourswec andistinguish betweenaclusterwithahaloandadoublecluster. 74

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ofthesumofthethreepopulations(eld,cluster1,andclus ter2).Thecutodistanceis locatedat d field 1 : 5 ( field ).Asbefore,ifthecentersareseparatedfromeachother byadistancetwicetheradiusofthelargerclusterthenourm ethodwillidentifythemas individualentities,otherwisetheywillbeidentiedason edoublecluster.InFigure 3-20 wepresentthecasewheretheclustercentersarecloseenoug hformergingtooccur.The structureseeninthedistributionofNNseparationsissimi lartothatobtainedfroma clusterwithahalo,sowecannotdiscernbetweenahaloorthe inruenceofasecondary clusterbysolelyanalyzingtheNNdistribution.However,b yperformingananalysisofthe contourlevelscorrespondingtoregionsoftheNNdistribut ion(asshowninFigure 3-14 ), wendthatthedensitypeaksoftheindividualclustersares tillidentiable,asshownin thebottomrightcontourplotofFigure 3-20 Assuch,withthismethodwecanidentifyclusters,measuret heirproperties(size, numberofmembers)and,whensignicantinternaldensityst ructureispresent,distinguish betweenthepresenceofahalopopulationoranearbycluster 3.5.3AccountingfortheEectsofExtinction Realembeddedclustersaregenerallyfoundinregionsofele vatedextinction,soeects associatedwithextinctionneedtobeconsidered.Inthemol ecularcloudswhereour analysisofembeddedclustersisfocused,extinctionisdir ectlycorrelatedtotheregionsof highestmoleculargasdensity;aswasmentionedinChapter 1 ,thisgasisdistributedin anon-homogeneousmanner,oftendisplayingclumpy,patchy ,andlamentarystructures (see Alvesetal.2001 Lombardietal.2006 Lombardietal.2008 ).Evaluatingtheeects ofthislargevarietyofextinctionstructuresuponcluster simulationsiscomplex,andlies beyondthescopeofourwork.Instead,wefocusonanalyzingt hemoregeneraleectsof extinctionupontheidenticationofclustersthroughtheu seoftheNNMmethod. Wesimulatedtwosimplecasesofextinction:i)aclusterdee plyembeddedinasphere ofdarkmaterial,whichwassimulatedbythepresenceofcirc ularlysymmetricextinction, centeredontheclustercenter,havingitspeakvalueatthec enter,anddecreasingwith 75

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Figure3-19.Simulatingtwo,signicantlyseparated,die rentproleclusters.Clusterradii are0.5units,theirseparationis1.6units.Theverticalda shedlineindicates the d field 1 : 5 ( field )value;thedarkercontourinthelowerplothasa densitycorrespondingtothatvalue. 76

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Figure3-20.Simulatingtwoproximalclusterswithdieren tproles.Theverticallines correlatetothedensitiesshowninthebottomrightplot(th eclose-upimage ofthecluster).Thisgureshowsthatbystudyingthedistri butionofNN separationsinconjunctionwiththedensitycontourswecan distinguish betweenahaloandadoublecluster. 77

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r 2 ;andii)homogeneousextinctioncoveringthewholeregion. Foreachofthethreeradial densityproleswesimulatedaclusterofradius0.5inasqua reeldofsides2.5unitsin lengthandcontaining6000eldstars,andwevariedthenumb erofclustermembersfrom 1200to200instepsof200;wedidthisforextinctionvalueso f0,1,2,3,4and5.We simulatedatotalofapproximately120eldstounderstandt heeectsofextinctiononthe NNdistribution.Wendthatextinctioninruencesourobser vationsinthefollowingways: 1.Extinctionrstaectstheeldpopulation.Theeldpopu lationcontainsfainter sourcesthantheclusterpopulation(asshownbytheKLFsinF igure 3-3 ); thesesourceswillbethersttobecomeunobservableasexti nctionpushestheir magnitudesbeyondourcompletenesslimit.Thishastheeec tofmakingthecluster "standout"asthesurroundingeldpopulationbecomesspar ser; 2.Extinctioncausesunderestimationoftherealnumberofm embers; 3.Extinctionchangesthedistributionofseparations.The eectofsourcesfalling beyondthecompletenesslimitcausestheremainingsources tohavelargerNN separations.ThisisrerectedinthedistributionofNNsepa rationsby:1)awidening oftherangeofNNseparations;and2)ashiftingofthepeakst olargerseparations. Importantly,wendthatextinctioncannotaccountforthep resenceofasecondary peaksuchastheonesseenwhenweincludeahalocomponentorw hentwoclustersarein thesameeld.Innosimulatedscenariodidtheinruenceofex tinctiongeneratethesecond peak. Oftheeectsmentionedabove,theonewhichwehavenoticedt obethemost commonhasbeentheshiftingoftheeld-peak(thepeakcorre spondingtotheeld population)tolargerseparations;Figure 3-21 showsthiseect.Theplotswereobtained byapplyinganincreasingamountofuniformextinctiontoac lustereld. Inthechapterthatfollowswewillpresenttheresultsofapp lyingourNNMtoa catalogof43knownclusters.WeusetheNNMtoidentifythecl usters,measuretheir properties,andstudythepresenceofinternaldensitystru ctures. 78

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Figure3-21.Simulatingtheeectsofextinction.Theplots correspondtotheeects ofaddinganextinctionof0(upperleftpanel),2.5(upperri ghtpanel), 3.0(lowerleftpanel),and3.5mag(lowerrightpanel).Weno ticethat,as theextinctionbecomesmoresignicant,themaximaassocia tedwiththe eldpopulationdecreasesinintensityandshiftstotherig ht.Extinctionis spatiallyuniformfortheseplots. 79

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CHAPTER4 AUNIFORMSTUDYOFEMBEDDEDCLUSTERSWITHTHENNM InChapters 2 and 3 wedevelopedandtestedourautomatedmethodofcluster identicationandanalysis;inthepresentchapterwediscu sstheapplicationofourNNM toacatalogofnearbyembeddedclusters,andwepresentther esultsofthisstudy.This chapterbeginswithadescriptionoftheembeddedcluster(E C)catalogwhichservedas therepresentativesampleofyoungECs;wethendescribethe datawhichwasusedto analyzeeachcluster,followedbythepresentationanddisc ussionofourkeyresults. 4.1EmbeddedClusterCatalog ThreecriteriawereusedtoselectoursampleofECstobeincl udedinourcatalog: 1.Anembeddedclustermustbelocatedwithin < 1kpcoftheSun;thisisimportant fortworeasons:1)Theclusterpopulationwithin1kpchasbeenstudiedforse veraldecades,and thoughnotallclustersinthisdistancerangehavebeendete cted,itisbelievedthat ourpresentsampleconstitutesastatisticallycomplete,r epresentative,sampleofthe wholenearbyECpopulation;2)Photometricerrorsincreasewithincreasingmagnitudea ndsourcesgetfainter withtheirdistancefromtheobserver,theseerrorslimitth edepthandaccuracywith whichwecansampleacluster'spopulation.Byrestrictingo ursampletonearby clustersensuresusthatthepropertieswemeasureareaccur ate; 2.Asignicantnumberoftheseclustersmustbewell-studie d.Weimposethissothat weknowtheseareyoungECsandsothatwemaycompareourmeasu rementsto resultsfromotherstudies. 3.Theseclustersmustbeassociatedwithmoleculargasorwi thregionsofelevated extinction.Clustersolderthan5Myrsarerarelyassociate dwithmoleculargas ( Leisawitzetal.1989 )sothiscriteriaensuresthecluster'syouth. Usingtheembeddedclustercatalogsfromthethreewell-est ablishedreferences: LadaandLada ( 2003 ), Porrasetal. ( 2003 )(P03),and Bicaetal. ( 2003 ),weselectthose thatmeetourcriteria.Ourinitialcatalogconsistedof43c lustersandwepresentthesein table 4-1 80

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Table4-1.CatalogofClusterFields ClusterRADeclbDist Name(J2000)(Galactic)(pc) RhoOph16:27:01-24:36:41352:59:54.116:40:14.8139ChaI11:06:00-77:30:00297:11:58.4-15:49:03.2140MWC29718:27:39-03:49:5226:48:06.703:31:33.0250L122820:57:11+77:35:47111:40:11.720:13:13.3300SerpensSVS218:29:5601:14:4631:35:20.905:20:58.3300NGC133303:32:08+31:31:03158:44:27.0-19:57:31.6318IC34803:44:21+32:10:16160:26:51.8-17:49:32.3320NGC202405:41:42-00:53:46205:36:12.6-15:53:15.7400NGC206805:46:41+00:06:21205:17:41.0-14:19:01.2400NGC207105:47:10+00:19:19205:09:24.7-14:06:30.9400LKHalpha101*04:30:14+35:16:25165:21:19.9-09:00:25.1 450 NGC202305:41:44-02:14:31206:50:48.4-16:30:32.0480V380Ori05:36:28-06:44:46210:26:17.6-19:43:41.0480IRAS05401-100205:42:38-10:00:51214:16:11.0-19:47:02 .5480 IRAS243,24505:42:48-08:39:17212:59:17.3-19:09:34.84 80 L1641/KMS3505:37:54-06:57:00210:48:00.2-19:30:00.34 80 L1641/CKgroup05:40:47-08:06:15212:13:57.8-19:22:04. 4480 L1641N05:36:23-06:23:40210:05:39.2-19:35:22.7500L1641C05:38:46-07:01:40210:58:37.0-19:20:18.8500L1641S05:52:28-08:07:30213:35:11.6-16:46:27.2500Trap05:37:47-05:21:46209:17:02.7-18:48:53.6500S10620:27:25+37:21:4076:21:52.2-00:37:39.1600CB3405:47:01+21:00:25186:56:54.0-03:50:33.3600 81

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Table4-1.continued ClusterRADeclbDist Name(J2000)(Galactic)(pc) RCrA19:01:53-36:57:09359:55:56.4-17:50:58.6700L988e21:03:57+50:14:3890:31:16.002:15:48.0700CepA22:56:19+62:01:57109:52:25.302:06:55.1700IRAS08375-410908:39:21-41:19:53260:55:38.100:06:59. 4700 IRAS08404-403308:42:17-40:44:10260:47:43.400:55:06. 0700 IRAS08448-434308:46:35-43:54:30263:46:32.9-00:25:39 .8700 IRAS08470-424308:48:48-42:54:29263:15:02.200:30:50. 4700 IRAS08470-432108:48:48-43:32:29263:44:31.100:06:51. 8700 IRAS08476-430608:49:26-43:17:11263:37:01.000:21:52. 7700 IRAS08477-435908:49:33-44:10:45264:19:18.3-00:11:01 .6700 BBW192E08:53:09-42:13:03263:13:37.201:34:16.6700IRAS20050+272020:07:06+27:28:5965:46:48.6-02:36:32. 7725 HD21662922:53:15+62:08:45109:35:57.702:22:23.4725L121122:47:17+62:01:58108:55:27.002:35:09.3750VYMon06:31:07+10:26:05201:20:31.600:17:27.6800MonR206:07:46-06:22:59213:42:07.2-12:36:14.8800GGD12-1506:10:50-06:11:54213:52:48.6-11:50:22.5800NGC226406:41:03+09:53:07202:57:13.602:12:34.4800NGC2264South06:41:03+09:30:00203:17:48.402:02:01.18 00 AFGL49003:27:38+58:46:58141:59:56.301:49:07.4900 *LKHalpha101hasrecentlyhaditsdistancerevisedfrom800pcto450pc(see: Ladaetal.2009 ). 82

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4.1.1Usingthe2MASSSurvey ThispublicationmakesuseofdataproductsfromtheTwoMicr onAllSkySurvey, whichisajointprojectoftheUniversityofMassachusettsa ndtheInfraredProcessingand AnalysisCenter/CaliforniaInstituteofTechnology,fund edbytheNationalAeronautics andSpaceAdministrationandtheNationalScienceFoundati on. 2MASSprovidesuswithauniformdataset,allowingustomean ingfullycompare measurementsobtainedfordierentclusters;forthisreas onweuseddatafromthe2MASS survey.The2MASSsurveycompletedafullmappingoftheskyu singground-based near-infraredobservations.Thissurveywasanextensiono ftheTwoMicronSkySurvey ( NeugebauerandLeighton1969 )whichscanned70%oftheskyanddetected 5,700 celestialsourcesofinfraredradiation.The2MASSsurveyb eganitsobservationsin 1997andnishedmappingin2001;thenaldatareleasetookp laceinMarch2003. Twoteslescopeswerenecessaryforthecompleteground-bas edsurveyofthenightsky, onelocatedinthenorthernhemisphere,inMt.Hopkins,Ariz ona,andtheotherinthe southernhemisphere,inCerroTololo/CTIO,Chile.Thenal pointsourcecatalogcovers 99.998%oftheskyandcontainsaccuratepositionsandruxes for 300millionstarsand otherunresolvedobjects.2MASSobtaineduniformphotomet ricobservationsoftheentire skyinthreenear-infraredbands:J(1.25 ),H(1.65 )and K s (2.16 ).The2MASSsurvey wassponsoredbytheUniversityofMassachussetts,theInfr aredProcessingandAnalysis Center(IPAC),theNationalAeronauticsandSpaceAdminist ration(NASA),andthe NationalScienceFoundation(NSF).4.1.2ChoiceofFieldSizeandDataQuality Foreachclusterinthecatalog,weretrievedJ,H, K s measurementsforallsources locatedwithina2.5pcradiusofthepublishedclustercente r;dataretrievalfromthe 2MASSAll-SkyPointSourceCatalogwasperformedusingtheG ATORqueryservice. Knownyoungclusterstendtohavemeasuredsizessmallertha n1pcinlinearradius ( Bicaetal.2003LadaandLada2003 )sothe2.5pcradiuswasassumedtobesucient 83

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inordertosampleboththeclusterandthesurroundingeldp opulations.Thisextraction areawasappropriateforalltheeldswiththeexceptionoft heTrapeziumeld,forwhich weretrievedanappropriatelylarger2MASSareahavingarad iusof3.5pc. Foreachsourceidentiedinthe2MASSeldweretrieveditsr ightascension, declination,J-,H-,andK-bandmagnitudes,photometry-qu alityrag,andgalaxy-contamination rag.Weappliedaphotometry-qualityselectionofonlyacce ptingsourceswithphotometry ragsA,B,C,orD,andusedthe2MASSgalaxy-contaminationra gtominimize contaminationfromgalaxiesandotherextendedsources.Th efollowingdetailed descriptionsofeachragwasobtainedfromthe2MASSAll-Sky DataReleaseExplanatory Supplement:User'sGuide.A -detectionsinanybrightnessregimewherevalidmeasureme ntsweremade(read rag="1","2",or"3")withsignal-to-noiseratios jhk snr > 10andmeasurement uncertainties jhk cmsig < 0 : 10857; B -detectionsinanybrightnessregimewherevalidmeasureme ntsweremade(readrag= "1","2",or"3")with jhk snr > 7AND jhk cmsig < 0 : 15510; C -detectionsinanybrightnessregimewherevalidmeasureme ntsweremade(readrag= "1","2",or"3")with jhk snr > 5AND jhk cmsig < 0 : 21714; D -detectionsinanybrightnessregimewherevalidmeasureme ntsweremade(readrag= "1","2",or"3")withno jhk snr or jhk cmsig requirement; The2MASSmagnitudesforwhichtheJ,H, K s -bandsarecompleteto99%for countingsourcesare,respectively,15.8magnitudes,15.1 magnitudes,and14.3magnitudes. Thephotometryerrorsbecomesignicantformagnitudesgre aterthanthislimit..In ordertokeeptheseerrorstoaminimumwelimitedourdatatos ourcesfallingwithinthe completenesslimit. 4.2ResultsofApplyingtheNearestNeighborClusterDetect ionMethod Havingretrieveda2MASSdatatableforeachclustereldint heinitialcatalog,we thenappliedtheNNMtothesetables;next,wewillpresentth edetectionsoftheclusters. 84

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Figure4-1.Imageofatypical2MASSdataqueryoutput.Thisp articularquerywas forsourceslocatedwithina27arcminuteradiusoftheNGC13 33cluster. Wewantedtomaketheprogramasecientaspossiblesoitsinp utwasthe unalteredoutputofthequeryasshowninthisgure. 85

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4.2.1ClusterDetections Ofthe43mainclusterspresentinTable 4-1 ,3werenotdetectedbytheNNMdueto insucientdensityenhancementinthoseelds:RhoOph,MWC 297,andL1641S. Inadditiontothe"main"clusterswefoundatotalof28newcl usters.Newclusters werelocatedinthesameeldofviewasthemaincluster,soth eirprojectedseparations fromthemainclusterarenomorethan5pc,butitisuncertain iftheseareassociated withthemainclustersandthuswecannotbesureoftheirdist anceortheirage.Forthese newclustersweimposedadditionalcriteriatodeterminewh ethertheyshouldbeincluded inthecatalog.Weusethefractionofinfraredexcesssource s( IRx frac )andtheextinction ineachclusterasindicatorsofitsyouth;theassociationb etweenacluster'sageandits IRx frac hasbeenestablishedusingJHKLcolors( Haischetal.2001 ),revealingthatthese twopropertiesareinverselycorrelated.Usingthemainclu stersasareferencesample ofknownyoungclustersweimposeaminimum IRx frac of5%andaminimumV-band extinctionof2maguponthissampleofnewclusters. Weappliedonefurtherrestrictionwhichwasthatthemeasur edcoreradiusmust besmallerthanthetotalradius,inordertoremovedetectio nsofspuriousclusterswhich showupasextremelyextendedlow-densitycontourshavingn ocenterofdensity.Thislast restrictionalsoeliminatedthemainclusterBBW192E.This clusterisknowntobelocated inanebulahavingastrongspatialvariationofextinctiona ndapeakK-bandextinction ashighas14magnitudes( Burkertetal.2000 );thismayaccountforwhywecouldnot accuratelydetectitwith2MASS. Thenewclusterswhichsatisfyourcriteriaareassumedtobe atthesamedistance asthemaincluster;ournalcatalogthusconsistedof52clu sters,ofwhich13arenew detections.4.2.2DistributionsofClusterProperties Wederivedthefollowingpropertiesforeachclusterandpre sentthevaluesinTable 4-2 : 86

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1)equivalentradius, r e (seeSection 4.2.2.1 );2)density,orcore,radius, r c (see Section 4.2.2.2 );3)density-prole, (seeSection 4.2.2.3 ;4)circularityorisoperimetric quotient(IQ)(seeSection 4.2.2.4 ;5)numberofmembersandmasses(seeSection 4.2.2.5 ); 6)fractionofsourcesexhibitinginfraredexcess(seeSect ion 4.2.2.6 );and7)average extinction(seeSection 4.2.2.7 ).Inadditiontothesepropertieswealsoperformedan individualanalysisofeachcluster'sinteriordensitystr ucture,andwepresentthisanalysis forasampleofclusters(seeSection 4.3 ). Wewereinterestedinseeingifthepropertiesofthenewclus tersfollowedsimilar trendstothemainclusters,soinmostcasesweshowthedistr ibutionsofthemainclusters separatefromthatofthenewclusters.4.2.2.1EquivalentRadius Wedeneequivalentradiusasbeingtheradiusofacirclewho searea, A c ,is equivalenttothatboundbythecluster-deningcontour;th emathematicalexpression isshowninEquation 4{1 .WeshowthedistributionofequivalentradiiinFigure 4-2 wheretheplotontheleftisonlyforthemainclustersandthe oneontherightisforboth thenewclusters(dashedline)andthefullcatalog(solidli ne). r = r A c (4{1) Forthemainclusters,wendthattheequivalentradiusdist ributionextendsfrom 0.08pcto1.76pc;thereisonlyonecluster(Trapezium)with radiuslargerthan1.1pc soinFigure 4-2 weonlyshowthedistributiontoamaximumof1.2pc.Thedistr ibution presentsthreepeaks,locatedat0.4pc,0.6pc,and1.0pc;th emedianequivalentradiusis 0.61pcandtheaverageis0.66pc. Fornewclusters,thedistributionissimilarbutlessbroad ,extendingfrom0.1pcto 0.9pcandpresentingonlyonepeak,thispeakislocatedat0. 4pc,thesamevalueasthe rstpeakinthedistributionofmainclusters;themedianva lueis0.49pcandtheaverage radiusis0.48pc. Bicaetal. ( 2003 )alsostudiedthesizesofinfraredstarclustersand 87

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Figure4-2.Distributionsofequivalentradiiareshownfor dierentpopulations.Thepanel ontheleftisformainclustersonly,whereasthepanelonthe rightshowsthe combineddistribution(solidline)andthedistributionfo rnewclusters(dashed line).Thedistributionsforthemainandthenewpopulation sfollowsimilar trends. stellargroupsandndthatthelineardiameterstronglypea ksat1pc;thisisinagreement withourndingthatmostclustershavearadiuscloseto0.5p c. Bicaetal. ( 2003 )used largerbinsizesof0.4pcsoitisnotpossibletocompareour ndingsinmoredetail. 4.2.2.2CoreRadius Thedistributionofthecoreradiicoversarangefrom0.03pc to0.69pcandisshown inFigure 4-3 ,wheretheplotontheleftisforjustthemainclustersandth eoneonthe rightisforboththenewclusters(dashedline)andthefullc atalog(solidline). Amongstthemainclusterpopulationweobserveoneprominen tpeaklocatedat 0.1pc,andonesmallerpeaklocatedat0.5pc;thedistributi onrapidlydropsafterthe prominentpeakandreacheszeroat0.75pc.Themediandensit yradiusis0.23pcandthe averageis0.28pc. Thedistributionofthecoreradiiforthenewclustersfollo wsasimilartrendwith itsprominentpeaklocatedat0.2pcandthesecondarypeakat 0.5pc;themediancore radiusis0.25pc,andtheaverageis0.27pc. 88

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Figure4-3.Distributionofcoreradii.Thepanelontheleft isformainclusterswhereas thepanelontherightshowsthecombineddistribution(soli dline)andthe distributionfornewclusters(dashedline).Thedistribut ionsforthemainand thenewpopulationsfollowsimilartrends. 4.2.2.3Density-Proles Whileanalyzingtheradialdensityprolesofclustersitbe cameapparentthatall clusterscouldbeclassiedaseitherhavinga centrallycondensed (C-type)proleora rat (F-type)prole.Wequantifythedegreeofcentralcondensa tionbyevaluatingthe ratio, ,ofthecoreradiustotheequivalentradius,asperEquation 4{2 .Thecoreradius (denedinEquation 2{5 )isadensity-weightedradiussoitissensitivetotheshape ofthe cluster'sdensitydistributionand,particularly,tothei ntensityofthepeak;thuswend thatcomparingittothetotalradiusprovidesagoodmeasure ofhowcentrallycondensed theproleis. valuesrangefrom0to1withvaluescloserto0indicatingamo recentrally condensedproleandvaluescloserto1indicatingaratterp role. = r c r e : (4{2) Tobetterunderstandthisparameterwemeasuredthevalueof for144simulated clusters;36ofthesesimulationsdidnotincludeextinctio n(foreachofthethreeproles thenumberofmemberswasvariedfrom1200to100instepsof10 0)and108simulations includedextinction(foreachofthethreeprolesthenumbe rofmemberswasvaried 89

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Figure4-4.Distributionsofstructureparameter forthreedistinctproles.Thethree distributionsinthisgureshowushowtheparameter issensitivetothe radialdensityproleofthecluster.Theleftmostdistribu tionisforclusters havinga 1 r 2 prole,thisdistributionpeaksforverysmallvaluesof .The isolatedbincenteredat0.55isforaclusterwhoseaveraged ensityis7times fainterthantheaverageo-elddensity,thusitsdensitya ndequivalentradii havelargeerrors,leadingtoerrorsinevaluating .Themiddledistribution isfora 1 r prole,andtherightmostdistributionisforaconstantpro le;we noticethateachdistributionpeaksatdistinct -values. from1200to200instepsof200andtheextinctionwasvariedt o0,1,2,3,4,5.)Figure 4-4 showsthedistributionof forthethreedensityproles.Theleftmostpanelisfor a 1 r 2 prole,thereisastrongpeakata of0.1andmostoftheclustershave values between0.1and0.3;thereisoneisolateddetectionata of0.55whichisforanextremely low-densitycluster.Themiddlepanelisfora 1 r prole,andwenoticethatthepeaknow occursathighervalues(0.25)thanforthepreviouspanel;a gain,alldetectionsbutoneare locatedinawelldenedrangefrom0.15to0.35andthedetect ionat0.6isagainfroma verylow-densitycluster.Therightpanelisforaratprole ,whilethepeakisnowlocated atanevenhigher valueof0.55andhasanarrowerrangefrom0.55to0.65.Theis olated binobservedinthedistributionsfor 1 r 2 and 1 r prolescorrespondstoaclusterwhose averagedensityis7timesfainterthantheaverageo-eldd ensity,makingitsmeasured propertiesunreliable.Asisclearfromthesedistribution s,eachradialdensityprole generatesadistributionpeakingatadistinct value;thedistributionsofa 1 r 2 proleand a 1 r prolehaveoverlappingrangesof valuesbut,withtheexceptionofverylow-density clusters,theseareclearlyseparatefromtherangeobtaine dforratproles. 90

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Figure4-5.SameasFigure 4-4 butincludingextinction.Weusedthesameclustersas inFigure 4-4 andappliedextinctionvaluesvaryingfrom0to5magnitudes ; thereare36simulationsforeachprole.Extinctionismode ledascircularand centeredontheclusterpeak,decreasingwith r 2 Wealsoevaluated forclusterswithextinction;weshowthoseresultsinFigur e 4-5 Extinctionwassimulatedasdecreasingwith r 2 ,centeredontheclustercenterandvarying from0to5magnitudesinK-band(0to50magnitudesinV-band) ;theclusterradius was0.5unitsandthenumberofstarsineachclustervariedfr om1200to200.Wend thattheparameter stilldiscernsbetweencentrallycondensedandratcluster swhenwe includeextinction. Throughthesesimulations,weverifythat,forclusterswit hclearlydenedradial proles,theparameter providesuswithagoodmeasureofthecentralcondensationo fa cluster'sprole,andthatitallowsustodistinguishbetwe enratandcondensedclusters. InFigure 4-6 wecomparethedistributionof obtainedfromoursimulationstothat obtainedfromourclustercatalog.Thetoppanelisforthesi mulatedclusters;withthe exceptionofthetwoveryfaintsimulatedclusters,allvalu eslowerthan0.4weregenerated byclustershavingeithera 1 r 2 proleora 1 r prolewhereasvalueslargerthan0.4were fromclusterswithaconstantprole.Thetwolowerpanelssh owthedistributionof for theclustersinourcatalog;thedistributiononthelowerle ftisformainclusterswhereas onthelowerrightweshowthedistributionsforboththefull catalog(solidline)andthe newclusters(dashedline).Wenoticethatthe distributionsforourcatalog,forboth mainandnewclusters,exhibitthesamedouble-peakedstruc tureasthatpresentinthe simulatedclustersandthatbothdistributionsspanapprox imatelythesamerange.One 91

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Figure4-6.Distributionsofstructureparameter forbothsimulatedandrealclusters. Inthetoppanelsweshowthedistributionof forthesimulatedclusters;the leftpanelisfor36non-extinctedclusterswhereastherigh tpanelisforclusters includingextinctionandismadeupof106clusters.Valuesl owerthan 0.5 weregeneratedbyclustershavingeithera 1 r 2 proleora 1 r prolewhereas largervalueswerefromclusterswithaconstantprole.The lowergures showthedistributionof fortheclustersinourcatalog.Thedistribution onthelowerleftisformainclusterswhereasonthelowerrig htweshowthe distributionsforbothnewclusters(dashedline)andthefu llcatalog(solid line).Abinsizeof0.1wasusedtosampleallofthesedistrib utions. distinctionisthatthedistributionforourcatalogexhibi tsacontinuumofvaluesextending from0.74to0.1,whereasinthesimulatedclustersthereisa cleargapdiscerningbetween C-typeandF-typeclusters;thisisunderstandableinlight ofSection 3.5 ,wherewe demonstratedthatfactorssuchasextinction,halos,andap roximalclustercanaltera cluster'smeasureddensityproles.Assuch,weexpectreal clusterstodisplayalarger varietyofproles(translatedintoalargerrangeof values). Usingthesimulationsasareferencewedeneda valueof0.45asbeingthe boundarybetweenC-andF-typeclusters;thisvaluecorresp ondstotheapproximate locationofthetroughintheuppermostpanelsofFigure 4-6 .Usingthisclassicationwe 92

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Figure4-7.Contourplotsfortwoclusterswithdierentiso perimetricquotients.Thetop gureshowsthecontourplotfortheTrapeziumcluster,whic hhasanIQof 0.25.ThelowergureshowsthecontourplotfortheS106clus ter,whichhas anIQof0.87.S106isthecontourattheverycenteroftheeld ndthat64%ofthemainclustersand33%forthenewclustersa reclassiedasC-type; 54%oftheclustersinthecombinedcatalogareC-type.These resultsindicatethatthere isahigherfractionofrat-typedetectionsamongstthenewc lustersthanamongstthe mainclusters.4.2.2.4Circularity Wealsousedacluster'scircularityasanothermeasureofit sstructure;circularitywas evaluatedusingtheisoperimetricquotient,IQ,whichisam easureofhowmuchtheshape ofacontourdeviatesfromaperfectcircle. IQ =4 A=P 2 (4{3) IQisdenedastheratiooftheshape'sareatotheareaofacir clehavingthesame lengthperimeter;themathematicalexpressionforIQissho wninEquation 4{3 ,whereA istheareaoftheshapeandPisthelengthofitsperimeter.IQ canhavevaluesranging from0to1,withvaluescloserto1representingmorecircula rcontours(1beingreserved foracircle)andvaluescloserto0beinglesscircular(0res ervedforaninnitelylongand 93

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Figure4-8.Distributionofcircularity.Thetoppanelisth edistributionoffortheclusters inourcatalog,thebottom-leftpanelisforthesimulatedcl usterswithno extinctionincluded,andthebottom-rightpanelisforsimu latedclusterwith extinctionincluded.Thesimulatedclustersareallcircul arthusweexpect theirvaluestobecloseto1;thelargestdeviationsfrom1oc curforclusters havingalowdensity-ratio,forwhichblendingwiththeoeldismore signicant. narrowshape).TheclustersinourcataloghaveIQvaluesran gingfrom0.24to0.91,the medianIQvalueis0.57,andthereare8clusterswithanIQhig herthen0.8.InFigure 4-7 wecomparethestronglycircularS106cluster,whichhasanI Qvalueof0.87,withthe TrapeziumcontourwhichishighlyirregularandhasanIQofo nly0.25. Thecircularityparameterwasalsostudiedwiththeaidofcl ustersimulations;in Figure 4-8 weshowthedistributionofIQforourmainclustersandforas ampleof simulatedclusters.Thesesimulatedclusterswerecircula r,ofradius0.5units,andplaced amongstasquarebackgroundof2.5unitsinlengthandcontai ning6000eldstars;we simulatedeldswithoutextinction(36elds)andwithexti nction(106elds)andwe measuredhowwelltheIQparametercoulddetectthatthesecl usterswerecircular.36 94

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eldsweresimulatedwithoutextinction,12eldsforeachr adialdensityprolewith thenumberofclustermembersvaryingfrom1200to200,and10 6eldssimulatedwith extinction,extinctionvaluesfrom0to5magnitudeswereap plied.Aperfectlycircular clustershouldhaveanIQof1.0.However,wedonotidentifya nyclusterwiththatvalue; insteadwendthebulkoftheclustershavingIQsbetween0.6 and0.9withacouple ofclustersshowingIQsof0.3and0.5.Thelargesterrorsinm easuringIQoccurfor clustershavingalowdensity-ratio,which,weremindther eader,indicatesthepresence ofsubstantialblendingbetweentheclusterandtheeld.Th isinabilitytodetectthe clustersasbeingperfectlycircularistobeexpectedandsh owsthat,throughourmethod ofmappingthestellarnumberdensity,wecan,atbest,measu reanapproximationof thecluster'srealphysicalshape.Oncetheclusterisplace damidstaeldofstars,and excludingthepossibilityofidentifyingeveryindividual clustermember,itsshapebecomes impossibletoaccuratelytrace. TheaveragevalueofIQis0.62forC-typemainclustersand0. 47forF-typemain clusters.Amongstthenewclustersthesevaluesare,respec tively,0.65and0.44;this indicatesthatC-typeclustersarerounderthanF-typeclus ters;therecouldbeabias presenthereinthatweexpecttheboundariesofF-typeclust erstobemoreaectedthan C-typeclustersbyblendingwiththebackground.4.2.2.5NumberofMembers MembershipwasestimatedfromK-bandluminosityfunction( KLF)methods.With justtheK-bandmagnitudewecannotdistinguishbetweenaso urcethatisphysically associatedwiththeclusterandcontaminant(onethatissim plyintheline-of-sight); however,wecanusetheKLFtoobtainanestimateofthetotaln umberofcluster members.Thenumberofmembersisestimatedbyrstassuming thatthespatialnumber densityofcontaminantsintheclusteristhesameasthatmea suredinacontroleld. TherststeptothismethodisobtainingtheK-bandmagnitud eforallsourceslocated withinthedenedclusterboundaryandwithinthenearbycon troleld.Wenotethat 95

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Figure4-9.Numberofclustermembersclassiedinto3categ ories.Thegureontheleft showshowmanyclusterswerefoundineachofthosecategorie swhereasthe gureontherightshowshowmanystarsbelongtoclustersfal linginthose samecategories.Wend,inagreementwithliterature,that eventhoughlarge clusters( N> 100)arenotthemostabundantofthethreecategories,they contributesignicantlymoretothetotalstellarpopulati onthansmallclusters andstellargroupscombined. thecontroleldshouldbechosenfarenoughfromthecluster suchthattheyareinno wayassociated,butcloseenoughsuchitisrepresentativeo fthecontaminationseeninthe cluster.OnceasuitablecontroleldischosenthenitsKLFi sconstructedandscaledto theareaofthecluster.Finally,wemustconsidertheeects ofextinction;sincethecluster isgenerallyfoundinaregionofconsiderableextinctionan ycontaminantslocatedinthe clusterboundarywillhavefainterK-bandmagnitudesthani ftheywereobservedinthe controleld.Inordertoaccuratelyaccountforcontaminat ionthecontroleldKLFmust beshiftedtohighermagnitudes(extincted)bytheaveragee xtinctionfoundwithinthe clusterboundaries. Applyingthismethodforeachclustereldwendanaveragen umberofmembersof 132formainclusters,52fornewclusters,and111fortheful lcatalog.Amongstthemain clusters,theaveragenumberofmembersforthoseidentied asC-typeclustersis156, andforthoseidentiedasF-typethisis90;forthenewclust ersweobtain55members forC-typeand50forF-type.InFigure 4-9 weshowtwohistogramswhichhighlightthe distributionofclustermembersforourclusters.Wedivide ourclustersinto3categories 96

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accordingtotheirnumberofmembers,N;thesecategoriesar ethesameasthoseinP03. Thosecategoriesare:1)stellargroups(5 100).Theleftpanelshowshowmanyclustersarefoundineach ofthose3categories,andwecanseethatmostofourdetectio ns(25clusters)fallinthe categoryofsmallclusterswhereaslargeclustersandstell argroupshavesimilarnumberof detections(14and13respectively).Thepanelontherights howshowthetotalnumber ofstarsaredistributedacrossthosesamecategories,here wenoticethatthelargeclusters contributevastlymore(68%)tothetotalstellarpopulatio nthaneithersmallclusters (27%)orstellargroups(5%). Weexpecttobemostcompletefordetectionsofsmallandlarg eclustersandwe anticipatethatthetruenumberofstellargroupsisinfactl argerthanwhatwehave detected.Alargernumberofstellargroupswouldalterthed istributionintheleftpanel, increasingthenumberofclustersintherstbin,thoughthe rstbinoftherightpanel wouldalsoincreasethedistribution'soverallshapewould mostlikelyremainthesame, itwouldrequireaverylargenumberofnewstellargroupsino rdertocausesignicant changeintheappearance.P03ndsignicantlymorestellar groupsthanwedo(52%of theirregionsbelongtothe5
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Figure4-10.Figurecorrelatingacluster'smasstoitsnumb erofmembers.Themain clustersarerepresentedbystarswhereasthenewclustersa rerepresentedby squares;thesolidlinerepresentsa1:1relationship. IRx frac ),completenesslimits,anddistances.Themodelassumesth atallclusters followasimilarInitialMassFunction(IMF),thattheyfoll owtheevolutionarytracks of D'AntonaandMazzitelli ( 1994 ),and,asper LadaandLada ( 2003 ),thatameancluster ageof1-2Myrscanbeadopted;theTrapeziumcluster'sIMFis usedasreferencesince ithasbeenextensivelystudied.InFigure 4-10 weshowhow,byusingthesemodels,the massesarerelatedtothenumberofmembers,weseethattheco nversionfollowsalinear relationshipwithaslopeclosetounity. Inthesamewaythatastar'sevolutionandfatearedetermine dbyitsmassupon reachingthemainsequence,soacluster'sevolutionandfat earegreatlydeterminedby thedistributionofmassesspannedbyitsstellarmembers;t hisdistributionisknownas theinitialmassfunction(IMF).Theemergingparadigmhase mbeddedclustersasthe fundamentalunitsofstarformation,andthesearetiedtoth emassivemolecularcoresin theGMC.Tostudytheseweconstructtheembeddedclustermas sdistributionfunction (ECMDF)whichistheanalogueoftheIMFbutforclusters.The ECMDFisdenedby LL03as M ec dN dlog TheECMDFisofparticularimportancebecauseitallowsusto identifywhether thereisaspecicmass-rangeofclustersresponsibleforth ebulkofthestar-formation. TheworkofLL03pointstotwomainfeaturesintheECMDF:1)th eexistenceofasharp 98

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Figure4-11.ECMDFfortheclustercatalog.Thedistributio nintheleftpanelshows theembeddedclustermassdistributionfunction(ECMDF)fo rallclusters inmyclustercatalog.Thissamedistributionisshowninthe rightpanel bythedashedline,thesolidlineistheECMDFobtainedbyLL0 3;LL03 truncatedtheirECMDFat35sources.Wendgoodagreementbe tweenthe twodistributionsandwenotethattheabsenceofabinatlog( Mass)=3is solelybecausewemeasuredalowermassforTrapeziumthandi dLL03. dropolocatedatapproximately20-50 M ,indicatingthatsmallerclusterscontribute lesstothetotalstellarcontent;and2)thefactthattheECM DFisratformassesranging fromintermediate(50 M )tohighmasses(1000 M ),indicatingthat,eventhoughvery populousclustersarerare,theircontributiontothetotal stellarmassissignicant. IntheleftpanelofFigure 4-11 weshowtheECMDFforournalcatalogandinthe rightpanelwecompareourfunctiontothatofLL03,thetwodi stributionscorrelatewell. WenotethatLL03imposedaminimumnumberofclustermembers of35whichexplains whytheirECMDFistruncatedforlowermasses;wealsolackth ebinathighmasses, thisbinisduetooneclusteronlywhichistheTrapeziumclus ter,forwhichwemeasurea slightlylowermassthanLL03.4.2.2.6FractionofInfraredExcessSources J-,H-,and K s -bandmagnitudeswereusedtodeterminewhetherasourceexh ibits signicantinfraredexcessemission(IRx).The IRx frac isdenedasthefractionoftotal clustermembersthatexhibitsignicantinfraredexcess,w hereasourcehassignicantIRx ifitsatisesthecriteriainEquation 4{4 .Weusethe Cohenetal. ( 1981 )reddeninglaw 99

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Figure4-12.Distributionoffractionofinfraredexcessso urces.Thedistributiononthe leftisforthemainclusterswhereasthedistributiononthe rightisforboth thenewclusters(dashedline)andthefullcatalog(solidli ne).Theaverage IRx frac is22%formainclustersand17%fornewclusters. inaccountingforeectsofinterstellarextinctionuponso urcecolors.Wendthatthere isnegligiblecontaminationfromthebackgroundintermsof IRxsourcessowedonot background-correctour IRx frac ( J H ) < 1 : 692 ( H K )(4{4) Figure 4-12 showsthedistributionof IRx frac valuesamongsttheclustersinour dataset.Thedistributionof IRx frac formainclustersshowsonepronouncedpeaklocated at15%followedbyasteadydrop-ointhe IRx frac ;themaximum IRx frac is47%.The distributionfornewclustersalsoshowsonepeakbutlocate datsmaller IRx frac values; themaximum IRx frac fornewclustersis39%.Theaverage IRx frac is22%forthemain clustersand17%forthenewclusters. InthepanelsofFigure 4-13 westudyapossiblecorrelationbetweenthefractionof IRx frac sourcesand ;inthesepanelsthemainclustersarerepresentedbystar-s ymbols whereasthenewclustersarerepresentedbybox-symbols.In theupperleftpanelweshow thetrendforallclusters,weincludeasolidlinewhichrepr esentstheaverage IRx frac forbinsofsize0.1in andwenoticeafainttrendindicatingthatclusterswithhig her 100

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Figure4-13.Correlationbetweenthefractionof IRx frac sourcesand ;thePearson coecientforthiscorrelationis-0.429.Inthesepanelsth emainclusters arerepresentedbystars,whereasnewclustersarerepresen tedbyboxes.The solidlineintheupperleftpanelistheaverage IRx frac forbinsofsize0.1in .Inthetwolowerpanelswedistinguishbetweenmain(lowerl eft)andnew clusters(lowerright).Intheupperrightgureweconsider increasingvalues ofminimum IRx frac andwecomparethenumberofC-typeandF-type clustershavingvalues IRx frac greaterthanthatminimum. havelower IRx frac .Inthelower-leftandlower-rightpanelswediscernbetwee nthemain andnewclusters;apossibletrendbetweenthesetwoparamet ersismostevidentinthe lower-rightpanel,forthenewclusters.Theupper-rightpa nelshowstheratioofC-typeto F-typeclustersfordierentcluster-sets;asweconsidero nlyclusterswithhigher IRx frac valueswendthatC-typeclustersincreasinglydominateth ecluster-set.ThePearson coecientforthiscorrelationis-0.429.4.2.2.7AverageExtinction WeusedEquation 4{5 tomeasuretheaverageextinctionforeachcluster.Theterm intrinsic isasource'sintrinsicH-Kcolor,wemeasuredthisforsourc esina nearbycontrol-eld;fortheterm cluster wemeasuredtheH-Kcolorforeach 101

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Figure4-14.Distributionofaverageextinction.Thepanel ontheleftisforthemain clusterswhereasthepanelontherightisforboththenewclu sters(dashed line)andthefullcatalog(solidline). clustersource,makingsuretoexcludesourcesexhibitingI Rxsincethosewouldprovide incorrectmeasurementsoftheline-of-sightextinction. Av =15 : 87 [ cluster intrinsic ](4{5) ThedistributionofV-bandextinctioncoversarangeof34ma gnitudeswiththebulk oftheclustershavingextinctionvaluesbetween5and20mag ;thedistributionhasone mainpeaklocatedat15magandthemedianextinctionis15mag nitudes.Themainand newclustersshowasimilardistributionofextinctionvalu esandtheirmedianvalueisthe same,15magnitudes.Thedistributionofaverageextinctio nacrossourdatasetisshownin Figure 4-14 TheaverageextinctionamongstC-typemainclustersis19ma g,andforF-typemain clusters,12mag;fornewclustersthesevaluesare16magand 11mag,respectively.These valuesindicatethatC-typeclustersare,onaverage,moree mbeddedthantheF-type clusters.4.2.2.8CorrelatingEquivalentRadiusandNumberofMember s Inadditiontothedistributionswepresentacorrelationwh ichwendtoexist betweencluster'sequivalentradiusanditsnumberofmembe rs.Intheupperpanelof 102

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Figure4-15.Figurecorrelatingthetotalsizeofaclustert othenumberofmembersin thatsamecluster.Themainclustersarerepresentedbystar swhereasthe newclustersarerepresentedbysquares.Thelinesareobtai nedfroma relationofconstantsurfacestellardensity: R ( N )= R 111 ( N 111 ) 1 2 .Thesolid linehas R 111 =0.62pc,theaverageequivalentradiusforthefullcatalog andthedashedlineshavevaluesof1.77pcand0.09pc,respec tivelythe maximumandtheminimumvaluesofthesamedistribution. Figure 4-15 mainclustersareshownasstars,andnewclustersasboxes;w eobservea clearcorrelationbetweenthesetwopropertiesforboththe mainandnewclusters.This correlationindicatesthatastheclustersizeincreasesso doesthenumberofcluster members;thetwoparametershavearelationshipofconstant surfacenumber-density, whichweshowinEquation 4{6 .ThelinesshowninFigure 4-15 arelinesofconstant surfacedensity. N 1 R 2 1 = N 2 R 2 2 (4{6) Wendthatourlinesofconstantsurfacenumber-densityfol lowtherelationship showninEquation 4{7 ,whereR(N)istheequivalentradiusforaclusterofNstars. We 103

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calculatethat R 111 =0 : 62pcistheaverageequivalentradius,and111istheaverage numberofsourcesfortheclustersinthecatalog.Thegures howsthatthereissome spreadtothiscorrelationbutthatalltheclustersfallwit hinthedottedlines;theselines havethesamefunctionaldependenceasthesolidlineandhav ethevalues: R 111 =1.77pc and0.08pc;theseare,respectively,themaximumandminimu mvaluesoftheequivalent radii.InEquation 4{8 weexpresstherelationshipofconstantsurfacenumber-den sitythat theoverallcatalogfollows. R ( N )= R 111 ( N 111 ) 1 2 (4{7) ( N R 2 ( N ) ) Full =92 stars=pc 2 (4{8) Wendthattheaveragedensityis 100 stars pc 2 inaccordancewith densitiesseeninotherregions( Strometal.1993 Ladaetal.1991b ).Inthetwolower panelsofFigure 4-15 westudytheroleofthecluster'sstructureinthisrelation shipby distinguishingbetweentheC-typeandF-typeclusters.Wen oticethat,thoughboth catalogsarewelltbythesolidline,theF-typeclusterste ndtolieabovethesolidline andtheC-typeclustersbelowtheline;thisindicatesthatt herelationshipofconstant surfacenumber-densityholdsforbothtypesofclusters,an dthatF-typeclustershavea surfacedensitythatislowerthanC-typeclusters.InEquat ions 4{9 and 4{10 weshowthe relationshipswhichC-typeandF-typeclusters,respectiv ely,willfollow. ( N R 2 ( N ) ) C type =123 stars=pc 2 (4{9) ( N R 2 ( N ) ) F type =55 : 6 stars=pc 2 (4{10) Weaddthatasimilarrelationshipexistsbetweenclustersi zeandclustermass becausemassandnumberofmembersarecorrelatedasseeninF igure 4-10 104

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4.3AnalysisofDensityStructureinIndividualClusters Inthissectionweperformanindividualanalysisofacluste r'sinternaldensity structure,asindicatedbythedistributionofNNseparatio ns,forasampleofclusters fromourcatalog.Using wehavequantiedacluster'sdegreeofcentralcondensatio n butthisonlytellsussomeinformationregardingacluster' sstructure;inparticular, wewereinterestedinansweringquestionssuchas:Isthepre senceofahalocommonin clusters?Canaclusterbeexhibitingaratprolebecauseth epresenceofastronghalo isunderminingitsmainpeak?Canratproleclustershaveap rominentpeaks?andCan aclusterhavesignicantinternaldensitystructuredespi teremainingstronglycentrally condensed? isameasureofahowprominentthecluster'sdensitypeakisi nrelationto itstotaldensitydistribution,butitdoesnottellusabout theshapeandstructureofthat remainingdistribution.Wecanobtaininformationaboutth atshapeandstructurefrom ananalysisoftheNNseparations. Weareparticularlyinterestedinlearningmoreaboutthede nsitystructurebecause ofhowthestructuremaybelinkedtotheformationand/orevo lutionscenarios.Aswas indicatedbyLL03,thepresenceofsignicantinternaldens itystructuremayindicatethat turbulence,asopposedtogravity,isthedominantenergyin thecluster'sformation;on theotherhand,clusterswhoseformation/evolutionisgove rnedbygravitationalenergyare thoughttoshowacentrallycondensedstructureandasmooth radialprolethancanbe welltbyapower-lawfunction(e.g., ( r ) r q ). LL03mentionNGC1333andNGC2264asexamplesofclusterswho sestructuremay indicateaturbulencedrivenformationscenario,andTrape zium,IC348,NGC2024,NGC 2071,andNGC2282asexamplesofclusterswheregravitation alenergymaydominate. Ourgoalisrsttoanalyzethesesameclustersusingthedist ributionofNNseparations andcompareourresultswiththoseofLL03,andthentoanalyz eotherclustersfromour catalog. 105

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Foreachofthefollowingclustersweshowonegurewiththre epanels;thesepanels areorganizedasfollows:i)intheupperleftpanelweshowac ontourplotofthesurface densityasmappedbytheNNM;ii)intheupperrightpanelweag ainshowthesurface densitycontourplot,butthistimeweshowaclose-upofthec luster(ifpossible)andthe contourscorrespondingtoseparationsindicatedinthebot tompanel;iii)inthebottom panelweshowthedistributionofNNseparationsfortheeld ,andweaddverticallines wherethedistributionshowsapointofinterestsuchasatro ughorwheretheeldand clusterpopulationsbegintoblend;thedottedhistogramis theNNdistributionforthe o-eld. Toavoidconfusion,apeakinthedistributionofNNseparati onswillbereferredtoas a maxima whereasapeakinthesurfacedensityplotswillstillbea peak .Wealsoclassify maximaas primary secondary ,or tertiary fromsmallerseparationstolargerseparations. 4.3.1ClusterNGC1333 Figure 4-16 isforclusterNGC1333.ThedistributionofNNseparationsf or NGC1333showstwomainmaximaleftwardofwhentheeldpopul ationbecomes signicant.Theprimaryislocatedat0.014degandhasalong tail,stronglyresembling thedistributionofa 1 r 2 prole;thesecondarymaximumisrat,resemblingthatofaha lo orofanearbycluster.Thespatialdensitydistributionsho wstheexistenceoftwopeaks, however,thesecondpeakissmallerinradiusandreachesamu chlowerpeakintensity. CombiningtheanalysisoftheNNdistributionwiththesurfa cedensitydistributionwe concludethatthiseldismadeupoftwoclusters.Oneofthes eisstronglycentrally condensed(probablyhavinga 1 r 2 prole)andtheotheriseithera 1 r oraratprole. Additionally,wemeasurea valueof0.23indicatingthat,despiteitsinternaldensity structure,NGC1333isstronglycentrallycondensed.Weals omeasurean IRx frac of32% andanextinctionof20mag,theseareinaccordancewiththek nowledgethatNGC1333 isaveryyoungandembedded.Theseresultsareinalignmentw iththoseof Ladaetal. 106

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Figure4-16.DensitycontoursanddistributionofNNsepara tionsforNGC1333.The upperleftcontourplotshowsthedistributionofsurfacede nsityforthefull regionobservedwith2MASS.Theplotonthebottomshowsthed istribution ofNNseparationsforvaluessmallerthantheo-eldpeak;t heverticallines indicatevaluesofseparationswhichareofinterest,these areeitherattroughs orwheretheo-eldbecomessignicant.Theverticallines arelocatedat 0.055,0.041,and0.027deg.Thecontourplotontheupperrig htshowsthe contourlevelsassociatedwiththosesameverticallines. 107

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( 1996 ),whoperformedanear-infraredsurveyofthissameregion, clearlyidentifyingtwo clusters.4.3.2ClusterNGC2264 Figure 4-17 isforclusterNGC2264.Wendthisclustertobestronglystr uctured, thisisseeninboththesurfacedensityplotsandthedistrib utionofNNseparations.In analyzingthevaluesofinterest,indicatedbythevertical lines,weonlynoticeonedistinct troughlocatedat0.029deg;thiscorrespondstowherethee ldpopulationbeginstoblend withtheclusteredpopulation.The valueforthisclusteris0.69,indicatingthatitisan F-typecluster,the IRx frac is28%andtheextinctionis7mag;LL03classifythiscluster ashierarchical.4.3.3ClusterNGC2264SouthRegion Figure 4-18 isforclusterNGC2264South.Thesurfacedensityplotsshow what appeartobetwoveryproximalclusters,onewithasignican tlymoreprominentpeak thantheotherandappearingtohavearatterradialprole.T hedistributionofNN separationsshowsthreeregionsofinterestwhichweindica tewiththeverticallines.NGC 2264Southseemstobeagoodexampleoftwoprominentcluster slocatedtoocloseto eachothertobediscernible. ThepresenceofsignicantstructureintheNNdistribution isinaccordancewithour measured of0.63;theseareinaccordancewithLL03whoalsoclassifyt hisclusterare hierarchical.Wemeasurean IRx frac valueof20%andanintermediateextinctionof15 mag.4.3.4TrapeziumCluster Figure 4-19 isfortheTrapeziumcluster.TheTrapeziumclusterisclass iedas centrallycondensedbyLL03andisconsideredanexampleofa clusterwithsignsofhaving aformationdrivenbygravitationalenergy;furthermore,t hisisaclusterforwhichahalo componenthasbeendetected( Muenchetal.2003b ,hereafterML03).Inagreementwith thisclassication,ourdistributionofNNseparationscle arlyidentiesastrongmaximaat 108

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Figure4-17.DensitycontoursanddistributionofNNsepara tionsforNGC2264.The upperleftcontourplotshowsthedistributionofsurfacede nsityforthefull regionobservedwith2MASS.Theplotonthebottomshowsthed istribution ofNNseparationsforvaluessmallerthantheo-eldpeak;t heverticallines indicatevaluesofseparationswhichareofinterest,these areeitherattroughs orwheretheo-eldbecomessignicant.Thelinesarelocat edat0.29,0.245, and0.21deg.Thecontourplotontheupperrightshowsthecon tourlevels associatedwiththosesameverticallines. 109

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Figure4-18.DensitycontoursanddistributionofNNsepara tionsforNGC2264South. Theupperleftcontourplotshowsthedistributionofsurfac edensityfor thefullregionobservedwith2MASS.Theplotonthebottomsh owsthe distributionofNNseparationsforvaluessmallerthantheo -eldpeak; theverticallinesindicatevaluesofseparationswhichare ofinterest,these areeitherattroughsorwheretheo-eldbecomessignican t.Thelines arelocatedat0.25,0.19,and0.11deg.Thecontourplotonth eupperright showsthecontourlevelsassociatedwiththosesamevertica llines. 110

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verylowseparations,typicalofsteeppower-lawproles.H owever,thedistributiondoes notshowthelongtailcharacteristicofasteepprole,inst eaditrisesslightlythenfalls toreachatrough,thenrisesandfallsagainbeforeblending withtheeldpopulation; thisbehaviorclearlytsourmodelsofasteepprolecluste rwithanunderlyinghalo population.Thecontourplotindicatesthatthesourceswhi chpopulatethesecondary andtertiarymaximaarelocatedaround(andunderlying)the mainpeaks.Weaddthat F}ureszetal. ( 2008b )havedescribedthestellarandgaseoussubstructureasori ginating froma"nonuniformgravitationalcollapsetoalamentaryd istributionofgas".Despite ourclassicationofthisclusterascentrallycondensedwe canseesignicantinternal substructure,bothintermsofthedensitycontours(toptwo panelsofFigure 4-19 )andin termsoftheNNdistribution(bottompanelofsamegure),wh ichmaybeinagreement withtheobservationsof F}ureszetal. ( 2008b ). Wemeasurea valueof0.31,indicatingthepresenceofapower-lawprole ,a IRx frac of21%andanextinctionof12mag.Furthermore,webelieveth atthepresenceof thehalopopulationmaycontributetoratteningtheprole.4.3.5ClusterIC348 Figure 4-20 isforclusterIC348.IC348isconsideredtobewelltbyapow er-law prole(LL03),thusbeinganexampleofaclusterwithagravi ty-drivenformation scenario.The valueforthisclusteris0.4,indicatingthatitcanbetbya power-low prole,inaccordancewiththeLL03result.Ananalysisofth eNNdistribution,however, showssignicantinternaldensitystructure;wendthedis tributiontohave3signicant maximaapproximatelyequidistantfromeachother.Sinceth ereisnosecondarypeakin thesurfacedensityplotswhichmightindicatethepresence ofotherclusters,thisclusteris anothergoodcandidateforhavingahalopopulation. WeaddthatIC348andNGC1333arebothlocatedinthesamemole cularcloud; thefactthatweclassifybothasbeingcentrallycondenseda ndhavingsignicantinternal structuremaysuggestthatthesetwoclustershavehadsimil arformationscenarios. 111

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Figure4-19.DensitycontoursanddistributionofNNsepara tionsforTrapezium.The upperleftcontourplotshowsthedistributionofsurfacede nsityforthefull regionobservedwith2MASS.Theplotonthebottomshowsthed istribution ofNNseparationsforvaluessmallerthantheo-eldpeak;t heverticallines indicatevaluesofseparationswhichareofinterest,these areeitherattroughs orwheretheo-eldbecomessignicant.Thelinesarelocat edat0.40,0.27, and0.11deg.Thecontourplotontheupperrightshowsthecon tourlevels associatedwiththosesameverticallines.,theratioofav erageo-eld densitytoaverageclusterdensityis1:38.2 112

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Figure4-20.DensitycontoursanddistributionofNNsepara tionsforIC348.Theupper leftcontourplotshowsthedistributionofsurfacedensity forthefullregion observedwith2MASS.Theplotonthebottomshowsthedistrib utionof NNseparationsforvaluessmallerthantheo-eldpeak;the verticallines indicatevaluesofseparationswhichareofinterest,these areeitherattroughs orwheretheo-eldbecomessignicant.Thelinesarelocat edat0.05, 0.041,0.033,and0.024deg.Thecontourplotontheupperrig htshows thecontourlevelsassociatedwiththosesameverticalline s.,theratioof averageo-elddensitytoaverageclusterdensityis1:3.5 113

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Additionally,itisknownthatIC348issignicantlyolder, havingbeenproducingstars continuouslyfor5-7Myr.TheagedierencebetweenIC348an dNGC1333mayalsobe associatedtoIC348havingmoremaximainitsNNdistributio n. AhalopopulationaroundIC348hasbeensuggestedbyML03who noticeda ratteningoftheclusterproleforlargeradii.However,wh etherthispopulationisolderor youngerisinconclusive,with Herbig ( 1998 )observingaslightagegradientpointingtoan olderhalo,butML03ndingthattheinfraredexcessfractio ninthehaloislargerthanin thecore,implyingthatthehalomaybeyounger.4.3.6ClusterNGC2024 Figure 4-21 isforclusterNGC2024.Thevalueof forthisclusteris0.17,indicating ittobeastronglycentrallycondensedcluster,welltbyap ower-lawfunction,thisisin accordancewithLL03.TheNNdistribution,however,showst heexistenceofsignicant internaldensitystructure.Werstpointoutthepresenceo ftwoverystrongmaxima locatedataround0.01deginseparation.Thenwenoticethat ,aftertheNNdistribution fallssharplyfrom0.01to0.015deg,itbeginsrisingagainb eforefallingtoasecondtrough at0.03deg,thisbroaderpeakisindicativeofthepresenceo fahalopopulation.The IRx frac andextinctionvaluesforthisclusterare,respectively,3 2%and25mag. 4.3.7ClusterNGC2071 Figure 4-22 isforclusterNGC2071.NGC2071hasa of0.25,indicatingits strongcentrallycondensedprole,an IRx frac of38%andanextinctionof19mag.The distributionofNNseparationsdoesshowastrongmaxima,ch aracteristicofapopulation followingapower-lawprole,butwithoutthelongtail,ins teadthedistributionrattens outrapidlyandshowsanothersmallmaximabeforejoiningth eeldpopulation.The contourplotsshowtheexistenceoftwopeaks,thismayindic ateadoubleclustersuch asNGC1333.Thesecondmaximamaybeduetotheweakerpeaksoi tisinconclusive whetherthisclusterhasahalo. 114

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Figure4-21.DensitycontoursanddistributionofNNsepara tionsforNGC2024.The upperleftcontourplotshowsthedistributionofsurfacede nsityforthefull regionobservedwith2MASS.Theplotonthebottomshowsthed istribution ofNNseparationsforvaluessmallerthantheo-eldpeak;t hevertical linesindicatevaluesofseparationswhichareofinterest, theseareeither attroughsorwheretheo-eldbecomessignicant.Theline sarelocated at0.042,0.030,and0.016deg.Thecontourplotontheupperr ightshows thecontourlevelsassociatedwiththosesameverticalline s.,theratioof averageo-elddensitytoaverageclusterdensityis1:25. 1 115

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Figure4-22.DensitycontoursanddistributionofNNsepara tionsforNGC2071.The upperleftcontourplotshowsthedistributionofsurfacede nsityforthefull regionobservedwith2MASS.Theplotonthebottomshowsthed istribution ofNNseparationsforvaluessmallerthantheo-eldpeak,t heverticallines indicatevaluesofseparationswhichareofinterest;these areeitherattroughs orwheretheo-eldbecomessignicant.Thelinesarelocat edat0.044, and0.027deg.Thecontourplotontheupperrightshowstheco ntourlevels associatedwiththosesameverticallines.Theratioofaver ageo-elddensity toaverageclusterdensityis1:10.1 116

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4.3.8ClusterS106 Figure 4-23 isforclusterS106.ClusterS106isknowntobeaveryyoungcl uster (1 2 x 10 6 yr)embeddedin 20magofvisualextinction.Wemeasurean IRx frac of 24%,anextinctionof12mag,anda of0.38.ThedistributionofNNseparationsshows onlyonestrongmaximafollowedbyasteadydrop-ountilitm eetstheeldpopulation; thedrop-oseemstobeslowerthanthatexpectedfromapower -lawprolebutwecannot tellfromtheNNdistributionwhetherthereisornotanyothe rstructuresuchasahalo population.WealsoindicatethattheregiontothesouthofS 106isstronglyextinctedand that2MASSmaynotbedeepenoughtoaccuratelysamplethiscl uster. 4.3.9ClusterLKH 101 Figure 4-24 isforclusterLKH 101.The valueforthisclusteris0.24,indicating ittobestronglycentrallycondensed,the IRx frac valueis21%andtheextinctionis18 mag.ThedistributionofNNseparationsshowsamaximaat0.0 07degfollowedbya plateau,indicativeofasteepproleoverlappingwithatle astonesecondarypopulation;a pronouncedtroughat0.025degmayindicatethepresenceofa halo. 4.3.10ClusterGGD12-15 Figure 4-25 isforclusterGGD12-15.Similarlytothepreviouscluster, theNN distributionisindicativeofacentrallycondensedcluste r(amaximafollowedbyalong tail)withahalopopulation,shownbythesignicantstruct ureleftwardof0.023deg.We measurea valueof0.33inaccordancewithaC-typecluster,aswellasa n IRx frac value of31%andanextinctionof11mag. 4.4Discussion/Conclusion InthischapterwehaveappliedourNNM,asdevelopedandtest edinChapters 2 and 3 ,toacatalogof43nearbyembeddedclusters;wendthatourN NMisaneective methodforsystematicallydetectingembeddedclusters. Inadditiontothedetectionoftheknownclusterswealsodet ected13newclusters. Sincewehadnoinformationregardingthenatureofthesenew clusterswehadsome 117

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Figure4-23.DensitycontoursanddistributionofNNsepara tionsforS106.Theupper leftcontourplotshowsthedistributionofsurfacedensity forthefullregion observedwith2MASS.Theplotonthebottomshowsthedistrib utionof NNseparationsforvaluessmallerthantheo-eldpeak;the verticallines indicatevaluesofseparationswhichareofinterest,these areeitherattroughs orwheretheo-eldbecomessignicant.Thelinesarelocat edat0.015, and0.010deg.Thecontourplotontheupperrightshowstheco ntourlevels associatedwiththosesameverticallines.Theratioofaver ageo-elddensity toaverageclusterdensityis1:7.4 118

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Figure4-24.DensitycontoursanddistributionofNNsepara tionsforLKH 101.The upperleftcontourplotshowsthedistributionofsurfacede nsityforthefull regionobservedwith2MASS.Theplotonthebottomshowsthed istribution ofNNseparationsforvaluessmallerthantheo-eldpeak;t heverticallines indicatevaluesofseparationswhichareofinterest,these areeitherattroughs orwheretheo-eldbecomessignicant.Thelinesarelocat edat0.015, 0.025,and0.035deg.Thecontourplotontheupperrightshow sthecontour levelsassociatedwiththosesameverticallines.Theratio ofaverageo-eld densitytoaverageclusterdensityis1:17.3 119

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Figure4-25.DensitycontoursanddistributionofNNsepara tionsforGGD12-15.The upperleftcontourplotshowsthedistributionofsurfacede nsityforthefull regionobservedwith2MASS.Theplotonthebottomshowsthed istribution ofNNseparationsforvaluessmallerthantheo-eldpeak;t hevertical linesindicatevaluesofseparationswhichareofinterest, theseareeitherat troughsorwheretheo-eldbecomessignicant.Thelinesa relocatedat 0.033,0.023,and0.0175deg.Thecontourplotontheupperri ghtshows thecontourlevelsassociatedwiththosesameverticalline s.,theratioof averageo-elddensitytoaverageclusterdensityis1:6.6 120

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apprehensionastowhetherthesewere,infact,real,young, embeddedclusters;however, wendthatthepropertiesofthesenewclustersfollowsimil artrendstothoseofthemain clusters,providingevidenceinsupportoftheirinclusion amongstthemainclusters.We ndthatthenewclustersshowsimilardistributionsforequ ivalentradius,coreradius, degreeofcentralcondensation,fractionofinfraredexces ssourcesandextinction;on theotherhand,newclustershaveahigheraveragevalueof thanthemainclusters (0.55comparedto0.41)andalowervalueof(3.12ascompare dto10.8).Theseresults indicatethat,intermsoftheirspatialsurfacedensity,ou rnewclustersareratterand lessprominentthanthemainclusters;wesuggestthisasapo ssiblereasonforwhy theseclusterswerenotpreviouslyidentied.Alternative ly,thesenewobjectsmaybe substructureorlowerdensityextensionsofthemaincluste rs;inacomparativeanalysis ofourresultsforclusterNGC2068withthoseobtainedby Lada ( 1990 )wendthatthe newclusterintheNGC2068eldcoincideswithafeaturewhic h Lada ( 1990 )identifyas belongingtothecluster.Thefactthatitisdiculttodisti nguishbetweentwoindividual clustersandaclusterwithsignicantsubstructure(orsub -clusterswithinasinglecluster) wasalsoobservedby Allenetal. ( 2007 ). Wendthatourmeasurementsofclustersizesandmassesarei nagreementwith previousstudiessuchasthatby Bicaetal. ( 2003 ).Categorizingourclustersintostellar groups,smallclustersandlargeclusterswendagreementw ithP03inthatthevast majorityofyoungstarsbelongtolargeclusters;thisempha sizestheimportanceof studyingthoseentitiesinordertobetterunderstandthepr ocessesinvolvedinstar formation. Weintroducedanewmethodforevaluatingacluster'sdegree ofinternalstructure, andtheassociatedparameter: ;inaddition,weperformedpower-lawtstosurface densityradialprolesforeachcluster( A.2 ).Comparingtheparameter totheexponent ofthepower-lawts,(seeFigure A-52 ),wendtheexistenceofadirectcorrelation betweenthetwoparameters.ThiscorrelationhasaSpearman 'srankcorrelationcoecient 121

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of0.773witha1 : 93 10 11 probabilityofbeingachancecorrelation.Suchpositive correlationindicatesthat isagoodtracerofthesteepnessofacluster'ssurfacedensi ty radialprole. Usingtheparameter wehaveclassiedthedensityprolesofourclustersinto centrallycondensed(characterizedbyproleswhichfollo wapower-law)andrat;wend that64%ofthemainclustersarecentrallycondensedwhichi ndicatesthatthemajorityof knownclusterscanbetbypower-lawproles.This,mostlik ely,representsalowerlimit onthetruepercentagebecausewendthatextinctionhasthe abilitytochangeadensity prole,makingacentrallycondensedclusterlookratter.I ftheclusterformingprocess wereturbulence-drivenwewouldexpecttondmorelamenta rystructuresasopposedto themoreregular,centrally-concentratedstructureswhic hdominateourstudy.Inorderto evaluatetheaccuracyofthisvalueweperformedanerrorana lysis,similartoabootstrap method,oneachofourelds.Ourerroranalysisconsistedof generatingalternateversions ofstellardistributionswhichcouldbeseen.Foraeldcont ainingNstars,ourmethod randomlypicksNstarsfromthateld;onceastarispickedit spositionisloggedand thatstarisreplaced,thusthesamestarcanbepickedsevera ltimes.Sincesomeofthose Npickswillbeofthesamestar,theneweldwillhavelesssta rsthantheoriginaleld; thoughthestellardistributionwillresembletheoriginal eld,itwillnotbethesame.This processofgeneratinganeweldisrepeatedastatistically signicantnumberoftimes,and foreacheldthecoreandequivalentradiiandthetauvaluew eremeasured.Thisprovides uswithawayofevaluatinghowrobustourmeasuredvaluesofc oreradius,equivalent radius,andtauareforeacheld.Thismethodwasappliedtoa llofourclusterelds. Thiserroranalysisshowedusthatthepercentageofmainclu sterswhicharecentrally condensedisintherangeof59%to74%. Webelievethatourndingsareinagreementwithacluster-f ormingscenariosuchas theoneproposedby HartmannandBurkert ( 2007 )whosuggestthatgravitationalcollapse playsanessentialroleinstarclusterformation. 122

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ComparingC-andF-typeclustersintermsoftheirfractiono finfraredexcess sources,extinctionandcircularitywendthatC-typeclus terstendtobeassociatedwith highervaluesforallthreeofthoseparameters(extinction IRx frac ,andIQ).Considering extinctionand IRx frac asindicatorsofembeddednessandage,respectively,thism ay suggestthatmorecentrallycondensedclustersarealsoyou nger,moredeeplyembedded insurroundingmolecularmaterialandmorecircularthanth eirrat,F-type,counterparts. ItisinterestingtonotethatclusterstudiesusingSPITZER seemtoindicatethatthe youngeststellarpopulationsaredistributedinalamenta rystructure,notacentrally condensedone.Inordertobetterunderstandhowthesetwore sultstietogetherweneed toobtainbetterageestimatesforourcatalogthroughimpro ved IRx frac measurements usingadierentwavelength,suchasL-band,toprovidealar gerwavelengthbaseline. OurresultsfromusingthedistributionofNNseparationsto studyacluster'sinternal structureindicatethatthepresenceofahalocomponentisc ommon.62%ofourclusters haveaNNdistancedistributionwhichistoonoisytopermita goodevaluationofwhether ithasahaloornot,theseclustersareeithertoofaintorthe 2MASSdetectiondoesnot sampletheclusterwellenough.50%oftheremainingcluster shaveaNNdistribution resemblingthatofahalocomponent;wedividetheseremaini ng14clustersinto3 prominentonesand11faintones.Allthreeprominentcluste rsand36%ofthefaint clustershaveaNNdistributionindicativeofahalobeingpr esent,theNNdistributions oftheremaining64%ofthefaintclustersshowsignsofahalo butareunclearandneed furtheranalysis.Thoughtheconceptofahaloisnotnew,the reisnoagreeddenition ofahalocomponent.Wendthatauthorsusetheterm"halo"to refertoanextended regionoflowerdensitysurroundingthemoreprominent,hig hdenseregionofthecluster ( Verschuerenetal. ( 1990b ), HillenbrandandHartmann ( 1998 ), Allenetal. ( 2007 )).ML03 performedwhatisperhapsthemostdetailed,andpossiblyth eonlyquantitative,analysis ofthehaloforanembeddedcluster.Theauthorsseparatedth eIC348clusterregioninto twosubdivisions:coreandhalo;theybasedthisdivisionup onananalysisofthecluster's 123

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surfacedensityradialprolewhereupontheauthorsnotice dthattheinnerportionofthe clusterhadasteeperprolethantheouterportion.Subclus ters,surroundingIC348,had beenidentiedby LadaandLada ( 1995 )andML03interpretthehaloasbeingmadeup ofthesesurroundingsubclusters.Theexistenceofahaloco mponenthadbeenpreviously suggestedforclustersIC348,NGC2362,andTrapezium(ML03 );wendouranalysis forIC348andTrapeziumtobeinagreementwiththeML03hypot hesis.Furthermore, weprovideevidenceforhalosinotherclusters;ofthe10clu stersstudiedby Allenetal. ( 2007 )usingSPITZER,theauthorsconsiderthatatleast8(80%)an dpossibly9(90%) havehalos.Unfortunately,theseauthorsdonotdescribeth eirdenitionofahalo,which makesitimpossibleforustoperformacomparisonbetweenou rdenitionandtheirs. Forcentrallycondensedclusterswecanfrequentlyidentif ythemainstructures{themain clusterproleandthehalo{whereasforratclusterstheana lysisoftheNNdistributionis generallymorecomplicatedandoftentimesinconclusive. Thespatialcoincidenceofthetwopopulations(coreandhal o)indicatesthatthey mustbephysicallyrelated,yetitisunclearhow.Thefactth atweseethishalopopulation associatedwithveryyoungclustersmayindicatethatitise itheralreadypresentatthe timeofformationorthatittakespartinthesameformationm echanismshapingthe cluster,aconclusionalsosharedby Allenetal. ( 2007 ).Anotheroptionisthatwemay beobservingtheeectsofmasssegregation,wherethecentr alpopulationiscomprised ofhighermassstars,andthehalooflowermassstars.Massse gregationcouldbeapart ofthecluster'sformationmechanismorofitsevolution;sp ectraofstarsbelongingtothe dierentregions(centralandhalo)wouldbenecessarytote stthishypothesis. Thischapterhasprovideduswiththetoolsnecessaryforstu dyingclusterstructure andithasshownusthataclusters'densitystructurecanoft enbeunderstoodinterms ofacoreandahalo;however,wedonothaveenoughinformatio ntounderstandhow thecoreandhaloarephysicallyrelated.InChapter 5 weapplythesesamemethodsof detectionandanalysistostudytheyoungstellarpopulatio ninagiantmolecularcloud. 124

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Wedothiswiththeaimofobtainingamorecompleteunderstan dingofthelargescale stellarstructureofwhichclusters,suchastheonesinthis chapter,areanimportantpart. Thiswillallowustobettercomprehendourdetectionsofhal ocomponentsandtheirrole inclusterstructure. 4.5TablesofResults 4.5.1ClusterProperties Intable 4-2 wehaveusedtheletter"M"todenotemainclusters,uponwhic hthe eldsarecentered,andtheletter"N"todenotenewclusters Using ,asanindicatoroftheclusterprole,togetherwiththemea suredvalues ofandTable C-3 ,wehaveestimatedpercenterrorsforthetotalsizeandnumb erof members;wepresentthosevaluesintable 4-2 .Tobeconservative,aminimumpercent errorof2%isgiven,evenwhenthemeasurementsinthesimula tionsshowzeropercent error. 125

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Table4-2.DetectedClusters Name R Eff R Core NumofMassIRxFraction Av IQ (pc)Members( M )(%)(Mag) NGC1333(M)0.59(2)0.13114(4)5532200.2314.90.76 IC348(M)1.09(3)0.45322(6)1451670.413.50.26 NGC2024(M)0.85(12)0.16390(1)26919250.1225.10.66NGC2068(M)0.46(2)0.2380(6)3519180.493.70.61NGC2071(M)0.49(2)0.1281(2)4419200.2510.10.81 TRAP/ONC(M)1.77(6)0.551518(2)81923150.3138.20.25 L1641N(M)0.54(2)0.2732(5)154030.492.80.69 S106(M)0.31(2)0.1372(2)4521100.407.40.87 RCrA(M)0.60(26)0.0619(8)1731340.1016.10.83L988e(M)0.67(2)0.49104(5)522540.742.150.37 CepA(M)0.95(2)0.35173(5)11010140.378.40.54 MonR2(M)1.01(8)0.19297(2)29525300.1930.00.68 GGD(M)1.02(6)0.33158(2)12021170.336.60.67 NGC2264(M)1.32(8)0.78238(7)1553070.593.00.38 NGC2264South(M)1.04(6)0.65229(2)17221150.635.60.44 LKH(M)0.52(2)0.13140(2)8415150.2417.30.65 AFGL490(M)0.62(6)0.1427(2)2515180.225.20.88 Cha(M)0.24(20)0.0411(4)52890.1613.90.66 KMS35(M)0.71(8)0.5077(3)6416250.696.40.45 CKGroup(M)0.64(20)0.2030(3)1520230.313.50.67NGC2023(M)0.48(2)0.1323(4)6447340.2613.00.91 V380Or(M)(M)0.43(2)0.2329(6)1418110.533.10.75 IRAS05401-1002(M)0.64(6)0.3168(5)3328160.494.70.36 IRAS243245(M)0.69(20)0.2350(2)2620210.344.60.27 CB34(M)0.37(5)0.1132(5)1822120.309.80.68 IRAS08375-4109(M)0.81(2)0.59100(5)8817150.741.90.24IRAS08404-4033(M)0.42(20)0.1444(2)3814150.334.30.61IRAS08448-4343(M)0.50(2)0.2697(6)5818130.538.50.43 126

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Table 4-2 continued Name R Eff R Core NumofMassIRxFraction Av IQ (pc)Members( M )(%)(Mag) IRAS08470-4243(M)0.61(4)0.13102(2)6114100.229.70.42IRAS08470-4321(M)0.56(2)0.2274(2)4616140.387.90.32IRAS08476-4306(M)0.47(2)0.1357(2)5417150.287.70.44IRAS08477-4359(M)0.31(6)0.1027(2)2618180.326.50.87 IRAS20050+2720(M)0.34(4)0.1265(2)6625240.358.40.78 HD216629(M)1.00(2)0.69128(5)781290.691.80.26 L1211(M)0.46(2)0.2836(5)228140.611.90.51 VYMon(M)0.67(6)0.2871(5)8131150.415.10.27 SerpensSVS2(M)0.079(26)0.0313(6)639290.393.30.84 L1641C(M)0.77(20)0.5368(2)3518160.692.50.42 L1228(M)1.06(2)0.5539(5)182170.521.60.71 NGC2024(N)0.33(2)0.1718(3)82230.5311.10.42NGC2068(N)0.31(2)0.2425(6)20520.786.50.41 AFGL490(N)0.92(2)0.5655(6)499150.613.00.57 KMS35(N)0.52(2)0.3930(5)14760.742.00.42 CKGroup(N)0.83(2)0.5857(5)4616160.692.40.47 V380Ori(N)0.50(200.3635(6)1714150.732.50.29 IRAS05401-1002(N)0.61(2)0.2454(5)2620160.391.90.63IRAS08375-4109(N)0.55(20)0.43128(2)708100.774.80.45IRAS08375-4109(N)0.35(8)0.1450(3)2916130.408.10.75IRAS08448-4343(N)0.49(2)0.2074(5)4028130.402.30.47IRAS08470-4243(N)0.40(6)0.2531(2)161320.626.40.35IRAS08470-4321(N)0.32(6)0.1028(5)1639210.313.90.57 L1211(N)0.39(14)0.2627(10)1711150.661.40.48 MandNindicatemainandnewclusters,respectively%errorsforsizesandnumberofmembersshowninparenthesis127

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Table4-3.ComparisonwithValuesinLiterature NameRadiusN (pc) NGC13330.59(0.49)113(143) IC3481.09(1.0)304(300) NGC20240.85(0.88)391(309)NGC20680.46(0.86)69(192)NGC20710.48(0.59)81(105) Trapezium1.76(1.9*)1567(1740) L1641N(I)0.53(0.33)33(43) 4.5.2ComparingResults Intable 4-3 IcomparethevaluesobtainedbytheNNMtothosepresentinli terature. Valuesinparenthesiswereobtainedfrom LadaandLada ( 2003 ). *LL03havetheTrapeziumsizelistedas3.8pc,throughpriva tecommunicationwith theauthorswebelievethistobeanerror-havingbeenlisted asthediameterandnotthe radius.4.5.3CutoValues InTable 4-4 wepresentthecutovalueschosenforeachoftheclusterel ds.Sources whichareseparatedfromtheir20thNNbyadistancegreatert hanthecutovalueare consideredtobelongtotheo-eldwhereassourcesseparat edfromtheir20thNNbya distancesmallerthanthecutoarepotentialclustermembe rs. 128

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Table4-4.CutoValues NameDistanceCutoDistanceCutoDistance (pc)(deg)(pc) ChaI1400.080.20 SerpensSVS23000.0170.0 L12283000.140.74 NGC13333180.0550.31 IC3483200.050.28 NGC20244000.0450.32NGC20684000.040.28NGC20714000.040.28 LKHalpha1014500.030.42 L1641/KMS354800.050.42 L1641/CKgroup4800.0650.55 NGC20234800.050.42 V380Ori4800.050.42 IRAS05401-10024800.050.42 IRAS243,2454800.0580.49 L1641C5000.050.44 Trap5000.0350.30 L1641N5000.0450.39 CB346000.030.32 S1066000.0150.16 129

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Table 4-4 continued NameDistanceCutoDistanceCutoDistance (pc)(deg)(pc) IRAS08375-41097000.030.37IRAS08404-40337000.0250.30IRAS08448-43437000.0230.30IRAS08470-42437000.0250.30IRAS08470-43217000.0250.30IRAS08476-43067000.0250.30IRAS08477-43597000.0250.30 BBW192E7000.0250.30 IRAS20050+27207000.0180.23 RCrA7000.040.49L988e7000.020.24 CepA7000.030.37 HD2166297250.030.38 L12117500.0280.37 VYMon8000.0280.39 MonR28000.0280.39 GGD12-158000.0330.46 NGC22648000.0290.40 NGC2264South8000.0250.35 AFGL4909000.0350.55 Themaximumnearestneighbourseparationforthecutodist anceis0.049pc Theminimumnearestneighbourseparationforthecutodist anceis0.002pc Theaveragenearestneighbourseparationis0.0085pc 130

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CHAPTER5 APPLYINGTHENNMTOMONOCEROSOB1 5.1MotivationandIntroductiontoMonOB1 TwoofthemainresultsfromtheapplicationoftheNNMtothes tudyofembedded clusters(fromChapter 4 )havebeen:i)thattheNNMiseectiveatdetectingclusters oversmall( < 5pc)areasandii)thatyoungclustersexhibitsignicantin ternalstructure. Ourmotivationforthiscurrentchapteristo:i)testtheapp licationoftheNNMfor identifyingmultipleclustersspreadoutacrossanentireg iantmolecularcloud(GMC);ii) seehowprevalentthosestructuresareinaGMCasawholeandi ii)tobetterunderstand thedistributedandclusteredmodesofstarformationbysam plingthedistributionof youngsourcesinaGMC. Inordertoobtainfurtherinsightintothesegoalswenotonl yneededtostudy clustersinthecontextoftheirGMCsbutwealsoneedtobecap ableofdistinguishing theyoungstellarpopulationswithinacluster.AswesawinC hapter 4 ,singlewavelength observationsdonotpermitustodiscernbetweenthosesourc esbelongingtothecluster andthosebelongingtotheeld;multi-wavelengthobservat ions,however,permitusto constructastar'sspectralenergydistribution(SED)whic hcan,inturn,beusedto distinguishayoungstellarobject(YSO)fromaeldstar.Th euseofastar'sSEDasa toolforclassifyingitsevolutionarystagehasbeenoutlin edinSection 1.2 ;asmentioned inthatsection,thewavelengthrangemostsensitivetothes tar'sevolutionarystageisthe infrared( LadaandWilking1984 ). WiththeuseoftheinstrumentFLAMINGOS( Elston1998 Elstonetal.2003 ) operatinginthenear-infrared,weperformedamulti-wavel engthanalysisoftwolarge star-formingregions,theRosetteMolecularComplex(RMCresultspresentedin Roman-Zu~nigaetal. ( 2008 )-hereafterR08)andtheMonocerosOB1association(Mon OB1)whichisthefocusofboththischapterandofChapter 6 .Morespecically,wehave usedmeasurementsofasource'smagnitudeinthethreenearinfraredbandsJ,H,andK, 131

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tosamplethestellarpopulationanddetectthepresenceofn ear-infraredexcessemission (IRx);IRxisaknownsignatureofYSOs;thus,withFLAMINGOS ,weareabletomap thespatialdistributionofYSOs. MonOB1is,itself,partofalargerstructureknownastheNor thernMonoceros Region;MonOB2,whichhoststhenearbyRosettenebulaandth eMonocerosLoop,is alsopartofthissameregion.BoththeRMCandMonOB1havebee nthestudyofmany surveyssincetheybothhostprominentstarformingregions :theRMCbeingdominated bytheRosetteNebula,abrightHIIregionhostingthepromin entOBclusterNGC2244, andMonOB1,hostingtheyoungclusterNGC2264.Despitethei robservationalproximity (MonOB1isapproximately5degtothenorthoftheRMC),NGC22 64isnotphysically associatedwiththeprominentobjectsintheMonOB2eldsuc hasNGC2244.MonOB1 iscomposedoftwomainclouds,MonAandMonB,thetotalmasso fthismolecularcloud isatleast 3 : 7 x 10 4 M ( Dahm2008 ),andislocatedat800pc( LadaandLada2003 ), approximatelyhalfthedistancetotheRMC;inthisChapterw euseFLAMINGOStomap theyoungpopulationofbothMonAandMonB. 5.2FLAMINGOS TheFLoridAMulti-ObjectImagingNear-IRGrismObservatio nalSpectrometer (FLAMINGOS)isbothawideeldnear-IRimagerandamulti-ob jectspectrometer, conceived,designed,andbuiltattheUniversityofFlorida intheyear2000;itsclaim-to-fame beingthatitistheworld'srstfullycryogenicnear-IRspe ctrometer( Elston1998 ). FLAMINGOSwasbuiltwithaspecicobjective:tomapthestel larpopulationsofnearby GMCsusingbothnear-infraredobservationsandmulti-obje ctspectroscopy. 5.2.1Specications Photometrically,FLAMINGOSoperatesinasimilarwaveleng thrangeas2MASS(J, H,K,or K s ,usingtheCIT/CTIOphotometricsystem),butwithimproved sensitivity (depth)andresolution,andthereforedecreasedamountofp hotometricerrors.The FLAMINGOSKbandoperatesat2 : 2 m whereasthe2MASS K s bandoperatesat 132

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2 : 16 m ,thislargerbaseline(fromJ-toK-band)makesFLAMINGOSmo resensitiveto excessemissionthan2MASS.Spectroscopically,itsgrisma ndlterwheelsallowitto performsimultaneousnear-infraredspectroscopyofmulti pleobjects( 30)atresolutions ashighas3600. TheFLAMINGOSinstrumentusesa2048x2048pixeldetectorwh ich,whenused initsimagingmodeattheKittPeakNationalObservatory(KP NO)4metertelescope, resultsinapixelscaleof0.3 00 /pixelwitha21 0 x21 0 eldofview(FOV).Whenmountedat the2.1metertelescopetheFOVis10 0 x10 0 andthepixelscaleis0.6 00 /pixel. 5.2.2GoalofFLAMINGOS ThestudyofGMCsusingFLAMINGOSwasencompassedinthesurv ey: Toward aCompleteNear-InfraredSpectroscopicandImagingSurvey ofGiantMolecularClouds (PIE.A.Lada).TheGMCsobservedinthissurveywere:Perseu s,OrionA,OrionB, MonocerosOB1,RosetteGMC,GemOB1,andCepheusOB35.2.3Observations TheFLAMINGOSsurveywascarriedoutfrom2001to2007atthe2 .1mand4.0m telescopesoftheKPNO,whereFLAMINGOSisacomissionedins trument.Themajority oftheimagingwasperformedatthe2.1mtelescope,wherethe FOVislarger,whereasthe majorityofthemulti-objectspectroscopywasperformedat the4.0mtelescope. MyinvolvementwiththeFLAMINGOSobservationsbeganatthe endof2002with myrstobservingruncominginthewinterof2003;intotalIw enton9observingrunsto theKPNOtelescopestotalingin95nights. WithFLAMINGOSattheKPNO2.1mtelescopeweobservedtheMon OB1region overthecourseof52partialnights;24nightswerededicate dfortheMonAregion; coverageofMonOB1intermsoftheindividual,21 0 x21 0 ,FLAMINGOSeldsisshownin Figure 5-1 .Wealsoobservedfourcontrol-elds;thesearelocatedat: 1)RA=06:34:49.9, Dec=09:12:31.4,2)RA=06:41:13.8,Dec=12:01:20.3,3)RA= 06:46:36.8,Dec= 10:28:9.8,and4)RA=06:36:44.2,Dec=12:16:48.5.InTable B.4 wepresenttheaverage 133

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Figure5-1.DivisionofMonocerosintoFLAMINGOSelds.The MonOB1complexwas dividedintothetworegionsMonAandMonB,witheachbeingsu bsequently dividedintomultipleelds.Eacheldis21 0 x21 0 ,theFOVofFLAMINGOS attheKPNO2.1mf/7telescope. 134

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photometryerrorsandtheirstandarddeviationsforthethr eebandsandthefourcontrol elds. Astarcatalogisobtainedforeveryeldobserved;henceour MonOB1dataismade upof52ofthesestarcatalogs,25fortheobservationsofMon A,23forMonB,and4for thecontroleld.Thesecatalogswerethenmergedintotwon alcatalogs,onecovering 2.43deg 2 ofMonAandtheothercovering1.18deg 2 ofMonB;inadditiontothesewealso obtainedstarcatalogsforthefourcontroleldsinorderto evaluatethecontributionof theeldtoourobservations. Weaimedfor1000secondsofon-sourceintegrationtimeinea chlterachievedby obtainingindividual,short,ditheredexposures,whichwe relateroverlayedtoincrease thesignal-to-noiseratio.Theindividualditherexposure swereof60secondsfortheJ andHltersand20or30secondsfortheKlter;shorterexpos uresweretakenwiththe Klterbecausesaturationinthisbandoccursfasterthanwi thJandH,duetohigher thermalbackground.Saturationtypicallyoccursformagni tudesbelow11.0magnitudes inJ,H,andK;IRarraydetectorshavearegionofoptimalfunc tioningandwhenthe number-of-countsperpixelrisesabovethislevelthepixel becomessaturated,nolonger correctlyestimatingtheincomingintensity.Tocompensat efortheseshorterexposures wetookatleastdoublethenumberofimagestakenfortheothe rtwobands;undergood seeingconditionswetook16framesforbothJandHand32forK DetailsoftheseobservationsfortheMonocerosregioncanb eseeninAppendixA. 5.2.4ReductionofData EachFLAMINGOSimageisa16MegabyteFITS(FlexibleImageTr ansportSystem) le,thismeantthateachnightofobservingsuppliedaveryl argeamountofdata;data reductionandphotometrywereperformedusingautomatedpr ocessingpipelines. Thetwomainpipelinesusedforthedatareductionwere:i)an imagereduction pipeline(nicknamedLongLegs)andii)aphotometryandastr ometrypipeline(nicknamed PinkPack).Thesewerebothwritteninthecommonlyusedcomp uterlanguageIRAF 135

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(ImageReductionandAnalysisFacility),writtenandsuppo rtedbyagroupatthe NationalOpticalAstronomyObservatories(NOAO)inTucson ,Arizona. LongLegswasprogrammedbyCarlosRom a n-Z u ~ n igaandhasthreedistinctphases. 1.Intherstphasedefectiveimagesandbadpixelsareremov ed,a3rddegree polynomiallinearizationcorrectionisappliedtoeachima ge,andbadpixelmasksare createdusingthedarksandtherats. 2.Inthesecondphaseimagesarecombinedtocreateaskyimag e,andsky-subtraction isperformed.Dataiscombinedandsourceswithverylargeru xesareremoved, creatingnewlocalskyframes.Asecondpassofskysubtracti on,ratelddivision, andshift-and-addcombinationisalsoperformed. 3.InthethirdphasegeometricdistortionsoftheIRarrayar ecorrectedforbyusinga sixthorderChebyshevpolynomial;thedistortion(andthus thecorrection)isradial, centeredapproximatelyat[3000,2400]inthe4096x4096ima ge.Theprogramfor applyingthiscorrectionwasdevelopedbyAndreaStolte.Th enalimageisfreeof geometricdistortions,resampledtotwicetheoriginalsiz e,andtrimmedintonal framesof4096x4096pixels. PinkPackwasprogrammedbyJoannaLevine( Levine2006 ),andperformsstellar prolettingphotometryonthenalproductoftheLongLegs program;the2MASS AllSourceCatalogReleaseisusedtondbothafullphotomet riccalibrationandan astrometricsolution.Inaddition,PinkPackmakesanalme rgedcatalogcontainingthe objectID,nalRA&Deccoordinates,pixelpositionsforthe Kbandimage,photometry forallbands,andprolettinguncertainties. TheMonocerosdatausedinmyanalysiswasreducedbyNoahRas hkind,ChrisFoltz andAndreaStolte;thenalcatalogswerepreparedbyAndrea Stolte. 5.2.5PhotometricSelectionCriteria Severalselectioncriteriawereappliedtothetwonalcata logsinordertoremove sourceshavinglargeerrorsintheirphotometry.Ourrstse lectioninvolvedremoving sourceswhoseastrometryisaccuratebutforwhomvaluesofJ ,H,orKbandphotometry couldnotbedetermined;thesesourcesareidentiedbynull J,H,orKmagnitudevalues. Oursecondselectioncriteriaremovedsourceswithlargeph otometricerrors;todothis webinnedthemagnitudesin0.25magnitudebins,obtainedth emeanerrorandstandard 136

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Figure5-2.J,H,KFLAMINGOSphotometryerrorsforMonA(lef tcolumn)andMonB (rightcolumn)catalogs.Theverticallineindicatestheli mitforsaturation;the horizontallinesarelocatedat0.04and0.06magnitudesofp hotometricerror. deviationforeachbin,andremovedanysourceswhosephotom etricerrorstrayedmore than3sigmafromthemeanvalue.Weshowthisselectionforth ethreebandsinFigure 5-2 ;thesolidcurveindicatesthemeanerrorforeachbinandthe standarddeviationfor thatbinisshownbythesmallsolidverticalline;thedot-da shedlineisthe3 forthe errorsineachbin.Ourerrorsstaybelowthe0.06magnitudeh orizontaldashedlinefor K < 15.75;weconsiderthatvaluetodenethe optimalrange Thethirdselectioncriteriaremovedsaturatedsources;th edetectorreachesits saturationlimitmorerapidlyintheH-bandthaninJorKsowe removedallsources havingH < 11.0.InFigure 5-2 weshowthedistributionofFLAMINGOSphotometry errorswithmagnitude,wheretheverticaldashedlineindic atesthelimitforsaturation. Withthefourthselectioncriteriaisimportantforourcolo ranalysis,wewantedto makesurethatnotonlythephotometricerrorineachlteris lowbutthattheerror intheJ-HandH-Kcolorsarealsolow;thisisimportantbecau seweusethecolors 137

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Figure5-3.FLAMINGOScompletenesslimitestimate.Weesti mateourcompleteness limitbywheretheKLFbeginstodecline.Thisestimateisfor thesources whichsatisfyourphotometriccriteriaandarelocatedinth econtroleld. toevaluatethepresenceofIRxineachsource.Thecolorunce rtaintiesare: J H = ( 2 J + 2 H ) 1 2 and H K =( 2 H + 2 K ) 1 2 andwerequiredthesetobesmallerthan0.1mag. WealsolimitedourcatalogtosourceswithintheFLAMINGOSc ompletenesslimit; ourcompletenesslimitwasestimatedbybuildingaKLFforso urceslocatedinthecontrol eld(seeFigure 5-3 )andwhosephotometrysatisesourselectioncriteria.Wea dopt17.25 asourcompletenesslimit. Weperformedanevaluationofourphotometrybycomparingit tothatof2MASS. InFigure 5-4 wecomparemagnitudesandcolorsforthesourceswhichareob servedby bothFLAMINGOSand2MASSinourcontroleld.Wendgoodagre ementbetween themagnitudesforthethreelters;scatterisparticularl ystrongfortheK-bandbutwe attributethisto:i)wearecomparingtheFLAMINGOS2 : 2 m K-bandtothe2MASS 2 : 16 mK s band;andii)2MASSisonlyphotometricallycompleteto K s 14 : 3mag. FortheJ-Hcolorcomparisonwendthat98 : 4%ofthesourcesagreetowithin0.2 magnitudesandfortheH-Kcomparisonthisvalueis98 : 6%,indicatingagoodagreement betweenFLAMINGOSand2MASScolors.Thecolorcomparisonsa lsoseemtoshowa slightnegativeslope,thismayindicatetheexistenceofac olorterminthecomparisonof FLAMINGOSand2MASSphotometry. 138

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Figure5-4.ComparisonofFLAMINGOSphotometrywith2MASSp hotometry.This comparisonwasperformedforsourcesinthecontroleld. 139

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TheinitialcatalogfortheMonAregioncontained163,517so urces;afterthe applicationoftheseselectioncriteriathenalcontained 81,569sources.Theinitial MonBcatalogwasreducedfrom62,900to30,404andthecontro leldwasreducedfrom 8,685sourcesto5,769.TheMonAandMonBcatalogswerethenm ergedtomakeournal MonOB1catalog,uponwhichweappliedtheNNM;thenalMonOB 1catalogcontained 111,973sources. AnotherfactorwhichlimitedourspatialcoverageofMonOB1 wasopticaldegradation ofthedetector.Wefoundthatthephotometricsensitivityo ftheFLAMINGOSdetector degradedfromthecenterduetoareductioninopticalqualit y;thisaectedtheshapes ofthestarsinthoseregions.Weappliedaradialcorrection tothezeropointofthe photometriccalibrationinordertoaccountforthisdegrad ation;despitethecorrection wewereforcedtorejectmanysourcesinthoseregions.Thisd egradationoccurredmost stronglyontheleftedgeandtheupper-leftcorner.Theradi alcorrectionandsource rejectionwereperformedaspartofthedatareductionproce ssandsoourphotometric selectioncriteriawereappliedafterthis.5.2.6SpatialCoverageofMonOB1 Ofthe49FLAMINGOSeldsusedtomapMonOB1,only35wereacce ptedforthe nalcatalog;theothereldswererejectedbecausethequal ityofthedatawasnotgood. Badweatherduringtheobservationsorproblemswiththedet ector,specicallybadreads andthesoftwarecrashing,werethetwomorecommonissueswh ichcausedaeldtohave badqualitydata.InFigure 5-5 weshowthecoverageofMonOB1andindicate,with dashedlines,therejectedelds. Therejectionsduetoopticaldegradationandtherejection sofsaturatedsources causedournalcatalogtohaveadiscontinuousdistributio nofsources(gaps)asopposed toasmoothtransitionfromeldtoeld.Wewereconcernedth atsourceslocatednear thesegapscouldcausethedetectionof"fakeclusters";how ever,wendthatgapshave theeectofunderestimatingthelocalstellardensity,whe reasa"fakecluster"would 140

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Figure5-5.LocationofFLAMINGOSeldsfortheMonOB1regio n.Fieldsshownaslled werenotincludedinthenalcatalogeitherbecausetheywer enotobservedor becausetheywereobservedunderpoorconditions. requireanoverestimationofthedensity.InFigure 5-6 weshowasimpleillustrationof how,intermsoftheNNM,thepresenceofthesegapscausesthe localstellardensitytobe underestimated. Anotherconcernwasthatthesegapswouldnotallowustoaccu ratelysamplethe distributionofclusters;inordertoaccountforthiswei)r eplacedallsaturatedsourcesby 2MASSsources,andii)applieda"bed"of2MASSsourcestothe fullMonOB1region. InFigure 5-7 weshowthespatialcoverageofMonOB1beforeandaftersuppl ementing ourcatalogwith2MASS.ThepanelontheleftshowstheFLAMIN GOScoverageofMon OB1,andwenoticethatMonAhasgoodspatialcoveragebutwit hsomegapsinthe upperleftcornersoftheelds;thepanelontherightshowsF LAMINGOS+2MASS coverage. Weappliedthesamephotometryselectioncriteriadescribe dinSection 5.2.5 tothe 2MASSsources;inaddition,werestrictedthe2MASSsources tothe2MASScompleteness limitof K s < 14 : 3mag. 141

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A B Figure5-6.Eectsofimposingboundaryconditions.PanelA showsanexampleofa stellarregion,unaectedbyboundaryconditions,whereth edistancetothe 5thNNisbeingmeasured.Thedensityis N 1 =A whereNisthenumber ofsourcesinthecircle,notincludingthecentralsourceno rtheoneatthe circle'sedge;Aistheareaofthecircle.InpanelBthegreya reaindicates theimposedboundary;thesourcesinthatareaarenolongerc onsideredas neighbours.Theeecttobenoticedistheincreaseinthedis tancetothe5th NNwhichwilllowerthedensityestimate. Figure5-7.FinaldistributionofsourcescoveringMonocer os.Theleftpanelshowsthe distributionofFLAMINGOSsourceshavinggoodphotometry; therightpanel includesthebedof2MASSsources.Allsourcessatisfytheph otometriccriteria describedinSection 5.2.5 142

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5.3ANearestNeighborNear-InfraredAnalysisofMonOB1 5.3.1SpatialStructureofMonOB1 WerstdiscusstheoverallspatialstructureoftheMonOB1c loudbeforeentering intothestudyofitsstellarpopulations;todothisweconst ructedaNIRdustextinction mapusingtheNear-InfraredColorExcessRevisited(NICER) method(see LombardiandAlves 2001 );toobtaincompletespatialcoverage,weusedthecombined FLAMINGOS+ 2MASSdataset.TheMonOB1regionwasdividedintobinsmeasu ring2.1 0 x2.1 0 and, foreachbin,weaveragetheAvofallthestarsinsideofit,re sultinginoneextinction valueperbin.Visualextinction, A V ,wascalculatedforeachstarusingEquation 5{1 ; the( H K ) observed termisthecolorofthestarandthe( H K ) intrinsic termisthe medianinstrinsiccolormeasuredfromacontroleld.( H K ) intrinsic wasmeasuredat 0.187magnitudes.Weexcludedsourcesexhibitinginfrared excessemissionfromthese calculations;infraredemissionisindicativeofacircums tellardisksowecannotusethose sourcestoaccuratelyestimateline-of-sightextinction. TheextinctionmapispresentedinFigure 5-8 .ForMonA,theregionsofmoderateto highextinction(5-12mag)arefoundalongawell-denedNor th-Southridge;thisregion thenwidensoutandencompassesclusterNGC2264.ForMonBex tinctionisgenerally low( < 4mag)andpatchyexceptforoneregionmeasuring 2pcinlength,where extinctionpeaksat13mag;thisregionislocatedatRA=98.1 Dec=10.5.Wemeasure anaverageextinctionvalueof5magnitudesoverthewholeca talogbutnotethattheMon OB1extinctionmapisverystructuredsotheextinctionvalu eshavelargevariationsover smallseparations. A V =15 : 93 [( H K ) observed ( H K ) intrinsic ](5{1) WemustpointoutthatbecauseourcatalogconsistsoftheFLA MINGOSdataplaced ontopofa2MASSbedourextinctionmeasurementshavebeena ected.InFigure 5-9 wecomparetheabilitiesofa2MASScatalogandourFLAMINGOS +2MASScatalog 143

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Figure5-8.DustextinctionmapofMonOB1obtainedfromaFLA MINGOS+2MASS dataset.TheNICERprogramwithaNyquist-samplingboxof2. 1 0 x2.1 0 was usedtomakethismap. 144

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Figure5-9.Herewecomparetheextinctionvaluesobtainedf romusinga2MASS catalogandusingaFLAMINGOS+2MASScatalog.Theregionuse dfor thiscomparisoniscenteredonNGC2264andspanstherightas censionand declinationvalues:[100.0,100.5],[9.6,10.5]. inmeasuringextinctionvalues.Themainfeaturetonoticei nthisgureisthatthe FLAMINGOS+2MASScatalogcandetectsignicantlygreatere xtinctionvaluesthan the2MASScatalog(14magfortheFLAMINGOS+2MASSascompare dto6magfor 2MASS);forthisreason,theextinctionmapofFigure 5-8 ismostcompleteintheareas coveredbyFLAMINGOS.5.3.2EstablishingOurCatalogofIRxSources5.3.2.1Color-ColorDiagrams InFigure 5-10 weshowaschematiccolor-colordiagram(CCD)whichdescrib eshow weidentiedIRxsources,andinFigure 5-11 weshowacontourmapoftheJ-HvsH-K CCDforallsourcesinournalMonOB1catalog. Accordingtotheirevolutionarystage,sourceswillinhabi tdierentregionsofthe CCD.Thesolidblacklineatthebottomleftofthediagramrep resentsthemainsequence andthetwobranchesrepresentredgiantsanddwarfs.Thepar alleldashedlinesare linesofreddening andtheyindicatehowthepresenceofextinctionshiftsthel ocation ofthestarsinthisdiagram;mainsequencestarsobservedun derhighextinctionwillbe locatedinaregionknownasthereddeningband,locatedleft wardofthebluesectionand 145

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Figure5-10.JHKcolor-colordiagramshowinglocationofIR xregion.Thesolidblackline showingtwobranchesrepresentsthemainsequence,whereth ebranchesare thelinesfordwarfandgiantstars.Thedashedlinesareline sofreddening, andalongwiththearrowtheseindicatehowthepresenceofex tinctionwill shiftstarsinthediagram;mainsequencestarsshouldliele ftwardoftheblue regionandrightwardofthedashedline,inaregionknownast he reddening band .Objectslyingtotherightofthereddeningband,intheblue region, exhibitinfraredexcessemission.Thesolidlinesarethelo ciofthezeroage mainsequenceandthegiantbranchfrom BessellandBrett ( 1988 ).Thedot dashlineshowstheunreddenedTTaurilocusfrom Meyeretal. ( 1997 );the reddeningvectorsarefrom Cohenetal. ( 1981 ). rightwardofthedashedline.Wehaveassumedthereddeningl awof Cohenetal. ( 1981 ) forallCCDs;thisreddeninglawistruefortheCITphotometr icsystem,sincethatisthe systeminwhichthelawwasderived,howeverwefoundthatthe choiceofthereddening lawdidnotmakeadierenceinourstudy.Theblueregionindi cateswheresources exhibitingIRxemissionwillbelocated;Equations 5{2 and 5{3 mustbothbesatisedfor asourceexhibitingsignicantIRx. 146

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( J H ) < 1 : 692 ( H K )(5{2) ( J H ) > (0 : 47 ( H K ))+0 : 46(5{3) LadaandAdams ( 1992 )ndthattheblueregionisprimarilypopulatedbyClassI sourcesandclassicalT-Tauristars(CTTS).Finally,webri ngattentiontothedot-dash linewhichbeginsatthelowerbranchofthemainsequenceand denesthelowerbounds oftheblueregion;thislineisknownastheclassicalTTauri locusbecause,asshownby Meyeretal. ( 1997 ),CTTSwilloccupythisverynarrowregionoftheJ-HvsH-KCC D. ApplyingtheaboveselectioncriteriawendthatournalMo nOB1catalog contained3,339IRxsources.Weexpectyoungembeddedclust erstohaveasignicant fractionoftheirpopulationlocatedintheblueregion,and ,fromFigure 5-11 ,wesee thatMonOB1doescontainasignicantpopulationofIRxsour cestotherightofthe reddeningband.Wealsonoticethattheregiontotheleftoft hereddeningbandis populated;thisregionisrepresentedinFigure 5-10 bythegreencolor.Accordingto LadaandAdams ( 1992 ),forastartobelocatedinthisregionwouldrequire"physi cally implausibleconditions,"makingitaforbiddenregionfory oungstars.Thefactthatwe dondsourcestotheleftoftheredenningbandindicatesthe presenceofphotometric errorsinourcolormeasurements.Weexpecttheeectsofsca ttertobringstarsfromthe reddeningbandrightward,intotheregionofIRxemission,a ndsowefurtherrestrictour samplebyonlytakingthosesourceslocatedatmorethan2tim esthestandarddeviation oftheH-Kcoloruncertaintytotherightofthereddeningban d;the"dashdotdotdot" linesinFigure 5-11 indicatethisadditionalrestriction. Theamountofscatterisdirectlycorrelatedtothedepthtow hichwesampleour eldsbecausephotometryerrorsincreasewithmagnitude;s cattercanbeminimized byapplyingacutinourmaximummagnitude,andinFigures 5-12 and 5-13 weshow CCDsforthedierentmagnitudecuts.Figures 5-12A 5-12B and 5-12C areforaK-band 147

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Figure5-11.ContourplotoftheCCDforsourceshavingK < 17.25.Thesourcesincluded herefollowthephotometryrestrictionsdescribedinsect 5.2.5 .TheNyquist samplingboxusedtomapthecolor-colordiagrammeasured0. 1magx0.1 mag.Thetwo"dashdotdotdot"linesshowtheadditionalrest rictionwhich limitstheeectsofscatter;asourcemustbelocatedtother ightofthemost rightwardoftheselinesinordertobeconsideredashavingI Rx. 148

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magnitudecutof14.50mag,Figures 5-12D 5-12E and 5-12F foramagnitudecutof15.25 mag,Figures 5-13A 5-13B and 5-13C foramagnitudecutof15.75mag,andFigures 5-13D 5-13E and 5-13F foramagnitudecutof16.50mag. NextwepointoutanddiscussthetwomainfeaturesoftheseCC Ds:i)thepopulation lyinginthereddeningband,andii)thescatterintheFLAMIN GOScolors.InFigure 5-12A theobservationsareonlyslightlydeeperthanthe2MASScom pletenesslimit;we seethatthereddeningbandisstronglypopulated,indicati ngthepresenceofextinction whichisshiftingthecolorsofmainsequencestarsintothis region;wealsonoticeasmall butdistinctbulgeintotheregionofIRx.Figure 5-13E isfor16.5 < K < 17.25;herewe observethattheCCDisclosetocircularbutstillshowingan elongationalongtheTTauri locus.Thedistributionofcolorsbecomesveryroundforthe faintestmagnitudesbecause thephotometricerrorsincreasewithincreasingmagnitude ,thusgeneratingmorescatter incolorestimates.Forthecontrol-eld,itisevidentthat thesestarsoccupytheregion oftheCCDcorrespondingtothemainsequence;thisisexpect edsincethecontrol-eld wasremovedfromthecloudandthussuerslittleextinction .AnalyzingFigures 5-12F and 5-13F wepointoutthatthecontroleldsdocontainsomeIRxsource s;thesesources arelocatedalongtheCTTSlocusandcannotbeaccountedforb yconsideringscatterin FLAMINGOScolors,sincethereisnocorrespondingscattert owardslowerH-Kvalues. TheIRxsourcesobservedinthecontroleldsareseenforfai ntmagnitudeswhereas,for theoneld,weobserveIRxsourcesatallmagnitudes. Wewillbereferringtofourdatacuts;thesearei)the 2MASScut ,K < 14.5,going justslightlydeeperthanthe2MASScompletenesslimit;ii) the conservativecut ,K < 15.25, going0.75magdeeperthan2MASS;iii)the optimalcut ,K < 15.75,stayingwellwithinthe FLAMINGOSoptimalrangeofmagnitudes;andiv)the deepcut ,whichextendstowhere the3 errorsreach0.1magnitudes,K < 16.5.EachcutdividestheIRxpopulationintoa bright groupanda faint group;withthefaintgrouphavingmagnitudesextendingall the waytotheFLAMINGOScompletenesslimitof17.25magnitudes .LookingatFigures 5-12 149

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A B C D E F Figure5-12.Color-colordiagramsforthemagnitudecutsK < 14.5andK < 15.25.Therst twocolumnsarefortheMonOB1population;therightcolumni sforthe controleld.TheNyquistsamplingboxusedtomapthecolorcolordiagram measured0.1magx0.1mag. 150

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A B C D E F Figure5-13.Color-colordiagramsforthemagnitudecutsK < 15.75,andK < 16.5.Therst twocolumnsarefortheMonOB1population;therightcolumni sforthe controleld.TheNyquistsamplingboxusedtomapthecolorcolordiagram measured0.1magx0.1mag. 151

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and 5-13 asthreecolumns,then,thecolumnontheleftcontainstheCC Dsforthebright populationwhereasthecolumninthemiddlecontainsCCDsfo rthefaintpopulation. Weusedthebrightpopulationtotracetheboundariesofthec lusters,sincethosesources havelesscolorscatter,andthenweincludedthefaintpopul ationfortheclusteranalysis; clusterdetectionwillbefurtherexplainedinSection 5.4 5.3.2.2DepthofEachCut AsmentionedinSection 5.1 ,MonOB1isknowntobeyoungbuttoalsohavean agespreadof10 7 yr;assuch,weexpecttobesensitivetosourceswithagesbet ween 0.5Myrand10Myr.Weusethisagerangetogetherwithevoluti onarymodelsby D'AntonaandMazzitelli ( 1997 )andanaverageextinctionof5visualmagnitudes determinedfromourNICERmaptoestimatethemasssensitivi tyofoursurvey;we showthosevaluesinTable 5-1 .Sincewehaveseenthattheextinctionvariessignicantly weexpectourlimitingmagnitudetoalsobestronglydepende ntupontheregionstudied. Wewereparticularlyinterestedinevaluatingwhetherwewe resensitivetostarsat thehydrogen-burninglimit(0.08 M )becausethisalsomarksthehighestmassfora browndwarf.Browndwarfsareobjectswithmasseslowerthan theHBLyethigherthan 13Jupitermasses;theprocessesleadingtobrowndwarfform ationarestillunclear,sowe wereinterestedinwhetherwecouldaddressthistopicthrou ghastudyofthebrowndwarf distribution.Wendthat,assumingavisualextinctionof5 mag,boththeoptimaland thedeepcutsaresensitiveto2Myr,andyounger,browndwarf s;at5Myrsonlythedeep cutcanpickupthoseobjects.5.3.2.3DistributionofIRxSources WenowlookathowtheIRxsourcesarespatiallydistributedt hroughoutMonOB1; inTable 5-2 wepresentthenumberofsourceswithgoodphotometryandthe number ofsourceswithIRxforthefourmagnitudecuts.Wenotethato fallthedetectedIRx sourcesonly15arefromthe2MASScatalog;2MASSIRxsources represent7.1%ofthe IRxsourcesfortheconservativecut,3.3%fortheoptimalcu t,and0.75%forthedeepcut. 152

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Table5-1.PhotometricLimits Age-0.5Myr MagnitudeLimit(Mag)Mass( M ) 14.50.1 15.250.0815.750.05 16.50.03 Age-1Myr MagnitudeLimit(Mag)Mass( M ) 14.50.1 15.250.0815.750.06 16.50.04 Age-2Myr MagnitudeLimit(Mag)Mass( M ) 14.50.2 15.250.115.750.07 16.50.05 Age-5Myr MagnitudeLimit(Mag)Mass( M ) 14.50.35 15.250.3015.750.15 16.50.075 Age-10Myr MagnitudeLimit(Mag)Mass( M ) 14.50.5 15.250.0515.750.2 16.50.1 Evolutionarymodelsby D'AntonaandMazzitelli ( 1997 ) andavisualextinctionof5magwereused 153

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Table5-2.NumberofSourcesExhibitingInfraredExcess MagCutNo.SourcesNo.IRxSources 14.534866210 15.254868745215.7562097856 16.5896871994 NumberofIRxsourcestoK < 17.25is3339 Thereare152MASSIRxsourcesinourregion Weconsiderthecontributionof2MASStobenegligiblewhena nalyzingthedistribution ofIRxsourcesfortheoptimalanddeepmagnitudecuts.Weals opointoutthatinthe combinedcontrol-eldsweidentifyzero(0)IRxsourcesfor the2MASScut,7forthe conservativecut,26fortheoptimalcut,and83forthedeepc ut. InFigures 5-14 ,and 5-15 weshowthedistributionofIRxsourcesforthefour magnitudecuts;inthenextsectionwewilldiscusshowtheNN MusedfortheIRx sourcesdieredfromthatappliedinChapter 4 .Wewanttopointouttheabsenceof coverageinonesquareeldlocatedintheMonBregion,thisi sField11.Theabsence ofFLAMINGOScoveragecanbeseeninFigure 5-7 andwasduetopoorobserving conditions.Thoughthiseldiscoveredbythe2MASSbed,the absenceofFLAMINGOS coverageisverynoticeableinourdistributionofIRxsourc essincenoIRxsourcesare foundinthisregionusingthe2MASSmagnitudecut.5.3.3AdaptingtheNNMtoIRxStudies ExpandingtheNNMfromhowitwaspresentedinChapter 2.2.4 toamulti-wavelength (IRx)analysiswasperformedinacollaborationwithCarlos Roman-Zu~nigaforstudying theclusteredpopulationinRMC(seeR08).Thereweresigni cantdierences,both technicallyandconceptually,fromtheoriginalmethod;we discussthoseherebefore presentingtheresults. OnemaindierencewastheuseofIRxsources,asopposedto K s -bandsources,to identifytheECs.Forinstance,intheMonOB1analysisweuse dIRxsourcestoidentify clustersandtracetheirboundaries,whereasinChapter 4 theanalysiswasperformedon 154

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Figure5-14.DistributionofIRxsourcesforthe2MASScutan dfortheconservative cut.Weexpectverylittlebackgroundcontaminationforthe setwocuts;for K < 14.5noIRxsourceswerefoundinthecombinedcontrolelds, andfor K < 15.25only7werefound. 155

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Figure5-15.DistributionofIRxsourcesfortheoptimalcut andforthedeepcut.At thispointweexpectsomeoftheIRxsourcestobeduetobackgr ound contamination;fortheoptimalmagnitudecutwefound26IRx sourcesin thecombinedcontroleldsandforthedeepcutwefound83. 156

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thedistributionof K s -bandsources.Oneadvantagethisapproachhadoverthe K s -band analysiswasthereductionofeldsourcecontamination;al thoughwestillndIRxsources intheeld,theseareinmuchfewernumbersthanwitha K s -bandstudy.Ontheother hand,itisnotknownwhetherthedistributionofIRxsources inclustersmirrorsthatof K s -bandidentiedsources,sothecomparisonofclusterprope rtiesobtainedbythetwo methodsmustbedonewithcaution. Anotherimportantdierenceisthatwearelesssensitiveto clusterswithasmall numberofmembers.AswesawinChapter 4 ,theseyoungclusterstendtohavelow IRx frac values(the IRx frac distributioninSection 4.2.2.6 peakedat15%),whichmeans thataclusterwith100membersandan IRx frac of10%willonlyhave10IRxmembers. Inordertobemoresensitivetosmallerclusterswehaveused aj-valueof10insteadof 20;thiswasdonefortheRMC(seeR08).Aj-valueof10optimiz estheNNMtoclusters havingatleast10sources;forclusterswith IRx frac valuesintherangeof10%-50%,this limitsourdetectionstoclustershavingatotalnumberofso urcesbetween20-100.As discussedinChapter 2 ,loweringthej-valuemakesusmoresensitivetosmaller(in terms ofnumbersources)densityructuations.Wehadavoidedther egimeofsmallructuations inChapter 4 becauseitisstronglyinruencedbyrandomructuationsinth epopulous backgroundeld;however,backgroundcontaminationissig nicantlyreducedwhentracing onlytheIRxpopulation.Inthefollowingsectionweapplyth eNNMandpresentthe resultsofouranalysis. 5.4Results WeperformtwodistinctstudiesontheMonOB1populationofI Rxsources:i)we identifyclustersandmeasuretheirproperties(Section 5.4.2 );andii)westudythespatial distributionoftheIRxpopulation(Section 5.4.3 );thesetwoapproachesarecomparableto theonesperformedontheECcataloginChapter 4 InordertoidentifytheclustersinMonOB1wehaveusedtheco nservativecut (K < 15.25)andtheoptimalmagnitudecut(K < 15.75);ofthefourcuts,thesetwoprovide 157

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thebestbalancebetweendepthandminimizingcolorerrors. Wedon'tusethedeepcut forclusteridenticationbecauseofitslargercolorscatt eranditshigherbackground contamination.ThelargercolorscatterinthedeepcutCCDs meansthatwearemore likelytoincludefalseIRxsources;thiscanhaveasignica nteectonalocalscale,where acoupleoffalsedetectionsmayskewthecorrecttracingofa clusterboundary.However, weassumedthatthelargescaledistributionofIRxsourcesi snotsignicantlyaectedby theinclusionofasmallfractionoffalseIRxsource;asares ult,forthestudyofthespatial distributionofIRxsourceswehaveincludedresultsfromth edeepcut.Thehighnumber ofIRxsourcesdetectedinthecontroleldatK < 16.5is,inpart,duetothelargercolor scatterpresentatthismagnitudecut;however,wealsoexpe ctsomecontaminationto comefromobjectswhicharenotYSO(wediscussthisfurtheri nSection 5.5 ). 5.4.1DistributionofNNSeparations InFigure 5-16 wepresentthedistributionsof10thNNseparationsfortwom agnitude cuts;thesedistributionswereusedtodeterminethecutos eparationwhichdenesthe clusterboundary.Thechoiceofthecutovaluewasperforme dinasimilarmannerto whatwasusedinChapter 4 andisshowninFigure 5-16 bythesolidverticalline. UsingthecutovaluewedividedtheIRxpopulationinto highdensity sourcesand lowdensity sources;inFigures 5-17 and 5-18 weagainshowthedistributionofIRx sourcesforeachmagnitudecutbutthistimewedistinguishb etweenhighandlowdensity sources.TheblackdotsrepresentthelocationofalltheIRx sourcesdetectedforeach magnitudecutwhereasthereddotsrepresenttheIRxsources havingNNseparations smallerthanthecutovalue;thereddotstracethelocation oftheclusters. The2MASScutpicksoutthreeregionsofIRxsourceswithinMo nOB1;thelargestof theseislocatedatRA=100.20,Dec=9.70.Theconservativec utidentiesthreeregions withred(highdensity)sources,thesamethreeasforthe2MA SScut.Whenwelookat theoptimalcut(K < 15.75)weidentify5regionswithhighdensity;thethreemai nones correspondtotheoneslocatedatlowercutsandthefourthis locatedatRA=100.30, 158

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Figure5-16.Distributionof10thNNdistancesfortheconse rvative(K < 15.25)andoptimal (K < 15.75)cuts.Thedottedlineindicatestheo-eldpeakwher easthesolid lineindicatesthecutovalue,choseninasimilarwaytoCha pter 4 159

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Dec=11.15.Finally,atthedeepcutwend 18regionscontainingclustersofhigh densitysources. 160

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Figure5-17.ClusteringofIRxsourcesforthe2MASScutandf ortheconservativecut. Sourcesshowninredhavelocaldensitieshigherthanthecut ovalue,while sourcesinblackhavedensitieslowerthanthecuto. 161

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Figure5-18.ClusteringofIRxsourcesfortheoptimalcutan dforthedeepcut.Sources showninredhavelocaldensitieshigherthanthecutovalue ,whilesources inblackhavedensitieslowerthanthecuto. 162

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5.4.2PropertiesofClustersIdentiedinMonOB1 Wedetected3clusterswiththeconservativecut(K < 15.25)andfourwiththeoptimal cut(K < 15.75);onlyoneoftheseisdistinctfromtheonesdetecteda tK < 15.25.InFigures 5-19 to 5-24 wepresentcontourplotsconstructedusingthe10thNNsurfa cenumber density,aCCDforallsourceswithmagnitudesdownto17.25, aCCDforallsources brighterthanthemagnitudecut,aKLFforallIRxsourcesint hecluster,andKLFs comparingtheclusterandtheo-eldpopulations. 163

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Figure5-19.Cluster1-withK < 15.25 Figure5-20.Propertiesofcluster1-withK < 15.25 164

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Figure5-21.Cluster2-withK < 15.25 Figure5-22.Propertiesofcluster2-withK < 15.25 165

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Figure5-23.Cluster3-withK < 15.25 Figure5-24.Propertiesofcluster3-withK < 15.25 166

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WemapthelocationoftheclustercentersinFigure 5-25 andinFigure 5-26 weuse SKY-MAPtolookforcorrespondencebetweenourdetectionsa ndknownobjects. ThepositionofCluster1(Figure 5-19 )closelycorrelateswiththererectionnebulae IC446,Cluster2(Figure 5-21 )hasnocorrespondingobjectandCluster3(Figure 5-23 ) correspondstothecenterofthewell-studiedclusterNGC22 64.IC446belongstothe MonR1associationwhichisbelievedtobeatasimilardistan ceandrelatedtotheMon OB1association. NGC2264andIC446areobservedintheupperpanelofFigure 5-26 butCluster2 canonlybeobservedininfrared(lowerpanel).Intheupperp anelwelocatethecluster centersusingyellowboxes,inthelowerpanelusingblackst ars. InTable 5-3 wepresentvaluesfortheclustercenters,numberofbrightI Rxsources, totalnumberofIRxsources,numberofclustermembers,equi valentradius,coreradius, centralcondensationstructurecoecient ,fractionofsourcesexhibitingIRxinthe clusterandvisualextinction.Theclustercenterwasobtai nedusingEquation 2{3 equivalentradiususingEquation 4{1 ,thecoreradiususingEquation 2{5 ;forthenumber ofmembersweusedKLFmethodsdescribedinSection 4.2.2.5 .ThenumberofIRx sourcesandthe IRx frac arebothcorrectedforbackgroundcontamination;wend2IR x sourceswithK < 15.25and75IRxsourcesforK < 17.25inthecontroleld(areaofcontrol eldis0 : 101448deg 2 ).Althoughthebright(K < 15.25)sourceswereusedtoidentifyand tracetheclusterboundaries,weusedallsourcesdowntothe FLAMINGOScompleteness limittomeasuretheclusterproperties. WealsoneedtoaddressconcernsarisingfromtheFLAMINGOSc overagenotbeing spatiallyhomogeneousand,thus,ataconsistentcompleten esslimit.Ourclusterswere situatedoverFLAMINGOSgaps,thismeantthatthesecluster swereonlypartially sampledtoadepthof17.25(andfullysampledtoadepthof14. 3duetothe2MASS bed).Thispartialcoverageaectedourestimatesforthenu mberofmembersbecauseour backgroundcorrectionassumedasamplingdepthof17.25. 167

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Table5-3.ClusterDetectionsforConservativeCut ClusterIDRADec N bright IR N IR N R E R C IRx brightfrac A v (J2000)(pc)mag 1-IC44697.89829710.468200281352662.271.190.74285 2-Cluster299.03109710.963748241179861.911.190.68163 3-NGC2264100.205989.70851151113337593.712.300.73225 ValuesbelowareforKLFstruncatedat14.5mag 1-IC44697.89829710.468200191351652.271.190.74104 2-Cluster299.03109710.963748131171981.911.190.6832 3-NGC2264100.205989.7085115753337543.712.300.738.54 Totakethisintoaccount,wevisuallymeasuredtheareaofth egaps;subtracting thisareafromthetotalclusterareagaveustheclusterarea sampledto17.25.Forthe control-eldKLFsubtractionwenormalizedKLF-binssmall erthan14.3tothefullcluster areaandKLF-binslargerthan14.3tothecorrectedclustera rea. Additionally,forClusters1and2wendthatthecontrol-e ldKLFdoesnotfully matchthebackgroundcontributionseenintheclusterKLFs; thisismostpronouncedfor Cluster2.Webelievethatthisisnotarealeectbutismostl ikelyduetoacombination of1)adicultyinaccuratelymeasuringthefaintendofaKLF duetothedistance atwhichMonOB1islocated;and2)thedieringdataqualityo fthecontroleldand theeldswhichmakeuptheclusters.Inordertoestimatethe totalnumberofcluster membersaswellasthefractionofsourcesexhibitinginfrar edexcess,wehavetruncated theKLFsat14.5(thevalueatwhichtheKLFsforbothCluster1 and2tendtozero);we presentboththevaluesofthefullKLFsubtractionandthetr uncatedKLFsubtractionin Table 5-3 168

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Figure5-25.Locationofclustercentersasmeasuredusingt heNNmethodandthe conservativemagnitudecut(K < 15.25).WealsoaddedthelocationofCluster 4whichistheonlynewclusterdetectedwhenusingtheoptima lmagnitude cut(K < 15.75 169

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Figure5-26.Locationofclusterdetectionsascomparedtot woimagesadaptedfrom SKY-MAP(Wikisky).SKY-MAPdoesnotprovidethedetailsfor the observationsthatledtothepictureshownintheupperpanel ;thelower panelisfromtheinfraredskysurvey,IRAS.Intheupperpane lwelocatethe clustercentersusingyellowboxes,inthelowerpanelusing blackstars. 170

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5.4.3AStudyoftheClusteredvsDistributedStarFormation OurstudyofembeddedclustersinChapter 4 showedusthatananalysisoftheNN separationscanhelpusidentifythepresenceofdierentpo pulationsinaclustereld; however,ouranalysisinthatchapterwaslimitedbothphysi cally,bytheboundariesofthe clustereld,andbecausewewereusingasingle-lter.Inth ischapterwediscusstheuseof thedistributionofNNseparationstoidentifydierentpop ulationswithinMonOB1;for thisanalysiswewillusetheconservativecut(K < 15.25),theoptimalcut(K < 15.75)and thedeepcut(K < 16.5). IntheupperpanelofFigure 5-27 ,weshowthedistributionofNNseparationsforthe conservativecut;wenoticesignicantstructure,interms ofpeaksandtroughs,similarto whatwasobservedinChapter 4 .Specically,thereisabroadpeakwithatail,centered at0.15/0.16deg.Weassociatethiswithabackgroundcontam inantpopulationsincethese starshavesimilarseparationstothedistributionofstars inouroeld.Thedashedline locatedat0.121degliesatthetroughtotheleftofthebackg round,andwasthevalue usedfortheclusterdetectionatthebeginningofthischapt er.Asimilarcriteriawasused fordetectingclustersinChapter 4 .Thedistributionofsourceseparations,forseparations shorterthanthebackgroundseparationsexhibitstwodisti nctpeaks,oneat0.05degand thesecondat0.11.Thesolidlineinthegureislocatedat0. 085deg,thetroughformed bythesersttwopeaks.Thelowerpanelshowswhereeachpopu lationislocated;the redsourcesareforNNseparationssmallerthantherstvert icalline,theblacksources forseparationsbetweentherstandsecondlines,thegreen forseparationsbetweenthe secondandthird,andtheyellowforseparationslargerthan thedottedline.Intermsof theirspatialdistribution,theredpopulationisverytigh tlypackedintowhatwedene asa corepopulation ;theblackpopulationfollows,forthemostpart,asimilarb utmore spreadoutdistributiontotheredandwedeneitasthe halopopulation ;thegreen populationisgenerallynearbytheredandtheblackbutwith aneverlooserassociation 171

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Figure5-27.DistributionofNNseparationsfordierentpo pulationsinMonOB1.The sourceshavinga10thNNseparationsmallerthanthatindica tedbythe solidline(intheupperpanel)areshowninred,sourceshavi ngseparations betweenthesolidandthedashedlinesareshowninblack,sou rceswith separationsbetweenthedashedandthedottedlineareshown ingreenand sourceswithseparationslargerthanthatindicatedbythed ottedlineare showninyellow. 172

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andwedeneitasthe aggregatepopulation ;theyellowshowsnoevidentstructureandwe deneitasthe eldpopulation Wehavechosentheterminologyof"core"and"halo"basedont heworkpresentedin Chapter 4 .Similarlytowhatwasseeninthatchapter,thedistributio nofNNseparations forIRxsourcesgenerallyshowstwopeaksforseparationssm allerthanthoseofthe o-eld;onedeningthecorepopulationandtheothertheha lo.Theterm"aggregate" isbasedontheworkof Strometal. ( 1993 ); Strometal. ( 1993 )ndapopulationof about1500youngstarsdistributedthroughoutL1641,aswel lassevenaggregatesandone embeddedcluster. AsimilaranalysisforcutsofK < 15.75andK < 16.5isshowninFigure 5-28 .Inthis Figureweseethatthepopulationsobservedforthedeepcutc loselyfollowthoseobserved attheconservativeandoptimalcut;thisgaveuscondencet hattheobservedstructures werenotsimplytheresultofbackgroundcontamination.Web elievetheretobesignicant backgroundcontaminationforthedeepcut,butwedonotthin kitwouldi)overwhelmthe structuresobservedatmoreconservativecuts;orii)showu pastightclusters.InSection 5.5 wepresentfurtherdiscussionontheeectsofbackgroundco ntamination. Inordertoanalyzethepropertiesofthesourcesineachpopu lationwestudytheir KLFs,J-Hcolordistributions,andCCDs.Wesaw,inSection 5.3.2 ,thatanalyzingthe CCDofapopulationallowsustodiscernbetweenthosesource sbelongingtothemain sequenceandthosehavingIRx,InFigure 5-29 weshowtheCCDsforthefourdierent populations;wenoticethatfromthecorepopulationtothe eldpopulationthereare fewerIRxsourceswithhighcolors;theeldseemstohavesom esourceswithhighcolors butlessthanthecore.Theseresultsindicatethat:1.ThereisatrendofprogressivelylowerJ-HandH-Kcolorsw hengoingfromthe coretothehalototheaggregatepopulation.Thisindicates thatthecoreismore embeddedandhashigherinfraredexcessthanthehaloandthe aggregates. 2.Theeldpopulationalsocontainsafewsourceswithhighe xtinctionandwith excess;however,takingintoaccountthattheeldpopulati oncontainsoverdouble 173

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Figure5-28.SameasFigure 5-27 butforK < 15.75andK < 16.5. 174

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Figure5-29.Color-colordiagramsforIRxpopulationsinth econservativecut.Thesolid linesarethelociofthezeroagemainsequenceandthegiantb ranchfrom BessellandBrett ( 1988 ).ThedotdashlineshowstheunreddenedTTauri locusfrom Meyeretal. ( 1997 ),thereddeningvectorsarefrom Cohenetal. ( 1981 ). 175

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thenumberofsourcesthantheclusteredpopulation,thefra ctionofsourceswith highextinctionandexcessintheeldismuchlessthaninthe clusters. Anothermethodofobtaininginformationaboutthedierent stellarpopulationsis throughtheuseoftheJ-Hcolordistribution( Strometal.1993 );inFigures 5-30 and 5-31 wepresenthistogramsoftheJ-Hcolorsfortheeachpopulati on.ThetwopanelsinFigure 5-30 areforallsourcesinthecontrol-eldandintheMonOB1cata log(withK < 15.25). ThecontourmapinFigure 5-13F clearlyshowsthepresenceofsourceshavingJ-Hvalues correspondingtotherstpeak;thesecondpeakcorresponds towherethemainsequence branchesintotheredgiantanddwarfloci.Intherightpanel weonlyseeonepeaklocated ataJ-Hcolorvalueapproximatelyhalfwaybetweenthetwope aksofthecontrol-eldand aslightbulgetotheright;weinterpretthisdistributiona sbeingtheresultofapopulation thatisdominatedbymain-sequencestarsbutbulgingtohigh erJ-Hcolorsduetothe presenceofasignicantpopulationofyoungsources. InFigure 5-31 weshowthedistributionsfortheIRxsources,wheretheleft panelis forthecontrol-eldwhich,aswesawinFigure 5-13F ,containsasmallpopulationofIRx sourceslocatedalongtheTTaurilocus.ThepresenceoftheT Tauristarsisrerectedin themainpeakofthedistribution,andweattributeasolidbl acklinetothispeakwhich wewilluseinthediscussionofthenextdistributions;thev erticaldottedlineindicates whatwebelievetobeweak-lineTTauristars(WTTS).Whenobs ervingtheJ-Hcolor distributionforallIRxsourcesinMonOB1wenoticethatthe mostpronouncedpeak (dashedline)islocatedjustrightwardofthesolidvertica lline,weattributethispeak tothepresenceofareddened(embedded)CTTSpopulation.Th esedistributionsshow signicantstructureforJ-Hvalueslargerthanthemainpea k;someofthisstructurewe attributetothethepopulationofCTTSobservedundervaryi ngdegreesofextinctionand somewebelievetobeClassIsources.Wendthatthecorepopu lationcontainsthemost signicantamountofsourcesrightwardofthedashedlinean dinferthatthecorecontains theyoungestsources. 176

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Accordingto LadaandAdams ( 1992 ),theyoungerClassIsourcestendtohave aJ-Hcolorgreaterthan1.5.Assuch,weusethepercentageof sourceshavingaJ-H colorgreaterthan1.5tocomparetheagesofthepopulations ;weshowtheseresults inTable 5-4 .Wendthatthecorepopulationcontainsthehighestpercen tage,with 32.5%followedbythehalowith20%,theaggregatealso20%an dthentheeldwith 8%.Thismayindicatethatthecorepopulationistheyounges t,followedbythehaloand aggregatepopulationsandthentheeldpopulation.Figure 5-31 showshowtheJ-Hcolor distributiondiersamongstthefourpopulations. 177

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Figure5-30.J-Hdistributionsforpopulationsintheconse rvativecut;they-axisrangeis notthesamefortheseplots.WeshowtheJ-Hdistributionfor allsources havingK < 15.25belongingtothecontrol-eldandforsourceshaving K < 15.25belongingtotheon-eld. Figure5-31.J-HdistributionsforIRxpopulationsintheco nservativecut;they-axisrange isnotthesamefortheseplots.WeshowtheJ-Hdistributions forsources withK < 15.25inthecontrol-eld,intheon-eldandforK < 15.25sources locatedinthecore,halo,aggregateandeldpopulations. 5.4.4MeasuringtheFractionofStarsinClusters WecalculatethefractionofIRxstarsassociatedwithclust eredstarformationby comparingthenumberofIRxsourceswithinclusterboundari estothenumberofIRx sourcesoutsideofthoseboundaries. ForthisestimateweuseourcalculationofthetotalMonOB1a rea;thiswasobtained byaddingthecorrectedareasforeachFLAMINGOSeld.Wend atotalusableareaof 2.955115deg 2 178

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Table5-4.NumberofSourcesinEachPopulation PopulationTotal(J-H) > 1.5(J-H) < 1.5(J-H) > 1.5 NNN% MagcutK < 15.25 Core123408332.5 Halo50104020 Aggregate65135220 Field214171977.9 Fortheconservativecutwend3clusters;theseoccupyatot alareaof0.363deg 2 (12.3%ofthetotalarea).IntermsofIRxsources,forthisma gnitudecutwendatotal numberof452 21inMonOB1;173 13(38.3%)arelocatedinsidetheclustersand279 17outside.Inordertoaccountforbackgroundcontaminatio nwescaledthenumberof IRxinthecontroleldtotheareaoftheclusters;hence,wee stimatethat143 12IRx sourcesarelocatedinclustersand68 8IRxsourcesareoutside.Therefore,forMon OB1thefractionofIRxsourcesinsideyoungclustersis68% 6%.Thisvaluecorrelates wellwiththevalueof60%obtainedbyR08fortheRMC. 5.5DiscussionofBackgroundContamination WefoundthatbygoingtodeepermagnitudesthenumberofIRxs ourcesrose signicantly;thiswasobservedforboththecontroleldan dtheMonOB1eld.Thisrise can,inpart,beattributedtoanincreasedsensitivitytoyo ungstarsoflowermass,such asbrowndwarfs;however,asimilarriseisobservedintheco ntroleld,indicatingthat backgroundcontaminationmustbeanimportantfactor. Onepossiblesourceofcontaminationisfromsourceshaving alargeFLAMINGOS colorscatter;suchsourceswouldbeshiftedfromtheredden ingbandintotheIRxregion. Inordertominimizethiseectweimposedabuerontheredde ningbandandonly acceptedsourceslocatedrightwardofthatbuer.Othersou rcesofcontaminationhave beenthefocusof Fosteretal. ( 2008 )(F08).F08studiedpossiblecontaminationfrom non-YSOswhenobservingintheinfrared;inparticular,F08 havelookedathowobjects suchasgalaxiesandAGNcouldpopulatesimilarregionsofth eCCDasYSOs.BothR08 179

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Figure5-32.ComparisonofIRxnumberdensitiesfortheMonO B1regionandforthe controleld.Theleftpanelshowsthenumberdensitiesfore achmagnitude cutandintherightpanelwehavesubtractedtheo-eldnumb erdensities fromthoseoftheon-eld.Insteadofassuminganaverageext inctionforthe eld,wehaveusedaprobabilitydistributionfunctionofth eextinctionin ordertomoreaccuratelyestimatetheo-eldcontribution andF08emphasizetheneedforcarefulbackgroundcorrectio nsevenwhenconsidering brightsources;andsimilarlytoR08,wetoondbrightIRxso urcesinthecontroleld. Thestepswetooktoaccountforbackgroundcontaminationar einagreementwiththose suggestedbyR08andF08. InFigure 5-32 weshowacomparisonofthenumberdensityofIRxsourcesinth e MonOB1regionandinthecontroleld;thenumberdensityisc alculatedbydividing thenumberofIRxsourcesfoundforeachmagnitudebythearea ofthecontrol-eld (forthedashedline)andtheMonOB1region(forthesolidlin e).Toaccurately estimatetheo-eldcontaminationwehavetakenintoaccou nttheeectsofextinction. ExtinctionreddensthedistributionofsourcesintheJ-Hvs H-KCCDsuchthathigher extinctiongeneratesmoreIRxdetections;sinceourspatia ldistributionofextinctionis nothomogeneous,wecalculatedtheextinctionprobability distributionfunction(EPDF). TheEPDFwasobtainedbycalculatingthepercentageofon-e ldsourceshavingdierent extinctionvalues.Thepanelontherightshowsthedierenc eofthesetwocurves,wend thatformagnitudesbetween14.5magand16.0magthereisadi erenceinthenumber densityofbetween50and100starspersquaredegreeandthat formagnitudesgreater than16.0magthedensityrises. 180

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5.6Discussion TheNNMhasprovenaneectivemethodfordetectingandanaly zingclustersin bothsmallregions(Chapter 4 )and,asseeninthischapter,largeregions.Itsapplicatio n ontheyoungstellarpopulationofMonOB1hasindicatedthre emainclustersofYSOs: therstliesinthelineofsightofIC446,theseconddoesnot haveaknowncounterpart andthethirdonecoincideswithNGC2264.TheNNMhasprovide duswithproperties forthesethreeclusters.TheknownclusterNGC2264isbyfar themostprominentof thethreefound;thisclusterholds68%ofthetotalnumberof clustermembers,and70% ofK < 14.5maginfraredexcesssources;itisnotuncommontondth emajorityofthe stellarpopulationlocatedwithinonlyoneorafewoftheclu sters.Thiswasalsoseen by Ladaetal. ( 1991b )intheL1630molecularcloud,where49%ofthetotalnumbero f membersbelongtojustoneofthefourclustersinthatcloud, andby Roman-Zu~nigaetal. ( 2008 )intheRosettemolecularcloud,ndingthat77%ofallembed dedstarswerelocated inthe5richestclusters(outofatotal12clusters). SimilarlytowhatwasfoundintheRosette,ourclustersarel argerthanothersin literature.Wendthattheequivalentradiusrangesfrom1. 91to3.71pc,withanaverage valueof2.63pcandthecoreradiusrangesfrom1.19to2.3pcw ithanaverageof1.56 pc.Forcomparison,inChapter 4 wefoundarangeof0.08to1.76pcandanaverageof 0.66pcfortheequivalentradius,andforthecoreradiusara ngeof0.03to0.69pcwithan averageof0.28pc. ClusterNGC2264wasalsostudiedinChapter 4 yetitwasconsideredasbeingtwo individualclusters,theNGC2264Northcluster(RA[06:41: 03],Dec[+09:53:07])andthe NGC2264Southcluster(RA[06:41:03],Dec[+09:30:00]).Up onthediscoveryofthehalo populationweareledtobelievethatthereisonlyonelargec luster. DahmandSimon ( 2005 )foundthedistributionofT-Tauristarstobeindicativeof adoubleclusteras opposedtotwoindividualclusters;ourvalueof3.71pcfort heequivalentradiusexceeds their2.5pcradius.Weestimateatotalof754clustermember sforNGC2264,thislies 181

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wellwithintheacceptedrangeinliteraturewherevaluesas highas1000membershave beenestimated( Dahm2008 ). Ouranalysisofthedistributionofnearestneighborsepara tionshasindicatedevidence forthepresenceoffourstellarpopulationsamongstthoses ourcesexhibitinginfrared excess;wehaveattributedtothesepopulationsthefollowi ngclassication:i)core,ii)halo, iii)aggregateandiv)eld.Thecoreandthehaloclassicat ionsfollowfromtheworkin Chapter 4 ,theaggregateclassicationforthepossibleassociation tothesamepopulation seenby Strometal. ( 1993 ). Wendthatthecoreandthehalopopulationsshowtightlyclu steredspatial distributions,theaggregatepopulationhasalesswell-de nedstructureandoftenforms arcs,whereastheeldpopulationshowsnosignsofspatials tructure.Wealsondthat: i)sourcesbelongingtothecorepopulationarealwaysspati allyassociatedwithahalo,an aggregate,and,inevitably,aeldpopulation,ii)sources classiedas"halo"arealways associatedwithanaggregateandaeldpopulationbutnotne cessarilyacorepopulation, andthatiii)sourcesclassiedasaggregatearealwaysasso ciatedwiththeeldpopulation andoftentimeswithahalo. Buildingcolor-colordiagramsandperformingJ-Hcolorcom parisonsforeachofthe fourpopulationswendthatthefractionofIRxsourceswith high( > 1.5)J-Hcolors decreasesfromthecoretotheaggregates.Wesuggestthatth ismayindicateanage gradient,wherethecorepopulationistheyoungestandthe eldpopulationtheoldest. Classicationintothefourpopulations(core,halo,aggre gate,eld)wasperformedfor progressivelydeeper(fainter)magnitudecuts;forthemos tpart,IRxsourcesdetectedat deepermagnitudesfollowthesamespatialdistributionasI Rxsourcesdetectedatbright magnitudes.Inotherwords,bygoingtodeepermagnitudeswe seeanenhancementofthe spatialstructuresobservedatbrightmagnitudes.Weinter pretthisasindicationthatthe low-massstarsfollowsimilarspatialdistributionsasthe highmassstars.Wespeculate 182

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thatthismaybeindicatingthatthemodesofformationgover ninglowandhighmass starsisthesame. Lastly,usingthesamemethodasinR08andaconservativemag nitudecut (K < 15.25),wecalculatethefractionofsourcesbornincluster stobe68% 6%;this impliesthatmostoftheIRxsourcesinMonOB1arelocatedinc lusters. 183

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CHAPTER6 ACOMPARISONOFRESULTSFORNGC2264 6.1IntroductionandMotivation ItisclearthatthedominantstarformingregioninMonOB1is NGC2264;this hasbeennotedbypreviousstudies,andourresultsfromChap ter 5 supportthis.Inthis chapterwediscusshowthedistributionofIRxsources,iden tiedusingFLAMINGOS, compareswithstellardistributionsfrompreviousstudies andcontributestounderstanding thestarforminghistoryofNGC2264. ThereisnopresentconsensusonwhetherNGC2264isbestcons ideredadouble-double clusteroraquadruple;itis,however,clearthatthisregio nishighlystructured(seeLL03 and WilliamsandGarland2002 ).AgeestimatesindicatethatNGC2264isyoung,with amedianageofjust3Myr;however,theregionalsoshowsevid enceforanagespreadof 5Myr.Thissupportsascenarioofmultipleepochsofstarfor mation;itislikelythatthe NGC2264containssourcesformedfromolder( 5Myr)episodesofstarformationaswell asrecent( 3Myr)andevencurrentepisodes. Evidenceofongoingstarformationcomesfromthenumerouse mbeddedclusters ofprotostars,molecularoutrows,andHerbig-Haroobjects thathavebeendetectedin thisregion;withthetwomostprominentsitesofstarformat ionhavingbeenidentied surroundingIRS1andIRS2.Thetotalstellarpopulationfor thiscomplexclusteris estimatedtobeashighas1000memberswithasignicantfrac tionbeingsubstellar ( WilliamsandGarland2002 ,LL03, Dahm2008 ).Evidenceof236substellarmass candidateswasfoundby Kendalletal. ( 2005 );onlyafewoftheseobjectshavereliable 2MASScounterpartsbecausetheirestimated K s -bandmagnitudesaremuchfainter thanthe2MASScompletenesslimit.Assuch,thereisevidenc efortheexistenceofan undetectedlow-masspopulation. ToseehowourFLAMINGOSobservationsandanalysistwithth ecurrentstar formationscenarioinNGC2264wehavecomparedthedistribu tionofIRxsources(found 184

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usingtheNNMontheFLAMINGOSobservations)todistributio nsof2MASS-detected sourcesandSPITZER-detectedsources(ClassIsources,Cla ssIIsourceswithanemic disks,andClassIIsourceswiththickdisks).Forthedistri butionof2MASSsourceswe haveusedresultsobtainedfromtheapplicationoftheNNMsh owninChapter 4 ;whereas fortheSPITZERcomparisonweusedatableofsourcesprovide dtousbyPaulaTeixeira ( Teixeira2008 ). Wewillshowthiscomparisonforthreedierentmagnitudecu ts:i)K < 15.25,ii) K < 15.75andiii)K < 16.5;byusingdierentmagnitudecutsweareobservingdie rent masssensitivitylimits.ReferringbacktoTable 5-1 ,arangeofagesfrom0.5Myrto5 Myrwillcorrespondtothefollowingrangesinmass:i)forth eK < 15.25cut:0.08M -0.30M ,ii)fortheK < 15.75cut:0.05M -0.15M andiii)fortheK < 16.5cut: 0.03M -0.05M .Intheestimatesabovewehaveusedthe D'AntonaandMazzitelli ( 1997 )evolutionarymodelsanda5magnitudesofvisualextinctio n.Wenotethatthese estimatesaresensitivetoboththeevolutionarymodelused andtotheextinction;thislast parameter,aswehavementioned,variesconsiderablythrou ghouttheNGC2264region. 6.2MappingtheMolecularStructure Weconsiderthemolecularcloudastherootofallthestarfor mationthathas occurredandthatwilloccur;forthisreason,werstmapthe extinctioninthisregionand willuseitthroughoutthevariousdatacomparisons. TheextinctionmapfortheNGC2264regionofMonOB1isshowni nFigure 6-1 ;in ordertocreatethismapwehaveusedallsourcesintheFLAMIN GOS+2MASScatalog toadepthofK=15.25magnitudes.Similarlytotheprocedure discussedinSection 5.3.1 wemeasuredtheline-of-sightextinctionthroughmeasurem entsoftheH-Kcolorandusing Equation 5{1 ;theeldwasthenbinnedintoresolutionelementsof2.79 0 x2.79 0 (0.65 pc 2 ). Wenotethati)similarmapswereconstructedfordepthsofK= 15.75,16.5magnitudes andtheseshownodierence,andii)6FLAMINGOSimageswereu sedtoimagethis region,sothe2MASSbedusedtosupplementFLAMINGOSdataha sminimalinruence 185

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Figure6-1.ExtinctionmapoftheNGC2264region.Weshowthe locationofSMon,IRS 1,IRS2andtheedgeoftheFoxFurnebula. inthisanalysis.Also,inthismap,weshowthelocationsoft hemainfeaturesinthis region;thesefeaturesare:i)theO7VmultiplestarSMon,ii )thedeeplyembedded early-typeinfraredsourceIRS1(Allen'ssource),iii)inf raredsourceIRS2,astarforming coreassociatedwithaprotostellarcluster,andiv)theedg eoftheFoxFurnebula.The stellarobjectsSMon,IRS1andIRS2haveeachbeenassociate dwithclusters. Figure 6-1 showsthatthemolecularmaterialintheNGC2264regionisdi stributed alongaNorth-Southridge;therearetwoveryprominentenha ncementsinextinction, whereextinctionrisesabove9magnitudesinV-band,andwe ndthattheycoincidewith IRS1andIRS2.Thiswouldindicatethattheclustersassocia tedwithIRS1andIRS2 aredeeplyembedded.SMonislocatedinaregionoflowerexti nction( 5magandclose totheedgeoftheFoxFurnebula. WenowlookatthedistributionofIRxsourceshavingK < 15.25;thisisshownin thetwopanelsofFigure 6-2 .Intheleftpanelweshowthedensitycontoursforthe 186

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Figure6-2.TheNGC2264regionwithIRxsources,K < 15.25.Theleftpanelshowsthe contoursofNNdensityforIRxsources;therightpanelshows thelocationof IRxsources,bluesourcesbelongtothe"core"population,g reensourcestothe "halo",whitetotheaggregateandblacktotheeld. distributionofIRxsources.Wendthatthecontoursclosel yfollowtheextinctionmap; therearetwopeaksinthecontourlevelssurroundingthesou rcesIRS1andIRS2and thenthereisabroadpeaklocatedontheedgeoftheFoxFurneb ula.Intherightpanel weshowthelocationoftheindividualIRxsourceswhereweha veusedbluesquaresto indicatethe"core"population,greensquarestoindicatet he"halo"population,white squarestoindicatethe"aggregate"populationandblackfo rtheeld.Inthispanelwe canclearlyseethatthecorepopulationispreferentiallyl ocatedinthevicinityofthe knownclustersassociatedwithIRS1,IRS2,andSMon.Wepoin toutthepresenceofa corepopulationlocatedattheveryedgeoftheFoxFurnebula .Theslightlylowerdensity halopopulationcloselyfollowstheNorth-Southmolecular ridgewhiletheaggregate populationispreferentiallylocatedaroundtheridge,int heregionsoflowerextinction( < 4 mag). InFigures 6-3 and 6-4 weshowthesametwoplots(IRxdensitycontoursand distributionofIRxsources)forthemagnitudecutsofK < 15.75andK < 16.5,respectively. Goingtothesedeepercutsallowsustoprobealower-masspop ulation.Themainfeatures 187

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Figure6-3.SameasFigure 6-2 butforK < 15.75 Figure6-4.SameasFigure 6-2 butforK < 16.5 188

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observedinFigure 6-2 arealsoobservedintheseplots;namely,theconcentration of IRxsourcesaroundIRS1,IRS2,andSMon.Inaddition,wenoti cethepresenceofa considerablenumberofIRxsourcesextendingfromtheFoxFu rnebulatolowervaluesof declination;wewillrefertothisfeatureastheNGC2264Lob e.Wenoticethatthelobe becomesparticularlyevidentinthepanelsofFigure 6-4 ;inthese,thelowerregion(lower indeclination)ofthelobebecomespopulatedtothepointwh ereitrivalsthedensities foundaroundIRS1andIRS2.AlsofromtherightpanelofFigur e 6-4 weidentifya groupofIRx"core"IRxsourcesalongthemolecularridge;we labelthegroupandthe lobeonourmaps. WenowcomparethedistributionofIRxsourcestodistributi onsofsourcesidentied using2MASSandSPITZER.Forthe2MASScomparisonwehaveplo ttedthecluster contoursasdenedinChapter 4 ;thecontoursherewerechosenusingthecutovalue andtheytracethesurfacenumber-densityofsourcesidenti edinthe K s -band.Forthe SPITZERcomparisonsweusetheclassicationofsourcesint o:i)ClassIIthickdisk,ii) ClassIIanemicdiskandiii)ClassI,asperformedbyPaulaTe ixeira( Teixeiraetal.2006 (T06)). Thecomparisonwith2MASSisshowninthetwopanelsofFigure 6-5 ;inthe upper-leftpanelwecompare2MASSwiththeIRxsourcesident iedatK < 15.25mag, intheupper-rightpanelwithIRxsourcesidentiedatK < 15.75magandinthelower panelwithIRxsourcesidentiedatK < 16.5mag.IneachofthesepanelswendthatIRS 1andIRS2arewelltracedbyboth2MASSand,aswesawbefore,o urIRxobservations; theclustersurroundingSMon,however,doesnotshowaclear match.ForSMon,we observethatonlythelower(lowerdeclinations)regionoft he2MASScontourhasa signicantnumberofIRxsources;thisregionalsohasapart ialoverlapwiththeedgeof FoxFurnebulaanditispossiblethatthesetworesultsareco nnected.Anotherfeature,in thisgure,thatmayhelpusunderstandtheconnectionbetwe enthe2MASScontours,the IRxdistributionandtheFoxFurnebulaisindicatedbythear row;intheregionindicated 189

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Figure6-5.Comparisonof2MASScontoursandIRxsourcesfor the15.25magcut (upper-leftpanel),the15.75magcut(upper-rightpanel)a nd16.5magcut (lowerpanel). 190

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Figure6-6.LocationofCIIAnemic/ThickDiskandCISources ,K < 15.25 bythearrow,wendaseriesof 8IRxsourcesalllocatedalongtheveryedgeofboththe 2MASScontourandtheFoxFurnebula. Inthenaltwogures(Figures 6-6 and 6-7 weshowthelocationoftheSPITZER-identied sourcesoverlayeduponthenearestneighbourIRxdensityco ntoursforthe15.25magand 16.5magcuts.Wedonotincludethe15.75magcutinthisanaly sisbecauseweconsider itsdensitycontourstobesucientlysimilartothoseshown heretonotwarrantan separatediscussion.Thethreecategoriesdistinguishedh ereare:i)opticallythickdisks, 191

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Figure6-7.SameasFigure 6-2 butforK < 16.5 192

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ii)anemicdisksandiii)ClassIsources;weaddthat,source swiththickdisksarealso referredtoasClassIIsources,andanemicdisksourcesareC lassIII.Fromthecatalogs providedbyT06,116sourceshaveanemicdisks,217havethic kdisks,and12areClassI sources;wecomparethelocationsofeachpopulationtotheI Rxdistribution. ObservingtheupperleftpanelofFigures 6-6 wenoticethatthethickdisksources closelyfollowboththeIRxnumber-densitycontoursandthe North-Southmolecularridge; furthermore,thereseemstobeasignicantpopulationofth ickdisksourceslocatedat theintersectionoftheIRxcontourswiththeFoxFurnebula. Anemicdisks(upperright panel)alsolieovertheIRxcontoursbutdonotseemtobeasco nstrained(asthethick disks)tothesamedistribution.ThereareveryfewClassIso urces(lowerpanel)and weseetheirdistributionfocusedaroundIRS1andIRS2,corr elatingwellwiththeIRx contoursforthatregion. Figure 6-7 showsasimilarcomparisonbutforadeeperpopulationofIRx sources;we noticeafewfeatureswhicharedistinctfromthoseinFigure 6-6 duetothepresenceofthe "group"and"lobe"featurespreviouslyidentied.Wendth atthegroupcoincideswell withnumerousthickdisksources;ifwecomparewiththeuppe rleftpanelofFigure 6-6 (K < 15.25)wenoticethatthosesourcesdidnothaveacorrespond ingIRxcontourpeak astheydoforK < 16.5.ThefactthatthispeakintheIRxcontourlevelsonlyap pearsfor deeperobservationsmayindicatethattheseyoungClassIIs ourcesarealsooflower-mass. WealsonoticethatthethickdisksourcesalsofollowtheIRx contoursleadingup(higher declinationvalues)fromtheFoxFuredgetoanotherpeakint heIRxcontourlevels(we indicatethisregionwithanarrow).Thesewouldindicateth atthedistributionofIRx sourcescloselyfollowsthatoftheClassII(thickdisk)sou rces;ontheotherhand,we noticeasignicantpresenceofthickdisksourcessurround ingSMonforwhichthereisno correspondingpeakinIRxnumberdensity.Infact,theIRxco ntoursseemtoformanarc structureinthevicinityofthebrightOstarSMon.Wealsono ticethatthelowerpart ofthelobeonlycoincideswithafew( < 5)thickdisksourcesand 8anemicdisksources; 193

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sincethecoincidencewiththeotherthicksourceswasgood, wesuggestthatthelobe sourcemayhavemagnitudeswhicharetoofaintfortheSPITZE Rlimits.Finally,wepoint outthat,forallmagnitudecuts,thereisaclosecorrelatio nbetweentheIRxdensitiesand ClustersIRS1andIRS2. 6.3Conclusion ThedistributionofIRxsources,asanalyzedusingtheNNM,c loselyfollowsthe molecularcloud,asmeasuredbytheextinctionmap.Thiscoi ncidencebetweenIRxand extinctionisespeciallynoticeableforIRxsourcesbelong ingtothe"core"and"halo" populationsasdenedinChapter 5 .Aclosecorrelationisalsoobservedbetweenthe distributionofIRxsourcesandtheknownclustersIRS1andI RS2;thiscorrelationis seeninthevariousmagnitudecutsforwhichIRxdistributio nsweregenerated.Infact, fortheregionsurroundingclustersIRS1andIRS2,wendgoo dagreementbetween IRxsources,2MASSnumber-densitycontours,thedistribut ionofthickdisksources,and thedistributionofClassIsources;anemicsourcesshowasl ightlylesstightindicationof clusteringforthatregion. FortheknownnorthernclustersurroundingSMon,however,w ehaveobserved signicantdierencesinthedistributionsofstellarpopu lations.Ourresultsindicate thatIRxsourcesarenotprevalentintheimmediatesurround ingsofSMon,onlywhere the2MASScontourassociatedwiththeSMonclustermeetsthe FoxFurnebuladowe ndasignicantnumberofIRxsources.Webelievethatthisr egionattheveryedgeof theFoxFurnebulaisahighdensityregion,formedfromtheme etingofapressurewave originatingSMonandthenebula.T06hadnoticedthecoincid enceofthethickdisk number-densityenhancementandtheFoxFurnebulaandhadpo intedoutthatthismay beindicativeofsequentialstarformation(SSF);thefactt hatwedetectthepresenceofa coreIRxpopulationforthissameregionmayindicatethepre senceofYSOsinthenebula andthussupporttheSSFscenario. 194

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Finally,wendthestrongpresenceofanIRxlobeandanIRxgr oupaswesample atdeepermagnitudesandsuggestthatbysamplingatdeeperm agnitudeswearepicking uplower-massstarsinthisregion;assuch,thesefeatures( thelobeandthegroup)may correspondtoclustersorgroupsoflow-massIRxsources.Es timatingtheextinctionat 5magfurtherindicatesthat,ifrealYSOs,theseobjectsmay havemassesinthebrown dwarfrange. 195

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CHAPTER7 SUMMARYANDFUTUREWORK Insummary,wehavedevelopedanewmethod(thenearestneigh bormethod,NNM) ofsystematicallydetectingandanalyzingyoungembeddedc lusters;thisisanovelway ofstudyingclusterssowehaveperformedMonteCarlosimula tionstounderstandits rangeofapplicability.Ourmethodiswellsuitedforstudyi ngacluster'sinternaldensity structureandwehaveappliedittounderstandthestructure of43knownclusters.Our analysishasshownthat50%oftheclustersprominentenough tosignicantlysample theirNNdistributionhaveaninternaldensitystructurewh ichcanbebestunderstood consideringacore+halomodel.Thisincludessomeofthewel lknownclusterssuchasIC 348,NGC2024,Trapezium,NGC2071,NGC1333,S106.Wefoundt hatthemajority (64%)ofourclustershaveaninternaldensitystructurecat egorizedascentrallycondensed, astructurewhichissuggestiveofagravitation-drivenfor mationscenario;furthermore,we ndthatyoungerclustersaremorecentrallycondensed.Add itionally,duetotheeectsof extinction,weconsiderthistobealowerlimitontherealva lue. Inordertobetterunderstandthisscenariowehavesurveyed thepopulationofyoung starsinthenearbymolecularcloudMonocerosOB1.Applying ourNNMtotheYSOs inthiscloudhasprovidedevidenceforthepresenceoffourd istinctpopulations:core, halo,aggregateanddistributed;ananalysisoftheinfrare dcolorssuggestsapossible agedierencewiththecorebeingyounger,followedbytheha loandthentheaggregate. Finally,wehavelookedinmoredetailatthespatialdistrib utionofthesepopulationsfor thewellknownclusterNGC2264,andcomparedthesetothedis tributionofknownyoung sources.Ourresultsindicateatightcorrelationbetweent hecore+halopopulationandthe thickdiskClassIIsources;thisfurtherindicatesthatthe sepopulationsareindeedyounger andthatthehaloisprobablyaproductofstarformationinst eadofclusterevolution. Thisresearchpointstoseveralavenuesoffuturework.Ourd evelopmentandanalysis ofthenearestneighbourmethodhasshownittobeanexcellen ttoolforthestudyof 196

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stellarclusters,beingabletoprovidemeasurementsoffun damentalclusterparameters. However,weaddthatthenearestneighbourmethodisnotrest rictedtothestudyof stellarregionsandthatwewouldliketoseeitsapplication tofurtherourunderstandingof otherdistributionssuchasthoseofgalaxies. ThemodelsgeneratedinChapter 3 representarststeptowardunderstandingwhat componentsmakeupacluster;weproposethatthesemodelssh ouldbecontinueduntil theclustersbeinggeneratedcloselyresembleknowncluste rs.Themodelshavebeen fundamentalinourunderstandingoftheapplicationofthen earestneighbouranalysis,we believethatthenearestneighbourmethodcanprovidefurth erinsightsintoclusterstudies sowesuggestcontinuingsimilartests. The K s observationsofclusters,presentedinChapter 4 ,provideuswithonlya shortbaselinewithwhichtoaccuratelymeasureinfraredex cessand,thus,inferrelative ages.Inordertobetterstudytheexistenceofapossiblecor relationbetweenthecluster's structure,asmeasuredbytheparameter ,anditsagewesuggestobtainingL-band observations. InordertofurtherunderstandtheresultsinChapter 5 wesuggestobtaining spectroscopicobservationsofsourcesineachpopulation; spectrawouldallowusto measureagesandmassesfortheseobjectsand,thus,testour results.Additionally,we recommendre-imagingCluster4andobtainingspectraofits membersinordertobetter understandit. Finally,Chapter 6 hasrevealedthreefeaturesofinterestforfutureresearch .These are:theregionattheedgeoftheFoxFurNebulawhichmaybein teractingwiththe strongO-starpressurewaveoriginatingfromSMonandmaybe asiteofyoungstar formationandii)thelobeandthegroupwhichshowupinthedi stributionofIRxdensity andmayalsobesitesofyounglow-massstars. 197

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APPENDIXA FURTHERRESULTSOFCLUSTERSOBSERVEDWITHNNM A.1ContoursandSourceDistributionsofClustersobserved with2MASS Thisappendixcontainsacatalogoftheclustersidentiedi nChapter 4 .Foreach clusterweshowtwogures:i)thegurelabeled"A"showsthe density(20thNNdensity) contours;thelowestlevelcontourisequaltotheaverageba ckgrounddensityandthe darkcontourhasadensityequaltothecutodensity,ii)the gurelabeled"B"showsthe distributionof20thNNseparations. 198

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AContourplotforNGC1333. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-1.NGC1333. AContourplotforIC348. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-2.IC348. 199

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AContourplotforNGC2024. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-3.NGC2024. AContourplotforNGC2068. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-4.NGC2068. 200

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AContourplotforNGC2071. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-5.NGC2071. AContourplotforTRAP. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-6.Trapezium. 201

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AContourplotforL1641N. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-7.L1641N. AContourplotforS106. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-8.S106. 202

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AContourplotforRCrA. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-9.RCrA. AContourplotforL988e. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-10.L988e. 203

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AContourplotforCepA. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-11.CepA. AContourplotforMonR2. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-12.MonR2. 204

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AContourplotforGGD. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-13.GGD12-15. AContourplotforNGC2264. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-14.NGC2264. 205

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AContourplotforNGC2264South. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-15.NGC2264South. AContourplotforLKH. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-16.LKH 101. 206

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AContourplotforAFGL490. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-17.AFGL490. AContourplotforCha. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-18.ChameleonI. 207

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AContourplotforKMS35. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-19.KMS35. AContourplotforCKGroup. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-20.CKGroup. 208

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AContourplotforNGC2023. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-21.NGC2023. AContourplotforV380Ori. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-22.V380OrimeleonI. 209

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AContourplotforIRAS05401-1002. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-23.IRAS05401-1002. AContourplotforIRAS243245. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-24.IRAS243,245. 210

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AContourplotforCB34. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-25.CB34. AContourplotforIRAS08375-4109. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-26.IRAS08375-4109. 211

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AContourplotforIRAS08404-4033. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-27.IRAS08404-4033. AContourplotforIRAS08448-4343. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-28.IRAS08448-4343. 212

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AContourplotforIRAS08470-4243. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-29.IRAS08470-4243. AContourplotforIRAS08470-4321. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-30.IRAS08470-4321. 213

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AContourplotforIRAS08476-4306. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-31.IRAS08476-4306. AContourplotforIRAS08477-4359. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-32.IRAS08477-4359. 214

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AContourplotforBBW192E. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-33.BBW192E. AContourplotforIRAS20050+2720. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-34.IRAS20050+2720. 215

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AContourplotforHD216629. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-35.HD216629. AContourplotforL1211. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-36.L1211. 216

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AContourplotforVYMon. BDistributionofsourceshavingseparationscloserthanthechosenvalue. FigureA-37.VYMon. A.2SurfaceDensityRadialProles Inthissectionwepresentcorrelationsbetweenclusterpar ametersaswellasradial prolesforeachcluster;powerlawfunctionsoftheformF(x )= x werettedtothe clusterproles. Ourradialproleslikelysuerfromtwoproblems:1)weusec ircularannulicentered ontheclustercenter,however,ourclustersaregenerallyn otcircular;2)thesurface densityofeldstarsisestimatedfromanalyzinganearbyre gion,however,thiscoulddier fromthatfounddirectlyintheline-of-sightofthecluster 217

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FigureA-38.RadialprolesofclustersCha,SVS2,NGC1333, andIC348.Powerlaw functionsoftheformF(x)= x werettedtoeachclusterprole.The x-axisisinunitsofthecluster'sequivalentradiuswherea sthey-axisisin unitsofthecluster'smean,20thNN,surfacedensity. 218

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FigureA-39.Radialprolesofclusters,NGC2024(mainclus ter),NGC2024(new cluster),NGC2068(maincluster),andNGC2068(newcluster ).Power lawfunctionsoftheformF(x)= x werettedtoeachclusterprole. Thex-axisisinunitsofthecluster'sequivalentradiuswhe reasthey-axisis inunitsofthecluster'smean,20thNN,surfacedensity. 219

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FigureA-40.RadialprolesofclustersNGC2071,LKH 101,KMS35(maincluster), andKMS35(newcluster).PowerlawfunctionsoftheformF(x) = x werettedtoeachclusterprole.Thex-axisisinunitsofth ecluster's equivalentradiuswhereasthey-axisisinunitsoftheclust er'smean,20th NN,surfacedensity. 220

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FigureA-41.RadialprolesofclustersCKGroup(mainclust er),CKGroup(newcluster), NGC2023,V380Orimaincluster),andV380Ori(newcluster). Powerlaw functionsoftheformF(x)= x werettedtoeachclusterprole.The x-axisisinunitsofthecluster'sequivalentradiuswherea sthey-axisisin unitsofthecluster'smean,20thNN,surfacedensity. 221

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FigureA-42.RadialprolesofclustersIRAS05401-1002(ma incluster),IRAS05401-1002 (newcluster),IRAS243,245,andL1641C(maincluster).Pow erlaw functionsoftheformF(x)= x werettedtoeachclusterprole.The x-axisisinunitsofthecluster'sequivalentradiuswherea sthey-axisisin unitsofthecluster'smean,20thNN,surfacedensity. 222

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FigureA-43.RadialprolesofclustersTrapezium,L1641N, CB34,andS106.Powerlaw functionsoftheformF(x)= x werettedtoeachclusterprole.The x-axisisinunitsofthecluster'sequivalentradiuswherea sthey-axisisin unitsofthecluster'smean,20thNN,surfacedensity. 223

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FigureA-44.RadialprolesofclustersIRAS08375-4109(ma incluster),IRAS08375-4109 (newcluster),IRAS08375-4109(newcluster),IRAS08404-4 033.Powerlaw functionsoftheformF(x)= x werettedtoeachclusterprole.The x-axisisinunitsofthecluster'sequivalentradiuswherea sthey-axisisin unitsofthecluster'smean,20thNN,surfacedensity. 224

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FigureA-45.RadialprolesofclustersIRAS08448-4343(ma incluster),IRAS08448-4343 (newcluster),IRAS08470-4243(maincluster),andIRAS084 70-4243(new cluster).PowerlawfunctionsoftheformF(x)= x werettedto eachclusterprole.Thex-axisisinunitsofthecluster'se quivalentradius whereasthey-axisisinunitsofthecluster'smean,20thNN, surfacedensity. 225

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FigureA-46.RadialprolesofclustersIRAS08470-4321(ma incluster),IRAS08470-4321 (newcluster),IRAS08476-4306,andIRAS08477-4359.Power lawfunctions oftheformF(x)= x werettedtoeachclusterprole.Thex-axisis inunitsofthecluster'sequivalentradiuswhereasthey-ax isisinunitsofthe cluster'smean,20thNN,surfacedensity. 226

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FigureA-47.RadialprolesofclustersBBW192E,IRAS20050 +2720,RCrA,andL988e. PowerlawfunctionsoftheformF(x)= x werettedtoeachcluster prole.Thex-axisisinunitsofthecluster'sequivalentra diuswhereasthe y-axisisinunitsofthecluster'smean,20thNN,surfaceden sity. 227

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FigureA-48.RadialprolesofclustersCepA,HD216629,L12 11(maincluster),L1211 (newcluster).PowerlawfunctionsoftheformF(x)= x werettedto eachclusterprole.Thex-axisisinunitsofthecluster'se quivalentradius whereasthey-axisisinunitsofthecluster'smean,20thNN, surfacedensity. 228

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FigureA-49.RadialprolesofclustersMonR2,GGD12-15,NG C2264,andNGC2264 South.PowerlawfunctionsoftheformF(x)= x werettedto eachclusterprole.Thex-axisisinunitsofthecluster'se quivalentradius whereasthey-axisisinunitsofthecluster'smean,20thNN, surfacedensity. 229

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FigureA-50.RadialprolesofclustersAFGL490(mainclust er),AFGL490(newcluster), VYMon,andL1228.PowerlawfunctionsoftheformF(x)= x were ttedtoeachclusterprole.Thex-axisisinunitsoftheclu ster'sequivalent radiuswhereasthey-axisisinunitsofthecluster'smean,2 0thNN,surface density. 230

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FigureA-51.Radialprolesofalltheclusters.Thex-axisi sinunitsofthecluster's equivalentradiuswhereasthey-axisisinunitsoftheclust er'smean,20th NN,surfacedensity. 231

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PearsonCorrelationCoecients CorrelationNegativePositive Null-0.09to0.00.0to0.09 Small-0.3to-0.10.1to0.3 Medium-0.5to-0.30.3to0.5 Large-1.0to-0.50.5to1.0 A.3CorrelationsbetweenClusterParameters Inthissubsectionwelookforcorrelationbetweenthepower -lawcoecient and variousclusterparameters( ,mass,numberofmembers,equivalentradius,coreradius, fractionofinfraredexcesssources,averageclusterextin ction,andmaximumdensity). Instudyingthecorrelationsbetweenclusterparameterswe haveusedboththePearson coecientandtheSpearman'srankcoecienttoevaluatethe strengthofacorrelation. Werefertocorrelationsasnull,small,medium,orlargeacc ordingtothevalueofthe Pearsoncoecient;thecutovaluesforeachcategoryaresh owninTable A.3 .The Spearman'scorrelationcoecientispossiblybettersuite dforourdata.Whereasthe Pearsoncoecientwillbe1(or-1)foralinearcorrelationb etweenthetwovariable, theSpearman'scoecientis1(or-1)wheneverthevariables arecorrelatedthroughany monotonicfunction.InadditiontotheSpearman'scoecien twealsopresentavalue,r, indicativeofthesignicanceofthecorrelation;thesigni canceisavalueintherange[0.0, 1.0]withsmallvaluesindicatingasignicantcorrelation A.3.1CorrelationsBetweenClusterParametersA.3.2CentralCondensationvsExtinction InFigure A-60 weshowtherelationshipbetweenaverageextinctionand ;thesolid lineshowstheaverageextinctionforbinsizesof0.1in ;themainclustersarerepresented bythestars,whereasnewclustersarerepresentedbythebox es. Wendatrendbetweenthesetwoparametersindicatingthate xtinctionincreasesas weconsiderclustersthataremorecentrallycondensed,the Pearsoncoecientislargeand negative(-0.506),theSpearman'scoecientis-0.489with asignicance2 : 34 10 4 .This 232

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FigureA-52.Correlationbetweenradialproleandtau.We ndalargepositivePearson coecientof0.774.Spearman'srankcorrelationcoecient is0.773with asignicanceof1 : 93 10 11 .Thislargecorrelationhavingasmallr strengthensouruseof asameasureofthesteepnessofacluster'sradial densityprole. FigureA-53.Correlationbetweenradialproleandmass.We ndamediumnegative Pearsoncoecientof-0.360.Spearman'srankcorrelationc oecientis-0.374 withasignicanceof6 : 29 10 3 233

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FigureA-54.Correlationbetweenradialproleandnumbero fsources.Wendamedium negativePearsoncoecientof-0.304.Spearman'srankcorr elationcoecient is-0.321withasignicanceof0.0205. FigureA-55.Correlationbetweenradialproleandequival entradius.Wendasmall negativePearsoncoecientof-0.186.Spearman'srankcorr elationcoecient is-0.135withasignicanceof0.340. 234

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FigureA-56.Correlationbetweenradialproleandcorerad ius.Wendamedium positivePearsoncoecientof0.371.Spearman'srankcorre lationcoecient is0.455withasignicanceof6 : 97 10 4 FigureA-57.Correlationbetweenradialproleandinfrare dexcessfraction.Wenda mediumnegativePearsoncoecientof-0.331.Spearman'sra nkcorrelation coecientis-0.425withasignicanceof0.0017. 235

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FigureA-58.Correlationbetweenradialproleandextinct ion.Wendamedium negativePearsoncoecientof-0.439.Spearman'srankcorr elationcoecient is-0.371withasignicanceof6 : 8 10 3 FigureA-59.Correlationbetweenradialproleandmaximum density.Wendalarge negativePearsoncoecientof-0.685.Spearman'srankcorr elationcoecient is-0.757withasignicanceof8 : 35 10 11 236

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FigureA-60.Correlationbetweenextinctionand .Mainclustersarerepresentedby thestarssymbols,whereasnewclustersarerepresentedbyt heboxes.The Pearsoncoecientislargeandnegative(-0.506).TheSpear man'scoecient is-0.489withasignicance2 : 34 10 4 .Thesolidlineistheaverage extinctionforbinsofsize0.1in trendisstrongerthantheonewith IRx frac fromFigure 4-13 .Similarlytothetrendseen with IRx frac ,therelationshipseemstoexistonlyforC-typeclusters,p ossiblyextending to valuesof0.55.Thisgureindicatesthatmorecentrallycon densedclustersarealso moreembedded.A.3.3ExtinctionvsInfraredExcessFraction InFigure A-61 weshowtherelationshipbetweenaverageextinctionand IRx frac ; themainclustersareshownasstarsandthenewclustersasbo xes.Weseeatrendof increasingextinctionwithincreasing IRx frac .WhenwediscernbetweenC-typeand F-typeclusterswendthatthistrendonlyholdsforthecent rallycondensedsample.We expectedtoseeatrendbetweenthesetwoparametersbecause itiswellestablished(LL03) thatyoungclustershavehigher IRx frac valuesandaremoredeeplyembeddedintheir natalmolecularmaterial;thefactthatonlytheC-typeclus tersshowapronouncedtrend mayindicatethatthisassociationbetweenyouthandembedd ednesshasdissipatedfor 237

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theF-typeclusters.ThePearsoncoecientforthiscorrela tionismediumandnegative (-0.401).TheSpearman'scoecientis0.322withasignica nceof0.0197. A.3.4EquivalentRadiusvsMass InFigure A-62 weshowtherelationshipbetweenclustersizeandmass,indi cating thatclusterswithlargerradiiarealsomoremassive;thist rendisseenforbothmainand newclusters,thesolidlineisthesameasasthatseeninFigu re 4-15 ( R ( N )= R 50 ( N 50 ) 1 2 ). Thepearsoncoecientfortherelationshipbetweenthesetw opropertiesislargeand positive(0.728).TheSpearman'scoecientis0.634withas ignicanceof4 : 53 10 7 A.3.5MaximumDensityvsMass InFigure A-63 weshowtherelationshipbetweenthepeakdensityregistere dinthe clusterandtheclustermass;mainclustersareshownasstar s,andnewclustersareshown asboxes.Weseethatbothdatasets,mainandnewclusters,fo llowsimilaroveralltrends ofincreasingmaximumdensitywithincreasingmass.Wealso noticethatfordensity valuesgreaterthan 55 stars arcmin 2 (shownbytheverticaldottedline)thetrendseemstorise sharply.ThePearsoncoecientforthesetwoparametersisl argeandpositive(0.728). TheSpearman'scoecientis0.542withasignicanceof3 : 36 10 5 InthebottompanelsofthisgurewedistinguishbetweenC-t ypeclustersand F-typeclustersFromthebottom-rightpanelwenoticethatF -typeclustersare,with theexceptionof1cluster,alllocatedatlog(density)valu eslowerthan5.3;fordensities smallerthanthisvalue,boththemainandnewclustersfollo wsimilartrends.Thedotted lineisthebestttothenewclustersandthedashedlineisth ettothemainclusters. TheC-typeclusters,inthebottom-leftpanel,spanthedens ityrangefrom4.0to 6.0andherewenoticethatthefeatureseenintheupperpanel isonlypresentamongst theseclusters.Thedotted,thedot-dashed,andthelongdas hedlinesindicatethebest tsto,respectively,thenewclusters,themainclusters,a ndthoseclusterswhichhave < 0 : 25.WeseethatthelesscentrallycondensedC-typeclusters followasimilartrend 238

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FigureA-61.Correlationbetweenextinctionand IRx frac forallclusters.Mainclusters arerepresentedbystars,whereasnewclustersarerepresen tedbyboxes.The solidlineistheaverageextinctionforbinsofsize10%.Int hetwolower panelsweshowthedistributionofC-typeandF-typecluster s;thedashed lineisthetforeachselection.ThePearsoncoecientfort hiscorrelation ismediumandnegative(-0.401).TheSpearman'scoecienti s0.322witha signicanceof0.0197. 239

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FigureA-62.Figurecorrelatingclustermassandclustersi ze.Thepearsoncoecientfor therelationshipbetweenthesetwopropertiesislargeandp ositive(0.728). TheSpearman'scoecientis0.634withasignicanceof4 : 53 10 7 Themainclustersarerepresentedbythestarsymbols,newcl ustersare representedbyboxes.Thesolidlineisthebestttothemain clusters whereasthedashedlineisthebestttothenewclusters. 240

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totheF-typeclustersbutthatthestronglycentrallyconde nsedclusters( < 0 : 25)havea distinctlysteepercorrelationbetweenmaximumdensityan dmass. A.3.6CorrelationBetweenMaximumDensityandNumberofMem bers Maximumdensityis,inturn,correlatedtothenumberofsour cesinsideacluster,this isshowningure A-64 .Again,boththenewandthemaindatasetsshowsimilartrend s indicatingthatthenumberofclustermembersincreasesast hecluster'smaximumdensity increases.ThePearsoncoecientforthesetwoparametersi slargeandpositive(0.690). TheSpearman'scoecientis0.496withasignicanceof1 : 86 10 4 A.3.7FractionofIRxSourcesvsCircularity InFigure A-65 weshowtherelationshipbetweenthe IRx frac andIQ(circularity); themainclustersareshownasstarsymbolsandthenewcluste rsasboxes.ThePearson coecientforthiscorrelationismediumandpositive(0.34 6).TheSpearman'scoecient is0.304withasignicanceof0.028.Toshowthegeneraltren dwehaveoptedtoshowa linetracingtheaveragevaluesof IRx frac for0.1sizeIQbins;weobservethat IRx frac doesnotchangesignicantlywithIQ. Inthetwolowerpanelsweagainlookathowclusterstructure playsaroleinthe correlationbydividingtheclustersintoC-typeandF-type ;wendthatthecorrelation onlyholdsforthecentrallycondensedclusters,astheF-ty peclustersonlyexhibitalotof scatter.A.3.8CircularityvsExtinction InFigure A-66 weshowtherelationshipbetweenaverageextinctionandIQ; themain clustersareshownasstarsandthenewclustersasboxes.The Pearsoncoecientfor thiscorrelationismediumandpositive(0.449).TheSpearm an'scoecientis0.401with asignicanceof3 : 19 10 3 .HereweseeafainttrendofincreasingIQwithincreasing extinction.Weagainopttoshowthetrendbyusingalinewhic htracesaveragevalues ofextinctionfor0.1sizeIQbins;wenoticeanoveralltrend ofincreasingextinctionwith increasingcircularity. 241

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FigureA-63.Figurecorrelatingmassandmaximumdensityfo rmainandnewclusters. Mainclustersarerepresentedbythestars,newclustersare representedby theboxes.ThePearsoncoecientforthesetwoparametersis largeand positive(0.728).TheSpearman'scoecientis0.542withas ignicanceof 3 : 36 10 5 242

PAGE 243

FigureA-64.Figurecorrelatingnumberofmembersandmaxim umdensity.Mainclusters arerepresentedbythestarssymbols,whereasnewclustersa rerepresented bytheboxes.Thesolidlineisthebestttothemainclusters whereas thedashedlineisthebestttothenewclusters.Thepearson coecient forthesetwoparametersislargeandpositive(0.690).TheS pearman's coecientis0.496withasignicanceof1 : 86 10 4 .Theleftpanelis forC-typeclustersandtherightpanelisforF-typecluster s,thetwo populationsfollowasimilarrelationshipforlog(Maximum Density) < 5.5 buttheC-typeclustersfollowasteeperrelationshipforhi ghervalues. 243

PAGE 244

FigureA-65.CorrelationbetweenthefractionofIRxsource sandIQforallclusters.Main clustersarerepresentedbystars,whereasnewclustersare represented byboxes.ThesolidlineistheaverageIRxforbinsofsize0.1 inIQ.The Pearsoncoecientforthiscorrelationismediumandpositi ve(0.346).The Spearman'scoecientis0.304withasignicanceof0.028.I nthetwolower panelsweshowthedistributionofC-typeandF-typecluster s,thedashed lineisthetforeachselection;weseethattheC-typeclust ersexhibita morewell-denedtrend,withlessscatterthanthatseenfor theF-type clusters. 244

PAGE 245

Inlookingatthelowertwopanelswendthat,aswasthecasei nthetrendbetween IRx frac andcircularity,onlythecentrallycondensedclustersfol lowarelationshipof increasingextinctionwithincreasingcircularity,where astheratclusterssimplyshowalot ofscatter.A.3.9CentralCondensationvsCoreRadius InFigure A-67 wepresenttherelationshipbetweenthecentralcondensati on, ,and thecoreradius;inthisgurethesolidlineistheaverageco reradiusforbinsofsize0.1in ,mainclustersarerepresentedbythestarssymbolsandnewc lustersarerepresentedby theboxes.ThePearsoncoecientforthiscorrelationislar geandpositive(0.684).The Spearman'scoecientis0.737withasignicanceof4 : 53 10 10 245

PAGE 246

FigureA-66.CorrelationbetweenextinctionandIQforallc lusters.Mainclusters arerepresentedbythestars;newclustersarerepresentedb ytheboxes. Thesolidlineistheaverageextinctionforbinsofsize0.1i nIQ.The Pearsoncoecientforthiscorrelationismediumandpositi ve(0.449).The Spearman'scoecientis0.401withasignicanceof3 : 19 10 3 .Inthe twolowerpanelsweshowthedistributionofC-typeandF-typ eclusters; thedashedlineisthetforeachselection.WeseethattheCtypeclusters exhibitawell-denedtrend,withlessscatterthanthatsee nfortheF-type clusters. 246

PAGE 247

FigureA-67.Correlationbetweencoreradiusand .Mainclustersarerepresentedby thestarssymbols,whereasnewclustersarerepresentedbyt heboxes.The solidlineistheaveragecoreradiusforbinsofsize0.1in .ThePearson coecientforthiscorrelationislargeandpositive(0.684 ).TheSpearman's coecientis0.737withasignicanceof4 : 53 10 10 247

PAGE 248

A.4AnalysisofStatisticalErrorsinCoreandEquivalentRa dii Weestimatethestatisticalerrorsassociatedwiththeequi valentandcoreradiiby usingananalysissimilartoabootstrapmethod.Thekeytoth ebootstrapmethodisto generatealternativeversionsofthestellardistribution swhichcouldbeseen.Foraeld containingNstars,ourmethodrandomlypicksNstarsfromth ateld;onceastaris pickeditspositionisloggedandthatstarisreplaced,thus thesamestarcanbepicked severaltimes.SincesomeofthoseNpickswillbeofthesames tar,theneweldwill havelessstarsthantheoriginaleld.Thisprocessofgener atinganeweldisrepeated astatisticallysignicantnumberoftimes,andforeachel dthecoreandequivalentradii andthetauvalueweremeasured.Thismethodwasappliedtoal lofourclusterelds. 248

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TableA-1.BootstrapAnalysisofStatisticalErrors CoreRadiusEquivalentRadiusTau Mean %ErrorMean %ErrorMean %Error Cha 0.0370.00359.50.220.00612.80.170.0169.5 SVS2 0.0300.00237.80.0.0760.00212.70.390.0317.9 L1228 0.500.0469.10.960.0353.60.520.0397.4 NGC1333 0.140.01813.40.560.00891.60.240.03213.2 IC348 0.390.06616.80.920.1516.00.430.1126.3 NGC2024 0.160.00452.90.800.0111.40.190.00532.7 NGC2024New 0.200.00442.20.350.0288.00.580.1017.4 NGC2068 0.210.0167.70.430.0122.80.490.0316.3 NGC2068New 0.170.05634.60.320.0298.90.510.1630.7 NGC2071 0.170.02614.90.790.0212.70.220.03214.7 LKH 0.150.01510.60.620.0254.10.230.0208.8 KMS35 0.410.06114.80.690.0385.50.590.07713.0 KMS35New 0.420.06816.20.690.0355.00.610.08513.9 CKGroup 0.160.0117.10.580.0274.50.270.0155.4 CKGroupNew 0.570.0203.60.800.0172.10.710.0202.8 NGC2023 0.130.0139.90.510.0183.60.260.02810.7 V380Ori 0.210.04922.70.390.0184.70.540.1121.7 V380OriNew 0.280.04917.70.460.0439.30.600.08013.2 IRAS05401-1002 0.210.03114.80.490.0336.70.430.04911.6 249

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Table A-1 continued CoreRadiusEquivalentRadiusTau Mean %ErrorMean %ErrorMean %Error IRAS05401-1002New 0.210.03215.60.500.0356.90.410.04511.1 IRAS243,245 0.200.06532.00.590.0579.60.340.09728.4 L1641C 0.470.06213.20.850.0698.10.560.0498.8 Trapezium 0.520.0468.81.480.1610.80.350.03610.3 L1641N 0.250.02510.10.470.0275.80.530.0458.4 CB34 0.110.00545.10.340.0133.90.310.0185.7 S106 0.130.01915.20.360.0256.80.340.0319.1 IRAS08375-4109 0.590.09115.40.770.07710.10.770.0607.8 IRAS08375-4109New1 0.600.2135.90.730.2027.70.790.1316.5 IRAS08375-4109New2 0.340.2881.00.510.2345.00.600.3050.0 IRAS08404-4033 0.130.02518.60.400.0112.70.330.06218.6 IRAS08448-4343 0.190.02311.90.450.0132.90.430.04811.3 IRAS08448-4343New 0.250.04216.80.460.0306.40.530.07013.2 IRAS08470-4243 0.120.0119.10.530.0224.10.230.0187.8 IRAS08470-4243New 0.260.1555.50.370.0349.20.720.4358.9 IRAS08470-4321 0.130.03828.10.450.0408.90.290.06120.9 IRAS08470-4321New 0.0700.02129.50.290.0217.30.240.05924.8 IRAS08476-4306 0.110.01312.00.430.0133.10.250.02810.8 250

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Table A-1 continued CoreRadiusEquivalentRadiusTau Mean %ErrorMean %ErrorMean %Error IRAS08477-4359 0.0930.009710.40.300.0113.80.320.03310.4 IRAS20050+2720 0.110.00756.60.320.00642.00.360.0215.9 RCrA 0.0630.00355.50.600.0152.50.110.00635.9 L988e 0.460.0286.10.610.0183.00.750.0344.6 CepA 0.350.0174.90.900.0121.30.290.0196.5 HD216629 0.630.0447.10.890.0323.60.710.0375.2 L1211 0.230.09742.20.390.0236.00.590.2441.3 L1211New 0.250.06526.00.380.0277.00.670.1623.9 VYMon 0.210.03416.00.550.0417.40.380.04511.2 MonR2 0.190.00532.80.960.01414.30.200.00512.6 GGD12-15 0.320.0226.90.950.0222.30.330.0206.1 NGC2264 0.740.0172.31.20.0252.10.620.0122.0 NGC2264South 0.640.06710.40.950.0363.80.680.0629.2 AFGL490 0.140.02517.60.580.0284.90.250.04317.2 AFGL490New 0.560.1934.00.790.0435.40.710.2636.6 251

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APPENDIXB DETAILSOFFLAMINGOSOBSERVATIONSOFMONOCEROS ThisappendixcontainsthedetailsoftheFLAMINGOSobservi ngrunsonthe MonocerosOB1regions,MonAandMonB.Wepresentthedatesin whicheacheldwas observed,thelterused,theexposuretime,thenumberofdi thers,thetotalexposure time,theairmassandtheseeing.InSection B.3 wepresenttherawandnalareaforeach oftheobservedelds.InSection B.4 wepresenttheaverageandstandarddeviationsfor thephotometryofeachcontroleld. B.1MonAObservations 252

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TableB-1.DetailsofMonAObservations FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) mona016:41:31.338:50:08.22002Dec21H60169601.581.329 000 mona01......2002Dec27J60169601.101.12975mona01......2002Dec21K354114351.241.217000mona026:41:31.339:10:08.22002Dec21H60169601.461.225 000 mona02......2002Dec27J60169601.121.253420mona02......2002Dec21K353512251.351.115000mona036:41:31.339:30:08.22003Jan31H60169601.251.217 000 mona03......2002Dec27J60169601.121.23365mona03......2003Jan31J60169601.361.23800mona03......2003Feb01J60169601.811.16000mona03......2003Jan31K353211201.180.924400mona046:41:31.339:50:08.22002Dec27H60169601.192.134 334 mona04......2002Dec27H30329601.291.520392mona04......2003Feb01H60169601.101.016800mona04......2002Dec27J60169601.141.353795mona04......2003Feb01J60169601.551.04500mona04......2003Feb01K353211201.091.129000mona056:41:31.3310:10:08.22003Mar26H60169601.121.52 2000 mona05......2003Mar26J60169601.091.95600mona05......2003Mar26J6095401.091.54400mona05......2003Mar26K35165601.141.3521000mona05......2003Mar26K35165601.181.3520000mona066:41:31.3310:30:08.22003Mar26H60169601.321.35 24000 mona06......2003Mar26J6074201.392.02900mona06......2003Mar26J6095401.501.83500mona06......2003Mar27J60169601.441.53600mona06......2003Mar26K35165601.241.3525000mona06......2003Mar26K35165601.261.3522500 253

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Table B-1 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) mona076:41:31.3310:50:08.22003Mar27H30164801.081.15 19000 mona07......2003Mar27H30164801.091.217000mona07......2003Mar27J60169601.081.115000mona07......2003Mar27J60169601.431.53900mona07......2003Mar27K35165601.111.328000mona07......2003Mar27K35165601.131.329000mona086:41:31.3311:10:08.22003Feb02H60169601.141.01 6500 mona08......2003Feb02J60169601.221.13400mona08......2003Feb02K353211201.071.328500mona106:40:10.228:50:08.22003Mar22H603219521.231.71 6000 mona10......2003Mar22J60169601.261.72800mona10......2003Jan01K30329601.191.415000mona10......2003Jan01K30329601.131.613500mona116:37:25.4410:33:0.02003Jan01H60169601.241.825 000 mona11......2003Feb01H602012001.221.018500mona11......2003Feb01J60169601.241.13000mona11......2003Jan01K303211201.231.713500mona11......2003Feb01K353211201.081.328500mona126:40:10.229:30:082003Jan03H60169601.121.61550 0 mona12......2003Jan03J60169601.151.62100mona12......2003Mar22K60169601.471.829000mona12......2003Mar23K35165601.191.525000mona12......2003Mar23K35165601.231.223000mona136:40:10.229:50:082003Mar03H60169601.101.51600 0 mona13......2003Mar23J60169601.491.053800mona13......2003Mar22K60169601.611.935500mona13......2003Mar23K35165601.271.1523000mona13......2003Mar23K35165601.331.123000mona13......2003Mar23K3541401.401.2524000mona146:40:10.2210:10:082003Jan03H60169601.081.6165 00 mona14......2003Jan03J60169601.211.72300mona14......2003Jan03K30329601.131.617500 254

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Table B-1 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) mona156:40:10.2210:30:082003Jan03H60169601.071.5180 00 mona15......2003Jan03J60169601.261.62300mona15......2003Jan03K30329601.131.718000mona166:40:10.2210:50:082003Jan03H60169601.081.6185 00 mona16......2003Mar23H60169601.481.2524000mona16......2003Mar23H6042401.701.129000mona16......2003Jan03J60169601.341.652300mona16......2003Jan03K30329601.091.618000mona176:40:10.2211:10:08.22003Jan04H60169601.401.53 5000 mona17......2003Mar24J60169601.171.52900mona17......2003Jan04K30329601.091.223000mona186:40:10.2211:30:08.22003Jan04H60169601.381.42 8000 mona18......2003Mar24J60169601.251.52700mona18......2003Jan04K30329601.091.120000mona196:42:52.4408:50:08.22003Jan04H60169601.251.22 7000 mona19......2004Jan30H60169601.531.420000mona19......2003Mar24J602012001.321.752900mona19......2004Jan30J60169601.901.23500mona19......2003Jan04K304814401.151.223000mona19......2004Jan30K353211201.191.315000mona216:42:52.449:30:08.22004Jan30H60169601.321.420 000 mona21......2004Jan30J60169601.911.23500mona21......2004Jan30K353211201.321.315000mona256:38:49.19:30:08.22003Dec27H60169601.111.5170 00 mona25......2003Dec27J60169601.211.32700mona25......2003Dec27K353411901.271.027000mona266:38:49.19:50:08.22003Dec27H60169601.101.4150 00 mona26......2003Dec27J601810801.271.32700mona26......2003Dec27K353612601.191.427000 255

PAGE 256

Table B-1 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) mona276:38:49.110:10:08.22003Dec27H60169601.101.414 000 mona27......2003Dec27J601810801.261.23000mona27......2003Dec27K353612601.121.227000mona286:38:49.111:10:08.22003Dec27H60169601.081.413 000 mona28......2003Dec27J601810801.371.253000mona28......2003Dec27K353211201.081.227500mona296:38:49.111:30:08.22003Jan28H60169601.441.252 6000 mona29......2004Dec22H602012001.222.017000mona29......2003Jan30J60169601.351.03200mona29......2004Dec22J602012001.442.23300mona29......2003Jan28K303410201.421.3525000mona29......2004Dec22K303610801.161.817000 monclus016:40:53.219:51:08.02003Jan28H60169601.291. 121000 monclus01......2004Jan30H60169601.081.511000monclus01......2003Jan30J60169601.521.04400monclus01......2004Jan30J60169601.091.51700monclus01......2003Jan28K303510501.211.327000monclus01......2003Jan28K303510501.211.327000monclus01......2003Jan29K353211201.111.127000monclus01......2004Jan30K353411901.111.415000monclus026:41:10.829:31:06.82003Jan28H60169601.261. 115000 monclus02......2003Jan28J60169601.541.45200monclus02......2003Jan28J601810801.651.35200monclus02......2005Jan01J60169601.181.826000monclus02......2003Jan28K303610801.331.3525000monclus02......2005Jan01K30329601.331.520000 256

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B.2MonBObservations 257

PAGE 258

TableB-2.DetailsofMonBObservations FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb016:37:27.9911:10:08.22003Jan28H60169601.271.25 21000 monb01......2004Jan28H6095401.071.510000monb01......2006Jan05H60169601.571.720000monb01......2006Jan05H6095401.511.720000monb01......2003Jan29J60169601.911.357000monb01......2004Jan28J6095401.071.61500monb01......2006Jan05J60169601.671.72500monb01......2006Jan05J6095401.641.72500monb01......2003Jan28K303811401.100.9527000monb01......2003Jan28K303610801.130.9527000monb01......2004Jan28K30257501.081.514000monb01......2006Jan05K30164801.341.220000monb01......2006Jan05K30164801.301.320000monb026:36:6.8811:10:08.22003Jan28H60169601.141.015 000 monb02......2004Jan31H60169601.551.627000monb02......2004Nov11H6016960-1.01.420000monb02......2006Jan05H60169601.181.320000monb02......2006Jan05H6095401.131.520000monb02......2003Jan29J60169601.781.45000monb02......2004Jan31J60169601.391.23000monb02......2004Nov11J6016960-1.01.42000monb02......2006Jan05J60169601.131.520000monb02......2006Jan05J6095401.091.520000monb02......2003Jan28K303510501.131.027000monb02......2004Nov11K35321120-1.01.522000monb02......2004Nov11K35165601.231.1523800monb02......2004Nov11K3551751.231.222800monb02......2006Jan05K30164801.281.320000monb02......2006Jan05K30164801.221.320000monb036:34:45.7711:10:08.22003Jan30H60169601.541.12 4000 monb03......2004Dec13H402510001.071.214000 258

PAGE 259

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb03......2006Jan05H60169601.071.520000monb03......2006Jan05H6095401.071.720000monb03......2003Jan29J60169601.571.64000monb03......2004Dec12J402510001.362.34000monb03......2004Dec12J60169601.201.52400monb03......2006Jan05J60169601.081.520000monb03......2006Jan05J6095401.071.54000monb03......2003Jan29K353211201.071.127000monb03......2004Dec13K205010001.091.220000monb03......2006Jan05K60169601.091.70monb03......2006Jan05K6095401.161.70monb046:33:24.6511:10:08.22003Jan29H60169601.251.32 9000 monb04......2003Jan29H40145601.911.328900monb04......2003Jan30H60169601.661.328000monb04......2004Dec13H602515001.091.212000monb04......2006Jan05J60169601.311.70monb04......2006Jan05J4093601.382.70monb04......2003Jan29J60169601.351.13600monb04......2004Dec13J60169601.191.62400monb04......2006Jan05J60169601.501.70monb04......2006Jan05K3593151.781.70monb04......2003Jan29K20326401.071.227500monb04......2004Dec13K605030001.161.220000monb04......2006Jan05K60169601.171.70monb04......2006Jan05K30164801.171.70monb04......2006Jan05K30164801.201.70monb04......2006Jan05K3092701.291.70monb056:32:03.5411:10:08.22003Jan29H60169601.101.32 4000 monb05......2004Dec13H402510001.101.214000monb05......2006Jan06H60169601.392.0524000monb05......2006Jan06H6095401.212.0524000 259

PAGE 260

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb05......2006Jan11H60169601.161.217000monb05......2006Jan11H6095401.192.317000monb05......2003Jan29J60169601.181.12900monb05......2004Jan05J60169601.131.72400monb05......2006Jan06J60169601.821.70monb05......2006Jan06J60169601.492.226000monb05......2006Jan11J6095401.402.226000monb05......2006Jan11J60169601.251.33200monb05......2006Jan29J6095401.291.23200monb05......2003Dec13K353211201.071.028000monb05......2004Jan05K205010001.431.220000monb05......2006Jan06K30164801.211.524000monb05......2006Jan06K30164801.161.524000monb05......2006Jan11K30164801.121.122000monb05......2006Jan11K30164801.141.322000monb066:30:42.4211:10:08.22003Jan29H60169601.111.11 6000 monb06......2006Jan06H60169601.101.520000monb06......2006Jan06H6095401.081.520000monb06......2006Jan11H60169601.341.223000monb06......2006Jan11H6095401.401.423000monb06......2003Jan29J60169601.172.12700monb06......2006Jan06J6095401.071.51800monb06......2006Jan06J60169601.072.01800monb06......2006Jan11J60169601.491.54500monb06......2006Jan11J6095401.611.54500monb06......2003Mar24K35165601.661.7525000monb06......2003Mar24K35165601.681.525000monb06......2006Jan06K30164801.141.524000monb06......2006Jan06K30164801.111.524000monb06......2006Jan11K20163201.741.523000monb06......2006Jan11K30164801.851.423000 260

PAGE 261

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb076:37:27.9910:50:08.22004Jan30H60169601.081.61 1000 monb07......2004Dec21H60169601.141.524000monb07......2006Jan06H601911401.091.717000monb07......2006Jan06H6095401.101.517000monb07......2006Jan11H60169601.191.221500monb07......2006Jan11H6095401.161.221500monb07......2004Jan30J60169601.081.41700monb07......2004Dec12J60169601.181.62500monb07......2006Jan06J60169601.072.02000monb07......2006Jan06J6095401.092.02000monb07......2006Jan11J60169601.131.34500monb07......2006Jan11J6095401.081.44500monb07......2004Jan30K353311551.081.515000monb07......2004Dec21K30329601.141.720000monb07......2006Jan06K30164801.161.522000monb07......2006Jan06K30164801.191.522000monb07......2006Jan12K30164801.081.320000monb07......2006Jan12K30164801.081.320000monb086:36:06.8810:50:08.22003Jan31H60169601.341.22 5000 monb08......2006Jan06H60169601.471.521000monb08......2006Jan06H6095401.511.521000monb08......2003Jan31J60169601.651.51200monb08......2006Jan06J60169601.321.53100monb08......2006Jan06J6095401.361.53100monb08......2003Jan31K353211201.341.425500monb08......2006Jan06K30164801.251.520000monb08......2006Jan06K30164801.321.520000monb096:34:45.7710:50:08.22003Jan31H60169601.100.91 4000 monb09......2004Dec21H60169601.111.424000monb09......2006Jan07H60169601.871.420000monb09......2006Jan07H6095401.751.420000 261

PAGE 262

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb09......2003Jan31J60169601.511.34000monb09......2004Dec21J60169601.231.72500monb09......2006Jan07J60169601.611.62000monb09......2006Jan07J6095401.391.92000monb09......2003Jan31K353813301.082.222000monb09......2004Dec21K30329601.122.619000monb09......2006Jan06K30164801.601.423000monb09......2006Jan06K30164801.861.423000monb106:33:24.6510:50:08.22003Jan31H601810801.071.1 14000 monb10......2003Jan31H60169601.071.114000monb10......2004Dec21H60169601.071.525000monb10......2006Jan07H6095401.171.810000monb10......2006Jan07H60169601.151.810000monb10......2003Jan31J60169601.541.54500monb10......2004Dec21J60169601.351.53000monb10......2006Jan07J60169601.281.32000monb10......2006Jan07J6095401.201.51800monb10......2003Jan31K353211201.071.222000monb10......2004Dec21K30329601.091.619000monb10......2006Jan07K30164801.131.420000monb10......2006Jan07K30164801.101.420000monb116:32:03.5410:50:08.22003Feb06H353211201.591.2 25000 monb11......2004Dec21H60169601.071.524000monb11......2006Jan07H60169601.071.416000monb11......2006Jan07H6095401.071.416000monb11......2003Mar25J60169601.131.24900monb11......2006Jan07J60169601.081.52000monb11......2006Jan07J6095401.091.52000monb11......2003Feb06K353211201.291.219000monb11......2004Dec21K30329601.071.519000monb11......2006Jan07K30164801.081.622000 262

PAGE 263

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb11......2006Jan07K30164801.071.622000monb126:30:42.4710:50:08.22004Dec12H402510001.201.4 22000 monb12......2006Jan07H60169601.161.318000monb12......2006Jan07H6095401.201.318000monb12......2004Dec12J402510001.291.64000monb12......2006Jan07J60169601.101.41900monb12......2006Jan07J6095401.131.121900monb12......2004Dec11K20255001.411.320000monb12......2004Dec11K20255001.581.520000monb12......2006Jan07K30164801.391.327000monb12......2006Jan07K30164801.451.327000monb136:37:27.0910:30:08.22004Jan31H60169601.651.62 8000 monb13......2006Jan08H60169601.081.313000monb13......2006Jan08H6095401.091.313000monb13......2004Jan31J60169601.371.23000monb13......2006Jan08J60169601.071.32000monb13......2006Jan08J6095401.071.32000monb13......2006Jan07K30164801.501.327000monb13......2006Jan07K30164801.641.327000monb13......2006Jan07K30164801.691.326000monb13......2006Jan07K30164801.831.826000monb13......2006Jan08K30164801.121.320000monb13......2006Jan08K30164801.151.320000monb146:36:06.8810:50:08.22005Jan06H60169601.091.52 0000 monb14......2006Jan08H60169601.491.425000monb14......2006Jan08H6095401.491.425000monb14......2004Dec24J60169601.102.82700monb14......2005Jan06J60169601.121.53000monb14......2006Jan08J60169601.221.32500monb14......2006Jan08J6095401.541.53000monb14......2005Jan06K353211201.091.514000 263

PAGE 264

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb14......2006Jan08K30164801.161.321000monb14......2006Jan08K30164801.201.321000monb156:34:45.7710:30:08.22006Jan08H60169601.781.53 5000 monb15......2006Jan09H60169601.671.515000monb15......2006Jan09H6095401.531.515000monb15......2006Jan28J60169601.531.53000monb15......2006Jan08J6095401.551.54000monb15......2006Jan09K30164801.431.517000monb15......2006Jan09K3092701.351.717000monb15......2006Jan09K3092701.301.717000monb166:33:24.6510:30:08.22005Jan06H60169601.211.53 0000 monb16......2006Jan09H60169601.191.213000monb16......2006Jan09H6095401.141.213000monb16......2005Jan06J60169601.201.53000monb16......2006Jan09J60169601.111.41600monb16......2006Jan09J6095401.101.31650monb16......2005Jan06K353211201.271.316000monb16......2006Jan09K30164801.251.422000monb16......2006Jan09K30164801.211.222000monb176:32:03.5410:30:08.22003Feb01H60169601.411.02 0000 monb17......2006Jan09H60169601.081.112000monb17......2006Jan09H6095401.081.212000monb17......2003Feb01J60169601.181.12500monb17......2006Jan09J60169601.081.31850monb17......2006Jan09J6095401.081.11850monb17......2006Jan09J6042401.071.31850monb17......2003Feb01K353211201.091.027600monb17......2006Jan09K30164801.091.218500monb17......2006Jan09K30164801.101.218500monb186:30:42.4210:30:08.22003Feb01H60169601.391.12 3000 monb18......2006Jan09H60169601.141.311500 264

PAGE 265

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb18......2006Jan09H6095401.171.111500monb18......2003Feb01J60169601.151.12500monb18......2006Jan09J60169601.211.12000monb18......2006Jan09J6095401.251.22000monb18......2003Feb01K353211201.131.128000monb18......2006Jan09K30164801.111.020000monb18......2006Jan09K30164801.121.020000monb196:32:03.5410:10:08.22006Jan09H60169601.471.31 8000 monb19......2006Jan09H6095401.561.523000monb19......2006Jan09J60169601.721.52500monb19......2006Jan09J6095401.941.62500monb19......2006Jan09K30164801.341.118000monb19......2006Jan09K30164801.421.118000monb206:30:42.4210:10:08.22006Jan10H60169601.091.61 8000 monb20......2006Jan10H6095401.091.618000monb20......2006Jan12H60169601.081.327000monb20......2006Jan12H60169601.091.627000monb20......2006Jan10J6084801.201.82500monb20......2006Jan10J60169601.151.82500monb20......2006Jan10J6095401.121.82500monb20......2006Jan12J6063601.111.64500monb20......2006Jan12J60169601.121.64500monb20......2006Jan12J6095401.141.54500monb20......2006Jan10K30164801.081.719500monb20......2006Jan10K30164801.081.919500monb20......2006Jan12K30164801.081.919500monb20......2006Jan12K30164801.081.620000monb20......2006Jan12K30164801.081.320000monb226:30:42.4210:10:08.22006Jan10H60169601.111.71 9500 monb22......2006Jan10H6095401.201.719500monb22......2006Jan20H60169601.281.829000 265

PAGE 266

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monb22......2006Jan20H6095401.361.829000monb22......2006Jan20H6031801.421.832000monb22......2006Jan30H60169601.321.512000monb22......2006Jan30H6095401.261.312000monb22......2006Jan10J60169601.221.83000monb22......2006Jan10J6095401.271.83000monb22......2006Jan12J60169601.171.54000monb22......2006Jan12J6095401.221.74000monb22......2006Jan13J60169601.441.52400monb22......2006Jan13J6095401.421.32400monb22......2006Jan10K30164801.092.019500monb22......2006Jan10K30164801.102.019500monb22......2006Jan12K30164801.531.722000monb22......2006Jan12K30164801.621.522000monb22......2006Jan13K30164801.621.316500monb22......2006Jan13K30164801.571.316500monbg26:36:47.4411:10:08.22004Jan28H6095401.111.612 000 monbg2......2006Jan11H60169601.141.122000monbg2......2006Jan11H6095401.131.122000monbg2......2004Jan28J60106001.111.81500monbg2......2006Jan11J60169601.101.32700monbg2......2006Jan11J6095401.081.12700monbg2......2004Jan28K30257501.101.68000monbg2......2006Jan11K30164801.201.120000monbg2......2006Jan11K35165601.181.120000monbg86:36:47.4410:50:08.22004Jan28H6095401.071.510 000 monbg8......2006Jan11H60169601.071.125000monbg8......2006Jan11H6095401.071.225000monbg8......2004Jan28J6095401.081.51200monbg8......2006Jan11J60169601.081.22700monbg8......2006Jan11J6095401.071.02700 266

PAGE 267

Table B-2 continued FieldRADecDateFilterExpDithersTotalExpAirmassSeeing Sky (J2000)(sec)(sec)( 00 ) monbg8......2004Jan28K30257501.081.38000monbg8......2006Jan11K30164801.081.220000monbg8......2006Jan11K30164801.091.220000 monbc26:41:10.829:31:06.82004Dec19H60169601.241.621 000 monbc2......2006Jan10H6053001.451.540000monbc2......2006Jan13H60169601.251.311000monbc2......2006Jan13H6095401.181.311000monbc2......2004Dec19J602313801.222.02200monbc2......2006Jan10J60169601.311.84000monbc2......2006Jan10J6095401.391.54000monbc2......2006Jan13J60169601.151.21800monbc2......2006Jan13J6095401.131.21800monbc2......2004Dec19K303410201.481.523000monbc2......2006Jan10K30164801.561.725000monbc2......2006Jan10K30164801.631.925000monbc2......2006Jan13K30164801.111.117000monbc2......2006Jan13K30164801.091.117000 267

PAGE 268

B.3AreasofMonOB1Fields B.4ControlFields 268

PAGE 269

TableB-3.RawandFinalAreasforMonocerosFields ClusterFieldRawAreaCorrectedArea MonA120020.1072130.101644MonA220020.1052190.0947453MonA320020.1048310.0943576MonA420020.1038760.0934710MonA520020.1052340.101858MonA620020.1022650.100797 MonA7mar20020.1047340.103331 MonA7dec20020.1052390.101570 MonA820020.1038640.0934286 MonA1020020.1042850.101483MonA1120020.1034170.0960715MonA1220020.1085120.106811MonA1320020.1026040.0833769MonA1420020.1031450.0996451MonA1520020.1031300.0995565 MonA16jan20020.1046360.101362 MonA1620020.1025630.0922004MonA1720020.1041640.0932423MonA1820020.1043830.0994723MonA2020020.1045650.0991708MonA2520030.1043960.0957037MonA2620020.1053650.0941705MonA2720020.1056360.101090MonA2820020.1026700.0863436 MonAclus120030.1044060.0878453MonAclus120040.1026990.0792683MonAclus220030.1026480.0835266MonAclus220040.1025710.0998551MonAclus220030.1079230.103718 269

PAGE 270

Table B-3 continued ClusterFieldRawAreaCorrectedArea MonB120030.1046070.0814732MonB120040.1113140.0797177MonB220030.1017460.0753925MonB220040.1111350.0860564MonB620020.1044040.0876826MonB720040.1035680.0628951MonB820030.1052100.0968976 MonB8g20040.1111160.0887485 MonB920020.1028260.0836119 MonB1020020.1051490.0848119MonB1120020.1040840.0872103MonB1320040.1038030.0948140MonB1720020.1024440.0867848MonB1820020.1023060.0827794 270

PAGE 271

TableB-4:AveragesandSTDevforMonocerosControlFields ClusterField ( J err ) ( H err ) ( K err ) err ( H K err ) CF10.0250.0160.0320.0170.0890.0450.250.059CF20.0310.0160.0450.0220.0680.0410.220.061CF30.0310.0180.0330.0200.0560.0340.170.052CF40.0240.0120.0310.0150.0380.0200.140.034 Oneld0.0230.0130.0260.0130.0310.0170.290.029 271

PAGE 272

FigureB-1.ComparisonofJ-bandphotometryerrorsforthef ourcontrolelds. InFigures B-1 B-2 and B-3 weshowtheJ,H,Kerrorsforthefourcontrolelds. 272

PAGE 273

FigureB-2.ComparisonofH-bandphotometryerrorsforthef ourcontrolelds. FigureB-3.ComparisonofK-bandphotometryerrorsforthef ourcontrolelds. 273

PAGE 274

FigureB-4.Locationsofsourcesforthefourcontrolelds. FigureB-5.DistributionofIRxsourcesforthefourcontrol elds. 274

PAGE 275

FigureB-6.KLFforthefourcontrolelds. FigureB-7.CombinedKLFforcontrolelds2,3and4. 275

PAGE 276

FigureB-8.CCDforthefourcontrolelds. FigureB-9.CMDforthefourcontrolelds. 276

PAGE 277

FigureB-10.CMDforthefourcontrolelds. 277

PAGE 278

APPENDIXC DETECTIONOFSMALLCLUSTERSUSINGJ=10 InthisappendixIpresentthetablesshowingthemeasuremen tofclusterproperties usingthej-valuej=10.Thoughj=10doesmeasurethecluster propertieswithgreater accuracythanj=20,weoptedforj=20becausej=10ismuchmor esensitivetothe presenceoffakeclusters{clustersgeneratedthroughrand omdensityructuations{whichwe wantedtoavoidwhenobservingrealelds. 278

PAGE 279

TableC-1.SimulatingClusters.Radius=0.1,j-value=10 N clus B : C Prole R err N err %% 201:11 1 r 2 160(80)25(15) 301:18 1 r 2 200(100)13(13) 401:23 1 r 2 210(130)18(5) 501:30 1 r 2 190(70)28(4) 201:9 1 r 200(50)25(22) 301:16 1 r 170(50)34(30) 401:28 1 r 200(70)44(40) 501:34 1 r 170(100)55(51) 201:8Cte200(70)25(0)301:19Cte170(60)33(3)401:34Cte220(90)40(0)501:36Cte170(90)56(0) Fieldhas1000membersN clus isthenumberofclustermembers B istheaveragebackgrounddensity C istheaverageclusterdensity R err istheerrorinmeasuringtheradius N err istheerrorinmeasuringthenumberofmembers Cutovaluewas d field 1 : 5 ( field )forallexcept thoseinparenthesisforwhichweusedthetrough 279

PAGE 280

TableC-2.SimulatingClusters.Radius=0.2,j-value=10 N clus B : C Prole R err N err %% 201:2 1 r 2 15(-)10(-) 301:4 1 r 2 45(15)3(17) 401:6 1 r 2 60(15)23(5) 501:7 1 r 2 5(10)16(24) 201:3 1 r 35(-)14(-) 301:5 1 r 50(15)37(27) 401:7 1 r 90(30)28(20) 501:8 1 r 65(30)10(4) 201:4Cte40(0)9(0)301:5Cte45(20)13(7)401:6Cte60(35)20(13)501:9Cte85(35)18(10) Fieldhas1000membersN clus isthenumberofclustermembers B istheaveragebackgrounddensity C istheaverageclusterdensity R err istheerrorinmeasuringtheradius N err istheerrorinmeasuringthenumberofmembers Cutovaluewas d field 1 : 5 ( field )forallexcept thoseinparenthesisforwhichweusedthetrough 280

PAGE 281

TableC-3.SimulatingClusters.Radius=0.3,j-value=10 N clus B : C Prole R err N err %% 201:1 1 r 2 10(-)23(-) 301:2 1 r 2 27(27)19(37) 401:3 1 r 2 10(7)46(3) 501:4 1 r 2 20(10)60(16) 201:1 r -(-)-(-) 301:2 1 r 3(-)7(-) 401:3 1 r 27(-)23(-) 501:4 1 r 27(7)18(6) 201:1Cte20(-)9(-)301:2Cte10(-)13(-)401:3Cte23(0)15(5)501:4Cte27(3)8(2) Fieldhas1000membersN clus isthenumberofclustermembers B istheaveragebackgrounddensity C istheaverageclusterdensity R err istheerrorinmeasuringtheradius N err istheerrorinmeasuringthenumberofmembers Cutovaluewas d field 1 : 5 ( field )forallexcept thoseinparenthesisforwhichweusedthetrough 281

PAGE 282

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BIOGRAPHICALSKETCH BrunoRicardoMaltaFerreirawasbornat7:45pm,onJune5th, 1978inLisbon, Portugal. Attheearlyageof5Brunomadehisrstinternationalrightt otheremoteArabian landsofOmanwherehewastospendhisformativeyears.Farfr omthecrowdsanddevoid oftracjams,OmanwastheperfectplaceforBruno.Itwasapl acewheredoorswere neverlockedandkeyswereleftincarignitions.Aplacewith vaststretchesofbeautiful beachandevenvasterexpansesofuntouchedsanddunes.Amid shingtripsandcamel ridesBrunogrewupslowlyinOman. BeingbothnaturallycuriousandendlesslystubbornBrunow asgiftedwiththetwo mainqualitiesnecessaryforbeingagoodstudent;thus,few werehisdicultiesinschool. Inthelastyearsofhighschool,however,whenmoststudents werebeginningtoprepare forcollegeentranceexams,Brunofoundhimselfwonderinga bouthisdirectioninlife, andhismotivationforstudyingwasatanall-timelow.Thisw astobehisrst"mid-life" crisis.HeisindebtedtoDr.KeithOrd,asternhigh-schoolp hysicsteacherwithasenseof humordrierthanthedunessurroundingtheschool,forshaki nghimoutofhisexistential (andacademic)stupor. WithdeliriousenthusiasmBrunoembeddedhimselfinallsor tsofbooks,fromoptics tocosmology,andathighschoolgraduationhewasbestowedt he"BestPhysicsStudent" award.Brunowasalsoadedicatedstudentoftennis,sowithh isjointacademicand athleticcurriculumhehadearnedhimselfapartialscholar shipatabeautifulcollegein SouthCarolina.Thiswasastepwhichheardentlydesiredtot ake,thoughitwasnotto becomearealityduetohisfather'sunwaveringopposition. AfterthirteenyearsinOman, andwithaheavyheart,Brunofoundhimselfonaplanereturni ngtohishomecountry, Portugal,tostudyattheUniversityofLisbon. HisexperienceofLisbonwasdiametricallyoppositetothat ofOman.Thequietof thesandduneswasreplacedbythecacophonyofindustrialso unds:ambulancesirens, 294

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carshornsandplanesryingoverhead,whilethecleanairwas replacedbybusandcar fumes.Sunsetshappenedoverbuildingsinsteadofbeaches, andeverythingalwayshadto belocked. In1996hebeganservinghistimeattheUniversityofLisbon, studyingforaphysics degree.Havingstudiedphysicsinhighschoolaccordingtot heInternationalBaccalaureate curriculum,Brunofoundthersttwoyearsofundergraduate classestobeatedious repetitionofwhathehadalreadylearned.Mathematics,ont heotherhand,wastaught withnauseatingdepthandrigor,andoftentimesbyRussiant eacherspossessingboth impeccablehandwritinganddisastrouspronunciation. TheveyearswhichittookforBrunotocompletethefour-yea rprogramwerealso veryformativeyearssocially.Thesocialtranquilitywhic hheexperiencedinOmanwas rapidlyreplacedbyathickturmoilcomprisedofbars,disco s,danceandmusicfestivals, amorousrelationships,all-nightstudyingsessionswithf riends,yogaparties,anda sproutingobsessionforrockclimbing.Thisperiodalsocoi ncidedwiththebeginningsof theinternetandBrunodoverightintothevirtualworldofch atroomsandmultiplayer gamesthatoccupiedthehoursandmindsofyoungstudents. Despiteallthedistractions,Brunomanagedtobeamongstth e0.5%ofstudents whograduateeachyearfromtheUniversityofLisbonwithade greeinphysics.Eagerto testhisskillsintheworldofresearch,Brunofoundhimself verylimitedbytheoptions providedinPortugal,havingtochoosebetweengraduatewor kincondensedmatter physicsorastrophysics.In2001hereluctantlybeganhisgr aduatestudiesinastrophysics, stillattheUniversityofLisbon,andhewasforthesecondti meinhislifefeelinglostand deeplyunmotivated. OnceagainfatewouldstepintoguideBruno.Overabottleofw ine,theyoung astrophysicistJoaoAlvesexplainedhowitwaspossibletod oashehaddoneandpursue astrophysicsgraduatestudiesintheUnitedStatesofAmeri ca.Withrenewedvigorfor travelingtothelandofopportunity,Brunotoldhisparents ofhisdecisionandjustafew 295

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monthslaterhequitthegraduatestudiesinLisbon.Onadayh eavywithhumidityin July2002BrunoarrivedinOrlando,Florida,andwasdrivenu pthedepressinglydesolate freewaytotheuniquecitycalledGainesville. EightyearspassedfromhisarrivalattheUniversityofFlor idain2002untilhis departurein2010.ThateightyearperiodinGainesvillesta ndsoutinBruno'slifeas deningthebeginningofhismanhood;itwasthersttimeBru nolivedbyhimself,far fromtheinruenceofhisparents,andthersttimehefelttru lyindependent. AttheUniversityofFloridaBrunobeganhisgraduatestudie sinastrophysics,under thesupervisionofElizabethLada.Thoughtherstyearswer etiresome,havingtoattend classesonthesametopicshehadpreviouslystudied,Brunoq uicklyfoundaresearch topicwhichfascinatedhim:embeddedstellarclusters.The remanylongdaysofcomputer programming,longnightsofobservingatthetelescopes,an dtripstoconferencesinexotic locations.Thislaborinlearningprogresseduntilthedayc amewhenhewasnolongerjust studyingwhatothershaddonebutalsocontributingtomanki nd'sscienticknowledge. Togetherwithhisscienticlearning,Gainesvilleprovide dthespaceandpeopleBruno neededtolearnabouthimself.Byconnectinginconversatio nwithpeoplesuchasHuxley Coulter,PaulLinn,andRafaelGuzman,Brunocametoabetter understandingofthe valueshebelievedinandhowtoliveinbetteralignmentwith them.Attheuniversity's outdoorpoolhereconnectedwithhischildhoodloveforswim ming,andattheGainesville RockGymhecontinuedfeedinghispassionforclimbing.Hedi scussedAynRandand chantedwiththeHareKrishnaswhilesittinginthegrassoft hePlazaoftheAmericas, adoptedavegetariandiet,learnedtomassageandcommunica teattheFloridaSchoolof Massageand,mostimportantly,becamefriendswithunforge ttablepeople(includinghis wifeUrsula). ThiseightyearperiodsawBrunotransitionfromanidealist icyouthincheckered pantswithathirstforbeingattheforefrontofscienticre searchtoagroundedman,a husbandandfather,withathirstforsavoringthepresent. 296

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InMayof2010Brunocompletedhismostarduousaccomplishme nttodate,his DoctorofPhilosophyinAstrophysics,amomentwhichwascel ebratedwithhislovedones, aglassofPort,andwithplentyofclimbing. 297