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Dependence of Galaxy Stellar Populations on Density at z=0.3-1.5

HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction to the density-morphology...
 The density-sed relation for spices...
 Density-sed relation for flamex...
 Age distribution of open clust...
 Appendix A: Catalogparse.c
 Appendix B: Maskfrac.pro
 Appendix C: Corrbrod.c
 Appendix D: Open cluster catalog...
 References
 Biographical sketch
 

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Iwishtothankallthepeoplewhohavemadethisworkpossible,includingmyfamily,friends,teachers,andcolleagues.Inparticular,IwouldliketothankBradleySchaeferfortakingthetimetoguidemethroughmyrstresearchpro-gram,helpmepublishmyrstpaper,andcreateanopportunityformetoattendgraduateschoolinastronomy,allwithverylittlereturnforhimself.IamalsodeeplygratefultoRichardElston,whotookmeonashisgraduatestudentandprovidedtheinspirationforthisproject,andwhoseinfectiousenthusiasmandheartfeltlaughterwillstaywithmeforever.IoweagreatdebtofgratitudetoAnthonyGonzalezforpickingmeupwhenmyresearchhadwanderedbadlyastrayandsettingmebackonthetruepathofscience,andforhisheroiceortstoensureasteadyowofresearchassistantfunding,butmostofallforhisamazingqualitiesasapersonandafriend. iv

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page ACKNOWLEDGMENTS ............................. iv LISTOFTABLES ................................. viii LISTOFFIGURES ................................ ix ABSTRACT .................................... xi CHAPTER 1INTRODUCTIONTOTHEDENSITY-MORPHOLOGYANDDENSITY-SEDRELATIONS ............................. 1 1.1BasicDescription ........................... 1 1.2LocalMeasurements ......................... 3 1.3WhatCausestheRelations? ..................... 4 1.4ExtendingStudytoHighRedshifts ................. 6 1.5Summary ............................... 10 2THEDENSITY-SEDRELATIONFORSPICESGALAXIES ...... 12 2.1Introduction .............................. 12 2.1.1AnAlternativetotheDensity-MorphologyRelation .... 12 2.1.2SPICESasaPrototype .................... 13 2.2Observations .............................. 13 2.3DensityMeasurements ........................ 14 2.3.1BasicOverview ........................ 14 2.3.2Star-GalaxySeparation .................... 15 2.3.3PhotometricRedshifts ..................... 18 2.3.4Two-PointAngularCorrelationFunction:Overview .... 22 2.3.5Two-PointAngularCorrelationFunction:SPICESCalcu-lations ............................ 25 2.3.6TranslatingtotheSpatialCorrelationFunction ....... 26 2.4GalaxySEDMeasurements ...................... 30 2.4.1OverviewofPhotometricTechnique ............. 30 2.4.2VisualMorphologies:DescriptionandConsistencyChecks 31 2.4.3ComparisonsofConnolly'sResultstoVisualMorphologies 36 2.5Results ................................. 39 v

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........ 44 3.1Introduction .............................. 44 3.2TheFLAMINGOSInstrument .................... 45 3.3SurveyandProgramDesign ..................... 46 3.4DataAcquisition ........................... 47 3.5DataProcessing ............................ 49 3.5.1InitialProcessing ....................... 49 3.5.2DarksandFlats ........................ 49 3.5.3SkySubtraction ........................ 50 3.5.4AlignmentandStacking .................... 51 3.5.5CombiningDatafromMultipleNights ............ 51 3.5.6AstrometryandPhotometry ................. 51 3.6TheCatalog .............................. 52 3.7CalculatingtheSpatialCorrelationFunction ............ 53 3.7.1MathematicalOverview .................... 53 3.7.2PhotometricRedshiftsandSEDClassications ....... 56 3.7.3TheFinalCatalog:catalogparse.c 57 3.7.4MaskingInformation:maskfrac.pro 62 3.7.5Aandr0Calculations:corrbrod.c 63 3.8Results ................................. 65 3.8.1EvolutionoftheSED-DensityRelation ........... 65 3.8.2EvolutionoftheERO-DensityRelation ........... 70 3.8.3GalaxyClusters ........................ 73 3.9DiscussionandConclusions ...................... 75 3.10FutureWork .............................. 76 4AGEDISTRIBUTIONOFOPENCLUSTERS .............. 78 4.1Introduction .............................. 78 4.2ComparisonofClusterCatalogs ................... 78 4.3SampleConstruction ......................... 80 4.4SampleOverview:AgesandLocations ............... 81 4.5SelectionEects ............................ 83 4.6FittingtheAgeDistribution ..................... 87 4.7Discussion ............................... 93 APPENDIX ACATALOGPARSE.C ............................. 99 BMASKFRAC.PRO .............................. 105 CCORRBROD.C ................................ 109 vi

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.............. 126 D.1Alessi .................................. 126 D.2Alessi-Teutsch ............................. 126 D.3Andrews-Lind.1,Antalova1,Arp-Mad.2,Aveni-Hunt.1 .... 126 D.4ASCC ................................. 127 D.5Basel .................................. 127 D.6Berkeley ................................ 127 D.7vandenBergh-Hagen(akavdBergh-HagenorBH) ......... 128 D.8Bica1-4,Biurakan1-2,Blanco1,Briceno1 ............. 129 D.9Bochum ................................ 129 REFERENCES ................................... 130 BIOGRAPHICALSKETCH ............................ 138 vii

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Table page 2{1SPICESFields ............................... 14 2{2Star-GalaxySeparation,SuccessRates .................. 16 2{3Star-GalaxySeparation,Spectroscopicvs.PhotometricSources .... 17 2{4Comparisonof\Double"MorphologyEstimates ............. 32 2{5PreliminaryResultsforLynx ....................... 40 3{1FLAMEXSubregions ........................... 60 3{2EROSpatialClusteringStudies ...................... 73 viii

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Figure page 2{1Comparisonofphotometricredshiftstospectroscopicredshifts. .... 20 2{2Redshifterrorhistograms. ........................ 21 2{3K0-bandKcorrections .......................... 28 2{4K0-bandevolutionarycorrections .................... 29 2{5SampleofHSTimages .......................... 31 2{6Visualmorphologyestimates. ...................... 33 2{7ComparisonofGIM2Dandvisualmorphologyestimates. ....... 35 2{8ComparisonofestimatedSED-typeswithvisualmorphologies. .... 37 2{9Redshiftdistributionofobjectswithvisualmorphologies. ....... 38 2{10PreliminaryresultsforLynx ....................... 39 2{11FinalSPICESresults(usingConnollySED-types) ........... 41 2{12FinalSPICESresults(usingvisualmorphologies) ........... 43 3{1IRACch2apparentmagnitudeversusredshift ............. 59 3{2FLAMEXdensity-SEDresults(exiblebins) .............. 66 3{3Overallr0vs.redshift ........................... 67 3{4NormalizedFLAMEXdensity-SEDresults(exiblebins) ....... 68 3{5FLAMEXdensity-SEDresults(xedbins) ............... 69 3{6LLdensity-SEDresults ....................... 70 3{7HistogramofEROsversusBrodwin'sSEDtypes ............ 72 3{8EROandnon-EROcorrelationlengthsversusredshift ......... 72 3{9Clusterr0valuesversusredshift ..................... 74 3{10Clusterr0valuesversusdetectionrating ................ 75 4{1Numberofclustersversusage ...................... 82 ix

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.................... 84 4{3Edge-ongalacticview ........................... 85 4{4Numberofclustersversusage,witht ................. 88 4{5Overalllnregressionlines ......................... 89 4{6Mid-termlnregression .......................... 94 4{7Short-termlnregression ......................... 95 4{8Lnregressionlinecomparison ...................... 96 4{9Clustersobservedandt ......................... 97 x

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1.1 BasicDescriptionThequestionofhowgalaxiesformedandevolvedisasubjectofmuchinteresttoextragalacticastronomersandastrophysicists.Competingtheoriesofmonolithiccollapse(Eggenetal.1962)andhierarchicalformation(e.g.,Peebles1974,1980)havelargelybeenresolvedinfavorofthelatter,butadisconnectremainsbetweenmodelsandobservations.Hierarchicalformationmodelsgenerallypredicttheevolutionwithredshiftofmassivedarkmatterhalos,whichrepresentthebulkofthematterintheuniverse,butthecorrespondencebetweentheseinvisiblehalosandthegalaxiesthatweactuallyobserveisnottypicallystraightforward.Asaresult,observationscontinuetoplayamajorroleinestablishingthepropertiesofgalaxiesandhowtheyvarywithredshift.TwoexamplesofthisthatIwilladdressinthisdissertationarethemorphologyofgalaxies(spiral,S0,elliptical,etc.)andtheirspectralenergydistributions(SEDs),andhoweachofthesedependsonthelocalgalaxydensity.Weobservegalaxiestodwellinregionsofwidelyvaryingdensity,fromsparseeldenvironmentstomassive,denseclusters.Earlyinvestigations(e.g.,Peebles1975)usedtheLickObservatorydata(ShaneandWirtanen1967)tostudytheautocorrelationofgalaxiesindetail,andDressler(1980)wasthersttoidentifythedensity-morphologyrelation,whereinthefractionofS0andellipticalgalaxiesrisessmoothlyasthelocalgalaxydensityincreases.Thisphenomenonisanindicatoroftheimportanceofenvironmentingalaxyevolution,oeringcluestothemechanismsbywhichthegalaxiesevolveintodierentmorphologicaltypes.Itwas 1

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long-arguedthattheclusterenvironmentisanimportantfactorinquenchingstarformationandestablishingthedensity-morphologyrelation,butinthepastdecadetherehasbeenagrowingbeliefthat\preprocessing"inthegroupenvironmentismoresignicant.Recentstudieshavegreatlyexpandedthelocal-Universestatisticsandpushedthestudyofthedensity-morphologyrelationtoz1,althoughlimitationsindeterminingmorphologyathighredshiftshavehamperedtheseeorts.Itisalsopossibletostudyarelatedphenomenonbyexamininghowthespectralenergydistributionsofgalaxiesvarywithdensity.TheSEDsarelargelyameasureofthestellarpopulationofthegalaxies,whichreectsthestarformationhistory.Thedensity-SEDrelationcanbeobservedwithvariouslevelsofprecision,includingdirectspectroscopy,spectralmodelingofmultibandphotometry,orsimplecolorclassication.Thelattertwoapproachesarevaluablebecauseofthespeedwithwhichtheinformationcanbeobtainedandbecauseoftheirrobustnesscomparedtomorphologicalestimatesathighredshifts.InthelocalUniverse,thereisaclosecorrespondencebetweengalaxymorphologiesandgalaxyspectraltypes(e.g.,Kennicutt1992),althoughthisconnectiondivergessomewhatathigherredshifts,whichitselfprovidesusefulinformation.Inpartsofthisdissertation,Itestthiscorrespondence(Chapter 2 )andmeasurethedensity-SEDrelationasafunctionofredshift(Chapters 2 3 ).Inallcases,densitymeasurementsaresometimesmadeintermsofsurfacedensityandsometimesintermsoftheangularorspatialcorrelationfunctions.Thelatteraremoreproperlyameasureofclusteringthanofdensityperse,butIwillsubsumeallofthesetechniquesundertheheading\densitymeasurements"throughoutthisdissertationforsimplicity.

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1.2 LocalMeasurementsDressler(1980)performedtherstmajorstudyofthedensity-morphologyrelation.Heinvestigatedthemorphologydistributionofthegalaxiesin55rich,nearbyclusters,mostlyfromAbell'scatalog(1958).Themorphologiesvariedsmoothlyovervemagnitudesofestimatedspacedensity,from10%/40%/50%spiral/S0/ellipticalinthickclumpswithintheclustersto60%/30%/10%inthediuseedgesoftheclusters,and80%/10%/10%fortheeldgalaxies(isolatedgalaxiesandloosegroups).Henotedthatthisrelationappearedtoholdregardlessofthedierencesbetweentheclustersinrichnessoroverallconcentration.PostmanandGeller(1984)extendedthisstudytolessdenseregions,wheretheyfoundthattherelationleveledoaround70%/20%/10%spiral/S0/elliptical.Thisindependenceatlowdensitiesisinterpretedasapplyingtoregionswherethecollapsetimetc=1:43=(G)0:5iscomparabletoorgreaterthantheHubbletime.Localstudiesofthedensity-SEDrelationndahigherdegreeofclusteringforquiescentgalaxiesthanforemission-linegalaxies(e.g.,Lovedayetal.1999;Magdwicketal.2003).Budavarietal.(2003)usesphotometrictstoSEDmodelsandsimilarlyndsgalaxieswithspectraltypescomparabletoellipticalgalaxiestobemorehighlyclusteredthanbluegalaxies.Thisisinaccordancewithexpectationsfromthedensity-morphologyrelation,asitreinforcesthecommonobservationthatpresent-dayspiralgalaxiesareactivelyformingstars,whilepresent-dayellipticalgalaxiesareevolvingrelativelypassively.Studiesoftheenvironmentaldependenceofgalaxycolor(e.g.,Kaumannetal.2003;Baloghetal.2004)ndared/bluebimodalcolordistributionthatcanbetbytwoGaussiandistributionsregardlessofsurfacedensityorluminosity.Thisdivisionsuggeststhatpresent-daytransformationsfrombluetoredgalaxiesmusttakeplaceoverashorttimescaleforbothfaintandbrightgalaxies.Thereisastrongincreaseinthefractionofredgalaxieswithincreasingsurfacedensity(at

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xedluminosities),from10-30%inthesparsestregionsto70%inthedensestregions.Themeancolorsoftheblueandredpopulationsshowlittletonochange,however. 1.3 WhatCausestheRelations?Theveryexistenceofthedensity-morphologyanddensity-SEDrelations,aswellasthecontinuityoftherelationsacrossfourordersofmagnitudeindensity,tellsusthatenvironmentalfactorsarefundamentaldriversindeterminingthepresent-daymorphologiesandspectralclasses.Identifyingthespecicphysicalfactorsresponsibleformorphologicalandspectralevolutionhasbeenanimportantobjectiveforastrophysicists.Foratime,natureversusnurturedebatesdominatedthediscussioninanattempttodeterminewhetherthekeyprocessestookplaceasthegalaxieswereforming(monolithiccollapse)orinlaterinteractionsbetweengalaxiesandotherpost-formationevolutionaryprocesses.Thelattertheory,knownashierarchicalformation,graduallygainedascendanceinthe1990sasnewobservationalcapabili-tieslentsupporttoit,anditisnowgenerallyaccepted.Manymodels(e.g.,Bensonetal.2001)havesuccessfullymatchedpresent-dayandhigh-redshiftobservationsusingcolddarkmatter(CDM)cosmologiesandhierarchicalformationassumptionsintheirinitialconditions,correctlypredictingvariationsingalaxynumbercountsandluminosityfunctions,galaxyclustering,etc.asafunctionofredshift.Newobservationsalsocontinuetosupporthierarchicalformation,suchasdiscoveriesofrecentstar-formationindistantearly-typegalaxies(e.g.,Bargeretal.1996;vandeVenetal.2003).Thereiscontinueduncertaintyabouttherelativeimportanceofthepossiblephysicaldriversforthedensity-morphologyanddensity-SEDrelations.Severalauthors(e.g.,Toomre1977;Roos1981)investigatedthepossibilitythatgalaxymergerscouldconvertspiralgalaxiesintoellipticalgalaxies.Whilethelarge

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velocitydispersionspresentinclustersprecludeecientmerging(e.g.,Merritt1984),themodernviewisthatclusterellipticalscanbeformedinthisfashionvia\preprocessing"inlower-dispersionsystemssuchasgroups.GunnandGott(1972)identiedrampressuregasstrippingasaprobablemeansofconvertingspiralgalaxiesindenseregionstoS0s.Asgalaxiespassthroughthehotgasoftheintra-clustermedium(ICM),thegalaxies'starsareessentiallyunaected,buttheirowngascloudsareblownoutanddispersed.Gasstrippingwouldonlybeeectivewithin250kpcoftheclustercore,wheretheICMisdensest,andsoitislesseectiveasanexplanationfortheS0sobservedinlow-densityenvironments,althoughLarsonetal.(1980)suggestthatspiralgalaxiesmayberefueledbytheinfallfromtenuousgasenvelopesandthattheseenvelopesmaybeeasilystrippedintidalinteractionsbetweengalaxies.Certainly,tidalinteractionshaveplayedsomeroleinestablishingthepresentrangeofmorphologies,whetherdirectlystrippingstarsormerelygas.Morerecentproposalsincludegalaxyharassment(e.g.,Mooreetal.1998),inwhichsmall,newly-infallingdiskgalaxiesinaclusteraredisruptedduringy-byencounterswithlargergalaxies.Thisresultsinstarburstsandthetransformationofthegalaxyremnantsviaangularmomentumlossintocompactgalaxies,probablydwarfspheroidals(dSph).Thistheoryismotivatedbytheexistenceofapopulationofsmall,disruptedspiralgalaxiesinclustersatz>0:3butnotinpresent-dayclusters.ThereisclearlynosinglephysicalmechanismthatcanexplainthefullHubblesequenceacrossvaryinglevelsofgalaxydensity.Thenextstepinenhancingourunderstandingofhierarchicalformationwillbetolearnmoreaboutthemechanisms'relativeimportanceandthetimescalesonwhichtheyoperate.Onenaturalmeansofdoingthisisbyextendingourstudytohigherredshift.

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1.4 ExtendingStudytoHighRedshiftsAstronomershavestudiedthedensity-morphologyrelationforovertwodecadesinourgalaxy's(comparatively)localneighborhood.Whatwedonotyetknow,though,arethedetailsoftheassemblyhistoryofmassivegalaxies,orhowearlythedensity-morphologyanddensity-SEDrelationswereinplace.Aconsiderablybroaderperspectivecanbegainedbylookingtohigherredshiftandearliertimesinouruniverse'shistory.Wecanobservehowtherelationshavebeenchangingoverbillionsofyears,andthiswilladdanewdimensiontothesnapshotevidencewehavefromourowntime.Thedensity-morphologyrelationbecomesdiculttostudyathighredshift,particularlywhenmakinganeorttodistinguishbetweenellipticalandS0galaxies.Nevertheless,wendthatclustersatintermediate-redshifts(z0:5)havesimilarfractionalpopulationsofellipticalgalaxiestopresent-dayclustersbutamuchsmallerfractionofS0galaxies(2-3timesfewer),withacorrespondinglyhigherfractionofspirals,althoughtherelationforirregularclustersislessclearthanforregular,dynamicallyrelaxedclusters(Dressleretal.1997).Themorphologicalsegregationbydensityinabroaderrangeofenvironmentsisstillreadilyapparentevenouttoz1,withfE+S0(thefractionofelliptical+S0galaxies)remainingcomparabletothepresent-dayfE+S0atlowandintermediatedensitiesatz1andatlowdensitiesatz0:5(Smithetal.,2005).Theauthorsproposeabasicmodelinwhichmostellipticalgalaxiesareformedathighredshift(z>2),whileS0saregraduallyformedbyaninfallingpopulationoflate-typegalaxies,althoughthisconclusionislimitedbytheirinabilitytovisuallydistinguishEandS0galaxiesatz=1,andthedominantmechanismofS0productionremainsunclear.Postmanetal.(2005)usetheAdvancedCameraforSurveys(ACS)ontheHubbleSpaceTelescope(HST)toenableadistinctionbetweenEandS0morphologies(albeitstillwithsignicantuncertainties).Theirresultsaregenerallyinaccordancewith

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Smithetal.(2005),buttheytentativelyndahigherfractionofS0galaxiesandalowerfractionofEsatz1,whichinuencestherelativeimportanceofthecandidateprocessesthatproducemorphologicaltransformations.Inparticular,therewouldbemoreroomforpairwisemergersofspiralstoplayamodestroleintheproductionofellipticalgalaxies.Acomplementaryviewfordierencesinthedensity-SEDrelationatinter-mediateredshiftsisgivenbyPoggiantietal.(1999).TheauthorsestablishasetofbasicSEDclassications,includingpassive/non-star-forminggalaxies,galaxieswithcomparableSEDstopresent-dayspirals,starburstgalaxies,post-starburstgalaxieswithlittlestar-formation,andgalaxieswhichcouldbeinterpretedeitheraspost-starburstgalaxieswithsignicantstar-formationorasdustystarburstgalaxies.Theyconcludethatgalaxiesinfallingintoclustersundergobothmorpho-logicalandSEDtransformations,butondierenttimescales.Asignicantfractionofclustergalaxiesatz0:5haveredcolorsandlittlestarformationbutspiralstructure,suggestingthatthephysicalprocess(es)responsibleforstarformationsuppressionactsonafastertimescale,byroughly1Gyr,thantheprocess(es)responsibleformorphologicalshifts(suchasram-pressuregasstrippingshiftingspiralstoS0s).Theauthorsalsonotethattherearemanymoregalaxieswith\post-starburst"SEDsinclustersthanintheeld,thoughgalaxieswith\dustystarburst"SEDsarefoundinbothclusterandeldenvironments.Theauthorsproposethat\post-starburst"andstar-forminggalaxiesinclustersarerecentlyacquiredandhavenotyethadtheirstar-formationquenched.Otherstudies(e.g.,Phlepsetal.2005;Meneuxetal.2006)alsoshedlightontheclusteringvariationsfordierentSED-typesatintermediateredshifts.Finally,thereareresearcherswhostudythisevolutionaryprocessbasedongalaxycolors.Inadditiontobeingeasilymeasurable,colorsexhibitatruebimodalitybetweenredandbluepopulations,whilespectralclassandmorphologies

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occupyamorecontinuousspectrum.Althoughtheydonotfocusondensityassuch,Belletal.(2004)studyUVgalaxycolorsandcolor-magdiagramsacrossabroadrangeofenvironmentsat0:2
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(LV<0:1LV),Kodamaetal.(2001,2003)locatethecolordivisionatalocaldensityof30galaxiesMpc2,i.e.inthelamentssurroundingtheclusterthattheystudied.Otherstudiesidentifysignicantgrowthofclusteringbetween02:3cuttotrackthe\opticalbreak."ThismethodisaninfraredcounterparttotheLymanbreaktechnique;itidentiesredshiftsatz>2basedonthe3625ABalmerbreakand4000ACaIIH+Kbreak.Theyspectroscopicallyverifyasmallsampleofvegalaxiesat2:4
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1.5 SummaryResearchersareclearlybeginningtoestablishanoverallpictureofgalaxyevolution,buttherearestillmanyuncertaintiesregardingtheresponsibleprocessesandtheirrespectivetimescales.Thereisalsosomeambiguityinattemptingtoestablishconnectionsbetweenstudiesthatfocusondierentredshiftsorareselectedindierentways.MyprojectcontributestoourunderstandingbyextendingthestudyofgalaxySEDclasses(estimatedusingtemplatespectraandmultiwavelengthphotometry)andtheirdependenceondensity.Itfollowstheevolutionofthedensity-SEDrelationwithredshiftfrom0:3
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theagedistributionofopenclusterswithintheMilkyWayanddrawsinferencesregardingthetimescalesofdissipationmechanisms.

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2.1 Introduction 2.1.1 AnAlternativetotheDensity-MorphologyRelationAnextensivestudyofthedensity-morphologyrelationathighredshiftsre-quiresanumberofassumptionsandapproximations.Oneproblemisthatthespatialdensityofgalaxiescannotbedirectlyascertainedwithouttime-consumingspectroscopy.Anotheristhattherest-frameopticalmorphologyofhigh-redshiftgalaxiescanonlybedeterminedwithdeep,high-resolution,near-infrared(NIR)imaging,suchasthatavailablewithNICMOSoradaptiveopticsonmajortele-scopes,andwide-areasurveysarenotreadilyachievable.Theseissuescanbecircumventedbyinsteadusingmultiwavelengthphotometricobservationsandstudyingtherelationbetweendensityandstellarpopulationratherthanmor-phology.Inplaceofspatialdensitiesderivedfromspectroscopicredshifts,Iobtainspatialcorrelationamplitudesbycalculatingthetwo-pointangularcorrelationfunctionforeachgalaxyandapplyingamathematicalinversion.Theresultsoerimpreciseinformationforaparticulargalaxybutrobuststatisticswhenappliedtoalargesample.Inplaceofvisualmorphologies,Iusespectralenergydistribution(SED)modelsfordierentgalaxytypes(E,S0,etc.)andestimationsoftheclosest-matchSEDtypeforeachgalaxy.Thishastheadvantageovervisualmorphologiesofbeinglesssubjective,anditisalsoeasiertomeasureathighredshifts.Thus,Ichoosetostudythe\spatialcorrelationamplitude-SEDtyperelation,"whichforconvenienceIcallthedensity-SEDrelation.Itisnotadirectsubstituteforthedensity-morphologyrelation,butthetwoarecloselyrelatedandrepresentsimilarphysicalprocesses. 12

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2.1.2 SPICESasaPrototypeInthisproject,Iusetwoastronomicalsurveys.TheSpectroscopicPhotometricInfrared-ChosenExtragalacticSurvey(SPICES),asmall,pencil-beamsurveythatincludesbothspectroscopicobservationsandhighresolutionphotometry,providesanidealmeansofcomparingthedensity-morphologyanddensity-SEDrelationsathigherredshift.Forredshiftsandgalaxyspectraltypes,atradeoexistsbetweenacquiringpreciseinformationforsmallsamplesusingspectroscopyandlower-precisiondataforlargesamplesusingmultibandimaging.InmymainstudyoftheFLAMINGOSExtragalacticSurvey(FLAMEX,discussedinChapter 3 ),Iemploythelatterapproach,usingphotometricredshiftsandSEDtypesderivedfrommultibandphotometrytoquantifythedensity-SEDrelationforalargestatisticalgalaxysample.PriortotheFLAMEXstudy,however,SPICESprovidesanimportanttestoftheconceptsthatareusedinthelargerstudy.AnimportantaspectofSPICESisthatithasbothfollowupspectroscopyandHubbleSpaceTelescope(HST)imaging.Asaresult,theaccuracyandprecisionofthephotometrictechniquescanbeestimated,andtheybecomeabetter-understoodquantitywhenworkingwithsurveysthatarebasedonphotometryalone(suchasFLAMEX).TheobservationsfortheSPICESprogramaredescribedinSection 2.2 .InSection 2.3 ,Ipresentthedetailsofthedensitymeasurements,includingacomparisonofthephotometricandspectroscopicredshifts.IthencomparetheSED-typesfromthephotometricredshiftswithHSTvisualmorphologiesinSection 2.4 ,beforepresentingthedensity-morphologyanddensity-SEDresultsandconclusionsinSection 2.5 2.2 ObservationsSPICESobservationsweretakeninB;R;I;z;J;andK0bandsattheKittPeakNationalObservatory's4-metertelescopeduring1997,usingtheInfrared

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Imager(IRIM).ThephotometriccutoemployedinthisstudyisK020:0(Vega),with1471sourcesdetectedbySExtractoratthe10levelin3"apertures.Thesurveyteamtookfollowupspectroscopicobservationsofroughlyhalfthesesourcesbetween1997and2001,whichwereusedbothtoeliminatestarsandtoestimatetheerrorsofourphotometricredshifts.Thesurveyconsistsoffoureldsindierentregionsoftheskywithacom-binedareaof105arcmin2.Table 2{1 liststhebasicdatafortheelds.Thephotometricsourcecountincludessomeobjectswhichwerenotusedinthecor-relationanalysis:probablestars,objectswithzphot>2:0,andsourceswithKMAGERR AUTORMS>0:5.Thesixthandseventhcolumnsseparatethesourcesstudiedwithfollowupspectroscopyintogalaxiesandstars.AsmallpercentageofthesesourcesandtheHSTsourcesareexcludedfromthephotometricsourcecountduetofaintnessorlocationoutsidethetrimmedSPICESimageboundaries.TheplatescalesfortheK0imagesare.471arcsec/pixafterrebinning(tomatchtheopticalCCD'splatescale)foralleldsexceptPisces,whoseplatescaleis.420arcsec/pix. Table2{1: SPICESFields Cetus02:59:00+00:12:2024.032918023224Lynx08:45:22+45:05:2525.742124250230Pisces23:10:25+00:41:2225.037020347277SA5713:07:04.1+29:36:16.530.2346180270 DensityMeasurements 2.3.1 BasicOverviewTodeterminethedensity-SEDrelation,itwasnecessarytoassignavaluetoeachSPICESgalaxyrepresentingthelocaldensityofneighboringgalaxies.Ichosetousetheamplitudeofthespatialcorrelationfunctionasestimatedfromaninversionofthetwo-pointangularcorrelationfunction.Thefollowingisadescriptionofthesecalculations,aswellasoftherelatedissuesofstar-galaxy

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separationandphotometricredshifts.SPICES'spectroscopicdataareanimportanttoolforthelattertwotopics.Section 2.3.2 discussesstar-galaxyseparation,describingtwodierentphotometricmethodsofidentifyingwhichsourcesaretruegalaxiesandwhicharemerelyforegroundstars;italsopresentstestsoftheeectivenessofthesetwoapproachesusingthespectroscopicSPICESdataforcomparison.Section 2.3.3 providesanoverviewofthephotometricredshiftsdeterminedforthegalaxies,withspectroscopictestsoftheiraccuracy.Section 2.3.4 givesamathematicaloverviewofthetwo-pointangularcorrelationfunction,whichisdirectlyobservable,andSection 2.3.5 providesdetailsofitscalculationfortheSPICESgalaxies.Section 2.3.6 coversthetwo-pointspatialcorrelationfunction,whichisinferredfromtheangularcorrelationfunctionandphotometricredshiftinformationandrequiresvariouscorrectionstoplaceallgalaxiesonanequalfooting. 2.3.2 Star-GalaxySeparationTooptimizethegalaxydensitymeasurements,wemustremovestarsfromthesourcecatalog.Inordertoremovethestarsbaseduponphotometricinformationalone,weconsideredtwoapproaches:selectionbasedonSExtractor'sneuralnetworkobjectclassication(theCLASS STARparameter)andselectionbasedoncolor(BIvs.IK0).SExtractorproducesavaluerangingbetween0(galaxy)and1(star)basedonthepoint-spreadfunction(PSF);objects0:95arecommonlyconsideredtobestarsinmostapplications,althoughthemethodgenerallyworksbetteratbrightermagnitudes.Thecolorselectionswerebasedonadoublecuto.Foreachobject'sIK0color,itsBIhadtoexceed2:974(IK0)+0:056and1:469(IK0)+1:200tobeclassiedasagalaxy.Totesttheeectivenessofthesetechniques,wecomparedtheirresultstotheinformationgainedfromspectroscopicfollowupfortheCetus,Lynx,andPisceselds,summarizedinTable 2{2 .SA57isomittedduetoitspaucityofspectroscopy.

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Table2{2: Star-GalaxySeparation,SuccessRates Cetus180/18020/236/18011/18011/2315/23Lynx230/24135/450/2411/24113/4516/45Pisces200/20332/472/2034/20330/4730/47 STARvalues;Itestedtwodierentcutosandfoundthataless-rigorousvalue(0.90)correctlyidentiesmorestars,butthatthereisaconcommittantincreaseinmistakesforgalaxies.ThecolorseparationismoreeectivethanSExtractor'sPSFclassication,correctlyidentifying98%ofthegalaxiesand76%ofthestars,althoughacombinationofthetwotechniquesprovestobeuseful.Adetailedinvestigationofthecaseswheretheseparationmethodsfailrevealsastrongdependenceonmagnitude.Forcolorseparation,manyofthestarsmistakenlyidentiedasgalaxiesareverybright.Forthethreeeldscombined,15/21starsareincorrectlyclassiedatK0<15:5,comparedto5/59at15:5K0<18:5and8/35at18:5K0.Fortunately,themistakesatK0<15:5allhaveCLASS STARvalues0:95.Notealsotheslightdropoineectivenessatfaintermagnitudes.Galaxieswereidentiedwithgreateraccuracyatbrightermagnitudes:only3/289wereidentiedasstarsatK0<18:5,comparedto11/338at18:5K0.SExtractor'sPSFclassicationissomewhatusefulforbrightobjects.Brightstarsinparticularareidentiedfairlyconsistently,andgalaxiesseldomhaveCLASS STARvalues0:95.CLASS STARbecomesrelativelyuselessatfaintmagnitudes,however,duetothelowsignal-to-noiseratios;forK018:5,noneof35starshaveavalue0:95andonlyonehasavalue0:90.Moregenerally,thestars'valuescannotbedistinguishedfromthoseofthegalaxies.

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Forthethreeeldscombined,thebestseparationalgorithmforourpur-posesistoremoveobjectsclassiedasstarsbycolorseparationandobjectswithCLASS STARvalues0:95.Applyingthisalgorithmtoourobjectswithspectroscopicinformationwronglyincludes11/115starsandwronglyexcludes14/624galaxiesfromourfullcatalog,or11/113starsand8/583galaxiesfromourK020:0catalog.Onenalissueistheextenttowhichtheseexperimentsarerepresentativeoffainterobjects,sincethepercentageofobjectswithspectroscopicinformationdeclinesatK018:5.66%oftheK018:5photometricsourcesinCetus,Lynx,andPisceshavespectroscopy,comparedwith33%for18:50:5(generallyveryfaintsourcesoronesnexttotheedge

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oftheimage),butretainingfaintsources.Thiscutreducedthetotalsourcesfrom794to737inCetus,from1505to1345inLynx,andfrom1957to1850inPisces.Mostofthese(thosewith20
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Themethodisalsobasedupontheuseofeigenspectraltechniques,determiningasmallnumberofbasisspectrawhichcanbecombinedindierentwaystocreatespectrawhichreproducevirtuallyanycolorobservations.Thisyieldsacontinuousdistributionoftemplatespectra,aswellasprovidinguswithquantiableerrors.Thus,wecancompareagalaxy'scolortotheseoptimizedtemplatespectratoestimatetheredshiftandSED-typephotometrically.FollowupspectroscopyinCetus,Lynx,andPiscesprovidedaccurateredshiftsfor625ofthegalaxies,providinganindependentassessmentoftheerrorsinourphotometricredshifts.Aplotofzspecvs.zphotforallthreeelds(Figure 2{1 a)yieldsalinearregressionslopeof1:05:06whentthroughtheorigin.Theaverageofthedeviationsz=jzspeczphotjisrelativelyhighat.27,althoughignoringtheextremeoutliers(z>1:0)reducesthisvalueto:19.ThedistributionofdeviationsisnotGaussian,butzavg<:22for68%ofthegalaxies.Figure 2{2 providesahistogramoftheresults.AsFigure 2{1 areveals,thegreatmajorityofphotometricredshifts>2werecatastrophicfailures,missingtheirtargetbyaconsiderablemargin(z1),andweregenerallyoverestimates.Thissuggeststhatgalaxiesinthefullsamplewithzphot>2shouldbediscardedasunreliable.However,itmustalsobenotedthatthisanalysis,basedongalaxieswithspectroscopicinformation,ispredisposedtowardbrightergalaxiesandprovideslittleinformationaboutthephoto-zcode'saccuracyinrelationtothefaintergalaxiesinthefullsample.Overall,zphotpredictionsforgalaxiesatzspec>0:8arejustasaccurateasforgalaxiesatzspec0:8.Forthehigh-zset,with242objects,(z)avg<:22for68%;forthelow-zset,with383objects,(z)avg<:24for68%.Thephotometricredshiftcodeisstillmakingrelativelyaccuratepredictionsforgalaxiesouttozspec'1:5.Itmaywellcontinuetobesuccessfulathigherredshifts,butwedonothavethemeansoftestingitextensively,andsogalaxieswithzphot>2areremovedfromthesample.

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Figure2{1: Comparisonofphotometricredshiftstospectroscopicredshifts.A)AllSPICESelds.B)Cetusonly.C)Lynxonly.D)Piscesonly.SA57hasbeenomittedduetoitssmallnumberofspectroscopicfollowups.

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Figure2{2: Redshifterrorhistograms,showingthejzspeczphotjvalues.A)AllSPICESelds.B)Cetusonly.C)Lynxonly.D)Piscesonly.E)Alllow-zgalaxies.F)Allhigh-zgalaxies.

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Panelsb-dinFigure 2{1 comparephotometrictospectroscopicredshiftsforthetargeteldsindividuallyinordertoassesstheconsistencyoftheresultsfromoneeldtoanother.Pisceshasthegreatestnumberofcatastrophicfailures,dominatedbyagroupofgalaxiesattrueredshiftsof0.5-1.5withzphot3.Lynxhasthefewestcatastrophicfailuresandconsequentlyhasalinearregressiontslopeof1:02:05,with(z)avg<:23for68%ofthegalaxies.Cetus,however,hadthebesttforthemajorityofitsobjects,andconsequently(z)avg<:16for68%ofthegalaxies;theslopeis1:07:13.ForPisces,(z)avg<:29for68%ofthegalaxies,andtheslopeis1:08:14.Thedierencesbetweenthethreeeldsarenoticeablebutnotexcessive.Theymaybeduetovariationsintheeectivenessofthephotometricredshiftcodewithdierenttypesofgalaxies.Forexample,Lynxhasclustersatz=.57andz=1.27,visibleinFigure 2{1 c,andasaresultithasahigherfractionofearly-typegalaxies.TheseconsiderationsarediscussedingreaterdetailinSection 2.4 .Anothersystematicweaknessofthecodeisatendencytounderestimateredshiftsatzspec<1,creatingthetriangularbulgeinthelowerleftcornerofFigure 2{1 a.Theoriginalintentwastousethesamemethodsandcodetoestimatepho-tometricredshiftsforthemainFLAMEXstudy.However,anothercollaborator'scodewaschoseninstead,asdiscussedinSection 3.7.3 .Asaresult,thetestsandvaluesderivedinthissectionarenotdirectlyapplicabletotheFLAMEXresults;theyare,however,indicativeoftheissuesanduncertaintiesassociatedwithpho-tometricredshifttechniquesandareusefulforanyfutureworkdoneusingtheBudavarietal.(2000)procedure. 2.3.4 Two-PointAngularCorrelationFunction:OverviewGalaxiestendtogrouptogetherinspace,andonewaytocharacterizethisdensityamplicationiswiththetwo-pointspatialcorrelationfunction.The

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function,representingthedensityamplicationofgalaxieswithinsomedistancerofareferencegalaxy,canbewrittenas(r)=Bggr,wherethenumberofneighboringgalaxiesinavolumeelementdVisn(r)dV=g[1+(r)]dV.TheBcoecientisknownastheamplitudeofthespatialcorrelationfunction;ifitiszero,thenthedensityofgalaxiesisindistinguishablefromtheaveragespatialdensity,g.Thefunctionisalsocommonlywrittenas(r)=(r=r0),wherethespatialcorrelationlengthr0=B1=.Thepowerlawformof(r)wasoriginallyderivedforrelativelylocalgalaxiesbasedontheLick(Shane&Wirtanen1967)andZwickycatalogs(Zwickyetal.1961-1968),with=1:77.SincewedonothavepreciseredshiftinformationformanyoftheSPICESgalaxies,wecannotcalculatethespatialcorrelationfunctiondirectly.Whatweactuallyobserveisthetwo-pointangularcorrelationfunction,whoseformcanbewrittenasw()=A(1),orw()=A:77.Thetotalnumberofgalaxiesfoundinsolidangledatanangulardistance(indegrees)fromthereferencegalaxyisn()d=Ng[1+A:77]d.Here,w()representsthefractionalincreaseofgalaxiesbeyondtheexpectedvaluesduetotheirtendencytoclustertogether.Asabove,ifthecoecientAiszero,thenthereisnosignicantdensityenhancementaroundthereferencegalaxybeyondtheaveragesurfacedensity,Ng(ingals=deg2).Integratingn()d=Ng[1+A:77]d,wecanwritenring()d=Ng21+A:77d=Ng2+Ng2A:23dwheretheleft-handexpressionstandsforthenumberofgalaxiesobservedinaninnitesimalringofwidthdwhichisdegreesawayfromthereferencegalaxy.(Ng2distheexpectednumberofgalaxiesinthering.)Forthetotalnumber

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ofgalaxiesinsidetheradius0,integratethisequationtogetntot(0)=Z002Ng+2Ng:23Aggd=Ng2+2 1:231:23Aggj00=Ng20+2 1:231:230AggAnimportantaspectofthismethodisthatitapproachestheangularcorre-lationfunctionfromthepointofviewofindividualgalaxies,derivingaseparatevalueforeachgalaxy.ThisapproachwasoriginallyusedbyLongairandSeldner(1979)toinvestigatetheenvironmentsofradioquasars,andthesametechniqueisusedinvarioussuccessorpapersthatstudythesameissues(e.g.,Yee&Green,1984;Woldetal.,2001).However,mostmodernstudiesthatareinterestedintheangularcorrelationfunction(e.g.,LeFevreetal.1996;Hudon&Lilly1996)applyanensembleapproach,designedtoproduceasinglecorrelationamplitude(A)foranentireeldorsurveyofgalaxies,orforaspecicsubsetofgalaxieswithinthesurveysuchasredgalaxies.Thistechniqueisverydierent,requiringthegenerationoflargesetsofrandompointswithintheareaofthesurveyandcomparingthedistancesbetweenallrandom-randompairs,galaxy-randompairs,andgalaxy-galaxypairs.Kerscheretal.(2000)provideanicesummaryofthenumerousvariationsofthistechnique.Forthisproject,itisdesirabletousetheLongairandSeldner(1979)methodtoderiveanangularcorrelationamplitudeforeachofthegalaxiesintheSPICESstudy,ratherthantheensembleapproach,sothatwecancross-referencetheamplitudeswiththeindividualSED-typesassignedtothegalaxies.ItisunclearwhethereitherthemeanormedianoftheindividualcalculationsofAcanbedirectlycomparedtoensemblecalculationsofAfromotherstudies,orwhether

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subtleissuesmaycreatesystematicdierencesbetweenthetwoprocedures'results;thistopicrequiresfurtherinvestigation. 2.3.5 Two-PointAngularCorrelationFunction:SPICESCalculationsTodeterminetheAvalues,Ifoundthebesttforvs.ntot()foreachindividual\reference"galaxy.Iemployedlinearleast-squaresttingusingtheGauss-Jordaneliminationmethodasoutlinedin,e.g.,Pressetal.(1992).Eachthad100datapointsrepresentingconcentric,equally-spacedcirclesaroundthereferencegalaxyandthenumberofgalaxieswithinthosecircles.However,anygalaxywhosephotometricredshiftdieredfromthereferencegalaxy'sredshiftbymorethan0:1zwasdiscardedforthesepurposes,asitwouldprobablynothaveanyclusteringconnectionwiththereferencegalaxy.Consequently,itwasnecessarytocalculateaveragedensityvalues(Ng)separatelyforeachreferencegalaxybasedsolelyongalaxieswithin0:1zofit.Forthispurpose,IderivedthedensitiesfromallfourSPICESeldsratherthanjustthereferencegalaxy'seldtolessenthepossibleeectsofcosmologicalvarianceuponasinglesmalleldofview.Thedensitydeterminationswerebasedontheentiregalaxypopulation,ratherthantryingtoidentifyclustersandisolatea(somewhatarbitrary)non-clusterbackgrounddensity.Correctionsweremadeforareasofthesurveywithpoordata.IcreatedamaskfortheSPICESeldsthatidentiedsurveyregionswithbadpixels,proximitytobrightstars,etc.Excludingtheseareas,thefourimagescombinedhad1,702,480usablepixels(using\equivalentpixels"forPisces,whichhadadierentpixelscalethantheotherelds).TheaveragegalaxydensityNgforalltheobjects,regardlessofredshift,was39;900gals/deg2atK0<20,includingasmallfractionofstars.Foreachreferencegalaxy,onapixel-by-pixelbasis,Iidentiedthefractionofeachsurroundingcirclethatwasgoodqualityandmultipliedthenumberof

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observedgalaxieswithinthecirclebythefraction'sreciprocaltoobtainanestimateofthetruenumberofgalaxies.ThemaximumanglethatIchoseforthetwasaxedangulardistanceof200pixelsinallcases(224pixelsforPisces),correspondingto94"(.76Mpcatz=1).AxedphysicaldistanceisimplementedintheFLAMEXstudy(seeSection 3.7 ),witheachgalaxy'smaximumdeterminedbytheangulardiameterdistanceDAatthegalaxy'sredshift,butthiswasnotdonefortheSPICESsurveyforthesakeofsimplicity. 2.3.6 TranslatingtotheSpatialCorrelationFunctionWithsphericalsymmetryassumptions,itispossibletotranslatethegalaxies'angularcorrelationamplitudes(A)intospatialcorrelationfunctionamplitudes(B),providingestimatesoftheactualphysicalscalesofclustering.Duetothewiderangeofredshiftsinvolved,thevisibilityoffaintgalaxiesvariesandthecorrespondencesbetweenphysicalscalesandangularscalesaredierent.Agalaxyluminosityfunction,modiedappropriatelybyKcorrectionsandevolutionarycorrections,helpstoplaceallgalaxiesonanequalfooting.Kcorrectionsareasubtractionfromagalaxy'sapparentmagnitudetoremovetheeectsofredshift.Thelightthatwereceivefromagalaxyinagivenlterwasactuallyemittedfromabluerandnarrowerregionofthespectrum.Thisdierenceisdeterminedbytheredshiftanddependsstronglyonboththelterandthegalaxytype.Oneadvantageofobservinginthenear-IRisthatthereislittlevariationintheKcorrectionsbetweenearly-typeandlate-typegalaxies.Additionally,thenear-IRKcorrectionsforbothtypesarenegativeformuchoftheredshiftregimeofinterest,sothatthegalaxiesarebrighterthanwouldbeexpectedbasedondistancealoneandarethusmoreeasilydetected.Althoughthelightwasemittedfromanarrowerpartofthespectrum(e.g.,halfaswideasthelterpassband,foraz=1galaxy),theuxfromthatregionofthespectrum

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(c.1100nmforaz=1galaxyseenintheKlter)issucientlygreaterthatitovercomestheformereects.(Incontrast,foropticalpassbandstheKcorrectionsarelargeandpositive.)DetailedSEDsarerequiredtocalculatethecorrections,andtherearetwogeneralapproaches.Well-studiedlocalgalaxiescanbecombinedintoSEDtemplates,suchasthoseofColemanetal.(1980),andthesetemplates(combinedwithmodelswhereobservationsareinadequate)canbeusedtoadaptthemagnitudethatwasactuallyobservedtothemagnitudethat\shouldhavebeen"observed.ThisapproachwasusedbyMannuccietal.(2001),forexample.Alternatively,SEDscanbeproducedentirelyfromstellarpopulationsynthesismodelssuchasthosecreatedbyBruzualandCharlot(2003),Devriendtetal.(1999),LeBorgneetal.(2004),andPoggianti(1997).FurtherinformationandusefuloverviewsaboutKcorrectionscanbefoundinPoggianti(1997)andHoggetal.(2002).EvolutionarycorrectionsaresimilartoKcorrections.Theyareanattempttoosettheevolutionaryeectsonagalaxy'sspectrum,whichchangesovertimebecausegalaxiesathighredshiftwereyounger,andoftenbluerandbrighter.Theyrequireevolutionarystellarpopulationsynthesismodels,likethosementionedabove.Themodelsdescribethechangeofagalaxy'sSEDwiththepassageoftimesincethegalaxy'sformation.Thisismeasuredinyears,notredshift;atranslationbetweenthetwoisrequired.Thus,evolutionarycorrections(unlikeKcorrections)dependonthechoiceofcosmologicalparameters.IderivedKcorrectionsandevolutionarycorrectionsfromBruzualandCharlot'sGISSEL96code(Bruzual&Charlot,1993)tostandardizethehigh-zgalaxieswiththoseinthelocaluniverse.Forsimplicity,Imodelledthegalaxieswithasingleburstofstarformationatz=5:4lasting0.1Gyrs,evolvingpassivelythereafter.IusedtheScalo(1986)initialmassfunction(IMF)forstars,amore-renedalternativetothebetter-knownSalpeter(1955)IMF.Thecosmological

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Figure2{3: parameterswereH0=72,q0=0:3,M=0:6,K=0:4,and=0:0.Notethatthesevaluesarederivedfromanoutdatedcosmology,andthemainFLAMEXstudyusedmorecurrentparametersbasedonthe1st-yearWilkinsonMicrowaveAnisotropyProbe(WMAP)ndingsfromSpergeletal.(2003).TheoutputofGISSEL96isaseriesofmodelledspectraatvariousageincrements;IwroteaprogramtoconvolvetheseSEDswiththeIRIMK0ltertransmissionfunctionandconvertthemintoevolutionaryandKcorrections.TheresultsareshowninFigures 2{3 and 2{4 alongwithcomparisonvaluesfromMannuccietal.(2001)andPoggianti(1997),aswellascorrectionsbasedonvariantsoftheinputparametersusedforGISSEL96toassesstheimportanceoftheiruncertainties.IemployedKochaneketal.'s(2001)K-bandSchechterluminosityfunctiontocorrectforgalaxiestoofainttoseeathighredshift.Thefunctionisofthe

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Figure2{4: 2{3 ,theplottedval-uesforPoggiantiareasimpleaverageateachredshiftofthevaluesforthevariousSEDtypeslistedinthatreference. form(L)dL=(L=L)eL=Ld(L=L)andtheparametersare=1:09,MK=23:39+5:0logh(forH0=100hkm/s/Mpc),and=0:0116h3Mpc3.Foreachoftheseparameters,lowervaluescorrespondtoasmallergalaxydensityperMpc3.TheuncertaintieslistedinKochaneketal.forMKhavethelargesteect,followedbyandthen.FollowingtheprocedureoutlinedinLongairandSeldner(1979),theangularcorrelationamplitude(A)foreachgalaxyistranslatedtoitscorrespondingspatialcorrelationamplitude(B)accordingtoA=2 ()1

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cosmology).TheresultingBvaluesserveasmeasurementsofthelocalgalaxydensity,withhighvaluesrepresentingstronglyclusteredregionsandlow(insomecasesnegative)valuesrepresentingunderdenseregions.Thesevaluesarematchedwiththegalaxies'SED-types,(whicharediscussedinSection 2.4 ),andtheresultsarepresentedinSection 2.5 2.4 GalaxySEDMeasurements 2.4.1 OverviewofPhotometricTechniqueMostoftheSPICESgalaxiesaretoofaintandpoorlyresolvedtomakevisualmorphologyestimates.Early-typeandlate-typegalaxiestypicallyhaveverydierentSEDs,sothatspectroscopycanhelptodistinguishbetweenthem.Ininstanceswherespectroscopyisnotavailable,however,itispossibletousemultiwavelengthphotometrytoestimatetheSED-types.Thistechniqueofusingthecolorstoidentifyandtrackmajorspectralfeaturesisverysimilartothatofphotometricredshifts,andmostprocedurescalculatebothredshiftandSED-typesimultaneously.ThealgorithmusedforSPICESisderivedfromBudavarietal.(2000)andisdiscussedinmoredetailinSection 2.3.3 .Thecode,writtenbyAndrewConnolly,assignsoneofveclassicationstoeachgalaxy:E,Sbc,Scd,Im,andstarburst.WecomparedConnolly'scolor-basedSED-typeswithtruemorphologiestogainsomeinsightintothesimilaritiesanddierencesbetweenthedensity-SEDrelationandthedensity-morphologyrelation.Section 2.4.2 describesasetofHSTvisualmorphologiesthatwewereabletoobtainforasampleoftheSPICESsources,anditprovidesdetailsontheobjects'classicationwithaparticulareyetowardself-consistencychecks.Section 2.4.3 thencomparesthevisualidenticationswiththeSEDestimatesmadebyConnolly'scode.

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Figure2{5: SampleofHSTimagesofSPICESgalaxies. 2.4.2 VisualMorphologies:DescriptionandConsistencyChecksTheSPICESgroupobtainedHSTfollowupimageryinordertodeterminegalaxymorphologiesvisually,withtheobjectiveofcomparingtheseresultstotheSED-typesofConnolly'seigenspectralmatchingcode.KatherineWu,AdamStanford,andIindependentlyclassied1001objectsasP:peculiar/merger,L:late-type,E:early-type,T:toosmalltodetermine,F:toofaint,orS:star.Wecreatedapostagestampforeachobjectandanalyzedit,adjustingtheintensityscalingandrangeasneededandemployingradialprolesaswellasvisualassessments.Wealsousedamosaicofnearby,classiedgalaxiesfromtheNearbyGalaxyCatalog(Freietal.,1996)asareference,projectingtheirappearancetoz=0:75:Figure 2{5 showsasampleoftheSPICESstamps.DuetooverlappingHSTelds,125oftheSPICESobjectswereimagedtwice,andsevenofthemwereimagedthreetimes.Sincethese\clones"receivedindependentvisualmorphologicalclassications,thisprovidesinformationabouttheself-consistencyofeachinvestigator'sestimates.Table 2{4 presentstheresults.

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Table2{4: Comparisonof\Double"MorphologyEstimates P31L31128E52127T4191340F791611S1165030 2{6 ).6%ofthetotalobjectswereagreedtobestarsbyallthreeinvestigators(2:5fordoubly/triplyestimatedobjects).Fortheotherclassications,thevaluesare:F4%,T5%,E5%,L25%,P8%.Thus,53%oftheobjectshadfullagreement.(92%had2/3agreement.)43%hadadeniteidentication(S/E/L/P),andofthese,14%werestars,12%wereearly-typegalaxies,57%werelate-typegalaxies,and18%werepeculiar

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Figure2{6: Visualmorphologyestimates.Thisgure(basedononecreatedbyKatherineWu)presentsthepercentageofobjectsassignedtoeachvisualmor-phologyclassbyeachinvestigator.Itishelpfulinassessingtheconsistencyandreliabilityoftheclassications,andalsoforidentifyingthestrongestuncertainties.

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galaxies.Thesenumberscanbetakenasroughestimatesforthepercentagesofeachclassinthesurvey'seld.However,thereareintrinsicuncertainties,apparentintheprecedingtwoparagraphs,andtherearealsosystematicuncertainties,asTandFdesignationsprobablyrepresentsomewhatdierentdistributionsofS/E/L/Pfromtheprecedingpercentages.Theseuncertaintiesareestimatedat3%baseduponmyidenticationnotes.ThereisafurtherselectioneectintheLynxeld,wheretheHSTeldswerechosentocoverregionswithdetectedclusters(abouthalfthetotalarea),sothatthedistributionofgalaxytypesisnot\random"inthateld.Theaverageredshiftofthefull-agreementE/L/Pobjectsisz=0:71,andthemedianisz=0:62(basedonspectroscopicredshiftswhereavailable,andphotometricredshiftsotherwise).Wealsocomparedouraveragedresultswithmorphologicalestimatesdeter-minedbyGIM2D,anIRAFpackagefordoing2-Dbulgeanddiskconvolutionforgalaxies.Wechoseoutputparameterstocorrespondtoeachofoursixcategories(S,F,T,E,L,andP).Figure 2{7 showstheresults.Thereisnoeasywaytosep-arateoutstarswithGIM2D,andmanyofitsT(tiny)identicationsshouldbeS(star).TheothermajordiscrepancyisthatGIM2Didentiedmanyfewergalaxiesasearly-type(89E)andmanymoreaslate-type(571L,142P)thanwedid(214E,402L,80P).Weplacedourdividinglinebetweenearlyandlategalaxiesatabulge/totalfractionof70%,whichiscorrectforthelocalUniverse.However,alowerfraction,possiblyassmallas40%,maybemoreappropriateforhigh-redshiftobservations.TheSPICESspectroscopicobservationsprovidedanadditionalcheckofouraccuracybytestingourabilitytovisuallyidentifystars.52sourcesintheHSTregionswerespectroscopicallyconrmedtobestars.Ofthese,37werevisuallyclassiedasstarswithfull,3/3agreement,and12wereclassiedasstarswith2/3agreement.Twowereconsideredtoosmalltoclassifyandonehadno

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Figure2{7: ComparisonofGIM2Dandvisualmorphologyestimates.Thisgure(createdbyKatherineWu)presentsacomparisonoftheGIM2Dclassicationsandthosemadebyeye.Eachvisualmorphologyclasswasassignedanumericalvaluebasedonaninitialestimateoftheir\discernability";S=-5,F=-2,T=-1,E=1,L=2,andP=3.Eachobjecthadthreevalues(onegivenbyeachinvestigator);thesewereaveragedforthepurposesofthisplot.Thenumbersintheguredisplaythequantityofobjectsineachbin.

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consensusvalue.Individualmisjudgments(E,L,orP)wererare,buttherewereveinstancesofEidenticationsandoneeachofLandP.Conversely,ofthe410spectroscopically-identiedgalaxies,threewereunanimouslyvisuallyclassiedasstars,andone(aquasar)wasclassiedasastarwith2/3agreement.Tengalaxiesreceiveda1/3starvote.Asanalternateperspective,95%(37of39)ofthespectroscopicobjectsvisuallyclassiedasstarsbyallthreeinvestigatorswereveriedtobestars,while92%(12of13)oftheobjectsclassiedasstarswith2/3agreementwereveriedtobestars.Theremainingthreeprovedtobegalaxies,oneofthemaquasar.Theseresultsindicateahighdegreeofprecisioninthevisualstar-galaxyseparation,withfewfalsepositivesornegatives. 2.4.3 ComparisonsofConnolly'sResultstoVisualMorphologiesHavingcompletedtheseassessments,theprimaryareaofinterestisacompar-isonofourvisualmorphologieswiththeresultsprovidedbyConnolly'seigenspec-tralcode(discussedinSections 2.3.3 and 2.4.1 ).Theprogramyieldsvaluesonascaleof0to4thatcorrespondtotemplatesasfollows:E(0),Sbc(1),Scd(2),Im(3),starburst(4).Figure 2{8 comparestheseresultswiththosefromourE/L/Pclassication.Forgalaxieswithfullagreementofvisualmorphologies,theaveragevaluesfromConnolly'scodewere.21forEgalaxies,1.07forLgalaxies,and1.81forPgalaxies.Forgalaxieswith2/3agreement,theaveragevalueswere.39forEgalaxies,1.13forLgalaxies,1.19forL/Pgalaxies,and1.66forPgalaxies.(TheL/Pcategoryisforgalaxieswheretheinvestigatorscouldnotagree,assigningoneLrating,onePrating,andone\other.")Inthe2/3agreementcase,theex-tremestendmoretowardthemiddle,sinceweareincludinggalaxieswithgreateruncertainty,butthedivisionsbetweenE,L,andParestillquiteclear.Anotherdesiredpieceofinformationistheextenttowhichredshiftaectsthecode'sresults.TheobjectswithHSTvisualmorphologiescoveraredshiftrangeouttoaboutz=1.5.(SeeFigure 2{9 .)Wesplittheobjectsintotwobins,z0:7

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Figure2{8: ComparisonofestimatedSED-typeswithvisualmorphologies.Thesegurestrackthefractionsof,e.g.,Egalaxies(HSTvisualidentications)thatwereassignedvariousgalaxytypesbyConnolly'sphoto-zcode.(Thetotalofeachcurve'svaluesis1.0.)Theprogramyieldsvaluesonascaleof0to4thatcorre-spondtotemplatesasfollows:E(0),Sbc(1),Scd(2),andIm(3).Anothertem-plate,star-forming(4),hadnomatchesinthissurvey.A)includesonlygalaxieswithafull,3/3agreementinthevisualidentications,whileB)includesallgalax-ieswith2/3orbetteragreement.Inbothcases,Evisualdesignationsstronglycorrelatedto`0'ratingsfromthephoto-zcode;veryfewEgalaxieswereassignedvaluesof1,2,or3.GalaxieswithLvisualdesignationspeakat`1',andgalaxieswithPdesignationspeakat`2'.C)andD)splitthegalaxypopulationintolowandhighredshiftbins(respectively)toseehowthecorrelationbetweenthevisualidenticationsandthephoto-zcoderatingschangeswithredshift.

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Figure2{9: Redshiftdistributionofobjectswithvisualmorphologies.Thishis-togramshowsthenumberofobjectswithvisualmorphologiesateachredshift,includingallnon-starobjects(T,F,E,L,&P),thosethathad2/3orbetterclassi-cationagreement,andthosewhichhad3/3classicationagreement. andz>0:7,anddeterminedthe2/3agreementresultsforeach,includedinFigure 2{8 .Forthelow-redshiftbin,theaveragevalueswere.33forEgalaxies,.94forLgalaxies,1.00forL/Pgalaxies,and1.51forPgalaxies.Forthehigh-redshiftbin,theaveragevalueswere.50forEgalaxies,1.35forLgalaxies,1.23forL/Pgalaxies,and1.72forPgalaxies.Thevaluesareshiftedhigherforhigherredshiftgalaxies,butthedistinctionsremainclear.(Thisisaninterestingphenomenom,worthyoffutureinvestigation.)Thereisalsoashiftinrawnumbers;thereareonlyhalfasmanyearly-typegalaxiesatz>0:7asatz0:7,whilethequantityoflate-typegalaxiesdecreasesonlyslightlyandthatofpeculiargalaxiesincreasesbyoverafactoroftwo.

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Figure2{10: PreliminaryresultsforLynx. HighSED-typevaluescorrespondedwelltolate-typegalaxies,butlowvaluesweredegenerateregardlessofredshift.ThisisduetodiskyredgalaxiessuchasS0sandspiralswithquenchedstar-formation.FortheFLAMEXanalysis(Chapter 3 ),itisthereforeimportanttokeepinmindthatwearelookingattherelationbetweendensityandstellarpopulationratherthandensityandmorphology. 2.5 ResultsIcalculatedtheamplitudeofthespatialcorrelation(B)foreverygalaxyintheSPICEScatalogthatmettherequirementsstatedinSection 2.2 andcomparedthemwiththeSED-typeresultsfromConnolly'scodetoexaminethedensity-SEDrelation.TheinitialresultsfromaLynx-onlystudyof205galaxies,displayedinFigure 2{10 andTable 2{5 ,werequitepromising.AlargerBcoecientcorrespondstoagreaterestimatedspatialdensityofgalaxiesinthevicinity;galaxiesinveryunder-denseregionsarelikelytoreceive

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Table2{5: PreliminaryResultsforLynx GalaxyType(z=0.0-0.8) GalaxyType(z>0.8) Elliptical Spiral/Irr. %Ell. Elliptical Spiral/Irr. %Ell. 0.5-0.7 15 1 94% 0 0 0.4-0.5 24 6 80% 6 2 75% 0.3-0.4 11 8 59% 4 3 57% 0.2-0.3 9 9 50% 6 6 50% 0.1-0.2 14 14 50% 18 22 45% Positive 0.0-0.1 29 27 52% 43 37 54% Negative 0.1-0.0 21 22 49% 14 21 40% 0.2-0.1 4 6 40% 2 3 40% 2{11 .ThecurrentversionofConnolly'sprogramoutputsadiscretevalueforeachgalaxyonascaleof0to4,correspondingtothefollowingSED-types:E(0),Sbc(1),Scd(2),Im(3),andstarburst(4).OnlyeightgalaxieswereassignedastarburstSED-type,andtheyareomittedfromtheresultshere.Theeectsofthedensity-SEDrelationcontinuetobevisibleatlowandhighredshifts,althoughthepointmustbestressedthattheSED-typesmaynotcorrespondwellwiththegalaxies'truemorphologiesathighredshifts(thisissue

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Figure2{11: FinalSPICESresults(usingConnollySED-types)atA)lowredshiftandB)highredshift.Thenumberlabelsindicatethequantityofgalaxiesrepre-sentedbyeachSED-type.Itisworthnotingthat,duetoadierentcalibrationprocedureinmycalculations,theBvaluesshouldnotbedirectlycomparedtothepreliminaryresultsforLynxinTable 2{5

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isaddressedinFigure 2{12 ).However,theSED-typesarestillprovidinguswithimportantphysicalinformationaboutthegalaxies,andthevalueswilllikelyhavesomeconnectiontothemorphologiesofthegalaxies'present-daycounterparts.Changesinthecorrelationfunctionamplitudefromlowtohighredshiftmanifestaslowerabsolutevalues,whichsuggestsagenerallymorehomogeneously-distributedpopulationofgalaxiesathighredshiftandisconsistentwiththehierarchical-clusteringscenario.However,thesamplesizeistoosmalltofurtherrenetheredshiftbinsandinvestigatethedetailsofthechangeswithtime.TheFLAMEXsurvey,discussedinChapter 3 ,hasthiscapability.Therewasconsiderablevariationbetweentheindividualelds.Thiswasdueinparttomyuseofallfoureldstodeterminetheaveragesurfacegalaxydensityatvariousredshiftsforthecorrelationamplitudecalculations,asopposedtolettingeacheldserveasitsownreferenceforsurfacedensity.Galaxiesinthedensely-populatedelds(particularlyLynx,withtwosignicantclusters)werelikelytohavehigherBsthangalaxiesinsparsereldssuchasSA57.AnaltopictoconsideristheconnectionbetweentheBvaluesandthedirectmorphologicalinformationthatwehavefromtheHSTobservations,ratherthantheindirectcolor-estimatedSED-types.AlthoughHSTobservationsacrossabroadregionarefarhardertocomebythanmultiwavelengthground-basedobservations,andthusinappropriateforlargesurveys,theSPICESsamplecanprovidedirectdataonchangesinthedensity-morphologyrelation.TheseresultsarepresentedinFigure 2{12 .Itisinterestingtonotethatthedensity-SEDrelationofthissampleismoreapparentathighredshiftsthanthedensity-morphologyrelation.Thisislikelyduetotheinherentdicultyinmorphologicallyclassifyingsmall,distantgalaxies,anditisastrongargumentforusingtheSED-densityrelationathighredshiftsasanalternativeorextensiontothelow-redshiftdensity-morphologyrelation.

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Figure2{12: FinalSPICESresults(usingvisualmorphologies)atA)lowredshiftandB)highredshift.ThelabelingconventionisthesameasthatusedinSec-tion 2.4.2 ,whereErepresentsearly-typegalaxies(EorS0),Lrepresentslate-typegalaxies,andPrepresentspeculiarormerginggalaxies.ThenumberlabelsindicatethequantityofgalaxiesrepresentedbyeachSED-type.

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3.1 IntroductionThelimitationoftheSPICESstudyisitssmallskycoverage;thenextlogicalstepistoextendthesamestudytoalargersurvey,wherestatisticspermitnerbinningbyredshiftandSED-type,andtheresultsaremorerobust.Thishasbeenmymainprojectandwillbediscussedhere.Numerousinvestigationshavestudiedtheeectsofenvironmentongalaxies'colors/SED-types.ExamplesincludespectroscopicsurveysinthelocalUniverse(e.g.,Madgwicketal.2003)andpencil-beamspectroscopicsurveysathigherredshifts(e.g.,Lovedayetal.1995;Meneuxetal.2006).Photometricstudieshavecalculatedspatialcorrelationfunctionsbyassumingaredshiftdistributionfromaspectroscopicsubsampleoraseparatesurvey(e.g.,Roche&Eales1999;Wilson2003;Coiletal.2004),oralternativelybyestablishingtheredshiftdistributionusingphotometricredshifts(e.g.,Firthetal.2002;Budavarietal.2003;Brownetal.2003;Phlepsetal.2005).Unfortunately,directcomparisonsbetweensurveysarecomplicatedbythevarietyofselectiontechniques;inparticular,resultsareoftenaectedbythestrongdependenceofr0onluminosity(Norbergetal.2002).IbasedmyprimaryworkondatafromtheFLAMINGOSExtragalacticSurvey(FLAMEX;Elstonetal.2006).FLAMEXwasanNOAOSurveyProgram(2001-2004)conductedattheKPNO2.1mtelescope.IthasanexceptionalcombinationofdepthandbreadththatpermitsanalysisoftheSED-densityrelation'sevolution(impossiblewiththelocalUniversesurveys)whileminimizingtheeectsofcosmicvariance(towhichSPICESandtheotherpencil-beamsurveysarevulnerable). 44

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Thischapterisorganizedaccordingtothefollowingdesign.Section 3.2 de-scribestheFLAMINGOSinstrumentusedforthesurvey.Section 3.3 describesthebasiccharacteristicsofFLAMEX,whileSections 3.4 and 3.5 providedetailsofthedataacquisitionandreductionprocess,respectively.Section 3.6 brieydiscussesthechoiceofcatalogforthisproject.Section 3.7 containsmyprocedureforcalcu-latingspatialcorrelations,includingamathematicaloverview,thenalcullingofthecatalogforusablegalaxies,andthedetailsofmyalgorithm'simplementation.Theresultsforthemaindensity-SEDevolutionstudyarepresentedinSection 3.8 ,alongwithinvestigationsintothebehaviorofextremelyredobjects(EROs)andclusters.InSection 3.9 ,Isummarizetheresultsandpresentconclusions,andIdiscusspossibilitiesforfutureworkinSection 3.10 3.2 TheFLAMINGOSInstrumentTheFLAMEXsurveyisnamedaftertheFloridaMulti-objectImagingNear-InfraredGrismObservationalSpectrometer(FLAMINGOS),anastronomicalinstrumentthatDr.RichardElstonbuiltattheUniversityofFlorida.FLAMIN-GOScanbeutilizedforbothphotometryandmulti-objectspectroscopy,thoughwereliedentirelyontheformerforoursurvey.Itsfastall-refractiveopticalsystemand20482048HgCdTeHAWAII-2CCDarraymakeFLAMINGOSahighlyeectiveimagerforstudiesrequiringawideeldofview(210x210ontheKPNO2.1mtelescope,with0.61"pixels).Therewereseveralchangestotheinstrumentthattookplacewhilethesurveywasinprogress.Animportantonewasthearrayitself;weusedanengineering-gradearraythroughFall2002,atwhichpointthescience-gradearraywasinstalled.Theengineering-gradearraywasperfectlyserviceableinmostrespects,butwasnotfullyfunctionalalongtheedges,andthisresultedinstripsmissingfromoursurveycoveragetakenwiththisarray.Asforthescience-gradearray,itevincedaberrationincertainregions,particularlytowardtheedges,andthe50%completenesslimits

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forindividualeldsoftenvariedbyuptohalfamagnitudeacrossthearea.TheJandKSlterswerechangedinJuly2003whenanewltersetwasboughtfortheinstrumenttoreplacethesetborrowedfromNOAOandGemini.Thishadnomajoreect,althoughthetransmissioncurvesofthetwosetsareslightlydierent.ThecurvesandotherinformationareavailableontheFLAMINGOSwebsiteathttp://amingos.astro.u.edu/. 3.3 SurveyandProgramDesignFortheFLAMEXsurvey,weobservedtwosubregionsoftheNOAODeepWide-FieldSurvey(NDWFS;Jannuzi&Dey1999;Deyetal.2006,inpreparation)intheBootesandCetusconstellations.TheNDWFSeldswerechosenduetothedeepopticalimagingthatwasinprogressintheseeldswhenthesurveybegan,withtheBWRIdatabeingessentialforderivingaccuratephotometricredshifts.TheNDWFSsurveyareaisalsothetargetofoneofthemostextensivepanchro-maticinvestigationsinallastronomy,withspace-andground-basedimagingandspectroscopicprogramsspanningradiotoX-raywavelengths(Rhoadsetal.2000;deVriesetal.2002;Hoopesetal.2003;Lonsdaleetal.2003;Eisenhardtetal.2004;Kochaneketal.2004;Pierreetal.2004;Houcketal.2005;Murrayetal.2005).Thenorthern(Bootes)eldinfactisoneofonlytwowide-areasurveyregionspresentlymappedbyChandra,GALEX,andSpitzer(withIRACandMIPS).TheAGNandGalaxyEvolutionSurvey(AGES;Kochaneketal.2006,inpreparation)alsoprovides17,000spectroscopicredshiftsatz<0:8acrosstheNDWFSarea.TheFLAMEXregionscoveratotalof7.1deg2.Each210x210eldwasimagedfortwohours(seeing<1:7")ineachoftheJandKSbands,allowingustoreachJ=22andKS=19.3.Thesurveyregionisroughlyafactoroftenlargerthananyexistingnear-infrared(near-IR)studiestocomparabledepth.WecombinedtheFLAMEXdatawiththeBW;R;andIbandNDWFSopticalimagingaswellas

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theInfraredArrayCameraShallowSurvey(IRACSS;Eisenhardtetal.2004)mid-infrared(mid-IR)SpitzerimagingtoderivephotometricredshiftsandSED-typeestimates(Brodwinetal.2006).Theseresultsarequiterobustduetothequantityofmultiwavelengthphotometricinformation.Therearestilllargeuncertaintiesforindividualgalaxies,butourstatisticalunderstandingofthez<1:5universehasbeengreatlyenhanced.Thecombinedsurveyisamajorassettotheastronomicalcommunityandwillhelptoresolveavarietyofissues;theevolutionofthedensity-SEDrelationismerelyoneofthese.Already,ithasbeenusedtodetectgalaxyclusterstoz1:5(Stanfordetal.2005),identifyz>5quasars(Cooletal.2006;McGreeretal.2006;Sternetal.2006,inpreparation),detectaeldbrowndwarf(Sternetal.2006,inpreparation),andconrmtherst350m-selectedgalaxy(Khanetal.2005).Thesurveyalsoprovidesthelargestexistingsampleofextremelyredobjects(EROs),asdiscussedinElstonetal.(2006). 3.4 DataAcquisitionFLAMEXobservationswereociallytakenover97nightsspreadacrossvariousseasons,althoughwecoordinatedwiththeNOAOSurveyProgram\TowardaCompleteNear-InfraredSpectroscopicandImagingSurveyofGiantMolecularClouds"(PI:Lada)inordertomaximizetheeciencyofbothprogramsaccordingtothetimeofnightthattheirrespectivetargetareaswereobservable.Only50%ofthetimeprovedtobeuseful,asweatherconditionsweremediocreoverall,withtelescopemechanicalfailuresandinstrumentsoftwareproblemsplayingsecondaryroles.Thispreventedusfromcompletingthefullplanned10deg2survey,butweobtained4:7deg2ofcoverageinBootesand2:4deg2inCetus.Wedidnotrequirephotometricconditions,butweattemptedtoimposeaseeinglimitofFWHM<1:5"usingconstantreal-timeassessments.Thislimitprovedtobediculttomaintainduetotelescopeconditionsandtheintrinsic

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aberrationofthedetectorarray.Itinitiallyledtosubstantialextensionstotheobservingtimeforaeld,inanattempttoobtainafulltwohoursthatobeyedthelimit.Thisrestrictionwaslaterrelaxed,althoughitremainedcommontotakeanextra10-20%oftotalexposuretimewhentheseeingconditionsweremediocre.Weobservedtheeldsdowntoanairmassof2.0,althoughtheseeingwouldoftendeterioratesignicantlybeforereachingthatpoint.Atthebeginningorendofeachnight,wetook10-15lamp-onandlamp-oateldimagesforKSandsometimesforJ;forsomeobservingseasons,wesimplyusedskyatsforJ.Wealsotook10-20darkframesforeveryexposuretime.Formostofthesurvey,wedidnottakeimagesofstandardstars,preferringtorelyonthe2-MicronAll-SkySurvey(2MASS;Skrutskieetal.2006)catalogforphotometriccalibration.(Ourlargeeldofviewfacilitatedthis.)WhenobservingasurveyeldintheKSband,wetypicallytook120-200individualexposurestoachievetwohoursoftotalexposuretime.Near-IRback-groundemissionishighandthedetectorsaturatesunlessexposuretimesarekeptshort.Theoutsidetemperaturehadthestrongesteectonthis.Itvariedacrossourvariousobservingrunsfrom-5to20C,andtheKSexposuretimesvariedaccordinglyfrom60secondstoaslittleas30seconds.Weattemptedtokeepthebackgroundcountsbelow30,000.Non-linearitycorrectionsweregenerallyeectivetobetterthan1%upto45,000counts,soourfaintgalaxieswereinnodangerofsaturation,butouruseof2MASSstarsforcalibrationrequiredthatwesetalowerlimit.Jbandobservationswerelesshamperedbyhighbackgroundcountsandgenerallyrequired85-100images(of90secondseach)pereld.TheseKSandJimagesweretakeninsets(e.g.,of25exposuresina55pointinggrid),withthetelescopeditheredslightlyforeachexposureinordertominimizetheeectsofdetectorirregularities.Ampliercross-talkandother\badreads"tooktheirtollon

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theusefuldata,typicallyaccountingfor5-25%oftheframestaken,dependingonthestateofhealthoftheinstrumentduringagivenobservingrun.Theimagesforagiveneldwereoftentakenondierentnightsorevenindierentyears,possiblywithdierentexposuretimes.Theprocessfortakingallofthisdisparaterawdataandreducingitintoasinglenishedimageforaeldwasnecessarilylengthyandintricate,andmanypeoplecontributedtothetimeandeortrequiredtocompletethisworkfortheentiresurvey.Anoverviewofthemethodbywhich1.5terabytesofrawdataweretransformedintonalresultsseemsappropriateanduseful,andfollowshereafter. 3.5 DataProcessing 3.5.1 InitialProcessingAfterthedataacquisition,weprocessedtheimagesattheUniversityofFlorida.Foreachnightofdata,weidentied\imagestacks,"eachcontainingalltheimages(a.k.a.frames)foragiveneldwithidenticalexposuretimes;wealsomadestacksoftheat-eldimages.Foreachimagestack,weundertookthefollowingsteps.First,weremovedanyindividualimageswithproblems,usuallystemmingfromdetectormalfunctions.(Thisrangedfrom5%to20%oftheframesaccordingtothedetector'sstateofhealth,whichvariedduringtheobservingruns.)Theremainingimageswerelinearized;thatis,wecorrectedthemforthedetector'sgraduallossofabilitytoregisteradditionalphotonsathighcountlevels. 3.5.2 DarksandFlatsNext,wecombinedthedarkimages(generally10-20)fortheimagestack'sex-posuretimeintoasingleFITSle.Wealsocombinedthedarkimagescorrespond-ingtotheat-eldexposuretimesintoasingleFITSle(#1)andsubtracteditfromeachoftheat-eldimages,combiningtheresultingsetofdark-subtractedat-eldimagesintoasingleFITSle.Thisyieldedasinglelerepresentingthedarkimagesandasinglelerepresentingtheatelds.Wedividedtheformerinto

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quadrantsandmadehistogramsofthepixelvaluesforeachquadrant.Basedonthehistograms,wechosepixelvaluerangesthatcorrespondedto\good"pixels.Thiswasasomewhatsubjectiveprocess,andtheformsofthehistogramschangedslowlyduringanobservingrunandsignicantlyfromoneruntothenext,buttheynormallyhadaclearlyidentiablepeak.Atypicalgoodpixelrangewas250-750counts.Wethenrepeatedtheprocedureforthecombinedat-eldimage.Inthiscase,thehistogramvalueswereexpressedasafraction.Avalueof1.0meantthatnoat-eldcorrectionwasneededforthatpixel.Typicalrangesofvaluesthatweconsideredacceptablewere.65-1.35.Thesehistogramtrimmingsprovidedinformationonwhichpixelswere\bad";pixelsnearthedetector'sedgesoralongtheboundariesofthedetector'ssubdivisionscommonlyhadproblems,andcertainindividualpixelsorpixelclustersdistributedsemi-randomlyonthedetectorcon-sistentlyreturnedgarbagevalues.Basedontheseresults,wecreatedabad-pixelmask,animagewhosevalueswereonly`1'or`0'basedonwhetherornotthepixelswereusable. 3.5.3 SkySubtractionForthenextstage,wesubtractedthecombineddarkimagecorrespondingtotheat-eldexposuretime(#1above)fromeachofthedataimagesandthenconductedan\initialpass."Eachresultingframehada\localskyframe"subtractedfromit,madebycombiningeightotherimageframes(withtheirosetsremoved).Theframesproducedbythisprocedurethenreceivedaat-elddivision.Next,weusedtheIRAF\daophot"task,whichfoundallobjects/pixelsthatweretoobrightandthencalculatedtheosetsofeachframerelativetotherst.Our\secondpass"consistedofcreating\object-freelocalskyframes,"forwhichwemaskedouttheobjectsandpixelsfromthepreviousstep.Wesubtractedtheseframesfromtheircorrespondingdataimagesandthenperformedaat-elddivisionontheresults.Thisgeneratedcorrectedversionsoftheindividualimages

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intheimagestack,andwecombinedthembasedontheirosetsintoasingleimagerepresentingthesummationoftheirexposuretimes. 3.5.4 AlignmentandStackingThenalstagehandledthenalalignmentandstackingoftheimages.Itresampledthepre-combineddatatohalf-sizepixelsandcentroid-correctedtheditherstoadjustforgeometricdistortionduetoimperfectionsintheFLAMINGOSopticalsystem.Forthisprocess,weusedtransformationmapsgeneratedfortheKPNO2.1mtelescopeineachyearofthesurvey,asanyadjustmentstotheinstrument(disturbingthepositionofthedetectorarrayorinstallingnewlters)couldalterthedistortion.Thecorrectionsenabledustoproperlyalignimagestakenindierentyearsandalsotodesignmasksinthefutureformulti-objectspectroscopy.Finally,weusedanintegershift-and-addapproachtorecombinetheseoversampledframesintoanal,quadruple-size(4096x4096pixels),trimmedimagewhichwasreadyforanalysis. 3.5.5 CombiningDatafromMultipleNightsAfterweperformedthisprocedureforalloftheimagestacksfromalloftheobservingnights,westillhadnalimagesofthesameeldfromdierentnightswhichhadtobecombined.Weweightedthemaccordingtotheseeing,zeropoint,andrmsnoiseaccordingtotheformulaw=100:4m0 3.5.6 AstrometryandPhotometryWemadeastrometriccalibrationswiththeassistanceofthePinkpackIRAFsoftwarepackagewrittenbycollaboratorJoannaLevine.Pinkpackidentied

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matchesbetweenthestarsinaeldandthe2MASSAllSkyDataReleasecatalog(Cutrietal.2003),usingtheseinaniterativeprocesstoderiveaplatesolutionforeacheldtoaccountfortheprojectioneectsofthethree-dimensionalskyuponthetwo-dimensionalCCDarray.First,thesoftwarecreatedanobjectcatalogfromtheimageandaposition-selectedstarcatalogfromtheonline2MASSinformation.Itthenmatchedthesetwocatalogsandcalculatedasecond-orderpolynomialtfortheplatesolution.Usingtheplatesolution,thesoftwareadjustedthecoordinatesandrematchedthetwocatalogs.Baseduponthis,analplatesolutionwasdeterminedusingafourth-orderpolynomialt,thecatalogswerematchedathirdtimetoassessthequalityofthet,andtheskycoordinatesfortheFLAMEXimageobjectswereoutput.Toperformthephotometry,weemployedtheSourceExtractorsoftwarepackage(SExtractor,Bertin&Arnouts1996).WeworkedindualimagemodefortheJandKSbands,constructingKS-selectedcatalogswitha0.76"FWHMgaussianconvolutionkernelanda5objectdetectionthreshold.Pinkpackcomputedthenalphotometriccalibrationusingtheaveragephotometricosetforcolor-selected2MASSstarsineacheld,weightedbythephotometricerrors,toestablishzeropoints.2MASSwasusedforourastrometricandphotometriccalibrationsinplaceoftheU.S.NavalObservatoryall-skycatalog(USNOB1.0)since,beinganinfraredsurvey,2MASStendedtogeneratemorematchingstars. 3.6 TheCatalogIchosetoworksolelyontheFLAMEXBootesregion,excludingtheCetusregion,becausetheNDWFSopticaldatahasnotyetbeenreleasedforCetus,andourcollaboratorMarkBrodwinhasderivedrobustphotometricredshiftsforBootesusingthecombinedNDWFS,FLAMEX,andIRACSSdata(Brodwinetal.2006).MyinitialintentwastobasemystudyontheFLAMEXKS-selected

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catalogs.However,thequalityoftheFLAMINGOSdetectorvariedwidelyacrossthearray,withsignicantcomaticaberrationneartheedges.Thisresultedindepthlimitsofoveramagnitudeworsecomparedtothecentralportionsoftheelds.Eachregion(BootesorCetus)alsoconsistsofnumerousadjoiningelds,resultinginacheckeredimagequalityacrossthefullsurveyarea.Forfurtherdiscussionoftheproblem,seeElstonetal.(2006).Choosingtoemployacutomagnitudecorrespondingtotheweakestcomponentsofourdatahadtheadvantageofsimplicity,butitwouldhavecausedaconsiderablelossofinformationatthehighestredshifts.Choosingtoretaintheinformationfromourdeeperimagingwouldprovidealargersampleofhigh-redshiftgalaxies,butIwouldhavetomakecorrectionsforthelessdeeplyimagedregionsinordertocorrectlycalculategalaxydensities,andthiswouldbeanarduousandinexactprocess.IoptedinsteadtousetheIRACSS4:5m-selectedcatalog.Itsimagequalityisuniformandconsequentlyrequiredfewcorrectionstostandardizetheresults.IwroteaprogramwhichtooktheIRACSScatalogasinputandthenoutputinformationforthesampleofgalaxiesthatIneededformystudy;thedetailsarediscussedfurtherinSection 3.7.3 3.7 CalculatingtheSpatialCorrelationFunction 3.7.1 MathematicalOverviewMyprocedureforcalculatingFLAMEXspatialcorrelationshasmanysim-ilaritiestothemethodusedforSPICES(discussedinSections 2.3.4 2.3.6 ).TheAcoecientsforindividualgalaxiesweredeterminedinalmostexactlythesamewaywithtwoimportantexceptions.First,themaximumangleforthetwascalculatedtocorrespondtoaphysicaldistanceof2.0Mpcinallcases,requiringcalculationsoftheangulardiameterdistanceDAatvariousredshiftsasdiscussedinSection 3.7.3 .The2.0Mpclimitwasacompromisebetweenencompassingalargerareaandavoidinglosingtoomanygalaxiesneartheregionboundaries,

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sinceIdiscardedgalaxieswithinthephysicaldistancelimitoftheboundariesforsimplicity.Thesecondexceptionisthatthedependentvariableusedforthetwasthenumberofgalaxieswithinthedannulusatdistance,notthenumberofgalaxieswithindistance.Thelatterapproach,usingconcentriccircles,resultedinthedependentvariable'svaluesbeingcorrelatedwitheachother,andsotheannulus-basedprocedurewaspreferredforthet.Thus,Ittheequationnring()d=Ng21+A:77d=Ng2+Ng2A:23d;wheretheleft-handexpressionstandsforthenumberofgalaxiesobservedinaninnitesimalringofwidthdwhichisdegreesawayfromthereferencegalaxy.(Ng2distheexpectednumberofgalaxiesinthering.)AswithSPICES,IdeterminedanaveragegalaxydensityNgforeachgalaxy'sredshiftcomposedofallthegalaxiesinthesurveyareawithin0:1z,sincegalaxiesoutsidethisrangewereunlikelytobephysicallyassociatedwithit.(Thispromptedmetoignoregalaxieswithbadzphotagswhencalculatingthecorrelationamplitudes.Inessence,Iknewthatthesegalaxieswerepresent,buttheirredshiftswerepoorlydetermined,andsoIchosenottocountthemas\neighboringgalaxies"accordingtomyconditions.)TheprocedurefortranslatingfromangulartospatialcorrelationsdieredinseveralwaysfromthatusedforSPICES.Tobeginwith,Iworkedintermsofthespatialcorrelationlengthr0ratherthantheamplitudeofthespatialcorrelationfunctionB.Thespatialcorrelationfunctioncanberepresentedaseither(r)=(r=r0)or(r)=Bggr,wherer0andBaresimplyrelatedaccordingtor0=B1=.Studiesthatfocusontheclusteringaroundindividualgalaxies,suchasLongair&Seldner's(1979)radio-loudquasars,generallyuseB,whilemoststudiesthatinvestigatelarge-scaleclusteringofensemblesofgalaxiesuser0.Iusethelatterhere,asIamgenerallyreferringtothelarge-scalestudiesforpurposesofcomparison.Ialsofollow,e.g.,Gonzalezetal.(2002)in

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introducingafunctionf(z)describingtheredshiftdependenceofgalaxyclustering,sothat(r)=(r=r0)(1+z)f(z).Thetermisfrequentlyrepresentedasf(z)=(1+z)(3+),where=0correspondstoclusteredgalaxiesmaintainingthesameproperdistancefromeachotherwithredshift,and=3correspondstogalaxiesmaintainingthesamecomovingdistancefromeachother.Iassumethelatterinallresultspresentedhere,inaccordancewith,e.g.,Brownetal.(2003);however,theresultsareessentiallyindependentofthechoiceofepsilon,generallyvaryingbylessthan1%between=0and=3.AmoresignicantchangefortheFLAMEXprocedureistheuseofcosmologi-calLimberinversionstostatisticallydeprojectthetwo-dimensionaldistributionofgalaxiesandderivespatialcorrelationlengths.FollowingGonzalezetal.(2002),theLimberequationisro=Ac H0(=2) (1=2)[(1)=2]8><>:Rz2z1(dN=dz)2E(z)DA(z)1f(z)(1+z)dz 3.7.5 .TheadvantageofthismethodoverthatdescribedinLongairandSeldner(1979)isthattheLimberinversionmakesuseoftheredshiftdistributionofthegalaxiesinsteadofassumingaSchechterluminosityfunctiontodeterminegalaxypopulationsatgivenredshiftsandmagnitudelimits.IimplementedoneotherchangeintheprocedureforconvertingfromAtor0.ForSPICES,eachgalaxy'sAvaluewasconvertedtoacorrespondingBvalue,and

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theresultsforagivenredshift+SEDbinwereaveraged.ForFLAMEX,alloftheAvaluesforgalaxiesinagivenredshift+SEDbinwererstaveraged,andthenthemeanAvaluewasconvertedtor0.Theorderisimportantduetothenon-lineardependenceofr0uponA.TheFLAMEXapproachmorecloselyresemblesthestandardensembletechniquesofotherlarge-scaleclusteringsurveysandenablesadirectcomparisonwiththeirresults.Ialsoexperimentedwithstackingbyannulus,whichisparticularlysimilartothestandardmethod.Sinceallthegalaxies'annuliwereatthesamephysicaldistances(100equallyspacedintervalsupto2Mpc),itwaspossibletoaddthenumberofneighboringgalaxiesfoundatacertaindistanceawayforallgalaxiesofagivenredshift+SEDbin.Thisproducedverysimilarr0valuestothenon-stackedmethodatredshifts0:5
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thefar-UVandmid-IRbasedonBruzualandCharlot(2003)models.Withlinearinterpolationsbetweenthebasictemplates,thetotalnumberofSEDclassesroseto19.EachgalaxywassimultaneouslytforredshiftandSED-type;theywereas-signedSEDvaluesof0-18,wheretheoriginaltemplateswere0=E,7=Sbc,13=Scd,16=Im,17=SB3,and18=SB2.ComparisonsofthephotometricredshiftswiththeAGESspectroscopicredshifts(primarilygalaxieswithz<0:8)demonstratedadispersionofz=0:230andz=(1+z)=0:170,whilea95%clippingtoremovetheeectsofcatastrophicerrorsresultsinz=0:079andz=(1+z)=0:061.Forasmallerin-housesampleof500spectroscopicredshiftsthatismorerep-resentativeofthefullredshiftrangeofthesurvey,theunclippeddispersionwasz=0:498andz=(1+z)=0:253andtheclippeddispersionwasz=0:127andz=(1+z)=0:081.Brodwinwentontosupplementtheseresultswiththosefromaneuralnetworkalgorithm(ANNz;CollisterandLahav2004)whichwasveryeec-tivewithintheAGESredshiftlimits,particularlyforstrongPAH-emittinggalaxiesandAGNwhicharenottwellbytheSEDtemplateset;however,thesevalueswerenotincorporatedintothisproject.ForfurtherdetailsaboutthephotometricredshiftsandSEDclassications,seeBrodwinetal.(2006). 3.7.3 TheFinalCatalog:catalogparse.cOnlyafractionofthesourceslistedinthefullcatalogwereusefulforthisproject,andsoIwroteaprogramcalledcatalogparse.c(seeAppendix A )tocullthroughitandoutputagreatlystreamlinedcatalog.Inthecode,Iimplementedthefollowingprocedure.First,Iimportedtwolesofusefulinformation.TherstlecontainedKmagnitudevaluesand4:5mKcolorvaluesvs.redshift.(KistheabsoluteK-bandmagnitudeoftheturnofortheSchechterluminosityfunctionforgalaxies;high-luminositygalaxiesandlow-luminositygalaxiesfollowdierentfrequencydistributionlaws,withhigh-luminositygalaxiesatbrightermagnitudesthanK

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andlow-luminosityatfaintermagnitudes.)Animportantissueforhigh-redshiftgalaxiesisthatthelightemanatingfromthemhasbeenstretchedtolongerwavelengths,sothatthepartofthespectruminwhichweobservethelightisnotthepartfromwhichitoriginated.TheadjustmentsthatmustbemadeforthiseectarecalledK-corrections;Poggianti(1997)hasagoodoverview.Additionally,evolutionarycorrectionsmustbemadetoaccountforthedierencesingalaxies'spectra/colorsearlierintheuniverse'shistory,whenbrighter,bluerstarsplayedalargerrole.Thesecorrectionscanbecalculatedwithoneofseveralpublicly-availablestellarpopulationsynthesiscodes;weusedGALAXEV(Bruzual&Charlot2003).Ourinputparameterswereforapassively-evolvingsingle-burstgalaxywhichformedatzf=3;weusedsolarmetalicity,Padova1994evolutionarytracks,andaSalpeter(1955)IMFfrom0.1to100solarmasses(seeFigure 3{1 ).(StandardalternativeswouldhavelittleeectintheredshiftrangeinwhichIaminterested,z1:5.)Theobjectiveofallthisistoestimatetheabsolutemagnitudesofthegalaxiesinmysampleandtoemployanabsolutemagnitudecuto.Thispreventstheinclusionoffaint,low-redshiftgalaxiesinmygalaxydensitycalculationsthatwouldnothavebeenobservedathigh-redshifts.Accordingtothemodelledcorrections,thefaintestapparent4:5mmagnitudethatanLgalaxywouldhaveatz1:5wouldbe17.23.(IusetheVegamagnitudesystemthroughout.)The4:5mmagnitudelimitoftheIRACSSdatais17.8.Therefore,IdiscardedallgalaxieswhichwerefainterthanL+0:57mag,usingthecorrectionsforeachgalaxy'sredshifttoidentifythegalaxy'sabsolutemagnitudeandthevalueofLatthatredshift.Thesecondleimportedintomyprogramcontainedcosmologicalangulardiameterdistances(DA)versusredshiftinintervalsofz=:001.DAisarepresentionofthephysicaldistancethatcorrespondstoagivenangulardistanceinthesky.IcalculatedthesevaluesfollowingHogg(2000),usingthefollowing

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Figure3{1: IRACch2apparentmagnitudeversusredshiftforanL*galaxy.TheplotisbasedonthestellarpopulationsynthesiscodeofBruzualandCharlot(2003)andappliesKandevolutionarycorrectionsforapassivelyevolvingL*galaxywithzform=3.ThedashedlineshowstheIRACSS5depthusing5"apertures(17.8mag),andthedottedlineshowsthefaintestmagnitudethatanL*galaxywouldhaveatanyredshiftlessthan1.5(17.23mag).

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cosmologicalparametersfromthe1st-yearWilkinsonMicrowaveAnisotropyProbe(WMAP)observations:M=0:27,=0:73,k=0,andH0=71km/s/Mpc(Spergeletal,2003).Myprogramthenreadandanalyzedtheinformationforeachofthe225,746objectsintheIRACSS4:5m-selectedcatalog.Ioutputinformationonlyforthoseobjectswhichmetcertainstrictconditions.First,theyhadtofallwithintheFLAMEXBootesregion,andspecicallywithinthreesubregionswhichrepresented3:55deg2ofthe4:7deg2Bootesarea,excludingareasclosetothesurveyboundariesandalsoasectionoftheFLAMEXsurveywhichextendedoutsidetheNDWFSandIRACSSsurveys.Only93,907objectsmetthiscondition.Table 3{1 presentstheskycoverageofthethreesubregions. Table3{1: FLAMEXSubregions RABounds Dec.Bounds Area(deg2) Subregion1 216:329167<<218:820833 33:062500<<33:641667 1.205 Subregion2 216:291667<<219:529167 33:641667<<34:350000 1.901 Subregion3 217:729167<<219:333333 34:350000<<34:686944 0.445 CLASSparameterinthebest-seeingNDWFSopticalband.Only77,075objectsmetthisstandard,whichwasaconservativecutreliabledowntoR23,designedtoerronthesideofretainingstarsratherthanremovinggalaxies.Somebright,unresolved,star-likeob-jectswerealsoretainediftheywererobustlyinthe\AGN-wedge"accordingtothemid-IRcolorcriteriadenedbySternetal.(2005),asthesearealmostcertainlyquasars.AsecondarycutreliedonIRACshapeinformationandwaseectiveonlyatbrightmagnitudes,butitruledoutanadditional169objects,leaving76,906.Finally,Iautomaticallydiscardedthoseobjectswithz<0:01.Theseweregenerallyobjects(starsinmanycases)whosephotometricredshiftprobabilitydistributionfromBrodwin'scodewasat,contributingnoclearinformation.Thisprocedureleft74,577galaxies.

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Thefollowingcutswereofamoresubjectivenature.Iremovedgalaxieswithz>2.Abovethisvalue,theredshiftuncertaintieswerelarge,thesamplesizesweresmall,andthegalaxieswerefaint.Ithereforedecidedthattheywouldnotreasonablybeusefulinmystudy.Thisreducedthetotalto60,592galaxies.Anadditional197galaxieswerediscarded,leaving60,395,iftheywereinamaskedregionforanyoftheopticalNDWFSbands(BW;R;andI)orch1(3:6m)orch2(4:5m)oftheIRACSSdata,sincethisrenderedtheirphotometricredshiftslesscertainandsinceIwouldlateruseacombinedmaskimageforallvebandswhenmakingcorrectionsforundetectablegalaxies.Ithenusedinformationfrommyrstimportedle(discussedabove)toremovegalaxieswhichwerefainterthantheconstantluminositythreshold,whichleft45,461galaxies.Thiscuttookalargetollongalaxiesatz<0:5,asmanyofthesewereintrinsicallyfaintgalaxiesthatwouldnothavebeenobservedathigherredshifts.Theremaininggalaxieswereallpotentiallyusefulformystudy,andIexportedtheirinformationintoanalcatalogle.However,only37,494ofthemcouldbeusedas\reference"galaxies,meaninggalaxiesforwhichcalculationsofAweremade.Theothergalaxieswerewithin2Mpcoftheregionedges;althoughIcouldhavecorrectedforthis,Ichosenottoforthesakeofsimplicity,andsothesegalaxieswereusedonlyinestimatingthedensitiesaroundreferencegalaxies.Ioutputthefollowinginformationforeachofthese45,461galaxies:GalaxyID,rightascension,declination,SEDtype,andzphot.Ialsoincludedabinaryagtoindicatewhetherthegalaxycouldbeareferencegalaxy,aswellasaagindicatingwhetheritmatchedourcriteriaforextremelyredobjects(EROs,discussedinSection 3.8 ).Finally,Iusedtherstimportedle(discussedabove)tooutputtheanglecorrespondingto2Mpcatthatgalaxy'sredshift.Inpractice,fewerthan45,461galaxieswereusedinthisstudy,asIdecidedtorestrictthenalversiontoaredshiftrangeof0:3
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onlygalaxieswithinthisrangecouldbereferencegalaxiesandonlygalaxieswithin0:2
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adaptedforuseonmultiplemachinessimultaneously,anditonlyneededtobererunifthenalcatalogwaschanged.ThebasiccodeisincludedinAppendix B 3.7.5 3.7.3 )anddeterminedtherelationatdierentredshiftsbetweengalaxies'SED-typesandtheirspatialcorrelationlengths.(TheprogramcodeisavailableinAppendix C .)Ibeganbyreadingmyfullcataloginfointolargearrays.Duringthisprocess,Ikepttrackofthenumberofgalaxiesineachz=0:1redshiftbin,whichwasnecessaryforthenextstep.IthencalculatedtheLimberinversionfactorforeveryredshiftinmyrangeofinterest(0:3
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Thenextstageinvolvedsettingupalinearleast-squaresttondtheAcoecient.Icreatedtwoarraysof100elementseach.Therstconsistedof100equally-spacedradii,representingthedistancestoconcentricannuliaroundthereferencegalaxyoutto2Mpc.Thesecondconsistedofthenumberofgalaxiesfoundwithineachofthe100annuli.Itwasnecessarytocorrectthesevaluesforregionswithpoordatausingtheoutputofmaskfrac.pro(Section 3.7.4 ),whichincludedanestimateofthefractionalunmaskedareawithineachannulusaroundeachgalaxy.If,forexample,95%oftheregioncomprisingacertainannulusofthereferencegalaxywasunmasked,thenthenumberofobserved,unmaskedgalaxieswithinthatannulusweremultipliedby1:0=0:95toproducea\truegalaxy"estimateforthe2tofA.Theprogramwouldalsoassignthereferencegalaxya\dataquality"valueof.95,whichwasusedinlatermeanAcalculationstosignifythatitonlypossesses95%oftheinformationcontentthatagalaxywithnomaskedregionsnearbywouldhave;itwouldthenbeweightedaccordingly.However,forpurposesofttingforanindividualgalaxy'sA,Iweightedtheannuliequally.Allofthereferencegalaxies'Avaluesweredeterminedindividually;corrbrod.cthenexportedinfoforeachgalaxyintoanoutputle,includingthegalaxyID,thenumberofneighboringgalaxies,thegalaxy'sAvalue,anestimateofthedataqual-itybaseduponthefractionalmaskingintheneighborhood,thegalaxy'sSED-typeandphotometricredshift,andaagcarriedoverfromtheoriginalcatalogthatindicatedwhetherthegalaxywasan\extremelyredobject"(ERO).Finally,thecodereadtheinformationbackinforpurposesofbinningitbyredshiftintervals(generallywithz=0:2width),whichwerefurtherdividedintoSEDbins.TheSEDbinscouldeitherbeexible,wheregalaxiesinadjoiningSEDbinswereau-tomaticallybinnedtogetherinsuchawayastomakeeverybinofequalsize,orxed,wherethesamepredeterminedSEDrangeswereusedforbinningthroughout,regardlessofbinsize.(AseparateprocedurewasusedforanalysisofEROs.)Allof

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theAvaluesforagivenredshift+SEDbinwereaveragedtogether,andtheresultwasthenmultipliedbytheappropriateLimberinversionfactorforthemeanofthegalaxyredshiftstoobtainasinglespatialcorrelationlength(r0)forthebin.(SeeSection 3.7.1 forfurtherdiscussion.)Therawdataforanalyzingthedensity-SEDrelationwasthusavailableforplottingandanalysis. 3.8 Results 3.8.1 EvolutionoftheSED-DensityRelationTheresultsoftheprimarydensity-SEDstudyareshowninFigure 3{2 .Thestandardformofthelocal-Universerelation,inwhichearly-typeSEDsaremorehighlyclusteredthanlate-typeSEDs,isclearlyvisibleatallredshifts.Theerrorsaredeterminedusingabootstraptechnique,inwhichthesetofAvaluesforagivenbinisusedasthesamplingpoolfor1000randomly-generatedsetsofAvalues(withreplacement).Foreachrandomset,IthenconvertthemeanAtor0throughtheLimberinversion,asusual.Iusethestandarddeviationofthe1000r0valuestoestablishanerrorestimate.Thereisnoconsistentchangewithredshiftintheslopeofthedensity-SEDrelation,althoughitisinterestingthatthehighestredshiftrangeappearstohavetheattestresults.Itisalsointerestingtonotethat,atintermediateredshifts(0:91:3(seeFigure 3{3 ).Oneplausibleexplanationforthisisthatthe4:5mLmodelevolutiondepictedinFigure 3{1 deviatesfromthetrueevolution,presumablyduetoitsassumptionofpassiveevolution.Ifmyxed-luminosityselectioncriteria(seeSection 3.7.3 )areinfactremovingslightlyhigher-massgalaxiesatz=1thanatz=0:5,thenthiswouldcausetheobservedriseinr0.InFigure 3{4 ,thedataisreplottedafterrenormalizingtoameanr0of4.69Mpc,consistentwiththelowestredshiftbin.Theplotagainsuggestsaslight

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Figure3{2: FLAMEXdensity-SEDresults(exiblebins).Thebinsinthisg-urearealltunedtohaveequalnumbersofgalaxiesforagivenredshiftrangeandroughlyequalnumbersofgalaxiesacrossredshiftranges,inthiscasearound1000(theexactnumbersareincludedinparenthesesinthelegends).Errorbarsarebasedonbootstrapsamplingasdescribedinthetext.ItisimportanttobearinmindthattheSEDtypesarebasedonnon-evolvedmodels.

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Figure3{3: Overallr0vs.redshift.Thisgureshowsthecombinedr0forallSEDvaluesineachredshiftbin,withstandardbootstraperrors,andtheincreaseinr0at0.9
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Figure3{4: NormalizedFLAMEXdensity-SEDresults(exiblebins).ThisgureissimilartoFigure 3{2 ,withtheexceptionthateveryredshiftbinhasbeenrenor-malizedsothattheirmeanr0valuesareequaltothatofthelowestredshiftbin,i.e.5.98Mpc.

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Figure3{5: FLAMEXdensity-SEDresults(xedbins).ThebinsinthisgurecoverxedrangesofBrodwin'sSEDclassicationvalues,namely0-2,3-6,7-10,and11-18.Theexactx-axisvalueisstilldeterminedbythemeanSEDclasswithineachbin,however,soslightosetsmaybeseen.

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Figure3{6: 3{2 thehighestredshiftbin.AneortataL2Lluminositycutwasabandonedduetoinsucientcandidatesformeaningfulbinningonthesenescales. 3.8.2 EvolutionoftheERO-DensityRelationAnotherquestionishowtheclusteringofEROschangeswithredshift,andhowitcomparestotheclusteringofnon-EROs.IidentifyEROsaccordingtothecriteriainElstonetal.(2006),namelyRKS>5(within6"apertures),JKS>1:2,andKS<19:5,resultinginfewmatchesforz<0:9.EROsarecommonlyconsideredtorepresenttwoseparatetypesofgalaxies:passive,evolvedsystemsatz=0:82:0anddustystarburstsatcomparableredshifts.AttheKSlimitthatweuse,theEROsarepredominantlypassivegalaxies.Inanyevent,asthereisnoSEDtemplateforthedustystarburstgalaxies,theyarealsogenerallyregisteredbyBrodwin'scodeasearly-typegalaxies.Figure 3{7 indicateshowtheEROsasawholearedistributedamongourSED-types.Inordertocompare

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thedensity-SEDrelationofEROswithnon-EROs,Irestrictedournon-EROsampletothosegalaxieswhicharedetectedinKS,andspecicallytothosewithKS<19:5,soastoacquireasimilarly-selectedset.TheresultsfortheseareplottedinFigure 3{8 .EROsaresubstantiallymoreclusteredthannon-EROsat0:95orRKS>5forselection;itisbasedonTable1fromBrownetal.(2005).Thesurveynamesrefertothefollowingstudies:FLAMEX,thisstudy;NDWFS,Brownetal.(2003);NTT-WHT,Daddietal.(2001);Subaru1and2,Miyazakietal.(2003)fordustystarburstandpassiveevolvedSEDsrespectively;andELAISN2,Rocheetal.(2002)fortheno-evolutionmodel.Valuesofr0areadjustedtoassumeH0=71,inaccordancewithmyplots.ThisstudyincludessubstantiallymoreEROsthananyothertodate.Themeasuredr0valuesaresmallerthanthosereportedinotherstudies.InthecaseofBrownetal.(2003),thismaybeduetothedierentmagnitudecuts;onlybrightergalaxiesareincludedthere,andastrongrelationbetweenspatialcorrelationandluminosityhasbeenidentiedbyNorbergetal.(2002).Asecondarycausemaybetheaddedselectionbyabsolutemagnitude,baseduponL>0:6Lat4:5m,usedinmyproject.Thespatialcorrelationlengthsfortheothersurveyscannotbereconciledwithmyndings;ifveried,thepresentresultswouldrequiresignicantmodicationstocurrentmodelpredictionsofthepresent-daydescendantsoftheEROpopulation.

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Figure3{7: HistogramofEROsversusBrodwin'sSEDtypes.0=E,7=Sbc,13=Scd Figure3{8: EROandnon-EROcorrelationlengthsversusredshift.Thebinsinthisgureareeachz=0.2wide.NotethattheEROr0valuesarebasedonallsur-roundinggalaxies;theseareERO-galaxycorrelations,notERO-EROcorrelations(asarecommonlyshowninstudies).Forsimplicity,thedatapointsareplottedatthebins'midpointsratherthanusingthemeanredshift;however,thishasanef-fectoflessthanz=0.01.Thenumericalvaluesindicatethenumberofgalaxiesrepresentedbyeachdatapoint.ThedottedlineisatheoreticalpredictionfromKaumannetal.(1999)forearly-typegalaxies.

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Table3{2: EROSpatialClusteringStudies FLAMEX0:9
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Figure3{9: Clusterr0valuesversusredshift.Eachdatapointrepresentsasetofcombinedr0valuesfromgalaxyclusterswithinagivenredshiftbin.Thenumericalvaluesrepresentthenumberofclustersrepresentedbyeachdatapoint,andthebinsinthisgureareeachz=0.2wide.Forsimplicity,thedatapointsareplottedatthebins'midpointsratherthanusingthemeanredshift. criteria.Theatnessoftheslopeindicatesthattheclustermasslimitisnotchangingquicklywithinourredshiftregime,althoughtheaveragerichnessofthesystemsmaypossiblybediminishingatz>1.Figure 3{10 comparestheindividualclusterr0valueswiththedetectionratingsassignedbyGonzaleztoassessthescatterbetweenthetwoquantities.Thereisavisiblecorrelation,butwithahighdegreeofscatterforthelower-signicancedetections.Negativer0valuesindicatethattheAvaluewasnegative,i.e.theneighborhoodlookslessdensethanaverage.ThisapparentdiscrepancyprobablyresultsfromastrongerluminositycutothanthatusedbyGonzalez,fromclusterswhosecentersarenotwell-dened,orfrommarginalclusterswhoseexternalsurroundingsareunusuallyunder-dense.Thereisnoapparentdierenceinthescatterathighversuslowredshifts.

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Figure3{10: Clusterr0valuesversusdetectionrating.Eachdatapointrepresentsanindividualgalaxycluster,comparingitsr0valuetothedetectionratingassignedbyGonzalez'code.Adetectionratingof1signiesathresholddetection,whilehighervaluesrepresentstrongerdetections. 3.9 DiscussionandConclusionsTheresultsshownaboveoerusefulinsightsintogalaxyevolution.Firstandforemost,thedensity-SEDrelationisestablishedbyz=1:5,withnosubstantiveevolutionbetweenthatepochandthepresent.Atthelatterredshift,thereshouldbelessthan1clusterwithM>1014solarmassesintheentireFLAMEXBootesregion.Hence,theSED-densityrelationisinplacepriortoclusterassembly.ThisisconsistentwiththeideathatthekeyparameterindeterminingtheSED(andmorphological)fractionislocaldensityratherthantherichclusterenvironment.Anotherimportantresultisthatthespatialcorrelationlengthsarenotstronglyevolvingacrosstheredshiftrange,suggestingstableclusteringforaxedluminos-itythreshold.Thisprogramoerstwoimportantbenetstotheoverallstudyofthedensity-SEDrelation.Byusinga4:5mselection,weareabletoselectasamplewitharoughlyconstantintrinsicluminosityovertheentireredshiftregime.Noprevious

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suchstudieswitha4:5m-selectedsampleexist.Inaddition,whilethestudylacksspectroscopicredshifts,theuseofphotometricredshiftsallowsustocoveramuchlargerarea,whichisnecessarytoprobeasucientvolumeofspacetoincludearepresentativesampleofmassivegalaxiesandtominimizetheunpredictableeectsofcosmicvariance.Moreover,becauseoftheextendedwavelengthbaselineusedtogeneratethephotometricredshifts,theredshiftuncertaintiesareonlyweaklydependentuponSED-typeandredshiftouttoz=1.5.TheEROresultsshowedtheexpectedaugmentationinclusteringforEROscomparedtonormalgalaxiesat0:9
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isalsoroomformoredetailedworkbeyondwhattheFLAMEXsurveyiscapableofachieving.Forexample,followupspectroscopyofselectedregionscanmeasurethesuccessofourphotometricredshiftsathighzandlookforsystematicerrorsinmuchthesamewayasIusedtheSPICESspectroscopy.Similarly,wecouldbenetfromreplicatingthesurveyphotometryinregionsimagedbytheHubbleSpaceTelescope'sAdvancedCameraforSurveystoassessthemorphologicalconnectionstoourSED-typesinavarietyofclusterandeldenvironments.Finally,pushingasubsetofthesurveyregiontogreaterdepthscouldprovidedividends,aswecouldestablishwhethertheapparentatteningofthedensity-SEDrelationshipatz>1:3isarealphenomenon.Therearealsoseparatebutrelatedprojectsthatmeritinvestigation.Althoughthefocusofthisworkwasnotspecicallyupontheevolutionofclustering,thereisagreatdealofongoingworkinthisareathatisattemptingtoestablishtheextenttowhichclusteringparameterschangewithredshift,andtheFLAMEXsurveyiswell-suitedforcontributingtothis.Ananalysisoftheevolutionoftheluminosityfunctionwithredshiftwillalsohelptodevelopthelargerpictureofgalaxyevolutionoverthepastninebillionyears.

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4.1 IntroductionOpenclustersareborninthemidstofgiantmolecularclouds,buttheydonotstaythereforlong.Thestarsdepartthecloudswithinafewmillionyearsandtravelthroughspacetogetherforatime.UnlikeOBassociations,thereisasignicantdegreeofgravitationalbindingforopenclusters,buttherearepotentialdisruptiveforcesthatwillunbindthemintheend.Manyclustersdissipatewithintenmillionyearsoftheirbirth,andalthoughafewareknownwithagesofbillionsofyears,theyrepresentonlyatinyfractionofthetotal.GasremovalbyOandBstars,concentrationofangularmomentuminacentralbinary,andgalactictidaldisruptionhaveallbeencitedascausesofclusterdissipation.Theprimarygoalofthisprojectistoinvestigatethesecausesandassesstheirrelativeimportance. 4.2 ComparisonofClusterCatalogsStatisticalstudiesoftheagesofclustersareamajorobservationalmeansofachievingthisgoal,andtheyrequireascompleteacatalogofclustersasiscurrentlyattainable.ThemostrecentcomprehensivepublishedcatalogisthatofLynga(5thed.,1987),listingall1162openclustersknownatthattimealongwithawidearrayoftheirproperties(whenavailable).However,manyadditionalobser-vationshavebeenmadeinthepastnineteenyears,bothrevisingandsupplement-ingthesevalues,sothattheLyngacatalogisnowoutofdate.OnecurrentsourceforclusterinformationistheWEDBAdatabase(http://obswww.unige.ch/webda),compiledandactivelymaintainedbyDr.Jean-ClaudeMermilliodandDr.ErnstPaunzen.Itencompassesavarietyofrecentobservations(esp.Loktin,Gerasi-menko,&Malisheva,2000;Dambis,1998;Malysheva,1997;Dutra&Bica,2000; 78

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andKharchenkoetal.2005).Morerecently,Diasetal.(2002)establishedasecondweb-basedcatalogofopenclustersatwww.astro.iag.usp.br/wilton(DAML02).TheprimarymotivationforDAML02wastopresentup-to-dateinformation,par-ticularlywithregardstothepropermotionsandradialvelocitiesofclusters.BothcatalogsaresubstantialimprovementsovertheLyngacatalog;WEBDA(asofthiswriting,May2006)has1746clustersandDAML02has1756clusters.Manydonotyethavedeterminedages,buttheweb-basedcatalogshaveincreasedthenumberfrom403(Lynga)to960(WEBDA)and861(DAML02);mostoftheimprovementherehascomefromstudiesperformedinthelastveyears.Kharchenkoetal.(2005)isparticularlyworthyofnote,astheypublishedaconsistentsetofobserva-tionsandparametersfor520clusters(ofwhich109werenewdiscoveries)basedontheAll-SkyCompiledCatalogof2.5MillionStars(ASCC-2.5,Kharchenko2001).ThequestionthatnaturallyarisesiswhetherWEBDAorDAML02isconsis-tently\better"thantheother;unfortunately,thereisnostraightforwardanswer.Bothcatalogsreceiveupdatesbasedoncurrentliterature,butDAML02usessomesourcesthatWEBDAdoesnotandviceversa.Eventheirnamingconventionsforclustersareslightlydierent;for21oftheASCCclusterslistedinWEDBA(10,22,32,41,42,44,47,49,50,68,86,89,92,96,97,103,106,112,118,124,and129),DAML02insteadusesthenamesfromtheiroriginaldiscoveriesbyAlessi,Alessi-Teutsch,Ferrero,Herschel,andTeutsch.Listsofcross-identicationscanbefoundonbothwebsites,thoughalittlediggingmayberequired.Regardingtheclusterparameters,suchasage,acompleteanalysisofthecatalogstodeterminethebestinformationwouldbeaformidableprojectinitsentirety.Inlieuofthis,Istudiedasubsetofthecatalogs,thoseclusters(withlistedageparameters)whoseidentiersbeganwith`A'or`B'.Ilookedforbasicpatternsinthecatalogs'useofsourcesinhopesofidentifyinga\superior"catalogoraneasywayofcombiningthebestinformationfromboth.Theinvestigationcomprised252and229clusters

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withagesintheWEBDAcatalogandDAML02catalog,respectively.Adetailedreport,brokendownbyclustername,islocatedinAppendix D .ThecomparisonofWEDBAandDAML02subsetsndsanumberofdier-encesbetweenthem,butneithercatalogisclearlysuperior.Botharesubjecttosporadictypos(Ifoundtwoforeachandreportedthemall),andinformationabouttheirreferencesisoccasionallydiculttolocate.Indnosimplealgorithmfordeterminingwhichagevaluethecatalogsusewhenmultiplestudiesareavailable.Whenthetwocatalogslistdierentagesforacluster,WEBDAusesmorerecentsourcesthanDAML02insomecases(Iidentied7),whiletheoppositeistrueinothercases(Iidentied4).Morecommonly,aclusterwillhaveanagelistinginWEDBAbutnotDAML02(22)orinDAML02butnotWEBDA(8).Inparticular,WEBDAismorelikelytoincludetheagesdeterminedbyKharchenkoetal.(2005).DAML02'snamingconventionsarepreferred,sincetheiridentiersareconsistentlybasedontheoriginaldiscoveries.DAML02'slistofremovedclusterscontainssomevaluableinformationthatisnotreectedintheWEDBAcatalog.Finally,DAML02includesagsforthevariousclusters,suchas\possibleglobularcluster"or\dubiouscluster,"whichcanbeusedtocullquestionablecandidatesfromadataset. 4.3 SampleConstructionThereiscurrentlynoclearstrategyforusingthetwocatalogstoconstructa\best"collectionofclusterages.Adetailedinvestigationlookingatthefullsetoflistingsinthecatalogsandassessingthequalityoftheagedeterminationmethodsusedinthevariousstudiesthattheyreferencewouldbeaformidableundertaking,althoughavaluableone,worthyoffuturework.Thesimplestalternativeistoselectalarge,self-consistentstudysuchasKharchenkoetal.(2005),whichalsoeliminatesinhomogeneitiesinthemethodsofagedeterminationbetweenvariousgroups.However,inthisstudy,Iacceptedgreatersystematicuncertaintiesin

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exchangeforalargersamplesize,namelyalltheopenclusterswhoseageswehaveareasonableestimateof.Accordingly,Iconstructedmyinitialsampleasfollows.IstartedwiththeWEBDAclusterswithagevaluesasabaseandaddedall(49)non-duplicateDAML02clusters(takingcaretoidentifycaseswherethenamingconventionsweredierent).Next,allclustersfoundinDAML02'slistofremovedclusters(9)weretakenoutofthesample.Ichosetoretainclustersaggedas\dubious"inDAML02,butIcouldequallywellhaveremovedthem.Theresultingsamplecontained997clusters. 4.4 SampleOverview:AgesandLocationsAbriefoverviewoftheclustersispresentedinFigure 4{1 (showingthenumbercountvs.age),whileFigures 4{2 and 4{3 showthespatialdistributionofclustersintheMilkyWay.InFigure 4{1 ,thereisanextremelysharpdropoofclusterswithintherst50millionyears,afterwhichtheycontinuetodecline,butmoreandmoreslowly.Thegraphcutsoatthetwobillionyearmark,butahandfulofclustersareseenasoldas8-10billionyears!Therisebetweenthe0-10millionyearbinandthe10-20millionyearbinisprobablyattributabletotheyoungest,embeddedclustersbeingmorediculttosee;88%oftherstbin'smembersareinthe5-10millionyearrange.Consequently,laterstatisticaltreatmentsinthispaperassumethebin'svaluetobedoublewhatisactuallyobserved.

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Figure4{1: Numberofclustersversusage

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Figure 4{2 showsthedistributionoftheclustersintheMilkyWay,fromatop-downvantagepoint.Notsurprisingly,thegreatestconcentrationisneartheSunat0,8500.ItisalsoworthnotingthatolderclustersdominatethesampleintheouterregionsoftheGalaxy,comparedtotheregionsinsidethesolarcircle,wheretherearerelativelyfewofthem(discussedbelow).Also,therearesignicantlymoreclusters(61%)onthepositivesideoftheX=0axis,whichisratherpuzzling,asthereisnoobviousreasonwhytheywouldbepreferentiallyseeninfrontoforbehindthesolarrevolutionpath.Thehypothesisthatyoungopenclusterstracespiralstructureisnowoutoffavor(e.g.,Janes&Adler,1982).Figure 4{3 isanotherpositionalmap,plottingtheclusters'radialdistancefromtheGalacticcenteragainsttheirzheightsoutoftheGalacticplane.Here,theeectsofagearequitedramatic;virtuallyalloftheclusters500+pcfromtheplaneareolderthan400millionyears,reinforcingtheideathatclustersforminthemidstofthethindisk,andgivinganindicationoftheirrateofdispersion.NotealsothatthedispersionisunambiguouslygreaterintheouterregionsoftheMilkyWay,asanyhighlatitudeclustersnearthesolarcirclewouldeasilyhavebeenidentied. 4.5 SelectionEectsUnfortunately,notalloftheseclustersarecreatedequal:thereareanumberofpotentialselectioneectsthatmustbeconsidered.Thewaysinwhichvariousauthorstreatthisproducesubstantialvariationsintheirresults.Therstselectioneectisthestraightforwardpredictionthatyoungerclusters,withtheirbrighter,bluerstars,willbemorereadilydetectedatlargedistancesthanolderclusters.Anotherproblemisthepotentialforobserverselection.Observersinterestedinstarformationmayspecicallyseekoutyoungclustersforagedetermination.Clustersatlowdeclinations(30degreesS)maybeundersampled,aectinghowmanyareseentowardtheGalacticcenter(dominatedbyyoungerclusters)andhowmanyareseentowardtheperiphery(whereolderclustersarecomparatively

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Figure4{2: Top-downgalacticviewofclusters

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Figure4{3: Edge-ongalacticview

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prevalent{seeFigure 4{2 ).JanesandAdler(1982)believethislongitudeeecttobenegligible,butitrepresentsthemostlikelycausefortheaforementioneddisparityinFigure 4{2 'sY-axisdistribution.DeterminingthemaximumradiusfromtheSunofacompletesample(oratleastarepresentativeone)canbeattemptedbystatisticaltests,particularlytheKolmogoro-Smirnovtest(Wielen,1971).Wieleninvestigatedtheagedistributionsforclustersintworegimes,0400millionyears)greatlydominatethedetectedpopulationsat2+kpc(seeFigure 4{1 ).ThisislargelyduetotheirgreaterzdispersionoutoftheGalacticdisk,sothatobserva-tionsofthemareeasier,andpossiblyalsoduetotheirtendencytobemoremassivethanaverage(hencebetterabletosurvive).Thenetresultisthatdistance-basedselectioneectsarediculttoparame-terize,andtosomeextentbalanceoneanotherout.Thisstudyassumesthatthey

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arenotproducingsubstantialeectsandretainsalloftheclustersforitsstatis-tics.BattinelliandCapuzzo-Dolcetta'scontentionraisesthequestion,however,ofwhetherweareseekinganall-inclusiveclusteragedistribution,orwhetheritwouldbemoreappropriatetoderivedierentonesfortheactiveandinactivestarformingregionsofourGalaxy.BinningbyGalacticradius,i.e.breakingtheprojectintoseveralmini-studies,wouldbefeasible,aswouldbinningbytheothermajorparameterthataectsagedistributions,namelyclusters'mass/density/starcounts(e.g.,Janes&Tilley,1988).Unfortunately,althoughthesedoprovideusefulqualitativeinformation,thestatisticssuerfromsmallsamplesizes.AsthemainintentofthisworkistoinvestigateglobalpropertiesoftheagedistributionovertheentirelifetimeoftheGalaxy,Itreatalltheclustersasasinglepopulation. 4.6 FittingtheAgeDistributionAcommonassumptionfortheagedistributionisthatittsaninverseex-ponentialcurve,withthenumberofsurvivingclustersbeinghalvedatregularintervals.Figure 4{4 presentsaplotoftheagedistributionupto2billionyears,inbinsof10millionyears(similartoFigure 4{1 ),withthebesttinverseexpo-nentialincluded(solidline).Someofthebinsizesarezero,whichtheexponentialregressionalgorithmisunabletohandle.Oneoptionwastouselargerbins,sothateverybinwouldhaveatleastonemember.Theconcernwiththisapproachwouldbethelossofresolutionatyoungerages,wherethestatisticsareotherwisemostreliable.Instead,a\smoothing"ofthebinswasemployed,sothatbinsofzerosizesharedthepopulationsoftheirneighboringnon-zerobins,producingmanybinsoffractionalsize.Thisiseasilyjustied,asmuchoftheclumpinessinthedistributionforlargeagesisduetostudieswhichexpressedagesinroundguressuchas1000Myrorlog(age)=8:9.Thesmoothingwasdonebyhandratherthanusingalterfunction,astheclumpinessdidnotlenditselftoanautomaticprocedure.I

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Figure4{4: Numberofclustersversusage,witht repeatedlycheckedtheresultsbyapplyinglargerbins,ensuringthatthesmoothedresultswerebroadlyconsistentwiththeobservationsoverlargespansoftime.Forexponentialdistributions,thenumberofclustersineachbinwillbeN=N0ect,whereN0istheoriginalnumberofclusters.Theconstantcisameasureoftherateofdecline,andthedistribution'shalf-lifeismeasuredbyt1=2=106:693=c.TakingthenaturallogarithmoftheequationforNyieldslnN=lnN0ct.Figure 4{5 plotsthislatterfunction,nowusinglinearregression(solidline)tonditsslope(-c)anditsy-intercept(lnN0).Itisapparentfromtheseguresthatthetisanextremelypooronefortherst200millionyearsorso.Thereareseveralpossiblecontributingfactorstothis.

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Figure4{5: Overalllnregressionlines

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Oneisthattheselectioneectsareintroducingadisproportionatenumberofoldclusters.Toaccountforthis,allclustersmorethan2kpcawaywhoseGalacticlatitude'sabsolutevalueisgreaterthan5degreesareremovedfromthesampleasbeing\tooeasytosee."Thetsarerecalculated(dashedlineonFigure 4{5 ,revisedsymbolsnotshown).Although42%ofthe1-2billionyearoldclustersarethusremovedfromthesample(only2.5%fromages0-1billionyears),theeectsareinvisibleinFigure 4{4 andunremarkableinFigure 4{5 ,sotheselectioneectisprobablynotamajorfactorunlessitisconsiderablymoredramaticthanestimated.AnotherpotentialhindrancetoagoodtwouldbevariationinthestarformationrateovertheMilkyWay'shistory.Otherauthorshaveassumedaconstantstarformationrateintheirinvestigations,butthenaturalexpectationwouldbethattheratewashigherearlierintheGalaxy'shistory.Iattemptedtominimizethiseectbyderivingthetsonlyfromclustersundertwobillionyearsofage.Ifthestarformationratewere,forexample,twiceashightwobillionyearsago,thenthesurvivingoldclustersshouldonlycounthalfasmuchinthestatistics,whichwouldsteepenthelogarithmicslopeinFigure 4{5 .Theeect,however,wouldbecomparabletothehighlongitudeselectioneectalreadymentioned,soitwouldberelativelyunimportantunlessthestarformationratehasdecreasedtoamuchgreaterextentthanthisexample.Themostprobablecauseforthepoortisthatthereismorethanonemechanismdisruptingopenclusters,whichoperateondierenttimesscales,sothatmultipleexponentialdecayratesarebeingcombinedtogether.Olderstudies(Wielen,1971;Lynga,1982;Janes&Adler,1982)comeupwithtypicalhalf-livesaround100-150millionyears,andthatderivedfromFigure 4{5 'sslopeiscomparableifsomewhatlarger:T1=2=106:693=:0023300millionyears.Piskunovetal.(2006)foundT1=2=25612usingasampleof652galaxieswithhomogenously-determinedages.Incontrast,BattinelliandCapuzzo-Dolcetta's

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study(1991)producedmuchshorterhalf-lives,roughlytenmillionyears.Theprimaryreasonforthisistherespectivesamplesused:moststudiesbasedtheirtsusingonlyolderclusters,typically50+millionyearsold,tryingtoavoidtheearlystageswhenopenclustersandOBassociationsoverlapandareindistinguishable.However,thedistinctionbetweenthetwoisfairlyarbitrary,withoutenteringintothetediousandfrequentlyimpossiblecalculationsofstarandgasmasses,properandradialmotions,anddistancesbetweenthestarstodeterminewhetherthegroupisboundornot.Forourpurposes,thedistinctionisnotanimportantconsideration,asthedissipationofassociationsmaybeconsideredanextremecaseoftheoverallclusterdissipationrate.Thesevariationsinhalf-lifewithandwithouttheyoungclusterssupporttheideathatdierentdisruptionmechanismsareatwork.Areasonablehypothesismightcallforbothashort-termmechanism,suchastheremovalofgasfromtheclusters'interiorbyOBstarsandsupernovashocks,unbindingthestars,andalong-termmechanism,suchasgalactictidaleectsorencounterswitheldGMCs.Theideaisthattheinverseexponentialdeclineduetogasremovalalonedoesnotasymptoticallyreachzero.ThereexistsasmallnumberofclustersinourGalaxywhicharesostronglyboundthattheywillneverbreakapartevenwhenalltheirgasisremoved,andwhicharethereforenotafactorinthisexponentialcurve.Insteadofzero,thegasremovalcurvewillasymptoticallydeclinetotheoriginalnumberofstronglyboundclusters.Theseclusterswillhavetheirownexponentialdeclinerateduetotidalinteractions,etc.,butitwillbeamuchslowerdecline.Theobservationsthatwemakearebasedonacombinationofbothdecayrates,andthetaskistoseparatethetwoeects.Infact,cursoryinspectionofFigure 4{5 suggeststhreeregimes:thelong-termeect(>300millionyearsorso)whichhaslargelydeterminedtheregressionline,anintermediate-termeect,andashort-termeectthattakesplaceonlyoverthe

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rstthirtymillionyearsorso.Toisolatethelong-termeect,Iusedtheclustercountsbetween400millionyearsand2billionyears,asbelow400millionyearsitbecomesmorediculttobesurethatshorter-termmechanismsarenotplayingarole.FittingalinetothispartofthesampleinFigure 4{5 givesashallowerslope,c=:00196:00007(comparedto.0023fortheoverallsample),withay-interceptof2:24:09,correspondingto9:4:9clusters.Thissuggeststhat,ofthenumberofclustersthatareformedeverytenmillionyearswithinourobservationalrange,roughly91/2clustersneverexperienceshort-ormid-termdisruption.Theysuertheirownextremelylong-termdecay,withahalf-lifeof35413millionyears.(Notethatthetrueerrorsizesaresomewhatlargerthanpresentedhere,asnoconsiderationistakenoftheerrorsinagedeterminations.)Thenextstepistodeterminethecorrespondingexponentialdistributionfortheseclustersandsubtractthatdistributionfromtheoverallagedistribution(Fig-ure 4{4 )toretainonlytheclusterswhichundergoshort-andmid-termdisruption.Thissubtractionofatteddistributionfromtheobservedonecanproducenega-tivenumbersatlateages,whenfewclustersareextant,andsmoothinghasbeendonetoaccountforthis,asabove,bringingallthevaluesabovezero.Figure 4{6 showstheremainingclusters.Notethatsmallerbinsizes(5millionyears)arenowbeingusedtotrytoretaininformationresolution,requiringcarewhenmakingcomparisonswiththe10millionyearbinsofthelong-termeects.Inparticular,theyvalueshavedierentmeaningsinFigures 4{5 and 4{6 ,althoughtheFig-ure 4{6 yvaluescaneasilybetransformedtotheir10millionyearbinequivalentfollowingy10=ln(2ey5).Theplot'suppercutoisat400millionyearssincethelongtermeectshavebeenremoved,andsothereshouldbeeectivelyzeroclustersleftatoldages.Thestatisticsforthemid-termeectsarebasedonthe50-300millionyearsubsetofthegraph.Earlierthan50millionyears,theshort-termeectsmaystillbesignicant,whilelaterthan300millionyears,\smallnumber

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statistics"aecttheslope,asmostofthemid-termclustersaregoneandinaccura-ciesinthelong-termslopehaveagreatereect.Usingtheregimeinbetween,atisfound(solidline)withslopec=:0066:0015andy-intercept1:91:29,corre-spondingto13:64:5clustersaectedbythemid-termdisruption(oftheclustersproducedeverytenmillionyears).However,atthisstageitisworthmakinganadjustmenttothey-intercept,takingittobeatanageof6millionyearsratherthanzero,asitisprobablynotmeaningfultodiscussclusterdisruptionduringtherstfewmillionyearsoftheirexistence,whentheyarefrequentlystillembeddedintheirhostclouds.Certainlytheavailablestatisticsareveryincompletebeforethistime.Thisreducestheaectedclustersto13:04:3.Thehalf-lifeofthiseectis10530millionyears.(Thedashedlinerepresentsthetthatwouldhavebeenobtainedwithoutthesubtractionofthelong-termclusters;itisalsobasedonlyonthe50-300millionyearregime.)Finally,theprocessisrepeatedtondtheshort-termstatistics.First,thenumberofclustersaectedbythelongermechanismsaresubtractedfromtheobservedsample(Nshort=Nobseyintlongclongage=10eyintmidcmidage=5,usingbinsizesof1Myr).NshortisplottedlogarithmicallyinFigure 4{7 .AswithFigure 4{6 ,thebesttisshownwithasolidline,andthetthatwouldhavebeenfoundwithoutsubtractingthelongereectsisshownbyadashedline.Onlytheregime6-30millionyearsisusedforthets.Thedeterminedslopeisc=:138:019andthey-intercept(at6millionyears)is3:09:27,correspondingto22070clusterspertenmillionyears.Thehalf-lifeisaveryshort5:0:8millionyears. 4.7 DiscussionThemodeltbythisanalysisisoftheformNtot=N0ec1tec2tec3t=N0e(c1+c2+c3)t.N0isfoundtobeontheorderof240(thesumofthethreey-intercepts),sothat240clustersareformedeverytenmillionyearswherewecanseethem.Oftheseclusters,91%dissipateonveryshorttime-scales,presumably

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Figure4{6: Mid-termlnregression

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Figure4{7: Short-termlnregression

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Figure4{8: Lnregressionlinecomparison duetogasremovalfromtheirinteriors,5%surviveratherlongerbutarebrokenupbysomemeansactingonatimescaleofroughly100millionyears,and4%surviveindenitelyuntilscatteredbyGalactictidaleects,GMCinteractions,andthelike.Figure 4{8 isaversionofFigure 4{5 showingthethreedierentlinets.Theiradditivecombinationisalsodelineated.Figure 4{9 istheimprovedversionofFigure 4{4 ,showingthenalt,whichisanexcellentmatchfortheobservations.Therearesomecaveatstobearinmind.Thestatisticaltreatmenthasnotbeenall-encompassing:thetrueerrorsareprobablyrathergreaterthanthevaluesgivenabove,whichshouldbeusedonlyforqualitativeandcomparativepurposes.Also,itislikelythattherearemorethanthreemechanismsforclusterdisruption,althoughitdoesnotseempossibletoimprovethisthree-mechanismmodelwithoutbetterqualityandquantityofobservations.Itshould,moreover,be

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Figure4{9: Clustersobservedandt

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rememberedthatthisprojectisunabletodiscernanythingaboutclustersintheinnerGalaxy;theseresultsapplyonlytomid-outerregionsoftheGalaxy.Finally,noconsiderationhasbeentakenforpossiblemigrationofclusters.Althoughinterestingintheirownright,theseresultsalsohavepossiblesignicanceforstarformationstudies.Theresilienceofclustersprovidesagreatdealofinformationabouthowtheywereformed,anditmayhelpmodelerstopindownthemysteryofwhyafewclusterscanformsotightlypackedthattheyremainboundevenaftertheirgasremoval.Moreover,studieslikethisonecanaidinunderstandingvariationsinstarformationoverthecourseoftheGalaxy'shistory.

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3.7.3 99

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/Itlooksthroughallcatalog&flagfiles(upto99)andidentifieswhichgalaxiesarewanted/ /Itoutputstheirinfo(id#,RA,Dec,SEDtype,photoz)toafilecalledcateric/ /ThisiscurrentlydesignedtoworkwithMarkBrodwin'scatalogs,nottheSPICESdata/ /Itnowusesastandardluminositycutoffsothatsmallnearbygals.areignored/ /Itnowincludesthecorrectsurveyregion,usingthreesubregionsoftheFLAMEXsurvey/ /Thisprogramisrunfirst,themmaskfrac.pro,thencorrbrod.c/ 5sig.flags.mask"/Filewheretheflaginfoislocated/ 5sig.mag"/Brodwin'sphotometrycatalog/ /Seealsofilebasecatandfileendcatbelowforfilenamesofthezpeakfiles/ peakfiles)/ main() /Ifso,itwillbeincludedinthecatericcatalog/ merp,/NumberofsourcesoutsidemyBootesregions/

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5sig.mag.README/ zpeakn0";/Theendofthefilenamesfortheinputzpeakcatalogdata/ /Readsiniracplezf3.datfile,w/Kcorrectionsvs.redshiftandLinfoforallfilters/ fscanf(fpkcorr,"%s",header); fscanf(fpkcorr,"%lf",&magnarray[x][y]); fclose(fpkcorr); fscanf(fpdist,"%s %s",&header,&header); %lf",&redshift[x],&angdiam[x]);/Here,angdiamistheangulardist.inkpc/deg/ fpout=fopen("junk","w");/Theoutputcatalogfile,withalldesiredinfo/ fscanf(fpphot,"%s",header);/Readstheheaderlineforflagfile/ %lf %lf",&nostarid,&blah2,&blah2); merp=merp2=merp3=merp4=0; fp2=fopen(FLAGFILE,"r");/Theflagfile/ sprintf(&filetens,"%d",catalogs/10); sprintf(&fileunits,"%d",catalogs%10); strcat(filebasecat,&filetens); strcat(filebasecat,&fileunits); //filebaseflag[x]=filebasecat[x];

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//fp2=fopen(filebaseflag,"r");/Theflagfile/ fscanf(fp,"%s",header);/Readstheheaderlineforcatalogfile/ /for(x=1;x<9;x++) fscanf(fp2,"%s",header);/Readstheheaderlineforflagfile/ /Usedforstoppingthewhileloop/ endfile=0.0; fscanf(fp2,"%lf",&eoftest2); fscanf(fp2,"%d",&flags[x]); fscanf(fpphot,"%lf",&phot[x]); fscanf(fpphot,"%d",&blah); fscanf(fpphot,"%lf",&blah2); gals[0]=eoftest; fscanf(fp,"%lf %lf %d %lf",&gals[1],&gals[2],&sed,&gals[3]); starcount++; %lf %lf",&nostarid,&blah2,&blah2);/MovestonextnonstargalaxyinMark'slist/ /Decideswhethergalaxyisusefulornot;note:add2toflagstogetequivalentinBrodwin'sREADME/ /Determineswhethergalaxyisinsurveyfield/ areaid=1; areaid=2; field=1; field=1; field=1; g merp2++;/Objectisastarorotherwiseweird/

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/Throwsoutfaintlowzgalsthatwouldn'thavebeenseenathigherredshifts/ /Ideally,thesewouldbeincludedincatericformaskassessmentpurposes,butkindofahassle/ weird problem. %lf %lf %dnn",gals[3],magnarray[x+1][0],x); kstar=(magnarray[x+1][2]magnarray[x][2])interpfrac+magnarray[x][2]; kcorr=(magnarray[x+1][10]magnarray[x][10])interpfrac+magnarray[x][10]; ch2star=kstar+kcorr; belowthresh++; g /Foreachgal.,determinestheangulardistancecorrespondingtoMAXDISTbasedonphotozanddistance.txtfile/ x++; maxang=angdiam[x]; decfactor=cos(gals[2]3.14157/180.0); /Detailsarefinetunedtogeometryofmycurrentsurveyarea,whichcouldchange;seedefinitionsaboveandp.36a/ /Notwatertight;mightnothandleverylowzwell,wheremaxang>.3degreesorso/ /Willneedseriousrevisionsif/whenimageedgescanbeproperlyaccountedfor,butthatisdesirable;thiserrsonsideofstrictness/ /Accountingforimageedgeswillalsosimplifythisprocessgreatly/ maxangra=maxang/decfactor; field2=1; field2=1; field2=1; field2=1;

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field2=1; odd is going on in the field2 calculation.nn"); field2=1; /Flags57=optical,11=ch1,12=ch2/ nonmask=1; merp4++; totrefgals++; /Criteria:RKs>5,JKs>1.2,Ks<19.5,(magnitudeerrorsalllessthan.5?)/ erotot++; fprintf(fpout,"%lf %lf %lf %d %lf %d %d %d %lfnn",gals[0],gals[1],gals[2],sed,gals[3],galref,nonmask,ero,maxang); totnumgals++; printf("Finished with catalog %d. Totnumgals is %d. Reference galaxies: %dnn",catalogs,totnumgals,totrefgals); fclose(fpphot); fclose(fpstar); fclose(fpout); printf("Total number of EROs: %dnn",erotot); printf("Not in Brodwin's nonstar file: %ld Outside Bootes region: %ld Star flag or z=0: %ld Bad photz flag: %ldnn",starcount,merp,merp2,merp3,merp4); printf("Galaxies (excluded from totnumgals count) that didn't meet the standard min. luminosity threshold: %dnn",belowthresh); to file 'cateric' with totnumgals as a header.nn"); fp=fopen("junk","r"); fpout=fopen("cateric","w");/Theoutputcatalogfile,withalldesiredinfo/ galaxiesnn",totnumgals);/Headerlinefor"cateric"file/ %lf %lf %d %lf %d %d %d %lfnn",&gals[0],&gals[1],&gals[2],&sed,&gals[3],&galref,&nonmask,&ero,&maxang); fprintf(fpout,"%lf %lf %lf %d %lf %d %d %d %lfnn",gals[0],gals[1],gals[2],sed,gals[3],galref,nonmask,ero,maxang); completed.nn"); system("rm junk");

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3.7.4 105

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;Itthendeterminestheirdistancesfromthereferencegalaxy,sortsthembythosedistances,andbinsthemaccordingtothenumberofannuli ;usedincorrbrod.c.Finally,itoutputsthefractionofmaskedpointsineachannulus. ;Theprogramalsochecksagridcoveringtheentiresampleareatodeterminewhatoverallfractionoftheareaisunmasked. ;Itshouldberunaftercatalogparse.candbeforecorrbrod.c. ;PartofthecodeisadaptedfromMarkBrodwin'sapplymask2coords.proprogram(email3/29/06),whichcomparescoordinatestotheIRACSS/NDWFS/ ;FLAMEXmaskFITSfiletotestthecoordinates'maskiness.Itismoreversatileandcanbeconsultedforfurtherinformation.Ituses ;proceduresfromtheIDLAstronomyLibrary(online). ;TheFITSfileisquitelargeandmayexceedsomecomputers'RAM.(Need>256MB?) ;Currentspeedtowholeimagepart(4arcsecspacing)is~8mins ;Currentspeedforindivgalspart(4arcsecspacing)is36refgals/minuteonKashmir(2200/hr) ;Weightcorrbrod.cfittingbinsbyoutputfracs? SPAWN,"date" ;;ReadMaskfile maskfile='/astro/data/manta0/eric/brodwinnew/mask ISS.fits.gz' print,"ReadingMaskFile..." hdr=headfits(maskfile) indx=where(strmid(hdr,0,6)eq'NAXIS1') indy=where(strmid(hdr,0,6)eq'NAXIS2') ximage size=reform(fix(strmid(hdr(indx),15,16))) yimage size=transpose(fix(strmid(hdr(indy),15,16))) cov=readfits(maskfile);;Readfitsfile;cancommentthisoutifalreadyread,sincetakesawhile extast,hdr,astr,noparams;ExtractastrometryfromFITSheader if(noparamsLT0)thenprint,'Problemw/FITSheader.' spacing=4./3600.;Distanceindegreesbetweensamplepoints DEGRAD=!PI/180.D;Usedtoconvertfromdegreestoradians wholeimage=0;Thesedeterminewhichpartsoftheprogramrun;canbeeitherorboth indivgals=1 ifwholeimageeq1thenbegin;Findsmaskdataforentireimage ;TheseareRAandDecboundariesfor3subdivisionsoftheFLAMEXregion;seep.36aandcatalogparse.c minrareg=[216.329167,216.291667,217.729167] maxrareg=[218.820833,219.529167,219.333333] mindecreg=[33.0625,33.641667,34.35] maxdecreg=[33.641667,34.35,34.686944] goodpixall=0L badpixall=0L print,'Samplingentiresurveyareaformasking...' fori=0,2dobegin goodpixalltemp=0L badpixalltemp=0L forstepdec=(mindecreg[i]+spacing/2.),maxdecreg[i],spacingdobegin raspacing=spacing/cos(stepdecDEGRAD) forstepra=(minrareg[i]+spacing/2.),maxrareg[i],raspacingdobegin tempra=stepra tempdec=stepdec ad2xy,tempra,tempdec,astr,x,y outsideimage=0 ifXlt0orXgtXimage sizeorYlt0orYgtYimage sizethenoutsideimage=1 ifoutsideimageeq0then$ ifcov[X,Y]eq0thengoodpixalltemp++$ elsebadpixalltemp++ ifoutsideimageeq1thenprint,"Warning:Imageboundaryexceeded(maskfrac.pro)" endfor endfor SPAWN,"date" print,'DonewithRegion#',i,goodpixalltemp,badpixalltemp,goodpixalltemp/(goodpixalltemp1.+badpixalltemp) goodpixall=goodpixall+goodpixalltemp badpixall=badpixall+badpixalltemp endfor print,'Fractionoffullareawithgood(unmasked)pixels:',goodpixall/(goodpixall1.+badpixall)

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ifindivgalseq1thenbegin;Findsmaskdataforindividualgalaxies ;;ReadCoordFile print,'Determiningmaskingforreferencegalaxies...' print,"ReadingCoordinates..." ANGBINS=100 DOUBLESAMPLE=.07ANGBINS+.01;(Rough)numberofANGBINSinthecenterwhichgetdoublesampled;currently~7% outputfracs=fltarr(angbins) goodpix=lonarr(angbins) badpix=lonarr(angbins) refid=0.0D refra=0.0D refdec=0.0D datafile='/astro/homes/eric/current/cateric' openr,lun,datafile,/GET LUN readf,lun,totnumgals openw,lunout,"/astro/data/manta0/eric/brodwinnew/maskfrac.txt",/GET LUN,WIDTH=10000 stop=0L fori=0L,totnumgals1dobegin readf,lun,refid,refra,refdec,sed,photz,refyes,maskno,eroyes,maxang ifrefyeseq1thenbegin outputfracs=outputfracs0.0 goodpix=goodpix0 badpix=badpix0 ra=refra dec=refdec mindec=refdecmaxangspacing/2. maxdec=refdec+maxang+spacing/1.99 forstepdec=mindec,maxdec,spacingdobegin radist=maxang/cos(stepdecDEGRAD);Adjustmentforcos(Dec)effect raspacing=spacing/cos(stepdecDEGRAD) minra=refraradistraspacing/2. maxra=refra+radist+raspacing/1.99 highdens=0;Usedtoseeifaregionneedshighdensitysampling(i.e.nearthecenter) forstepra=minra,maxra,raspacingdobegin radista=(steprara)cos((stepdec+dec)/2.DEGRAD) galdist=SQRT((stepdecdec)(stepdecdec)+radistaradista) bin=fix(galdist/maxangangbins) ifbinltangbinsthenbegin tempra=stepra tempdec=stepdec ;adxy,hdr,tempra,tempdec,X,Y;;convertcoordstopixelspace;adaptedtousead2xyinsteadforspeed ad2xy,tempra,tempdec,astr,x,y outsideimage=0 ifXlt0orXgtXimage sizeorYlt0orYgtYimage sizethenoutsideimage=1 ifoutsideimageeq0then$ ifcov[X,Y]eq0thengoodpix[bin]++$ elsebadpix[bin]++ ifoutsideimageeq1thenprint,"Warning:Imageboundaryexceeded(maskfrac.pro)" ;Thisparthandlesthedoublesamplingoftheinnerregions ifhighdenseq1thenbegin stepdec=stepdecspacing/2. stepra=stepraraspacing/2. highdens=0 endifelse$ ifbinltDOUBLESAMPLEthenbegin stepra=stepraraspacing/2. stepdec=stepdec+spacing/2. highdens=1 endif endif endfor

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if(stopMOD100)eq0thenprint,stop;Keepstrackof#refgalsconpleted stop=stop+1 outputfracs=goodpix/(goodpix1.+badpix1.) printf,lunout,refid,total(goodpix)/total(goodpix1.+badpix1.) printf,lunout,outputfracs endif if(iMOD1000)eq0thenprint,'Workingoncatericgalaxy#',i endfor FREE LUN,lun FREE LUN,lunout endif print,"Done!" SPAWN,"date" end

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3.7.5 109

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/ItautomatesthedeterminationofcorrelationcoefficientsA&ro/ /Usessmoothintegrationratherthanannulusbinning/ /DeterminesAbasedonafittothecumulativeexpectationsouttovariousdists.,ratherthantheoverallexpectationofgals./ /Omitsgalaxiesfromcorrelationconsiderationiftheirphotoz'sdon'tfallwithinacertainrangeofthereferencegal./ /9/04:RevisedcalculationofA:addeddatapointsforallradii,improvedhandlingofbadpixels/ /12/05:Improvedspeedbyonlysortinggalaxiespredeterminedtobew/inmaxangofreferencegal./ /2/06:RevisedtohandlemaskedregionsinFLAMEXandpartnersurveys/ /3/06:Revisedtousegalsuptoafixedphysical(notangular)distancefromreferencegalaxyforAcoeff.fit/ /ThisisdesignedtoworkwithMarkBrodwin'scatalog,nottheSPICESdata/ /Thisversionusesbinningbyannuliratherthancumulativecircles,useschisqfits,andstillkeepsthe/ /distancevaluesinanarray(ratherthansimplykeepingtrackofhowmanyfallintoeachannulus)/ /6/06:Revisedtousemaskfrac.proformaskingcorrections,basedonactualsamplingofBrodwin'smaskfitsfile./ /Don'tneednonrefgal.infoanymore,butIhaven'tchangedthisyet./ /7/06:AllAvaluesforeachbinaveragedbeforecalculatingr ofromtheaverages.Startingw/v.3.5,onlynewversionsareoutput./ /Theprogramusesthefilescateric(producedbycatalogparse.c)anddistance.txt(producedbydistance.c)/ /Italsousesmaskfrac.txt(producedbymaskfrac.pro)./ /7/06,v.3.5:Introducedbootstraperroranalysisandautomaticbinsizing/ /8/15/06,v.3.5:Implementedimportantfixtoro(z)calculation;f(z)inGonzalezeq.5(butnoteq.6)hasextragammainexponent/ /akaro(z)=ro(1+z)f(z)^(1/gamma)/ /CurrentsetupwillcauseSEDs1718tobeincludedinresults,butthiscanprobablybechangedeasily/ /fracdistmustbechangedtouseotherphysicaldistancelimitsbesides2Mpc/ /Thisdissertationversionisnotfullycleanedupandcommented.Ifyouwouldlikeanupdatedversionoftheprogram,pleasecontactmeat/ /mckerih@aya.yale.edu/ /TouseadifferentLluminositycutfromthedefault,changeINPUTFILEandMASKFRACTIONS/ oinMpc;for0,outputsA;0nolongerwellsupported/ o'sofAnthony'sindividualgalaxyclusterstoOUTPUTFILECLUSTbelow/ ovs.zcomparedtononEROs/

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/Limberinversionvariables/ /NewvariablesusedforannulusapproachtocalculatingA(i.e.notconcentriccircleapproach)/ /Limberinversionvariables/ o(z);seeGonzalezetal.eq.5/ o)^gamma/ unmaskfractot,

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gammaterm;/ThevaluefortheterminvolvingGammafunctionsintheLimberinversion(Gonzalezetal.eq6)/ /UsedwithnewapproachofcombiningtheA'sforabinintoasingleaveragevalue before transformingtor o/ obasedonaverageofallA'sforaredshiftbin,combiningallSEDs/ avgmaxang[ZBINS][SEDBINS]=f0.0g,/Usedwithnewapproachofcombiningeachannulusofallgalaxies/ fixsedbinupper[FIXNUMBINS+1]=f1,2,6,10,18g;/(1and)UpperlimitsofeachSEDrangewhenusingfixedSEDbins(i.e.FLEXBINS=0)/ //fixsedbinupper[FIXNUMBINS+1]=f1,18g;/UsefulforgettingresultscombinedforallSEDsinagivenredshiftbin/ //fixsedbinupper[FIXNUMBINS+1]=f1,18,19g;/Usefulforgettingclustervaluesorcomparingthemwithgalaxies/ ocalculatedusingLimberinversionandAcomputedasavg.ofallAsforthatz+SEDbin/ oforagivencombobin,basedonbootstraptechnique/ FILEfpout,fpoutraw,

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binhandler(void), erohandler(void); main() fscanf(fp,"%d %s",&totnumgals,&header); /Maygetdiscardedifmaskedareaandimageedgetechniquesgetrefined/ /Readsincatericcatalog/ %lf %lf %d %lf %d %d %d %lf",&gals[x][0],&gals[x][1],&gals[x][2],&sed[x],&gals[x][3],&refgal[x],&nonmask[x],&ero[x],&maxang[x]); rejectgals++; ",galsvsz[x]); %dnn",x+1); total nonmasked area in square degrees is: %.2fnn",subarea); printf("# of reference galaxies rejected due to being too close to image boundaries or above z=2.0: %dnn",rejectgals); fscanf(fpdist,"%s %s",&header,&header); fscanf(fpdist,"%lf %lf",&redshift[x],&angdiam[x]);/angdiamistheangulardist.(inkpc/deg.)ateachredshift/ /IntegratesGonzalezetal.equation;z1=zZRANGEandz2=z+ZRANGE/

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gammaterm=gammafn(GAMMA/2.0)/sqrt(PI)/gammafn((GAMMA1.0)/2.0);/DeterminestheGammafunctionterm/ denom=0.0; n1=0; n2=galsvsz[hi2+1]; dndz=n2/10.0/SHIFTBINWIDTH; denom+=n2/10.0;/Dividedby10.0becausethegalsvszbinsizesareafactorof10coarserthanSHIFTBINWIDTH$ distindex2=distindex; w/ distindex. %f %f %dnn",hi,z,distindex); angdist=(angdiam[distindex1]+angdiam[distindex21])/2.0/1000.0;/Averagedandconvertedfromkpc/degtoMpc/deg/ eval=sqrt(OMEGAMpow((1.0+z),3.0)+OMEGAKpow((1.0+z),2.0)+OMEGALAMBDA); numer+=pow(dndz,2.0)evalpow(angdist,(1.0GAMMA))fz(1.0+z)SHIFTBINWIDTH; limberval=(C/HUBBLEgammatermdenom/numer); fprintf(fplimber,"%f %fnn",hi,limberval); redshift2[y++]=hi; limbervalarr[y]=limberval; fplimber=fopen(LIMBERFILE,"r"); fscanf(fplimber,"%lf %lf",&redshift2[y],&limbervalarr[y]); fclose(fplimber); fp=fopen(OUTPUTBROD,"w"); fpmask=fopen(MASKFRACTIONS,"r"); fperr=fopen(ERRORFILE,"w"); fprintf(fpclust,"%5s %9s %11s %13s %9s %8s %14snn","ID","RA","Dec","Photoz","Acoeff","r o","n%Unmasked"); on object #%dnn",x);

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%lf",&maskid,&unmaskfractot); maskfile ID %f doesn't match cateric ID %fnn",maskid,gals[x][0]); galdistbins[y]=0; galdistbins[0]=1;/Referencegalaxywillbecountedinnearestannulus;thistakesthatintoaccount/ /Determinestheangulardistancetoeachgalaxy;optimizedforcatalogsortedbyDecl./ galdens=0.0; /Keepstrackof#galswithinZRANGE,usefulforfindingavg.galdensityforang.corr./ galdens+=1.0; galindex++; galdens+=1.0; galdist=sqrt(pow(radist,2.0)+pow((gals[x][2]gals[galindex][2]),2.0)); galdistbins[binindex]++; galids[goodgals]=galindex; galdists[goodgals]=galdist; goodgals++; ALERT1! %dnn",x); /Skimsthroughlastpartofcatalog,wheredeclinationvaluesaregreaterthanreferencegal'srange/

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galdens+=1.0; galindex++; neargals=0.0; galindex2=0; /Finds#galswithinfracdist&ZRANGE/ neargals+=1.0; unmaskedgals2++; galindex2++; ALERT2! %dnn",x); afunc[1]=pow(lfitx[i],(GAMMA21.0)); ym=lfity[i]a[0]afunc[0]; sig2i=1.0/pow(sig[i],2.0); wt=afunc[1]sig2i; covar[0][0]+=wtafunc[1]; beta[0][0]+=ymwt;

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covar[0][0]=pivinv; beta[0][0]=pivinv; a[1]=beta[0][0]; chisq=0.0; afunc[1]=pow(lfitx[i],(GAMMA21.0)); sum+=a[j]afunc[j]; chisq+=pow((lfity[i]sum)/sig[i],2.0); covar[0][0]=0.0; blah=PIgaldenspow(maxang[x],2.0); hi=PIgaldens(pow(maxang[x],2.0)+2.0/GAMMA2pow(maxang[x],GAMMA2)gals[x][4]); No galaxies found related to Galaxy %d ",x+1); fprintf(fperr,"%d Redshift: %.2f RA: %.2f Dec: %.2f ",x+1,gals[x][3],gals[x][1],gals[x][2]); fprintf(fperr,"Unmaskfractot: %.2f SED type: %d A coeff.: %fnn",unmaskfractot,sed[x],gals[x][4]); fprintf(fpclust,"%f %10f %10f %10f %10f %10f %10fnn",gals[x][0],gals[x][1],gals[x][2],gals[x][3],gals[x][4],physdist,dataquality); fprintf(fp,"%f %f %f %f %f %f %d %f %dnn",gals[x][0],neargals,gals[x][4],physdist,dataquality,nearneigh,sed[x],gals[x][3],ero[x]); zbina[ztype]+=gals[x][4]unmaskfractot; zbinavgz[ztype]+=gals[x][3]unmaskfractot; avgmaxang[ztype][sed[x]]+=maxang[x]unmaskfractot; avgdataqual[ztype][sed[x]]+=dataquality; g fclose(fperr); fclose(fpmask); fclose(fp); totnumgals=rejectgals; printf("# of reference galaxies rejected for the above reason or for masking problems: %dnn",rejectgals); printf("# of reference galaxies outside current min and max redshift limits (but included in totnumgals): %dnn",testz); finaltotgals=0; finalunmaskgals=0.0; fprintf(fpsave,"zbinunmaskgals: ");/Labelforsaveddata/ avgdataqual[x][hi2]/=galcounter[x][hi2];/Getstheaveragefractionofunmaskedarea/

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",zbinunmaskgals[x]);/Savedincasethispartofthecodedoesn'tneedtobererun/ %d",totnumgals); close(fpsave); // /ThisnewsectionidentifiestheflexibleSEDbinstobeusedforplotting/ fpsave=fopen(SAVEFILE,"r"); fscanf(fpsave,"%s",header2); printf("%s ",header2); printf("%lf ",zbinunmaskgals[y]); fscanf(fpsave,"%s %ld",header2,&totnumgals); printf("%s %dnn",header2,totnumgals); /ReadsinsavedLimbertransformations/ fplimber=fopen(LIMBERFILE,"r"); fscanf(fplimber,"%lf %lf",&redshift2[y],&limbervalarr[y]); fclose(fplimber); besttotdev+=pow(deviation,2.0);/Canexperimentwith1.0,etc.;2.0willreallyhurtBINSIZESthatcausebigleftovers/ totdev+=pow(deviation,2.0);/Canexperimentwith1.0,etc.;2.0willreallyhurtBINSIZESthatcausebigleftovers/ besttotdev=totdev;

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best bin size is %d unmasked galaxies. Residuals: ",bestbin); printf("%f ",deviation);/Fractionalremainderofgalaxiesateachredshiftrangewhenabinsizeofbestbinisused;lowerisbetter/ number of SED bins for each redshift bin is: "); binfrac=1.0; newbins[x]=(int)(zbinunmaskgals[x]/bestbin+binfrac); printf("%d ",newbins[x]);/ThenumberofSEDbinstobeusedforeachredshiftrange/ than SEDBINS; problem?) "); totbins+=newbins[x]; printf("The number of unmasked galaxies per SED bin for each redshift bin is: "); binsize[x][y]=zbinunmaskgals[x]/newbins[x];/ForFLEXBINS==1,allcomboSEDbinsizesaresameatagivenredshift/ ",binsize[x][0]); fpoutraw35=fopen(OUTPUTFILEPLOT35,"w"); fprintf(fpoutraw35,"%d (Approx. # gals. represented by each data point)nn",bestbin); fprintf(fpoutraw35,"%d (Redshift bins)nn",ZBINS); ",newbins[x]); fprintf(fpoutraw35,"(#sedbins for each redshift bin)nn"); fprintf(fpoutraw35,"AvgSEDntAvgAntStddevAntAvgr ontStddevr ont#galsnn");

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fpoutfixraw35=fopen(OUTPUTFILEPLOTFIXSED35,"w"); fprintf(fpoutfixraw35,"%d %d (Redshift and SED bins)nn",ZBINS,FIXNUMBINS); fprintf(fpoutfixraw35,"%d ",fixsedbinupper[x]); fprintf(fpoutfixraw35,"(0 and upper bounderies of each bin)nn"); fprintf(fpoutfixraw35,"SED boundsntAvgSEDntAvgAntStddevAntAvgr ontStddevr ont#galsnn"); i2=0; %lf %lf %lf %lf %lf %ld %lf %ldnn",&hi,&hi,&avals[i2],&hi,&unmaskvals[i2],&hi,&sedvals[i2],&zvals[i2],&erovals[i2]); g close(fp); finalunmaskgals=0.0; fprintf(fpout35," unmaskindex=zbina[x]=zbinavgz[x]=0.0; i=sedindex=binindexa=finalbinindex=0; zbintotgals[x]=0; zbinunmaskgals[x]=0.0; finalbinunmaskvals[finalbinindex]=unmaskvals[i]; finalbinsedvals[finalbinindex]=sedvals[i]; finalbinzvals[finalbinindex]=zvals[i]; finalbinerovals[finalbinindex]=erovals[i]; finalbinindex++; unmaskindex+=unmaskvals[i]; /UsesaveragedA's;doesn'tusestackedannuliforasingleA,whichistheoreticallypreferablebutdidn'tworkwellatz=0.30.5/ averagesed[x][binindexa]+=finalbinsedvals[j]finalbinunmaskvals[j]; avgdataqual[x][binindexa]+=finalbinunmaskvals[j];

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zbinavgz[x]+=averagez[x][binindexa]; averagea[x][binindexa]/=avgdataqual[x][binindexa];/Finishescomputationofweightedaverages/ averagesed[x][binindexa]/=avgdataqual[x][binindexa]; avgdataqual[x][binindexa]/=finalbinindex; obymultiplyingAwiththeLimberinversionfactor/ avgrnought=pow((averagea[x][binindexa]limbervalarr[y1]),(1.0/GAMMA));/physdisthereisr o/ avgrnought=pow(1.+averagez[x][binindexa],1.(3.+EPSILONGAMMA)/GAMMA);/AppliesGonzalezeq.5toaccountforclust.evol./ but this part of the code assumes that BINA=1; please fix.nn"); bootstraperr[x][binindexa]=bootstrap(finalbinavals,finalbinunmaskvals,finalbinindex); roerror=avgrnought/GAMMAbootstraperr[x][binindexa]/averagea[x][binindexa];/SeeAnthony's7/25/06email/ SED: %5.2f Avg. A coeff.: %8.5f ",averagesed[x][binindexa],averagea[x][binindexa]); fprintf(fpout35,"(+%8.5f) r o based on avg. A: %8.5f (+%8.5f) ",bootstraperr[x][binindexa],avgrnought,roerror); fprintf(fpout35,"# Gals.: %3d (w/ masking %.2f)nn",finalbinindex,finalbinindexavgdataqual[x][binindexa]); %d%d AvgSED: %5.2f ",fixsedbinupper[binindexa]+1,fixsedbinupper[binindexa+1],averagesed[x][binindexa]); fprintf(fpoutfix35,"Avg. A coeff.: %8.5f (+%8.5f) ",averagea[x][binindexa],bootstraperr[x][binindexa]); fprintf(fpoutfix35,"r o based on avg. A: %8.5f (+%8.5f) ",avgrnought,roerror); fprintf(fpoutfix35,"# Gals.: %3d (w/ masking %.2f)nn",finalbinindex,finalbinindexavgdataqual[x][binindexa]); zbintotgals[x]+=finalbinindex; zbinunmaskgals[x]+=((double)finalbinindex)avgdataqual[x][binindexa]; unmaskindex=binsize[x][binindexa]; finalbinindex=0; binindexa++; sedindex++; g obymultiplyingAwiththeLimberinversionfactor/ zbinavgz[x]/=zbinunmaskgals[x]; zbinrnought[x]=pow((zbina[x]limbervalarr[y1]),(1.0/GAMMA));/physdisthereisr o/ zbinrnought[x]=pow(1.+zbinavgz[x],1.(3.+EPSILONGAMMA)/GAMMA);/AppliesGonzalezeq.5toaccountforclusteringevolution/

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fprintf(fpout35,"Total gals: %d (w/ masking %.2f) Overall A: %f Overall r o: %fnn",zbintotgals[x],zbinunmaskgals[x],zbina[x],zbinrnought[x]); galaxies: %d (w/ masking %.2f) Overall A: %f ",zbintotgals[x],zbinunmaskgals[x],zbina[x]); fprintf(fpoutfix35,"Overall r o: %fnn",zbinrnought[x]); galaxies used: %d (w/ masking %.2f)",finaltotgals,finalunmaskgals); fprintf(fpoutraw35,"%d %d (Boundaries for yaxis (r o))",(int)(lowestro+20.)20,(int)(highestro+20.)19);/Usedforplotting/ close(fpoutraw35); galaxies used: %d (w/ masking %.2f)",finaltotgals,finalunmaskgals); fprintf(fpoutfixraw35,"%d %d (Boundaries for yaxis (r o))",(int)(lowestro+20.)20,(int)(highestro+20.)19);/Usedforplotting/ close(fpoutfixraw35); /Adaptedfrombinhandlercode,butprettyconsolidated,possiblybettercommented/ fpsave=fopen(SAVEFILE,"r"); fscanf(fpsave,"%s",header2); fscanf(fpsave,"%s %ld",header2,&totnumgals); /ReadsinsavedLimbertransformations/ fplimber=fopen(LIMBERFILE,"r"); fscanf(fplimber,"%lf %lf",&redshift2[y],&limbervalarr[y]); fclose(fplimber); i2=0; %lf %lf %lf %lf %lf %ld %lf %ldnn",&hi,&hi,&avals[i2],&hi,&unmaskvals[i2],&hi,&sedvals[i2],&zvals[i2],&erovals[i2]); i2;

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close(fp); This part of code assumes that SEDBINS>1nn"); fpoutero=fopen(OUTPUTFILEERO,"w"); fprintf(fpoutero,"Redshift ERO? AvgA StddevA Avgr o Stddevr o #gals #unmaskednn"); zbintotgals[x]=0; zbinunmaskgals[x]=0.0; finalbinunmaskvals[finalbinindex]=unmaskvals[i]; finalbinzvals[finalbinindex]=zvals[i]; finalbinindex++; g avgdataqual[x][binindexa]+=finalbinunmaskvals[j]; avgdataqual[x][binindexa]/=finalbinindex; obymultiplyingAwiththeLimberinversionfactor/ avgrnought=pow((averagea[x][binindexa]limbervalarr[y1]),(1.0/GAMMA));/physdisthereisr o/ avgrnought=pow(1.+averagez[x][binindexa],1.(3.+EPSILONGAMMA)/GAMMA);/AppliesGonzalezeq.5toaccountforclust.evolution/ but this part of the code assumes that BINA=1; please fix.nn"); oforforredshift+SEDbinusingbootstraptechnique/ bootstraperr[x][binindexa]=roerror=0.0; roerror=avgrnought/GAMMAbootstraperr[x][binindexa]/averagea[x][binindexa];/SeeAnthony's7/25/06email/ %d %8.5f %8.5f ",MINZ+(x+0.5)ZBINSIZE,binindexa,averagea[x][binindexa],bootstraperr[x][binindexa]); fprintf(fpoutero,"%8.5f %8.5f %d %.2fnn",avgrnought,roerror,finalbinindex,finalbinindexavgdataqual[x][binindexa]); g %d (Boundaries for yaxis (r o))",(int)(lowestro+20.)20,(int)(highestro+20.)19);/Usedforplotting/ close(fpoutero);

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Input problem in function gammafnnn");/Thisintegrationtechniquenotvalidforn<=0/ integrand+=pow(log(1.0/t),(n1.0))STEP; swap(galids,galdists,left,(left+right)/2); last=left; swap(galids,galdists,++last,i); swap(galids,galdists,left,last); qsort2(galids,galdists,left,last1); qsort2(galids,galdists,last+1,right); temp=galids[i]; temp2=galdists[i]; galids[i]=galids[j]; galdists[i]=galdists[j]; galids[j]=temp; galdists[j]=temp2; MAX+1.0)finalbinindex); problem with bootstrap. %dnn",randnum); avga[ind1]+=finalbinavals[randnum]finalbinunmaskvals[randnum]; totunmask[ind1]+=finalbinunmaskvals[randnum]; totunmask[ind1]/=finalbinindex;/Ideallyshouldusethisinnextsection,butwouldhavetolookuphow;prob.veryminoreffect/

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meanavga+=avga[ind1]; meanavga/=BOOTSTRAPNUM; sumdev+=pow((avga[ind1]meanavga),2.0); stddev=sqrt(sumdev/(BOOTSTRAPNUM1));

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4.2 .Itisarrangedbyclusternameandincludesallclusterswhosenamesbeginwith`A'or`B'. D.1 AlessiWEBDAhas13Alessiclusterswithlistedageparameters,whileDAML02has19.ThreeofWEBDA'sentries(Alessi6,9and13)donotappearintheDAML02list;Alessi6wasremovedfromDAML02becauseitwasfoundtobeanasterism.(Alessi9and13arecontainedinthemainDAML02catalog,buttheydonothavelistedages.)Alessi24,31,33,34,37,40,43,and44arelistedinDAML02,butnotinWEBDA;however,thisissimplytheresultofadierentnamingconvention,asmentionedabove,andtheycorrespondtoASCCclustersinWEBDA.Inallcases,WEBDA'sagesaretakenfromtheKharchenkoetal.(2005)study.DAML02usesacombinationofagesfromAlessietal.(2003)(Alessi2,3,5,8,and12)andKharchenkoetal.(2005)(Alessi20,21,24,31,33,34,37,40,43,44,andJ2327+55);thesourceoftheremainingclusters'ages(Alessi1,10,19)isunclear. D.2 Alessi-TeutschAlessi-Teutschclusters(Alessi-Teutsch3,5,7,8,9,11,12)areonlylistedinDAML02,butthisistheresultofadierentnamingconvention,asmentionedabove,andtheycorrespondtoASCCclustersinWEBDA.AlloftheagevaluescomefromKharchenkoetal.(2005). D.3 Andrews-Lind.1,Antalova1,Arp-Mad.2,Aveni-Hunt.1Andrews-Lindsay1,Antalova1,andAveni-Hunter1arepresent(withagevalues)inWEBDA,butnotinDAML02.Andrews-Lindsay1'sreferenceisin 126

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WEBDA'slistof\ClusterParametersfromtheLiterature"(CPLhenceforth),aheterogenousassortmentofstudies,mostlyfromthepastfewyears.WEBDA'svaluesforAntalova1andAveni-Hunter1arefromKharchenkoetal.(2005)(althoughAveni-Hunter1'sagehadatypo).TheageforArp-Madore2islistedinbothWEBDAandDAML02,whichuseavaluederivedbyLyngaratherthanamorerecentstudyintheCPL. D.4 ASCCWEBDAandDAML02have130and109ASCCclusters,respectively;how-ever,thedierenceisdueonlytodierentnamingconventions;21oftheclusterswerepreviouslydiscovered,asnotedabove.TheagevaluesareidenticalinbothcatalogsandarealltakenfromKharchenkoetal.(2005) D.5 BaselWEBDAandDAML02have15Baselclusterswithageparameters,andthevaluesallmatch.TheyaretakenfromagesderivedbyLynga,eventhoughsixoftheclusterswerestudiedbyKharchenkoetal.(2005). D.6 BerkeleyWEBDAandDAML02have55and51Berkeleyclusters,respectively.Sevenclusters(Berkeley4,15,25,42,57,71,and75)haveagelistingsinWEBDAbutnotDAML02.Berkeley4'svalueisfromKharchenkoetal.2005,andthevaluesforBerkeley25and75comefromtheCPL.TheagesforBerkeley15and71arederivedfromLyngadespitearecentCPLstudy.Berkeley42isontheDAML02listofremovedclusters,whereitislistedasaglobularclusterinsteadofanopencluster.Berkeley57isaduplicateofNGC7423andisrenamedassuchinDAML02.(NGC7423isnotlistedinWEBDA.)Threeclusters(Berkeley24,35,and78)haveagelistingsinDAML02butnotWEBDA;thesearefromarecentpreprintbyOrtolani(notlistedonastro-ph).

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Ofthe45clusterswithagelistingsinbothcatalogs,39havematchingvalues.WEBDA'sCPLgivesthereferencesformostofthem,althoughtherearesomeinstanceswheretwoorthreestudieshaveestimatedagesforagivencluster(Berkeley17,18,20,23,32,33,34,36,54,58,60,and73).Inthesecases,itisnotentirelyclearwhyWEBDAchoseaparticularstudy'svaluetobethebestestimateforinclusioninthemainlist.Themostrecentstudiesarenotnecessarilypreferred,andwhilestudiesthatinvolvedmorestarstendedtoprevail,thisisnotacompletelyreliableheuristic.TheagesforBerkeley31,39,62,65,82,86,87,94,and96aretakenfromLoktinetal.(2000),overridingmorerecentCPLvaluesinsomecases.Berkeley19'sageistakenfromtheoriginalLyngacatalog,Berkeley30'sagewasderivedbyLynga,andBerkeley59'sageistakenfromKharchenkoetal.(2005).Berkeley21'sageistakenfromarecentstudywhichappearstobeinadvertentlyomittedfromtheCPL.ThesourceofBerkeley70'sageisunclear.OfthesixclusterswhosevaluesinWEBDAandDAML02diered,two(Berkeley17and80)weretyposinDAML02;thevaluesarefromtheCPL.Fortheotherfourclusters'ages,WEBDAusesoldersources:Loktinetal.(2001)forBerkeley11and22,avaluederivedbyLyngaforBerkeley12,andaCPLpaperfrom1996forBerkeley66.Incontrast,DAML02usesCPLpapersfrom2002(Berkeley11and12)and2005(Berkeley22and66). D.7 vandenBergh-Hagen(akavdBergh-HagenorBH)13clustershaveagevaluesinWEBDAbutnotinDAML02.ForBH34,56,91,111,164,205,and221,thevaluescomefromKharchenkoetal.(2005).BH87and132havevaluesderivedbyLynga,whiletheagesofBH217and222arefromtheCPL.BH121wasremovedfromDAML02(althoughitisnotintheirlistofremovedclusters)asaduplicateofIC2944.(WEBDAhasentriesfor\both"clusters.)BH223'sageparameterinWEBDAisanerroneousduplicateofthevalueforBH222.

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Ofthesevenclusterswithagelistingsinbothcatalogs,sixhavematchingvalues.AgesforBH66,144,222,and245comefromtheCPL,andthoseforBH90and99aretakenfromLoktinetal.(2001).WEDBAandDAML02havedierentvaluesforBH23;WEBDA'sageisfromKharchenkoetal.(2005)andDAML02'svalueisfromDiasetal.(2002). D.8 Bica1-4,Biurakan1-2,Blanco1,Briceno1Bica1-4andBriceno1arelistedinDAML02butnotinWEBDA;theyarerecentdiscoveriesdocumentedin2003-2005papersbythediscoverers.Biurakan1hasanagelistinginWEBDAbutnotDAML02,takenfromKharchenkoetal.(2005).Biurakan2andBlanco1havematchingagevaluesinbothcatalogs,takenfromLoktinetal.(2001). D.9 BochumWEBDAandDAML02have13Bochumclusterswithageparameters,andthevaluesfor12ofthemmatch.TheagesforBochum2,4,10,11,13,14,and15comefromLoktinetal.(2001),thoseforBochum3,5,and12werederivedbyLynga,andtheCPLprovidedagesforBochum6and7.Bochum1haddierentagelistingsinWEBDAandDAML02;DAML02usestheLoktinetal.(2001)value,whileWEBDAusesamorerecentCPLvalue.

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IwasborninMoscow,Idaho,andgrewupinSanAntonio,Texas,withmymotherandthreeyoungerhalf-siblings.Myinterestinastronomystemmedfromaveryearlyageandwasfosteredbymymother,enthusiasticteachers,andthelocalplanetariumatSanAntonioCollege.IcanrememberaskingmymomtopretendthatIwassixyearsoldsothatIcouldattendtheadultplanetariumshows.Thosewerethe\good"ones,dealingwithcosmicquestionslikethenatureofblackholes,thelivesanddeathsofstars,andtheoriginandfateofthecosmos.IattendedYaleUniversityandexploredastronomyasanoption(alongwithcomputerscience,psychology,andhistory).Ididnotputenoughtimeintotheadvancedphysicsclassesandgraduatedin1995withadegreeinhistory,butIremainedatYaleforanadditionalthree-and-a-halfyearsworkingatmybelovedlibrary,spendingtimewithclosefriends,andparticipatinginmedicalexperimentstohelppayforpart-timephysicsclasses.ItwasanidyllictimethatIrememberfondly.Althoughstillnoteasy,thephysicsclassesweremuchmoremanageablewhentakenonlyoneortwoatatime.Dr.BradleySchaeferkindlytookthetimetoassistmeingainingresearchexperienceandinpublishingarst-authorpaper.In1999,IcametotheUniversityofFloridaforgraduateschoolinastronomy,whereIhavehadtheopportunitytolearn,performhigh-caliberresearch,andmakefriendswithawonderfulgroupofgraduatestudents.IwasalsogiventhechancetohelpcoordinatethePublicNightopenhousesattheCampusTeachingObservatoryforfouryears,whichItrulyenjoyed;itwasawayformetoreturnwhatIwasgivenbytheSACplanetariumsolongago.MylifehasbeenenrichedbothprofessionallyandpersonallybythepeoplewhomIhavemethere.Iwillbe 138

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sorrytoleave,butIwishthemallwell,andIlookforwardtowhateverthefuturemayholdforme.


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Title: Dependence of Galaxy Stellar Populations on Density at z=0.3-1.5
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0016022:00001


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Table of Contents
    Title Page
        Page i
        Page ii
    Dedication
        Page iii
    Acknowledgement
        Page iv
    Table of Contents
        Page v
        Page vi
        Page vii
    List of Tables
        Page viii
    List of Figures
        Page ix
        Page x
    Abstract
        Page xi
        Page xii
    Introduction to the density-morphology and density-sed relations
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
    The density-sed relation for spices galaxies
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
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        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
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        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
    Density-sed relation for flamex galaxies
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
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        Page 60
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        Page 63
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        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
    Age distribution of open clusters
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
    Appendix A: Catalogparse.c
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
    Appendix B: Maskfrac.pro
        Page 105
        Page 106
        Page 107
        Page 108
    Appendix C: Corrbrod.c
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
    Appendix D: Open cluster catalog comparison
        Page 126
        Page 127
        Page 128
        Page 129
    References
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
        Page 137
    Biographical sketch
        Page 138
        Page 139
Full Text











DEPENDENCE OF GALAXY STELLAR POPULATIONS
ON DENSITY AT z 0.3-1.5















By

ERIC HOWIE MCKENZIE


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006

































Copyright 2006

by

Eric Howie McKenzie
















I dedicate this work to Dr. Richard Elston, whose spirit is missed by all who

knew him.















ACKNOWLEDGMENTS

I wish to thank all the people who have made this work possible, including

my family, friends, teachers, and colleagues. In particular, I would like to thank

Bradley Schaefer for taking the time to guide me through my first research pro-

gram, help me publish my first paper, and create an opportunity for me to attend

graduate school in astronomy, all with very little return for himself. I am also

deeply grateful to Richard Elston, who took me on as his graduate student and

provided the inspiration for this project, and whose infectious enthusiasm and

heartfelt laughter will stay with me forever. I owe a great debt of gratitude to

Anthony Gonzalez for picking me up when my research had wandered badly -l i ,i,

and setting me back on the true path of science, and for his heroic efforts to ensure

a steady flow of research assistant funding, but most of all for his amazing qualities

as a person and a friend.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... ...... iv

LIST OF TABLES ................... .......... viii

LIST OF FIGURES ..................... ......... ix

ABSTRACT .............................. ..... xi

CHAPTER

1 INTRODUCTION TO THE DENSITY-MORPHOLOGY AND DENSITY-
SED RELATIONS ............................. 1

1.1 Basic Description ........................... 1
1.2 Local Measurements .......... .............. 3
1.3 What Causes the Relations? ......... ........ ... 4
1.4 Extending Study to High Redshifts ........ ......... 6
1.5 Sum m ary ..... ...................... 10

2 THE DENSITY-SED RELATION FOR SPICES GALAXIES ...... 12

2.1 Introduction ................... ........ 12
2.1.1 An Alternative to the D -iili ,-M-.rphology Relation .... 12
2.1.2 SPICES as a Prototype ............ .. .. .. 13
2.2 Observations. .................. .......... .. 13
2.3 Density Measurements .................. .... .. 14
2.3.1 Basic Overview .................. .... .. 14
2.3.2 Star-Galaxy Separation ............ .. .. .. 15
2.3.3 Photometric Redshifts ....... . . 18
2.3.4 Two-Point Angular Correlation Function: Overview . 22
2.3.5 Two-Point Angular Correlation Function: SPICES Calcu-
lations ...... ... .. .. .. ....... 25
2.3.6 Translating to the Spatial Correlation Function ...... 26
2.4 Galaxy SED Measurements ................ ...... 30
2.4.1 Overview of Photometric Technique . . 30
2.4.2 Visual Morphologies: Description and Consistency C('! 1:- 31
2.4.3 Comparisons of Connolly's Results to Visual Morphologies 36
2.5 Results .................. .............. .. 39









3 DENSITY-SED RELATION FOR FLAMEX GALAXIES ....... 44

3.1 Introduction ................... ....... 44
3.2 The FLAMINGOS Instrument ......... ........... 45
3.3 Survey and Program Design ........ ......... .... 46
3.4 Data Acquisition ................... .... 47
3.5 Data Processing .................. ......... .. 49
3.5.1 Initial Processing .................. .. 49
3.5.2 Darks and Flats .................. ... .. 49
3.5.3 Sky Subtraction .................. ... .. 50
3.5.4 Alignment and Stacking ............. .. .. 51
3.5.5 Combining Data from Multiple Nights . . .... 51
3.5.6 Astrometry and Photometry ................ .. 51
3.6 The Catalog ....... ...... ...... 52
3.7 Calculating the Spatial Correlation Function . . ... 53
3.7.1 Mathematical Overview .................. .. 53
3.7.2 Photometric Redshifts and SED Classifications ...... ..56
3.7.3 The Final Catalog: catalogparse.c . . 57
3.7.4 Masking Information: maskfrac.pro . . 62
3.7.5 A and ro Calculations: corrbrod.c ..... . . 63
3.8 Results ...... ............... ............. 65
3.8.1 Evolution of the SED-Density Relation . ... 65
3.8.2 Evolution of the ERO-Density Relation . .... 70
3.8.3 Galaxy Clusters ......... ...... 73
3.9 Discussion and Conclusions .................. ..... 75
3.10 Future W ork .................. ......... .. .. 76

4 AGE DISTRIBUTION OF OPEN CLUSTERS . . ...... 78

4.1 Introduction .............. . . ...... 78
4.2 Comparison of Cluster Catalogs .................. .. 78
4.3 Sample Construction .................. ... .. .. 80
4.4 Sample Overview: Ages and Locations .............. .. 81
4.5 Selection Effects ............... ........ 83
4.6 Fitting the Age Distribution ................ .... 87
4.7 Discussion ............... ..... 93

APPENDIX

A CATALOGPARSE.C .................. .......... .. 99

B MASKFRAC.PRO .................. . ..... 105

C CORRBROD.C .................. ....... ....... 109









D OPEN CLUSTER CATALOG COMPARISON ...... ...... 126

D.1 Alessi .................... ........... 126
D.2 Alessi-Teutsch ............... ... ........... 126
D.3 Andrews-Lind. 1, Antalova 1, Arp-Mad. 2, Aveni-Hunt. 1 . 126
D.4 ASCC ................... .. ........ 127
D.5 Basel ................... .. ... ........ 127
D.6 Berkeley .............. .... ........... 127
D.7 van den Bergh-Hagen (aka vdBergh-Hagen or BH) ........ 128
D.8 Bica 1-4, Biurakan 1-2, Blanco 1, Briceno 1 . . ... 129
D.9 Bochum .................. ............. 129

REFERENCES ................. ............... 130

BIOGRAPHICAL SKETCH ............. . . .. 138















LIST OF TABLES
Table page

2-1 SPICES Fields ................... ........ 14

2-2 Star-Galaxy Separation, Success Rates ................. .. 16

2-3 Star-Galaxy Separation, Spectroscopic vs. Photometric Sources ... 17

2-4 Comparison of "Double" Morphology Estimates ............ ..32

2-5 Preliminary Results for Lynx .................. .. 40

3-1 FLAMEX Subregions .................. ........ .. 60

3-2 ERO Spatial ('l-1 i nig Studies .................. ..... 73















LIST OF FIGURES
Figure page

2-1 Comparison of photometric redshifts to spectroscopic redshifts. .... 20

2-2 Redshift error histograms. .................. ..... 21

2-3 K'-band K corrections .................. ....... .. 28

2-4 K'-band evolutionary corrections ................ 29

2-5 Sample of HST images .................. ....... .. 31

2-6 Visual morphology estimates. ................ ..... 33

2-7 Comparison of GIM2D and visual morphology estimates. ...... ..35

2-8 Comparison of estimated SED-types with visual morphologies. . 37

2-9 Redshift distribution of objects with visual morphologies. ...... ..38

2-10 Preliminary results for Lynx .................. .. 39

2-11 Final SPICES results (using Connolly SED-types) .......... .41

2-12 Final SPICES results (using visual morphologies) . . ... 43

3-1 IRAC ch2 apparent magnitude versus redshift ............ ..59

3-2 FLAMEX density-SED results (flexible bins) . . ..... 66

3-3 Overall ro vs. redshift .................. ... ..... 67

3-4 N. .iii, ii. .1 FLAMEX density-SED results (flexible bins) ...... ..68

3-5 FLAMEX density-SED results (fixed bins) .............. ..69

3-6 L > L* density-SED results .................. .. 70

3-7 Histogram of EROs versus Brodwin's SED types . . ... 72

3-8 ERO and non-ERO correlation lengths versus redshift . ... 72

3-9 Cluster ro values versus redshift .................. .. 74

3-10 Cluster ro values versus detection rating ............... ..75

4-1 Number of clusters versus age .................. ..... 82









4-2 Top-down galactic view of clusters ............. .. .. .. 84

4-3 Edge-on galactic view .................. ........ .. 85

4-4 Number of clusters versus age, with fit ................ .. 88

4-5 Overall In regression lines .................. ...... .. 89

4-6 Mid-term In regression .................. ....... .. 94

4-7 Short-term In regression .................. ..... .. 95

4-8 Ln regression line comparison ................ . .96

4-9 (',l-I. observed and fit .................. ..... .. 97















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

DEPENDENCE OF GALAXY STELLAR POPULATIONS
ON DENSITY AT z 0.3-1.5

By

Eric Howie McKenzie

December 2006

C'!I ii: Anthony H. Gonzalez
M i ji Department: Astronomy

I investigate the evolution of galaxy clustering and dependence on environment

by comparing galaxies' spatial correlation lengths with their photometrically-

determined spectral energy distribution (SED) types. This complements work on

the density-morphology relation and expands our understanding of galaxy evolution

at high redshifts (z < 1.5).

I first report on 1141 galaxies from the Spectroscopic Photometric Infrared-

C(!..-. i Extragalactic Survey (SPICES). The SPICES spectroscopy is used to

judge the effectiveness of photometric star-galaxy separation and redshifts. Hubble

Space Telescope imaging provides visual morphologies of the galaxies for comparing

the density-morphology relation to the density-SED relation. Spatial correlation

function amplitudes are determined for each galaxy individually, as are SED-types

based on spectral template fitting, and the two are compared to produce a density-

SED relation. As expected from the density-morphology relation, galaxies with

early SED-types are shown to be substantially more prevalent than galaxies with

late SED-types in high density regions.









I then report on 41,837 galaxies from the FLAMINGOS Extragalactic Survey

(FLAMEX), extending the techniques developed in the SPICES survey to examine

the density-SED relation and its redshift dependence for a much larger sample. The

results indicate that the density-SED relation is already established by z = 1.5,

with no substantive evolution between that epoch to the present, and that the

relation is in place prior to cluster assembly. I also investigate how clustering differs

for extremely red objects (EROs) versus non-ERO galaxies and for L > L* versus

L > .6L* galaxies, and I compare the spatial correlation lengths for specific clusters

to the cluster detection significance.

Finally, I present a separate project on the dissipation rates of open star

clusters within our own galaxy. Studying the age distribution of the complete

sample of 997 clusters for which age values are available, I propose that clusters

are disrupted by at least three different mechanisms acting on different timescales:

a long-term mechanism that produces a cluster half-life of 354 13 million years,

a medium-term mechanism with a cluster half-life of 105 30 million years, and

a short-term mechanism with a cluster half-life of 5.0 .8 million years. I also

estimate that 220 70 clusters are formed per ten million years within our current

limits of observation.















CHAPTER 1
INTRODUCTION TO THE DENSITY-MORPHOLOGY AND DENSITY-SED
RELATIONS

1.1 Basic Description

The question of how galaxies formed and evolved is a subject of much interest

to extragalactic astronomers and .,-I i. .1,1,-ii i-1 Competing theories of monolithic

collapse (Eggen et al. 1962) and hierarchical formation (e.g., Peebles 1974, 1980)

have largely been resolved in favor of the latter, but a disconnect remains between

models and observations. Hierarchical formation models generally predict the

evolution with redshift of massive dark matter halos, which represent the bulk of

the matter in the universe, but the correspondence between these invisible halos

and the galaxies that we actually observe is not typically straightforward. As a

result, observations continue to pl i, a in i.j role in establishing the properties of

galaxies and how they vary with redshift. Two examples of this that I will address

in this dissertation are the morphology of galaxies (spiral, SO, elliptical, etc.) and

their spectral energy distributions (SEDs), and how each of these depends on the

local galaxy density.

We observe galaxies to dwell in regions of widely varying density, from sparse

field environments to massive, dense clusters. Early investigations (e.g., Peebles

1975) used the Lick Observatory data (Shane and Wirtanen 1967) to study the

autocorrelation of galaxies in detail, and Dressier (1980) was the first to identify

the density-morphology relation, wherein the fraction of SO and elliptical galaxies

rises smoothly as the local galaxy density increases. This phenomenon is an

indicator of the importance of environment in galaxy evolution, offering clues to the

mechanisms by which the galaxies evolve into different morphological types. It was









long-argued that the cluster environment is an important factor in quenching star

formation and establishing the density-morphology relation, but in the past decade

there has been a growing belief that "prepro'. -- ii, in the group environment is

more significant. Recent studies have greatly expanded the local-Universe statistics

and pushed the study of the density-morphology relation to z ~ 1, although

limitations in determining morphology at high redshifts have hampered these

efforts.

It is also possible to study a related phenomenon by examining how the

spectral energy distributions of galaxies vary with density. The SEDs are largely a

measure of the stellar population of the galaxies, which reflects the star formation

history. The density-SED relation can be observed with various levels of precision,

including direct spectroscopy, spectral modeling of multiband photometry, or

simple color classification. The latter two approaches are valuable because of the

speed with which the information can be obtained and because of their robustness

compared to morphological estimates at high redshifts. In the local Universe,

there is a close correspondence between galaxy morphologies and galaxy spectral

types (e.g., Kennicutt 1992), although this connection diverges somewhat at higher

redshifts, which itself provides useful information. In parts of this dissertation, I

test this correspondence (Chapter 2) and measure the density-SED relation as a

function of redshift (C'!i plters 2-3).

In all cases, density measurements are sometimes made in terms of surface

density and sometimes in terms of the angular or spatial correlation functions.

The latter are more properly a measure of clustering than of density per se, but

I will subsume all of these techniques under the heading "density measu ,', il -

throughout this dissertation for simplicity.









1.2 Local Measurements

Dressier (1980) performed the first 1i i .ri study of the density-morphology

relation. He investigated the morphology distribution of the galaxies in 55 rich,

nearby clusters, mostly from Abell's catalog (1958). The morphologies varied

smoothly over five magnitudes of estimated space density, from 10' / 11 '. /50'.

spiral/SO/elliptical in thick clumps within the clusters to 11' / :II;./10'. in the

diffuse edges of the clusters, and II,'. /10'./10(' for the field galaxies (isolated

galaxies and loose groups). He noted that this relation appeared to hold regardless

of the differences between the clusters in richness or overall concentration. Postman

and Geller (1984) extended this study to less dense regions, where they found

that the relation leveled off around 711'. /2 '- /10'-. spiral/SO/elliptical. This

independence at low densities is interpreted as applying to regions where the

collapse time tc = 1.43/(Gp)'5 is comparable to or greater than the Hubble time.

Local studies of the density-SED relation find a higher degree of clustering

for quiescent galaxies than for emission-line galaxies (e.g., Loved,-v et al. 1999;

Magdwick et al. 2003). Budavari et al. (2003) uses photometric fits to SED

models and similarly finds galaxies with spectral types comparable to elliptical

galaxies to be more highly clustered than blue galaxies. This is in accordance with

expectations from the density-morphology relation, as it reinforces the common

observation that present-div spiral galaxies are actively forming stars, while

present-div elliptical galaxies are evolving relatively passively.

Studies of the environmental dependence of galaxy color (e.g., Kauffmann et

al. 2003; Balogh et al. 2004) find a red/blue bimodal color distribution that can

be fit by two Gaussian distributions regardless of surface density or luminosity.

This division si.-.-- -I that present-di-v transformations from blue to red galaxies

must take place over a short timescale for both faint and bright galaxies. There is

a strong increase in the fraction of red galaxies with increasing surface density (at









fixed luminosities), from 10-3'i.l in the sparsest regions to ~ 7i' .I in the densest

regions. The mean colors of the blue and red populations show little to no change,

however.

1.3 What Causes the Relations?

The very existence of the density-morphology and density-SED relations, as

well as the continuity of the relations across four orders of magnitude in density,

tells us that environmental factors are fundamental drivers in determining the

present-d-v morphologies and spectral classes. Identifying the specific physical

factors responsible for morphological and spectral evolution has been an important

objective for astrophysicists.

For a time, nature versus nurture debates dominated the discussion in an

attempt to determine whether the key processes took place as the galaxies were

forming (monolithic collapse) or in later interactions between galaxies and other

post-formation evolutionary processes. The latter theory, known as hierarchical

formation, gradually gained ascendance in the 1990s as new observational capabili-

ties lent support to it, and it is now generally accepted. Many models (e.g., Benson

et al. 2001) have successfully matched present-di-v and high-redshift observations

using cold dark matter (CDM) cosmologies and hierarchical formation assumptions

in their initial conditions, correctly predicting variations in galaxy number counts

and luminosity functions, galaxy clustering, etc. as a function of redshift. New

observations also continue to support hierarchical formation, such as discoveries of

recent star-formation in distant early-type galaxies (e.g., Barger et al. 1996; van de

Ven et al. 2003).

There is continued uncertainty about the relative importance of the possible

physical drivers for the density-morphology and density-SED relations. Several

authors (e.g., Toomre 1977; Roos 1981) investigated the possibility that galaxy

mergers could convert spiral galaxies into elliptical galaxies. While the large









velocity dispersions present in clusters preclude efficient merging (e.g., Merritt

1984), the modern view is that cluster ellipticals can be formed in this fashion

via "preprocessiing in lower-dispersion systems such as groups. Gunn and Gott

(1972) identified ram pressure gas stripping as a probable means of converting

spiral galaxies in dense regions to SOs. As galaxies pass through the hot gas of

the intra-cluster medium (IC'\ ), the galaxies' stars are essentially unaffected, but

their own gas clouds are blown out and dispersed. Gas stripping would only be

effective within ~ 250 kpc of the cluster core, where the IC'\ I is densest, and so it

is less effective as an explanation for the SOs observed in low-density environments,

although Larson et al. (1980) -i--.-. -1 that spiral galaxies may be refueled by the

infall from tenuous gas envelopes and that these envelopes may be easily stripped

in tidal interactions between galaxies. Certainly, tidal interactions have pl i, d

some role in establishing the present range of morphologies, whether directly

stripping stars or merely gas.

More recent proposals include galaxy harassment (e.g., Moore et al. 1998), in

which small, newly-infalling disk galaxies in a cluster are disrupted during fly-by

encounters with larger galaxies. This results in starbursts and the transformation

of the galaxy remnants via angular momentum loss into compact galaxies, probably

dwarf spheroidals (dSph). This theory is motivated by the existence of a population

of small, disrupted spiral galaxies in clusters at z > 0.3 but not in present-d iv

clusters.

There is clearly no single physical mechanism that can explain the full Hubble

sequence across varying levels of galaxy density. The next step in enhancing

our understanding of hierarchical formation will be to learn more about the

mechanisms' relative importance and the timescales on which they operate. One

natural means of doing this is by extending our study to higher redshift.









1.4 Extending Study to High Redshifts

Astronomers have studied the density-morphology relation for over two

decades in our galaxy's (comparatively) local neighborhood. What we do not

yet know, though, are the details of the assembly history of massive galaxies, or

how early the density-morphology and density-SED relations were in place. A

considerably broader perspective can be gained by looking to higher redshift and

earlier times in our universe's history. We can observe how the relations have been

changing over billions of years, and this will add a new dimension to the snapshot

evidence we have from our own time.

The density-morphology relation becomes difficult to study at high redshift,

particularly when making an effort to distinguish between elliptical and SO galaxies.

Nevertheless, we find that clusters at intermediate-redshifts (z ~ 0.5) have similar

fractional populations of elliptical galaxies to present-d-, clusters but a much

smaller fraction of SO galaxies (2-3 times fewer), with a correspondingly higher

fraction of spirals, although the relation for irregular clusters is less clear than for

regular, dynamically relaxed clusters (Dressler et al. 1997). The morphological

segregation by density in a broader range of environments is still readily apparent

even out to z ~ 1, with fE+SO (the fraction of elliptical+SO galaxies) remaining

comparable to the present-d-,i fE+so at low and intermediate densities at z ~ 1

and at low densities at z ~ 0.5 (Smith et al., 2005). The authors propose a basic

model in which most elliptical galaxies are formed at high redshift (z > 2), while

SOs are gradually formed by an infalling population of late-type galaxies, although

this conclusion is limited by their inability to visually distinguish E and SO galaxies

at z 1, and the dominant mechanism of SO production remains unclear. Postman

et al. (2005) use the Advanced Camera for Surveys (ACS) on the Hubble Space

Telescope (HST) to enable a distinction between E and SO morphologies (albeit

still with significant uncertainties). Their results are generally in accordance with









Smith et al. (2005), but they tentatively find a higher fraction of SO galaxies and

a lower fraction of Es at z ~ 1, which influences the relative importance of the

candidate processes that produce morphological transformations. In particular,

there would be more room for pairwise mergers of spirals to pl .i a modest role in

the production of elliptical galaxies.

A complementary view for differences in the density-SED relation at inter-

mediate redshifts is given by P......i I1lI et al. (1999). The authors establish a set

of basic SED classifications, including passive/non-star-forming galaxies, galaxies

with comparable SEDs to present-d-v spirals, starburst galaxies, post-starburst

galaxies with little star-formation, and galaxies which could be interpreted either

as post-starburst galaxies with significant star-formation or as dusty starburst

galaxies. They conclude that galaxies infalling into clusters undergo both morpho-

logical and SED transformations, but on different timescales. A significant fraction

of cluster galaxies at z ~ 0.5 have red colors and little star formation but spiral

structure, i .i:. -1 ii-; that the physical processes) responsible for star formation

suppression acts on a faster timescale, by roughly 1 Gyr, than the processes)

responsible for morphological shifts (such as ram-pressure gas stripping shifting

spirals to SOs). The authors also note that there are many more galaxies with

I' .--starburst" SEDs in clusters than in the field, though galaxies with "d(11i-

starburst" SEDs are found in both cluster and field environments. The authors

propose that "post-starburst" and star-forming galaxies in clusters are recently

acquired and have not yet had their star-formation quenched. Other studies (e.g.,

Phleps et al. 2005; Meneux et al. 2006) also shed light on the clustering variations

for different SED-types at intermediate redshifts.

Finally, there are researchers who study this evolutionary process based

on galaxy colors. In addition to being easily measurable, colors exhibit a true

bimodality between red and blue populations, while spectral class and morphologies









occupy a more continuous spectrum. Although they do not focus on density as

such, Bell et al. (2004) study U V galaxy colors and color-mag diagrams across

a broad range of environments at 0.2 < z < 1.1. They find color bimodality at

all redshifts; the blue peak reddens with declining redshift (A(U V) ~ 0.5 from

z ~ 1 to the present di,-), and the number density of bright blue galaxies declines

rapidly, while that of faint blue galaxies remains roughly constant. Red galaxies

follow a "red sequence" along color-magnitude diagrams, and their mean color

reddens with declining redshift (0.3 mag in B from z = 1.1 to z = 0.2). They find

no rest-frame B band evolution in the luminosity function for red sequence galaxies

in this redshift range. This is at odds with a pure passive evolution scenario, in

which the luminosities would have decreased. At all redshifts z < 1, there are few

blue galaxies which are bright enough to passively fade into the bright red-sequence

galaxies seen at present-div-. The combination of the latter two observations

appears to require mergers to produce luminous red galaxies, but the paucity of

luminous blue galaxies requires the blue phase of such mergers to be very short,

which could be caused by either substantial dust levels or gas-poor progenitors.

With models, the authors succeed in reproducing the number densities of red,

blue, and ip' galaxies if the star formation in 5-10' of the blue population is

truncated per Gyr (via some unspecified process) within this redshift range. Faber

et al. (2005) expand this study and include extensive data on the blue galaxy

luminosity function. They confirm a rise in massive red galaxies at a fixed stellar

mass, while the number of massive blue galaxies has remained constant since z = 1.

Basing their argument on the fact that the low-mass progenitors of present-div

massive red galaxies must be visible at z < 1, they argue for a mixed model

that includes both gas-rich mergers of blue galaxies (whose star-formation is then

quenched, pushing them to the red sequence) and a lesser number of later gas-poor

mergers (moving them to brighter stages of the red sequence). At faint luminosities









(Lv < 0.1 LU), Kodama et al. (2001, 2003) locate the color division at a local

density of 30 galaxies Mpc-2, i.e. in the filaments surrounding the cluster that they

studied. Other studies identify significant growth of clustering between 0 < z < 2

(Coil et al. 2004) and a higher early-type fraction among small galaxies but not

large ones at z ~ 0.8 compared to the present dwi (Holden et al., 2006). This latter

phenomenon may be due to the quenching of star-formation, producing early-types,

or to the smaller galaxies fading below the study's fixed luminosity limit by z = 0.

Relevant galaxy evolution research has been done at still higher redshifts. For

example, McCarthy et al. (2004) identify 20 massive, old, red galaxies in a redshift

range of 1.3 < z < 2.2. They estimate the formation redshift of these galaxies to be

zf ~ 4 and find their spectra to be consistent with a single massive star-formation

episode. Another study (van Dokkum et al. 2003) uses a Js Ks > 2.3 cut to

track the "optical break." This method is an infrared counterpart to the Lyman

break technique; it identifies redshifts at z > 2 based on the 3625A Balmer break

and 4000A Ca II H+K break. They spectroscopically verify a small sample of five

galaxies at 2.4 < z < 3.5, with spectra indicative of evolved stellar populations

(older than Lyman break galaxies at comparable redshifts), and they find tentative

indications of significant clustering. Finally, Mobasher et al. (2005) report a J

band dropout galaxy whose SED is consistent with a massive red galaxy at z ~ 6.5,

formed in a short-term starburst at zf ~ 9! If true, then this galaxy would appear

to represent a population formed according to monolithic collapse principles.

However, these papers describe small samples, and the discussions of surface

density in the first two are very susceptible to cosmic variance issues. Depending on

their actual density, the galaxies may represent an extreme population, not widely

representative.









1.5 Summary

Researchers are clearly beginning to establish an overall picture of galaxy

evolution, but there are still many uncertainties regarding the responsible processes

and their respective timescales. There is also some ambiguity in attempting

to establish connections between studies that focus on different redshifts or

are selected in different v--, My project contributes to our understanding by

extending the study of galaxy SED classes (estimated using template spectra and

multiwavelength photometry) and their dependence on density. It follows the

evolution of the density-SED relation with redshift from 0.3 < z < 1.5 and helps

to determine whether the early-type population as a whole was established prior

to cluster formation or whether subsequent evolution in the cluster environment

has significantly altered the galaxy population. I examine 37,494 galaxies from an

infrared-selected survey with photometric information from optical to mid-infrared

wavelengths. The galaxies span both field and cluster environments, and the large

sky coverage of 3.6 deg2 lessens the effects of cosmic variance. I also discuss a

smaller survey used as a prototype for the main project; its followup spectroscopic

information and high-resolution HST imaging are useful in establishing connections

between the information gained from photometry alone (which is all that the larger

survey has) and information gained from higher-precision methods.

The rest of this dissertation is organized as follow. C'! lpter 2 gives an overview

of the prototype survey, discusses my methods for determining density, compares

the followup spectroscopic and HST data with the original photometric data,

and presents basic density-SED results, albeit for a small sample size. Chapter 3

introduces the main survey, including an overview of the data acquisition and

reduction, and then it describes my current algorithm for determining density,

presents the main density-SED relation results, and discusses them in the context

of galaxy evolution. Finally, C'! lpter 4 is a stand-alone project, which examines







11

the age distribution of open clusters within the Milky Way and draws inferences

regarding the timescales of dissipation mechanisms.















CHAPTER 2
THE DENSITY-SED RELATION FOR SPICES GALAXIES

2.1 Introduction

2.1.1 An Alternative to the D(i-il ,-M..-phology Relation

An extensive study of the density-morphology relation at high redshifts re-

quires a number of assumptions and approximations. One problem is that the

spatial density of galaxies cannot be directly ascertained without time-consuming

spectroscopy. Another is that the rest-frame optical morphology of high-redshift

galaxies can only be determined with deep, high-resolution, near-infrared (NIR)

imaging, such as that available with NIC\IOS or adaptive optics on 1n, ii tele-

scopes, and wide-area surveys are not readily achievable. These issues can be

circumvented by instead using multiwavelength photometric observations and

studying the relation between density and stellar population rather than mor-

phology. In place of spatial densities derived from spectroscopic redshifts, I obtain

spatial correlation amplitudes by calculating the two-point angular correlation

function for each galaxy and applying a mathematical inversion. The results offer

imprecise information for a particular galaxy but robust statistics when applied to

a large sample. In place of visual morphologies, I use spectral energy distribution

(SED) models for different galaxy types (E, SO, etc.) and estimations of the closest-

match SED type for each galaxy. This has the advantage over visual morphologies

of being less subjective, and it is also easier to measure at high redshifts. Thus, I

choose to study the -I111 i correlation amplitude-SED type relation," which for

convenience I call the density-SED relation. It is not a direct substitute for the

density-morphology relation, but the two are closely related and represent similar

physical processes.









2.1.2 SPICES as a Prototype

In this project, I use two astronomical survy-1; The Spectroscopic Photometric

Infrared-C'! -. i1 Extragalactic Survey (SPICES), a small, pencil-beam survey that

includes both spectroscopic observations and high resolution photometry, provides

an ideal means of comparing the density-morphology and density-SED relations at

higher redshift. For redshifts and galaxy spectral types, a tradeoff exists between

acquiring precise information for small samples using spectroscopy and lower-

precision data for large samples using multiband imaging. In my main study of the

FLAMINGOS Extragalactic Survey (FLAMEX, discussed in C'!i Ilter 3), I employ

the latter approach, using photometric redshifts and SED types derived from

multiband photometry to quantify the density-SED relation for a large statistical

galaxy sample.

Prior to the FLAMEX study, however, SPICES provides an important test

of the concepts that are used in the larger study. An important aspect of SPICES

is that it has both followup spectroscopy and Hubble Space Telescope (HST)

imaging. As a result, the accuracy and precision of the photometric techniques can

be estimated, and they become a better-understood quantity when working with

surveys that are based on photometry alone (such as FLAMEX).

The observations for the SPICES program are described in Section 2.2.

In Section 2.3, I present the details of the density measurements, including a

comparison of the photometric and spectroscopic redshifts. I then compare the

SED-types from the photometric redshifts with HST visual morphologies in

Section 2.4, before presenting the density-morphology and density-SED results and

conclusions in Section 2.5.

2.2 Observations

SPICES observations were taken in B, R, I, z, J, and K' bands at the Kitt

Peak National Observatory's 4-meter telescope during 1997, using the Infrared









Imager (IRIM). The photometric cutoff employ' ,1 in this study is K' < 20.0 (Vega),

with 1471 sources detected by SExtractor at the 10 level in 3" apertures. The

survey team took followup spectroscopic observations of roughly half these sources

between 1997 and 2001, which were used both to eliminate stars and to estimate

the errors of our photometric redshifts.

The survey consists of four fields in different regions of the sky with a com-

bined area of 105 arcmin2. Table 2-1 lists the basic data for the fields. The

photometric source count includes some objects which were not used in the cor-

relation analysis: probable stars, objects with Zphot > 2.0, and sources with K

MAGERR_AUTO RMS > 0.5. The sixth and seventh columns separate the sources

studied with followup spectroscopy into galaxies and stars. A small percentage

of these sources and the HST sources are excluded from the photometric source

count due to faintness or location outside the trimmed SPICES image boundaries.

The plate scales for the K' images are .471 arcsec/pix after rebinning (to match

the optical CCD's plate scale) for all fields except Pisces, whose plate scale is .420

arcsec/pix.

Table 2-1: SPICES Fields
Area Photom. Spectr. Spectr. HST
Field RA (B1950) Dec (B1950) (arcmin2) Sources Gals. Stars Sources
Cetus 02:59:00 +00:12:20 24.0 329 180 23 224
Lynx 08:45:22 +45:05:25 25.7 421 242 50 230
Pisces 23:10:25 +00:41:22 25.0 370 203 47 277
SA57 13:07:04.1 +29:36:16.5 30.2 346 18 0 270

2.3 Density Measurements

2.3.1 Basic Overview

To determine the density-SED relation, it was necessary to assign a value

to each SPICES galaxy representing the local density of neighboring galaxies. I

chose to use the amplitude of the spatial correlation function as estimated from

an inversion of the two-point angular correlation function. The following is a

description of these calculations, as well as of the related issues of star-galaxy









separation and photometric redshifts. SPICES' spectroscopic data are an important

tool for the latter two topics. Section 2.3.2 discusses star-galaxy separation,

describing two different photometric methods of identifying which sources are

true galaxies and which are merely foreground stars; it also presents tests of

the effectiveness of these two approaches using the spectroscopic SPICES data

for comparison. Section 2.3.3 provides an overview of the photometric redshifts

determined for the galaxies, with spectroscopic tests of their accuracy. Section 2.3.4

gives a mathematical overview of the two-point angular correlation function, which

is directly observable, and Section 2.3.5 provides details of its calculation for the

SPICES galaxies. Section 2.3.6 covers the two-point spatial correlation function,

which is inferred from the angular correlation function and photometric redshift

information and requires various corrections to place all galaxies on an equal

footing.

2.3.2 Star-Galaxy Separation

To optimize the galaxy density measurements, we must remove stars from the

source catalog. In order to remove the stars based upon photometric information

alone, we considered two approaches: selection based on SExtractor's neural

network object classification (the CLASSSTAR parameter) and selection based

on color (B I vs. I K'). SExtractor produces a value ranging between 0

(galaxy) and 1 (star) based on the point-spread function (PSF); objects > 0.95

are commonly considered to be stars in most applications, although the method

generally works better at brighter magnitudes. The color selections were based

on a double cutoff. For each object's I K' color, its B I had to exceed

2.974 (I K') + 0.056 and 1.469 (I K') + 1.200 to be classified as a galaxy.

To test the effectiveness of these techniques, we compared their results to the

information gained from spectroscopic followup for the Cetus, Lynx, and Pisces

fields, summarized in Table 2-2. SA57 is omitted due to its paucity of spectroscopy.









Table 2-2: --Galaxy Separation, Success : .:. ;
Color Separation .: Separation r : Separation
: Galaxy G > 0.95 G > 0.90 S > 0.95 S > 0.90
Cotlus 180/180 20/23 6/180 11/180 11/23 15/23
Lynx 230/241 35/45 0/241 1/241 13/45 16/45
Pisces 200/203 32/47 2/ :: 4/203 30/47 30/47

The two columns for color separation represent the type of object as verified

by spectroscopy, with the table entries showing the fraction of correct identifica-

tions by color alone. The profile separation columns present the fractions of verified

objects with high CLASSSTAR values; I tested two different cutoffs and found

that a less-rigorous value (0.90) correctly identifies more stars, but that there is

a concommittant increase in mistakes for galaxies. The color separation is more

effective than SExtractor's PSF classification, correctly identifying '. of the

galaxies and 7.' of the stars, although a combination of the two techniques proves

to be useful.

A detailed investigation of the cases where the separation methods fail reveals

a strong dependence on magnitude. For color separation, many of the stars

mistakenly identified as galaxies are very bright. For the three fields combined,

15/21 stars are incorrectly classified at K' < 15.5, compared to 5/59 at 15.5 <

K' < 18.5 and 8/35 at 18.5 < K'. Fortunately, the mistakes at K' < 15.5 all have

CLASSSTAR values > 0.95. Note also the slight dropoff in effectiveness at fainter

magnitudes. Galaxies were identified with greater accuracy at brighter magnitudes:

only 3/289 were identified as stars at K' < 18.5, compared to 11/338 at 18.5 < K'.

SExtractor's PSF classification is somewhat useful for bright objects. Bright

stars in particular are identified fairly consistently, and galaxies seldom have

CLASS_STAR values > 0.95. CLASS_STAR becomes relatively useless at faint

magnitudes, however, due to the low signal-to-noise ratios; for K' > 18.5, none of

35 stars have a value > 0.95 and only one has a value > 0.90. More generally, the

stars' values cannot be distinguished from those of the galaxies.










For the three fields combined, the best separation algorithm for our pur-

poses is to remove objects classified as stars by color separation and objects

with CLASSSTAR values > 0.95. Applying this algorithm to our objects with

spectroscopic information wrongly includes 11/115 stars and wrongly excludes

14/624 galaxies from our full catalog, or 11/113 stars and 8/583 galaxies from our

K' < 20.0 catalog.

One final issue is the extent to which these experiments are representative

of fainter objects, since the percentage of objects with spectroscopic information

declines at K' > 18.5. Ii' of the K' < 18.5 photometric sources in Cetus, Lynx,

and Pisces have spectroscopy, compared with 3 :;' for 18.5 < K' < 20 (and 2'. for

20 < K' < 21.5). It is possible that the selection criteria for spectroscopic followups

biases the results. To attempt to assess this, we examined the sources without

spectroscopy to determine whether they had roughly the same fractions of galaxies

and stars according to the separators as the sources with spectroscopy.

Table 2-3: Star-Galaxy Separation, Spectroscopic vs. Photometric Sources


Field Mag. Range
Cetus 18.5 < K'

18.5 < K' < 20

20 < K'

Lynx 18.5 < K'

18.5 < K' < 20

20 < K'

Pisces 18.5 < K'

18.5 < K' < 20

20 < K'


Phot./Spec.
Phot.
Spec.
Phot.
Spec.
Phot.
Spec.
Phot.
Spec.
Phot.
Spec.
Phot.
Spec.
Phot.
Spec.
Phot.
Spec.
Phot.
Spec.


Color star Profile (> .95)


10/60 (17%)
11/93 (1.".)
21/181 (1" .)
9/104 (* .)
35/293 (1_".)
0/6 (,'.)
7/38 (1' .)
28/155 (1.' .)
30/279 (11%)
18/122 (15%)
103/736 (1 i'.)
5/15 ( ; ;' .)
8/58 (1 .)
24/118 (.-_'i .)
44/283 (11.'.)
8/109 (7'.)
276/1259 (2' .)
3/23 (1 .)


6/60 (11,'.)
17/93 (1' .)
0/181 (i' .)
0/104 (i' .)
0/293 (I' .)
0/6 (1,'.)
2/38 (5%)
13/155 (>' .)
2/279 (1%)
0/122 (I, .)
0/736 (I' .)
0/15 (i' .)
5/58 (*' .)
32/118 ('7' .)
1/283 (, '.)
0/109 (i' .)
0/1259 (I' .)
0/23 (,I'.)


Profile (> .90)
11/60 (1.' .)
24/93 (_'.' .)
1/181 (1%)
2/104 (_".)
0/293 ( .)
0/6 (,i.)
3/38 ('.)
17/155 (11%)
4/279 (1. i'.)
0/122 (,i'.)
0/736 ( .)
0/15 (,i .)
6/58 (11,'.)
34/118 (_"' .)
1/283 (, '.)
0/109 (Ii .)
0/1259 ( .)
0/23 (1I'.)


Table 2-3 shows the results for each field, after removing all sources with K

MAGERR_AUTO RMS > 0.5 (generally very faint sources or ones next to the edge









of the image), but retaining faint sources. This cut reduced the total sources from

794 to 737 in Cetus, from 1505 to 1345 in Lynx, and from 1957 to 1850 in Pisces.

Most of these (those with 20 < K') were not used in the correlation study, but they

are included here as a matter of general interest for future work involving galaxy-

star separation. The table entries show the fractions of objects identified as stars

by three different selection methods: selection by color and SExtractor's profile

selection (using CLASS_STAR > .95 and the less-strict CLASS_STAR > .90). It

compares these fractions for sources with spectroscopy to the fractions for sources

with photometry only. The fractions are broadly similar, at least for Cetus and

Lynx, sl.--. -ii- i;- that the selection criteria for choosing sources for spectroscopic

followup did not significantly bias the above investigations.

2.3.3 Photometric Redshifts

SPICES was useful as a prototype and testing ground for the techniques that

I later employ on the much larger FLAMINGOS survey in C'! lpter 3. The most

important of these techniques is the use of photometric methods to simultaneously

determine redshifts and SED-types. The SPICES survey benefits from imaging

in six optical and near-infrared (near-IR) passbands, making it possible to track

in, I i spectral features like the 4000A break across a range of redshifts. One com-

mon approach is to use a large training set of galaxies with known (spectroscopic)

redshifts, find the colors which best correspond to each redshift and morpholog-

ical type, and then fit all photometrically observed galaxies to those colors via

interpolation. An alternative approach is to create entire SEDs from models or

thorough observations of local galaxies, and then use the SEDs to predict the colors

corresponding to various redshifts and morphologies. Our group melds the two

approaches using the methods of Budavari et al. (2000), starting with SEDs but

using an arbitrarily large training set of galaxies with spectroscopic redshifts to

improve the SEDs so that they can better predict and match our observed colors.









The method is also based upon the use of eigenspectral techniques, determining a

small number of basis spectra which can be combined in different v--v to create

spectra which reproduce virtually any color observations. This yields a continuous

distribution of template spectra, as well as providing us with quantifiable errors.

Thus, we can compare a galaxy's color to these optimized template spectra to

estimate the redshift and SED-type photometrically.

Followup spectroscopy in Cetus, Lynx, and Pisces provided accurate redshifts

for 625 of the galaxies, providing an independent assessment of the errors in our

photometric redshifts. A plot of spec vs. Zphot for all three fields (Figure 2-la)

yields a linear regression slope of 1.05 .06 when fit through the origin. The

average of the deviations Az = zpec Zphotl is relatively high at .27, although

ignoring the extreme outliers (Az > 1.0) reduces this value to .19. The distribution

of deviations is not Gaussian, but Az,,g < .22 for I.' of the galaxies. Figure 2-2

provides a histogram of the results.

As Figure 2-la reveals, the great 1ii i ii ly of photometric redshifts > 2 were

catastrophic failures, missing their target by a considerable margin (Az > 1),

and were generally overestimates. This sI:.--- -1-I that galaxies in the full sample

with Zphot > 2 should be discarded as unreliable. However, it must also be noted

that this analysis, based on galaxies with spectroscopic information, is predisposed

toward brighter galaxies and provides little information about the photo-z code's

accuracy in relation to the fainter galaxies in the full sample. Overall, Zphot

predictions for galaxies at Zspec > 0.8 are just as accurate as for galaxies at

zspec < 0.8. For the high-z set, with 242 objects, (Az),,, < .22 for 6.'. for the

low-z set, with 383 objects, (Az),,, < .24 for i.-'X. The photometric redshift code

is still making relatively accurate predictions for galaxies out to zspec 1.5. It may

well continue to be successful at higher redshifts, but we do not have the means of

testing it extensively, and so galaxies with Zphot > 2 are removed from the sample.






























> O





2 2 -
0 / 0/1









0 1 2 3 4 0 1 2 3 4
Spectr-z Spectr-z

C) SPICES Lynx Field D) SPICES Pisces field





























omitted due to its smal nnnber of sp. et... ii foioi .ups.
4 /




















0 1 2 3 4 0 1 2 3 4
Spectr-z Spectr-



Figure 2 1: CG'-}. ;: on of photometric redshifts to }* !- ***{*: redshifts. A)

All SP1C i fields. B) Cetus 1 C) Lynx only. D) Pisces only. SA57 hias been

omitted due to its small number of spect- ic followoups.































































0 .005.01 .01 .02 .03 .04 .05 .06 .07 .08 .09 1.0 1.0 2.0 3.0 4.0 0 .005.01 .01 .02 .03 .04 .05 .06 .07 .08 .09 1.0 1.0 2.0 3.0 4.0
Spec z-Phot. zl ISpec. z-Phot z


Figure 2-2: :i : :, error histograms, showing the zphpe z hot values. A) All
SPB I : fields. B) Cetus only. C) Lynx only. D) F. .. (-. .-. E) All low-z galaxies.
F) All high-z galaxies.









Panels b-d in Figure 2-1 compare photometric to spectroscopic redshifts

for the target fields individually in order to assess the consistency of the results

from one field to another. Pisces has the greatest number of catastrophic failures,

dominated by a group of galaxies at true redshifts of 0.5-1.5 with Zphot > 3. Lynx

has the fewest catastrophic failures and consequently has a linear regression fit

slope of 1.02 .05, with (Az),,g < .23 for -'- of the galaxies. Cetus, however, had

the best fit for the 1i i. iily of its objects, and consequently (Az),g < .16 for '.'.

of the galaxies; the slope is 1.07 .13. For Pisces, (Az),,g < .29 for i,-'- of the

galaxies, and the slope is 1.08 .14. The differences between the three fields are

noticeable but not excessive. They may be due to variations in the effectiveness of

the photometric redshift code with different types of galaxies. For example, Lynx

has clusters at z=.57 and z=1.27, visible in Figure 2-1c, and as a result it has a

higher fraction of early-type galaxies. These considerations are discussed in greater

detail in Section 2.4.

Another systematic weakness of the code is a tendency to underestimate

redshifts at zspec < 1, creating the triangular bulge in the lower left corner of Figure

2-la.

The original intent was to use the same methods and code to estimate pho-

tometric redshifts for the main FLAMEX study. However, another collaborator's

code was chosen instead, as discussed in Section 3.7.3. As a result, the tests and

values derived in this section are not directly applicable to the FLAMEX results;

they are, however, indicative of the issues and uncertainties associated with pho-

tometric redshift techniques and are useful for any future work done using the

Budavari et al. (2000) procedure.

2.3.4 Two-Point Angular Correlation Function: Overview

Galaxies tend to group together in space, and one way to characterize this

density amplification is with the two-point spatial correlation function. The









function, representing the density amplification of galaxies within some distance

r of a reference galaxy, can be written as (r) = B,,gr-, where the number of

neighboring galaxies in a volume element dV is n(r)dV = pg[1 + ((r)]dV. The B

coefficient is known as the amplitude of the spatial correlation function; if it is zero,

then the density of galaxies is indistinguishable from the average spatial density,

pg. The function is also commonly written as ((r) = (r/ro)-7, where the spatial
correlation length ro = B1/7. The power law form of ((r) was originally derived for

relatively local galaxies based on the Lick (Shane & Wirtanen 1967) and Zwicky

catalogs (Zwicky et al. 1961-1968), with 7 = 1.77.

Since we do not have precise redshift information for many of the SPICES

galaxies, we cannot calculate the spatial correlation function directly. What we

actually observe is the two-point angular correlation function, whose form can be

written as w(O) AO-(-1), or w(O) = AO77. The total number of galaxies found

in solid angle dQ at an angular distance 0 (in degrees) from the reference galaxy is

n(0)dQ NV[1 + AO--"]dQ. Here, w(0) represents the fractional increase of galaxies

beyond the expected values due to their tendency to cluster together. As above, if

the coefficient A is zero, then there is no significant density enhancement around

the reference galaxy beyond the average surface density, N, (in gals/deg2).

Integrating n(0)dQ = Ng[1 + A0- 771]d, we can write


n,,g,(0)d0 N 20 [1 + AO -77] d0 (Ng 270 + Ng 27TA023) dO

where the left-hand expression stands for the number of galaxies observed in an

infinitesimal ring of width dO which is 0 degrees away from the reference galaxy.

(N, 27OdO is the expected number of galaxies in the ring.) For the total number









of galaxies inside the radius 00, integrate this equation to get

0o
ntot(0o) J (27 N'0 + 2rNg0.23Agg) dO
Jo1
iNg o2 + ol.23A,,

= LN9, + 2323A99

An important aspect of this method is that it approaches the angular corre-

lation function from the point of view of individual galaxies, deriving a separate

value for each galaxy. This approach was originally used by Longair and Seldner

(1979) to investigate the environments of radio quasars, and the same technique

is used in various successor papers that study the same issues (e.g., Yee & Green,

1984; Wold et al., 2001). However, most modern studies that are interested in

the angular correlation function (e.g., Le Fivre et al. 1996; Hudon & Lilly 1996)

apply an ensemble approach, designed to produce a single correlation amplitude

(A) for an entire field or survey of galaxies, or for a specific subset of galaxies

within the survey such as red galaxies. This technique is very different, requiring

the generation of large sets of random points within the area of the survey and

comparing the distances between all random-random pairs, galaxy-random pairs,

and galaxy-galaxy pairs. Kerscher et al. (2000) provide a nice summary of the

numerous variations of this technique.

For this project, it is desirable to use the Longair and Seldner (1979) method

to derive an angular correlation amplitude for each of the galaxies in the SPICES

study, rather than the ensemble approach, so that we can cross-reference the

amplitudes with the individual SED-types assigned to the galaxies. It is unclear

whether either the mean or median of the individual calculations of A can be

directly compared to ensemble calculations of A from other studies, or whether









subtle issues may create systematic differences between the two procedures' results;

this topic requires further investigation.

2.3.5 Two-Point Angular Correlation Function: SPICES Calculations

To determine the A values, I found the best fit for 0 vs. ntot(O) for each

individual "reference" galaxy. I emploi-y, linear least-squares fitting using the

Gauss-Jordan elimination method as outlined in, e.g., Press et al. (1992). Each

fit had 100 data points representing concentric, equally-spaced circles around the

reference galaxy and the number of galaxies within those circles. However, any

galaxy whose photometric redshift differed from the reference galaxy's redshift

by more than 0.1 z was discarded for these purposes, as it would probably not

have any clustering connection with the reference galaxy. Consequently, it was

necessary to calculate average density values (N,) separately for each reference

galaxy based solely on galaxies within 0.1 z of it. For this purpose, I derived the

densities from all four SPICES fields rather than just the reference galaxy's field to

lessen the possible effects of cosmological variance upon a single small field of view.

The density determinations were based on the entire galaxy population, rather

than trying to identify clusters and isolate a (somewhat arbitrary) non-cluster

background density.

Corrections were made for areas of the survey with poor data. I created

a mask for the SPICES fields that identified survey regions with bad pixels,

proximity to bright stars, etc. Excluding these areas, the four images combined had

1,702,480 usable pixels (using "equivalent pi::- !- for Pisces, which had a different

pixel scale than the other fields). The average galaxy density N, for all the objects,

regardless of redshift, was 39,900 gals/deg2 at K' < 20, including a small fraction

of stars. For each reference galaxy, on a pixel-by-pixel basis, I identified the fraction

of each surrounding circle that was good quality and multiplied the number of









observed galaxies within the circle by the fraction's reciprocal to obtain an estimate

of the true number of galaxies.

The maximum angle 0 that I chose for the fit was a fixed angular distance

of 200 pixels in all cases (224 pixels for Pisces), corresponding to 94" (.76 Mpc

at z 1). A fixed physical distance is implemented in the FLAMEX study (see

Section 3.7), with each galaxy's maximum 0 determined by the angular diameter

distance DA at the galaxy's redshift, but this was not done for the SPICES survey

for the sake of simplicity.

2.3.6 Translating to the Spatial Correlation Function

With spherical symmetry assumptions, it is possible to translate the galaxies'

angular correlation amplitudes (A) into spatial correlation function amplitudes

(B), providing estimates of the actual physical scales of clustering. Due to the

wide range of redshifts involved, the visibility of faint galaxies varies and the

correspondences between physical scales and angular scales are different. A galaxy

luminosity function, modified appropriately by K corrections and evolutionary

corrections, helps to place all galaxies on an equal footing.

K corrections are a subtraction from a galaxy's apparent magnitude to remove

the effects of redshift. The light that we receive from a galaxy in a given filter

was actually emitted from a bluer and narrower region of the spectrum. This

difference is determined by the redshift and depends strongly on both the filter

and the galaxy type. One advantage of observing in the near-IR is that there is

little variation in the K corrections between early-type and late-type galaxies.

Additionally, the near-IR K corrections for both types are negative for much of

the redshift regime of interest, so that the galaxies are brighter than would be

expected based on distance alone and are thus more easily detected. Although

the light was emitted from a narrower part of the spectrum (e.g., half as wide as

the filter passband, for a z = 1 galaxy), the flux from that region of the spectrum









(c. 1100nm for a z = 1 galaxy seen in the K filter) is sufficiently greater that it

overcomes the former effects. (In contrast, for optical passbands the K corrections

are large and positive.) Detailed SEDs are required to calculate the corrections,

and there are two general approaches. Well-studied local galaxies can be combined

into SED templates, such as those of Coleman et al. (1980), and these templates

(combined with models where observations are inadequate) can be used to adapt

the magnitude that was actually observed to the magnitude that "should have

been" observed. This approach was used by Mannucci et al. (2001), for example.

Alternatively, SEDs can be produced entirely from stellar population synthesis

models such as those created by Bruzual and ('! I. ot (2003), Devriendt et al.

(1999), Le Borgne et al. (2004), and P. .-.-i 11i (1997). Further information and

useful overviews about K corrections can be found in P. .-.vi ili i (1997) and Hogg et

al. (2002).

Evolutionary corrections are similar to K corrections. They are an attempt

to offset the evolutionary effects on a galaxy's spectrum, which changes over time

because galaxies at high redshift were younger, and often bluer and brighter. They

require evolutionary stellar population synthesis models, like those mentioned

above. The models describe the change of a galaxy's SED with the passage of time

since the galaxy's formation. This is measured in years, not redshift; a translation

between the two is required. Thus, evolutionary corrections (unlike K corrections)

depend on the choice of cosmological parameters.

I derived K corrections and evolutionary corrections from Bruzual and

('! i o lot's GISSEL96 code (Bruzual & ('!i I!ot, 1993) to standardize the high-z

galaxies with those in the local universe. For simplicity, I modelled the galaxies

with a single burst of star formation at z = 5.4 lasting 0.1 Gyrs, evolving passively

thereafter. I used the Scalo (1986) initial mass function (IMF) for stars, a more-

refined alternative to the better-known Salpeter (1955) IMF. The cosmological












u aalpeter I bill. yrs.
Scalo 13 bill. yrs.
Scalo 10 bill. yrs.
0.2 Scalo 20 bill. yrs.
.... -Poggianti (average): Dotted line
"-.__ Mannucci (average): Dashed line
E 0 .4 -


-0.6


0 .8 ...
0.0 0.5 1.0 1.5 2.0
Redshift


Figure 2-3: K'-band K corrections. I used Bruzual and ('!C 1 lot's GISSEL96 code,
choosing a Scalo IMF and a "modern galaxy ai, of 13 Gyrs for the SPICES study,
but alternatives are plotted here for reference. Salpeter's IMF has essentially no
effect on the results, and even significantly different galaxy ages result in similar K
corrections. The models used by other authors reveal larger uncertainties, although
the values are still broadly similar. P. -.- ,li and Mannucci found K corrections for
different galaxy SED types and listed them independently; this graph uses a simple
average of the values.


parameters were Ho = 72, go = 0.3, QM = 0.6, 2K = 0.4, and fA = 0.0. Note

that these values are derived from an outdated cosmology, and the main FLAMEX

study used more current parameters based on the 1st-year Wilkinson Microwave

Anisotropy Probe (WMAP) findings from Spergel et al. (2003). The output of

GISSEL96 is a series of modelled spectra at various age increments; I wrote a

program to convolve these SEDs with the IRIM K' filter transmission function

and convert them into evolutionary and K corrections. The results are shown in

Figures 2-3 and 2-4 along with comparison values from Mannucci et al. (2001) and

P. .-.-ii 1 11 (1997), as well as corrections based on variants of the input parameters

used for GISSEL96 to assess the importance of their uncertainties.

I employ, l1 Kochanek et al.'s (2001) K-band Schechter luminosity function

to correct for galaxies too faint to see at high redshift. The function is of the












z'--.=. .4, SF 1.0 Gyr burst
0.5 '-. Poggianti (overage): Dotted line








0.0 0.5 1.0 1.5 2.0
Redshift


Figure 2-4: K'-band evolutionary corrections. I used Bruzual and C'!i, lot's GIS-
SEL96 code, choosing Zform, 5.4 and a single star formation burst lasting 0.1 Gyrs,
but alternatives are plotted here for reference. Different values for Zform and for the
burst duration have little effect on the results, which are also quite consistent with
the evolutionary corrections found by P. ,.-.-i ,,li As in Figure 2-3, the plotted val-
ues for P.,.-.i i,:li are a simple average at each redshift of the values for the various
SED types listed in that reference.


form O(L)dL = *(L/L*)eL1L*d(L/L*) and the parameters are a = -1.09,

Mk = -23.39 + 5.0 log h (for Ho = 100 h km/s/\!lpc), and Q = 0.0116 h3 Mpc-3.

For each of these parameters, lower values correspond to a smaller galaxy density

per Mpc3. The uncertainties listed in Kochanek et al. for Mk have the largest

effect, followed by 0 and then a.

Following the procedure outlined in Longair and Seldner (1979), the angular

correlation amplitude (A) for each galaxy is translated to its corresponding spatial

correlation amplitude (B) according to A y- 2[(-l)/2]1 D- (M*, z).

This translation is based on the correlation function's power law 7 = 1.77, the

average surface density of galaxies (N,) within 0.1 z, the galaxy's redshift, the

angular diameter distance (DA), and the galaxy luminosity function (((M*, z)). DA

depends on the values chosen for cosmological parameters, while ((M*, z) depends

on the K and evolutionary corrections (which in turn also depend on the chosen









cosmology). The resulting B values serve as measurements of the local galaxy

density, with high values representing strongly clustered regions and low (in some

cases negative) values representing underdense regions. These values are matched

with the galaxies' SED-types, (which are discussed in Section 2.4), and the results

are presented in Section 2.5.

2.4 Galaxy SED Measurements

2.4.1 Overview of Photometric Technique

Most of the SPICES galaxies are too faint and poorly resolved to make

visual morphology estimates. Early-type and late-type galaxies typically have

very different SEDs, so that spectroscopy can help to distinguish between them.

In instances where spectroscopy is not available, however, it is possible to use

multiwavelength photometry to estimate the SED-types. This technique of using

the colors to identify and track major spectral features is very similar to that of

photometric redshifts, and most procedures calculate both redshift and SED-type

simultaneously. The algorithm used for SPICES is derived from Budavari et al.

(2000) and is discussed in more detail in Section 2.3.3. The code, written by

Andrew Connolly, assigns one of five classifications to each galaxy: E, Sbc, Scd, Im,

and starburst.

We compared Connolly's color-based SED-types with true morphologies

to gain some insight into the similarities and differences between the density-

SED relation and the density-morphology relation. Section 2.4.2 describes a

set of HST visual morphologies that we were able to obtain for a sample of the

SPICES sources, and it provides details on the objects' classification with a

particular eye toward self-consistency checks. Section 2.4.3 then compares the

visual identifications with the SED estimates made by Connolly's code.









k I I?012, .i -l-. i s t S S Ia r n1it
W V C MI, 04 i





Figure 2-5: Sample of HST images of SPICES galaxies.
; : .. : .
l .- ,: .

wi '











2.4.2 Visual Morphologies: Description and Consistency C( 1.:

The SPICES group obtained HST followup imagery in order to determine

galaxy morphologies visually, with the objective of comparing these results to

the SED-types of Connolly's eigenspectral matching code. Katherine Wu, Adam

Stanford, and I independently classified 1001 objects as P: peculiar/merger, L: late-

type, E: early-type, T: too small to determine, F: too faint, or S: star. We created

a postage stamp for each object and analyzed it, adjusting the intensity scaling

and range as needed and employing radial profiles as well as visual assessments.

We also used a mosaic of nearby, classified galaxies from the Nearby Galaxy

Catalog (Frei et al., 1996) as a reference, projecting their appearance to z = 0.75.

Figure 2-5 shows a sample of the SPICES stamps.

Due to overlapping HST fields, 125 of the SPICES objects were imaged

twice, and seven of them were imaged three times. Since these "clones" received

independent visual morphological classifications, this provides information about

the self-consistency of each investigator's estimates. Table 2-4 presents the results.









Table 2-4: Comparison of "Double" Morphology Estimates
P L E T F S
P 31
L 31 128
E 5 21 27
T 4 19 13 40
F 7 9 1 6 11
S 1 1 6 5 0 30

The right-most diagonal shows the number of occasions where an investigator

gave the same designation to a galaxy both times (P/P, L/L, etc.). The remaining

data cells display the number of instances where the two estimates were not

identical. The handful of triple detections are also included (e.g., P/P/P P/P,

P/L/P P/L). As can be seen from this chart, L and S designations were fairly

robust, but peculiar galaxies could not be consistently discerned from late-types.

Early-type galaxies were also often confused with late-types.

For a galaxy whose first estimate was P, its second estimate was P .i.'. of the

time. The other values are as follows: L 71' '. E 5 !'1. T :;' F ,!' S 2-' (Note

that it is necessary to double the number of successful duplicate identifications

when determining these numbers, since each mistake affects two of the percentages

negatively.) Overall, our self-consistency was 67.5' Disparate identifications that

involve T or F and some other value are sometimes due to better image quality

in one of the two images, permitting a definite classification. Thus, the relations

between P, L, E, and S values are of greater interest.

Comparing the three investigators' estimates for each object provides both an

additional test and interesting statistics (see Figure 2-6). '.'-. of the total objects

were agreed to be stars by all three investigators (> 2.5 for doubly/triply estimated

objects). For the other classifications, the values are: F !'., T 5'., E 5'., L 25'-. P

s'. Thus, 5;:'. of the objects had full agreement. (9,2'. had 2/3 agreement.)

4;;'. had a definite identification (S/E/L/P), and of these, 11!'. were stars,

12'. were early-type galaxies, 57'. were late-type galaxies, and 1' were peculiar
























0 6 I I I I I
S.A.Stanford
m E.McKenzie
0.5 K.L.Wu
Full Agreement


0 0.4 -
0
0

S0.5 -


o 0 _

S0.2









Star Faint Small Early Late Peculiar
Morphological Type


Figure 2-6: Visual morphology estimates. This figure (based on one created by
Katherine Wu) presents the percentage of objects assigned to each visual mor-
phology class by each investigator. It is helpful in assessing the consistency and
reliability of the classifications, and also for identifying the strongest uncertainties.









galaxies. These numbers can be taken as rough estimates for the percentages of

each class in the survey's field. However, there are intrinsic uncertainties, apparent

in the preceding two paragraphs, and there are also systematic uncertainties, as T

and F designations probably represent somewhat different distributions of S/E/L/P

from the preceding percentages. These uncertainties are estimated at ;:'. based

upon my identification notes. There is a further selection effect in the Lynx field,

where the HST fields were chosen to cover regions with detected clusters (about

half the total area), so that the distribution of galaxy types is not "random" in

that field. The average redshift of the full-agreement E/L/P objects is z = 0.71,

and the median is z = 0.62 (based on spectroscopic redshifts where available, and

photometric redshifts otherwise).

We also compared our averaged results with morphological estimates deter-

mined by GIM2D, an IRAF package for doing 2-D bulge and disk convolution for

galaxies. We chose output parameters to correspond to each of our six categories

(S, F, T, E, L, and P). Figure 2-7 shows the results. There is no easy way to sep-

arate out stars with GIM2D, and many of its T (tiny) identifications should be S

(star). The other i i" r discrepancy is that GIM2D identified many fewer galaxies

as early-type (89 E) and many more as late-type (571 L, 142 P) than we did (214

E, 402 L, 80 P). We placed our dividing line between early and late galaxies at

a bulge/total fraction of 7i i' which is correct for the local Universe. However, a

lower fraction, possibly as small as 11I' may be more appropriate for high-redshift

observations.

The SPICES spectroscopic observations provided an additional check of

our accuracy by testing our ability to visually identify stars. 52 sources in the

HST regions were spectroscopically confirmed to be stars. Of these, 37 were

visually classified as stars with full, 3/3 agreement, and 12 were classified as stars

with 2/3 agreement. Two were considered too small to classify and one had no

















Comparison of Average Visual Morphology to
Automated GIM2D Morphology


402
600 -402
Average Visual Morphology 571
Automated GIM2D Morphology
500


400
O
-o
0
S 300 136
-m 259
214
89
200 -
80
142

68 67 74
100 0
0 24
0

Star Faint Small Early Late Peculiar
Morphological Type

Figure 2-7: Comparison of GIM2D and visual morphology estimates. This figure
(created by Katherine Wu) presents a comparison of the GIM2D classifications and
those made by eye. Each visual morphology class was assigned a numerical value
based on an initial estimate of their "discernability"; S=-5, F=-2, T=-1, E=1, L=2,
and P=3. Each object had three values (one given by each investigator); these
were averaged for the purposes of this plot. The numbers in the figure display the
quantity of objects in each bin.









consensus value. Individual misjudgments (E, L, or P) were rare, but there were

five instances of E identifications and one each of L and P. Conversely, of the 410

spectroscopically-identified galaxies, three were unanimously visually classified

as stars, and one (a quasar) was classified as a star with 2/3 agreement. Ten

galaxies received a 1/3 star vote. As an alternate perspective, 95'. (37 of 39) of

the spectroscopic objects visually classified as stars by all three investigators were

verified to be stars, while 9' -. (12 of 13) of the objects classified as stars with 2/3

agreement were verified to be stars. The remaining three proved to be galaxies, one

of them a quasar. These results indicate a high degree of precision in the visual

star-galaxy separation, with few false positives or negatives.

2.4.3 Comparisons of Connolly's Results to Visual Morphologies

Having completed these assessments, the primary area of interest is a compar-

ison of our visual morphologies with the results provided by Connolly's eigenspec-

tral code (discussed in Sections 2.3.3 and 2.4.1). The program yields values on a

scale of 0 to 4 that correspond to templates as follows: E (0), Sbc (1), Scd (2), Im

(3), starburst (4). Figure 2-8 compares these results with those from our E/L/P

classification. For galaxies with full agreement of visual morphologies, the average

values from Connolly's code were .21 for E galaxies, 1.07 for L galaxies, and 1.81

for P galaxies. For galaxies with 2/3 agreement, the average values were .39 for E

galaxies, 1.13 for L galaxies, 1.19 for L/P galaxies, and 1.66 for P galaxies. (The

L/P category is for galaxies where the investigators could not agree, assigning

one L rating, one P rating, and one "other.") In the 2/3 agreement case, the ex-

tremes tend more toward the middle, since we are including galaxies with greater

uncertainty, but the divisions between E, L, and P are still quite clear.

Another desired piece of information is the extent to which redshift affects the

code's results. The objects with HST visual morphologies cover a redshift range

out to about z=1.5. (See Figure 2-9.) We split the objects into two bins, z < 0.7












































Figure 2-8: Comparison <.: estimated 1i )-ty :with visual morphologies.
figures track the fractions of, c.g., E galaxies ( 1 visual identifications) that
were ::'d various galaxy types by Connolly's photo-z code. ( i ::- total of each
curve's values is 1.0.) Ti. program yields values on a scale of 0 to 4 that corre-
spond to templates as follows: E (0), ,c (1), Scd (2), and i::: (3). Another tenm-
i. star-forming (4), had no matches in this : A) includes only galaxies
with a full, 3/3 agreement in the visual itd ::. :. ;, while B) includes all galax-
ies with 2/3 or better agreement. In both cases, E visual designations strongly
correlated to '0' ratings i : the photo-z code; very i: E galaxies were assigned
values of 1, 2, or 3. Galaxies with L visual designations .1 at '1', and galaxies
with P designations peak at '2'. C) and D) ;:: the galaxy population into low
and high redshift bins (respecti-.-!-) to see how the correlation between the visual
identifications and the 1: -z code ratings (1:::: with redshift.














A: R t ds moorphs.
S m t 2/c+ agreements
a 3/3 agreement

80

0 60 -


40-






0.0 0.5 1.0 1.5 2.0
Redshift


Figure 2-9: Redshift distribution of objects with visual morphologies. This his-
togram shows the number of objects with visual morphologies at each redshift,
including all non-star objects (T, F, E, L, & P), those that had 2/3 or better classi-
fication agreement, and those which had 3/3 classification agreement.


and z > 0.7, and determined the 2/3 agreement results for each, included in Figure

2-8. For the low-redshift bin, the average values were .33 for E galaxies, .94 for

L galaxies, 1.00 for L/P galaxies, and 1.51 for P galaxies. For the high-redshift

bin, the average values were .50 for E galaxies, 1.35 for L galaxies, 1.23 for L/P

galaxies, and 1.72 for P galaxies. The values are shifted higher for higher redshift

galaxies, but the distinctions remain clear. (This is an interesting phenomenon,

worthy of future investigation.) There is also a shift in raw numbers; there are only

half as many early-type galaxies at z > 0.7 as at z < 0.7, while the quantity of

late-type galaxies decreases only slightly and that of peculiar galaxies increases by

over a factor of two.














51 90
-+\. +z>0.8
LU








50
LU
S 60
0 50 ,





0.6 0.4 0.2 0.0 -0.2
B Coefficient (Spatia Corr. Fn.)


Figure 2-10: Preliminary results for Lynx.


High SED-type values corresponded well to late-type galaxies, but low values

were degenerate regardless of redshift. This is due to disky red galaxies such as SOs

and spirals with quenched star-formation. For the FLAMEX analysis (C'! lpter 3),

it is therefore important to keep in mind that we are looking at the relation

between density and stellar population rather than density and morphology.

2.5 Results

I calculated the amplitude of the spatial correlation (B) for every galaxy in

the SPICES catalog that met the requirements stated in Section 2.2 and compared

them with the SED-type results from Connolly's code to examine the density-SED

relation. The initial results from a Lynx-only study of 205 galaxies, di-i1 li- 1 in

Figure 2-10 and Table 2-5, were quite promising.

A larger B coefficient corresponds to a greater estimated spatial density of

galaxies in the vicinity; galaxies in very under-dense regions are likely to receive









Table 2-5: Preliminary Results for Lynx
Density Galaxy Type (z=0.0-0.8) Galaxy Type (z>0.8)
B coeff. Elliptical Spiral/Irr. %Ell. Elliptical Spiral/Irr. %Ell.
0.5-0.7 15 1 0 0
0.4-0.5 24 6 .-I'. 6 2 7 .
0.3-0.4 11 8 4 3 5F.
0.2-0.3 9 9 6 6. .
0.1-0.2 14 14 '. 18 22 45%
Positive 0.0-0.1 29 27 5- 43 37 '
Negative 0.1-0.0 21 22 l'. 14 21 I '.
0.2-0.1 4 6 lI'. 2 3 I '.


negative values. (Calculations are performed with 0 in degrees.) The values for the

SED-types were on a continuum from zero to one, depending on the combinations

of eigenspectra needed to match the galaxies' colors. Values of 0.0-0.1 corresponded

roughly to elliptical and SO SEDs, and galaxies with those results are placed in

the "Elliptical" column, while values of 0.1-1.0 corresponded to late-type galaxies.

There is a dramatic shift toward dominance by elliptical SED-types in the denser

regions, as is expected from the traditional density-morphology relation. It is not

possible to draw conclusions about redshift dependence from this small sample; the

division is merely presented here because of its eventual importance in the later

FLAMEX study.

In 2003, the SPICES team produced a revised (and final) version of the

SPICES catalog, and Andrew Connolly also modified his SED classification code.

I compared these to the spatial correlation amplitudes of the galaxies in all four

fields, 1149 in all; the results are shown in Figure 2-11. The current version of

Connolly's program outputs a discrete value for each galaxy on a scale of 0 to 4,

corresponding to the following SED-types: E (0), Sbc (1), Scd (2), Im (3), and

starburst (4). Only eight galaxies were assigned a starburst SED-type, and they are

omitted from the results here.

The effects of the density-SED relation continue to be visible at low and

high redshifts, although the point must be stressed that the SED-types may not

correspond well with the galaxies' true morphologies at high redshifts (this issue



























A) SPICES results z=0.0-0.8) B) SPICES results (z>0.8)

0.6 228 0.6 -
0 Avg. B 0 Avg. B
m Median B m Median B
0.4 0.4 -
135

S0.2 0.2
U
(\ \ 247 164
8 0.0 0.0
m ~ 81 M m 46

0.2 0.2


-0.4 -0.4-


E Sbc Scd Im E Sbc Scd Im
Galaxy SED-Type Galaxy SED-Type


Figure 2-11: Final SPICES results (using Connolly SED-types) at A) low redshift
and B) high redshift. The number labels indicate the quantity of galaxies repre-
sented by each SED-type. It is worth noting that, due to a different calibration
procedure in my calculations, the B values should not be directly compared to the
preliminary results for Lynx in Table 2-5.









is addressed in Figure 2-12). However, the SED-types are still providing us with

important physical information about the galaxies, and the values will likely have

some connection to the morphologies of the galaxies' present-d iv counterparts.

('!I in,. in the correlation function amplitude from low to high redshift manifest as

lower absolute values, which -, .-.- I- a generally more homogeneously-distributed

population of galaxies at high redshift and is consistent with the hierarchical-

clustering scenario. However, the sample size is too small to further refine the

redshift bins and investigate the details of the changes with time. The FLAMEX

survey, discussed in C'! lpter 3, has this capability.

There was considerable variation between the individual fields. This was due

in part to my use of all four fields to determine the average surface galaxy density

at various redshifts for the correlation amplitude calculations, as opposed to letting

each field serve as its own reference for surface density. Galaxies in the densely-

populated fields (particularly Lynx, with two significant clusters) were likely to

have higher Bs than galaxies in sparser fields such as SA57.

A final topic to consider is the connection between the B values and the direct

morphological information that we have from the HST observations, rather than

the indirect color-estimated SED-types. Although HST observations across a broad

region are far harder to come by than multiwavelength ground-based observations,

and thus inappropriate for large survey the SPICES sample can provide direct

data on changes in the density-morphology relation. These results are presented in

Figure 2-12. It is interesting to note that the density-SED relation of this sample is

more apparent at high redshifts than the density-morphology relation. This is likely

due to the inherent difficulty in morphologically classifying small, distant galaxies,

and it is a strong argument for using the SED-density relation at high redshifts as

an alternative or extension to the low-redshift density-morphology relation.








43

















A) SP CES results (z-0.0-0.8) B) SP CES results (z>0.8)
70


0.6 \ 0.6 -
0 Avg. B o Avg. B
\ m Median B i Median B

t 0.4- 0.4-
o o

m 0.2 \ m 0.2 25



0.0 0.0



E L P E L P
Visual Morphology Visual Morphology


Figure 2-12: Final SPICES results (using visual morphologies) at A) low redshift
and B) high redshift. The labeling convention is the same as that used in Sec-
tion 2.4.2, where E represents early-type galaxies (E or SO), L represents late-type
galaxies, and P represents peculiar or merging galaxies. The number labels indicate
the quantity of galaxies represented by each SED-type.















CHAPTER 3
DENSITY-SED RELATION FOR FLAMEX GALAXIES

3.1 Introduction

The limitation of the SPICES study is its small sky coverage; the next logical

step is to extend the same study to a larger survey, where statistics permit finer

inning by redshift and SED-type, and the results are more robust. This has been

my main project and will be discussed here.

Numerous investigations have studied the effects of environment on galaxies'

colors/SED-types. Examples include spectroscopic surveys in the local Universe

(e.g., Madgwick et al. 2003) and pencil-beam spectroscopic surveys at higher
redshifts (e.g., Lovedw, et al. 1995; Meneux et al. 2006). Photometric studies have

calculated spatial correlation functions by assuming a redshift distribution from a

spectroscopic subsample or a separate survey (e.g., Roche & Eales 1999; Wilson

2003; Coil et al. 2004), or alternatively by establishing the redshift distribution

using photometric redshifts (e.g., Firth et al. 2002; Budavari et al. 2003; Brown et

al. 2003; Phleps et al. 2005). Unfortunately, direct comparisons between surveys

are complicated by the variety of selection techniques; in particular, results are

often affected by the strong dependence of ro on luminosity (Norberg et al. 2002).

I based my primary work on data from the FLAMINGOS Extragalactic Survey

(FLAMEX; Elston et al. 2006). FLAMEX was an NOAO Survey Program (2001-

2004) conducted at the KPNO 2.1m telescope. It has an exceptional combination

of depth and breadth that permits analysis of the SED-density relation's evolution

(impossible with the local Universe surveys) while minimizing the effects of cosmic

variance (to which SPICES and the other pencil-beam surveys are vulnerable).









This chapter is organized according to the following design. Section 3.2 de-

scribes the FLAMINGOS instrument used for the survey. Section 3.3 describes the

basic characteristics of FLAMEX, while Sections 3.4 and 3.5 provide details of the

data acquisition and reduction process, respectively. Section 3.6 briefly discusses

the choice of catalog for this project. Section 3.7 contains my procedure for calcu-

lating spatial correlations, including a mathematical overview, the final culling of

the catalog for usable galaxies, and the details of my algorithm's implementation.

The results for the main density-SED evolution study are presented in Section 3.8,

along with investigations into the behavior of extremely red objects (EROs) and

clusters. In Section 3.9, I summarize the results and present conclusions, and I

discuss possibilities for future work in Section 3.10.

3.2 The FLAMINGOS Instrument

The FLAMEX survey is named after the Florida Multi-object Imaging Near-

Infrared Grism Observational Spectrometer (FLAMINGOS), an astronomical

instrument that Dr. Richard Elston built at the University of Florida. FLAMIN-

GOS can be utilized for both photometry and multi-object spectroscopy, though

we relied entirely on the former for our survey. Its fast all-refractive optical system

and 2048 x 2048 HgCdTe HAWAII-2 CCD array make FLAMINGOS a highly

effective imager for studies requiring a wide field of view (21' x 21' on the KPNO

2.1m telescope, with 0.61" pixels).

There were several changes to the instrument that took place while the survey

was in progress. An important one was the array itself; we used an engineering-

grade array through Fall 2002, at which point the science-grade array was installed.

The engineering-grade array was perfectly serviceable in most respects, but was not

fully functional along the edges, and this resulted in strips missing from our survey

coverage taken with this array. As for the science-grade array, it evinced aberration

in certain regions, particularly toward the edges, and the 50'. completeness limits









for individual fields often varied by up to half a magnitude across the area. The

J and Ks filters were changed in July 2003 when a new filter set was bought for

the instrument to replace the set borrowed from NOAO and Gemini. This had no

1 i i"r effect, although the transmission curves of the two sets are slightly different.

The curves and other information are available on the FLAMINGOS website at

http://flamingos.astro.ufl.edu/.

3.3 Survey and Program Design

For the FLAMEX survey, we observed two subregions of the NOAO Deep

Wide-Field Survey (NDWFS; Jannuzi & Dey 1999; Dey et al. 2006, in preparation)

in the Bo6tes and Cetus constellations. The NDWFS fields were chosen due to the

deep optical imaging that was in progress in these fields when the survey began,

with the BwRI data being essential for deriving accurate photometric redshifts.

The NDWFS survey area is also the target of one of the most extensive panchro-

matic investigations in all astronomy, with space- and ground-based imaging and

spectroscopic programs spanning radio to X-ray wavelengths (Rhoads et al. 2000;

de Vries et al. 2002; Hoopes et al. 2003; Lonsdale et al. 2003; Eisenhardt et al.

2004; Kochanek et al. 2004; Pierre et al. 2004; Houck et al. 2005; Murray et al.

2005). The northern (Bo6tes) field in fact is one of only two wide-area survey

regions presently mapped by Chandra, GALEX, and Spitzer (with IRAC and

MIPS). The AGN and Galaxy Evolution Survey (AGES; Kochanek et al. 2006,

in preparation) also provides 17,000 spectroscopic redshifts at z < 0.8 across the

NDWFS area.

The FLAMEX regions cover a total of 7.1 deg2. Each 21' x 21' field was

imaged for two hours (seeing < 1.7") in each of the J and Ks bands, allowing us to

reach J=22 and Ks=19.3. The survey region is roughly a factor of ten larger than

any existing near-infrared (near-IR) studies to comparable depth. We combined the

FLAMEX data with the Bw, R, and I band NDWFS optical imaging as well as









the Infrared Array Camera Shallow Survey (IRACSS; Eisenhardt et al. 2004) mid-

infrared (mid-IR) Spitzer imaging to derive photometric redshifts and SED-type

estimates (Brodwin et al. 2006). These results are quite robust due to the quantity

of multiwavelength photometric information. There are still large uncertainties for

individual galaxies, but our statistical understanding of the z < 1.5 universe has

been greatly enhanced.

The combined survey is a major asset to the astronomical community and

will help to resolve a v iii' I. i of issues; the evolution of the density-SED relation is

merely one of these. Already, it has been used to detect galaxy clusters to z ~ 1.5

(Stanford et al. 2005), identify z > 5 quasars (Cool et al. 2006; McGreer et al.

2006; Stern et al. 2006, in preparation), detect a field brown dwarf (Stern et al.

2006, in preparation), and confirm the first 350/m-selected galaxy (Khan et al.

2005). The survey also provides the largest existing sample of extremely red objects

(EROs), as discussed in Elston et al. (2006).

3.4 Data Acquisition

FLAMEX observations were officially taken over 97 nights spread across

various seasons, although we coordinated with the NOAO Survey Program "Toward

a Complete Near-Infrared Spectroscopic and Imaging Survey of Giant Molecular

Clouds" (PI: Lada) in order to maximize the efficiency of both programs according

to the time of night that their respective target areas were observable. Only ~ 50'.

of the time proved to be useful, as weather conditions were mediocre overall, with

telescope mechanical failures and instrument software problems .1iv ing secondary

roles. This prevented us from completing the full planned 10 deg2 survey, but we

obtained 4.7 deg2 of coverage in Bo6tes and 2.4 deg2 in Cetus.

We did not require photometric conditions, but we attempted to impose a

seeing limit of FWHM < 1.5" using constant real-time assessments. This limit

proved to be difficult to maintain due to telescope conditions and the intrinsic









aberration of the detector array. It initially led to substantial extensions to the

observing time for a field, in an attempt to obtain a full two hours that ol ,' 1, -

the limit. This restriction was later relaxed, although it remained common to take

an extra 10-21n' of total exposure time when the seeing conditions were mediocre.

We observed the fields down to an airmass of 2.0, although the seeing would often

deteriorate significantly before reaching that point.

At the beginning or end of each night, we took 10-15 lamp-on and lamp-off flat

field images for Ks and sometimes for J; for some observing seasons, we simply

used sky flats for J. We also took 10-20 dark frames for every exposure time.

For most of the survey, we did not take images of standard stars, preferring to

rely on the 2-Micron All-Sky Survey (2MASS; Skrutskie et al. 2006) catalog for

photometric calibration. (Our large field of view facilitated this.)

When observing a survey field in the Ks band, we typically took 120-200

individual exposures to achieve two hours of total exposure time. Near-IR back-

ground emission is high and the detector saturates unless exposure times are kept

short. The outside temperature had the strongest effect on this. It varied across

our various observing runs from -5 to 20C, and the Ks exposure times varied

accordingly from 60 seconds to as little as 30 seconds. We attempted to keep the

background counts below 30,000. Non-linearity corrections were generally effective

to better than 1 up to 45,000 counts, so our faint galaxies were in no danger of

saturation, but our use of 2MASS stars for calibration required that we set a lower

limit. J band observations were less hampered by high background counts and

generally required 85-100 images (of 90 seconds each) per field. These Ks and J

images were taken in sets (e.g., of 25 exposures in a 5 x 5 pointing grid), with the

telescope dithered slightly for each exposure in order to minimize the effects of

detector irregularities. Amplifier cross-talk and other "bad reads" took their toll on









the useful data, typically accounting for 5-25' of the frames taken, depending on

the state of health of the instrument during a given observing run.

The images for a given field were often taken on different nights or even in

different years, possibly with different exposure times. The process for taking all

of this disparate raw data and reducing it into a single finished image for a field

was necessarily lengthy and intricate, and many people contributed to the time

and effort required to complete this work for the entire survey. An overview of

the method by which 1.5 terabytes of raw data were transformed into final results

seems appropriate and useful, and follows hereafter.

3.5 Data Processing

3.5.1 Initial Processing

After the data acquisition, we processed the images at the University of

Florida. For each night of data, we identified ii I,.- stacks," each containing

all the images (a.k.a. frames) for a given field with identical exposure times; we

also made stacks of the flat-field images. For each image stack, we undertook the

following steps. First, we removed any individual images with problems, usually

stemming from detector malfunctions. (This ranged from 5' to 211' of the frames

according to the detector's state of health, which varied during the observing runs.)

The remaining images were linearized; that is, we corrected them for the detector's

gradual loss of ability to register additional photons at high count levels.

3.5.2 Darks and Flats

Next, we combined the dark images (generally 10-20) for the image stack's ex-

posure time into a single FITS file. We also combined the dark images correspond-

ing to the flat-field exposure times into a single FITS file (#1) and subtracted it

from each of the flat-field images, combining the resulting set of dark-subtracted

flat-field images into a single FITS file. This yielded a single file representing the

dark images and a single file representing the flat fields. We divided the former into









quadrants and made histograms of the pixel values for each quadrant. Based on

the histograms, we chose pixel value ranges that corresponded to sood" pixels.

This was a somewhat subjective process, and the forms of the histograms changed

slowly during an observing run and significantly from one run to the next, but they

normally had a clearly identifiable peak. A typical good pixel range was 250-750

counts. We then repeated the procedure for the combined flat-field image. In

this case, the histogram values were expressed as a fraction. A value of 1.0 meant

that no flat-field correction was needed for that pixel. Typical ranges of values

that we considered acceptable were .65-1.35. These histogram trimmings provided

information on which pixels were "bad"; pixels near the detector's edges or along

the boundaries of the detector's subdivisions commonly had problems, and certain

individual pixels or pixel clusters distributed semi-randomly on the detector con-

sistently returned garbage values. Based on these results, we created a bad-pixel

mask, an image whose values were only '1' or O0' based on whether or not the pixels

were usable.

3.5.3 Sky Subtraction

For the next stage, we subtracted the combined dark image corresponding

to the flat-field exposure time (#1 above) from each of the data images and

then conducted an "initial pass." Each resulting frame had a "local sky fi ,i.I.

subtracted from it, made by combining eight other image frames (with their

offsets removed). The frames produced by this procedure then received a flat-field

division. Next, we used the IRAF "d ..p1hi..1 task, which found all objects/pixels

that were too bright and then calculated the offsets of each frame relative to the

first. Our "second 1p -- consisted of creating "object-free local sky frames," for

which we masked out the objects and pixels from the previous step. We subtracted

these frames from their corresponding data images and then performed a flat-field

division on the results. This generated corrected versions of the individual images









in the image stack, and we combined them based on their offsets into a single

image representing the summation of their exposure times.

3.5.4 Alignment and Stacking

The final stage handled the final alignment and stacking of the images. It

resampled the pre-combined data to half-size pixels and centroid-corrected the

dithers to adjust for geometric distortion due to imperfections in the FLAMINGOS

optical system. For this process, we used transformation maps generated for

the KPNO 2.1m telescope in each year of the survey, as any adjustments to the

instrument (disturbing the position of the detector array or installing new filters)

could alter the distortion. The corrections enabled us to properly align images

taken in different years and also to design masks in the future for multi-object

spectroscopy. Finally, we used an integer shift-and-add approach to recombine

these oversampled frames into a final, quadruple-size (4096x4096 pixels), trimmed

image which was ready for analysis.

3.5.5 Combining Data from Multiple Nights

After we performed this procedure for all of the image stacks from all of the

observing nights, we still had final images of the same field from different nights

which had to be combined. We weighted them according to the s. ir. zeropoint,

and rms noise according to the formula

100.4mo
W 7(FWHM)2'

where mo is the photometric zeropoint, FWHM is the full width half-maximum of

the point spread function (PSF) at the field center, and a is the rms noise in each

image.

3.5.6 Astrometry and Photometry

We made astrometric calibrations with the assistance of the Pinkpack IRAF

software package written by collaborator Joanna Levine. Pinkpack identified









matches between the stars in a field and the 2MASS All Sky Data Release catalog

(Cutri et al. 2003), using these in an iterative process to derive a plate solution for

each field to account for the projection effects of the three-dimensional sky upon

the two-dimensional CCD array. First, the software created an object catalog from

the image and a position-selected star catalog from the online 2MASS information.

It then matched these two catalogs and calculated a second-order polynomial fit for

the plate solution. Using the plate solution, the software adjusted the coordinates

and rematched the two catalogs. Based upon this, a final plate solution was

determined using a fourth-order polynomial fit, the catalogs were matched a third

time to assess the quality of the fit, and the sky coordinates for the FLAMEX

image objects were output.

To perform the photometry, we employ, ,1 the Source Extractor software

package (SExtractor, Bertin & Arnouts 1996). We worked in dual image mode

for the J and Ks bands, constructing Ks-selected catalogs with a 0.76" FWHM

gaussian convolution kernel and a 5a object detection threshold. Pinkpack

computed the final photometric calibration using the average photometric offset

for color-selected 2MASS stars in each field, weighted by the photometric errors, to

establish zeropoints.

2MASS was used for our astrometric and photometric calibrations in place of

the U.S. N i,'- Observatory all-sky catalog (USNO B1.0) since, being an infrared

survey, 2MASS tended to generate more matching stars.

3.6 The Catalog

I chose to work solely on the FLAMEX Bo6tes region, excluding the Cetus

region, because the NDWFS optical data has not yet been released for Cetus,

and our collaborator Mark Brodwin has derived robust photometric redshifts for

Bo6tes using the combined NDWFS, FLAMEX, and IRACSS data (Brodwin et

al. 2006). My initial intent was to base my study on the FLAMEX Ks-selected









catalogs. However, the quality of the FLAMINGOS detector varied widely across

the array, with significant comatic aberration near the edges. This resulted in

depth limits of over a magnitude worse compared to the central portions of the

fields. Each region (Bo6tes or Cetus) also consists of numerous adjoining fields,

resulting in a checkered image quality across the full survey area. For further

discussion of the problem, see Elston et al. (2006). C'! .. -ig to employ a cutoff

magnitude corresponding to the weakest components of our data had the advantage

of simplicity, but it would have caused a considerable loss of information at the

highest redshifts. C'!... -ig to retain the information from our deeper imaging

would provide a larger sample of high-redshift galaxies, but I would have to make

corrections for the less deeply imaged regions in order to correctly calculate galaxy

densities, and this would be an arduous and inexact process.

I opted instead to use the IRACSS 4.5/m-selected catalog. Its image quality

is uniform and consequently required few corrections to standardize the results.

I wrote a program which took the IRACSS catalog as input and then output

information for the sample of galaxies that I needed for my study; the details are

discussed further in Section 3.7.3.

3.7 Calculating the Spatial Correlation Function

3.7.1 Mathematical Overview

My procedure for calculating FLAMEX spatial correlations has many sim-

ilarities to the method used for SPICES (discussed in Sections 2.3.4-2.3.6). The

A coefficients for individual galaxies were determined in almost exactly the same

way with two important exceptions. First, the maximum angle 0 for the fit was

calculated to correspond to a physical distance of 2.0 Mpc in all cases, requiring

calculations of the angular diameter distance DA at various redshifts as discussed

in Section 3.7.3. The 2.0 Mpc limit was a compromise between encompassing a

larger area and avoiding losing too many galaxies near the region boundaries,









since I discarded galaxies within the physical distance limit of the boundaries for

simplicity. The second exception is that the dependent variable used for the fit

was the number of galaxies within the dO annulus at distance 0, not the number of

galaxies within distance 0. The latter approach, using concentric circles, resulted

in the dependent variable's values being correlated with each other, and so the

annulus-based procedure was preferred for the fit. Thus, I fit the equation


ni,(O)dO Ng 2 0 [1 + AO- 77] d0 (Ng 270 + Ng 27A0O23) d0,


where the left-hand expression stands for the number of galaxies observed in an

infinitesimal ring of width dO which is 0 degrees away from the reference galaxy.

(N, 27OdO is the expected number of galaxies in the ring.) As with SPICES, I

determined an average galaxy density N, for each galaxy's redshift composed of all

the galaxies in the survey area within 0.1 z, since galaxies outside this range were

unlikely to be physically associated with it. (This prompted me to ignore galaxies

with bad Zphot flags when calculating the correlation amplitudes. In essence, I knew

that these galaxies were present, but their redshifts were poorly determined, and so

I chose not to count them as ii, i!hl oring galaxies" according to my conditions.)

The procedure for translating from angular to spatial correlations differed

in several v--iv from that used for SPICES. To begin with, I worked in terms

of the spatial correlation length ro rather than the amplitude of the spatial

correlation function B. The spatial correlation function can be represented as

either i(r) = (r/ro)-~ or ~(r) = B,,Tr-, where ro and B are simply related

according to ro = B1/7. Studies that focus on the clustering around individual

galaxies, such as Longair & Seldner's (1979) radio-loud quasars, generally use

B, while most studies that investigate large-scale clustering of ensembles of

galaxies use ro. I use the latter here, as I am generally referring to the large-scale

studies for purposes of comparison. I also follow, e.g., Gonzalez et al. (2002) in









introducing a function f(z) describing the redshift dependence of galaxy < ,L-, li.- 1

so that (r) = (r/ro)- x (1 + z) x f(z). The term is frequently represented as

f(z) = (1 + z)-(3+,), where c = 0 corresponds to clustered galaxies maintaining
the same proper distance from each other with redshift, and c = 7 3 corresponds

to galaxies maintaining the same comoving distance from each other. I assume the

latter in all results presented here, in accordance with, e.g., Brown et al. (2003);

however, the results are essentially independent of the choice of epsilon, generally

varying by less than 1 between c = 0 and c = 7 3.

A more significant change for the FLAMEX procedure is the use of cosmologi-

cal Limber inversions to statistically deproject the two-dimensional distribution of

galaxies and derive spatial correlation lengths. Following Gonzalez et al. (2002),

the Limber equation is
{ -1
c F(7/2) (dN z)2E(z)DA(z)1-f (z)(1 + z)dz
o Ho r(1/2)[( 1)/2] [2 dNdz)dz] 2


where F is the Gamma function, dN/dz is the redshift distribution (the number of

survey galaxies in each dz redshift range), E(z) = [QM(1 + z)3 + Qk(1 + z)2 + QI]1/2

(adapted from Peebles 1993), and DA is the angular diameter distance (e.g.,

Hogg 2000). The cosmological parameters are taken from the 1st-year Wilkinson

Microwave Anisotropy Probe (WMAP) findings (Spergel et al. 2003): Ho

71 km/s/\ 1pc, IM = 0.27, 2k = 0, and QA = 0.73. Details of the calculation can

be found in Section 3.7.5. The advantage of this method over that described in

Longair and Seldner (1979) is that the Limber inversion makes use of the redshift

distribution of the galaxies instead of assuming a Schechter luminosity function to

determine galaxy populations at given redshifts and magnitude limits.

I implemented one other change in the procedure for converting from A to ro.

For SPICES, each galaxy's A value was converted to a corresponding B value, and









the results for a given redshift+SED bin were averaged. For FLAMEX, all of the

A values for galaxies in a given redshift+SED bin were first averaged, and then the

mean A value was converted to ro. The order is important due to the non-linear

dependence of ro upon A. The FLAMEX approach more closely resembles the

standard ensemble techniques of other large-scale clustering surveys and enables a

direct comparison with their results. I also experimented with stacking by annulus,

which is particularly similar to the standard method. Since all the galaxies' annuli

were at the same physical distances (100 equally spaced intervals up to 2 Mpc),

it was possible to add the number of neighboring galaxies found at a certain

distance away for all galaxies of a given redshift+SED bin. This produced very

similar ro values to the non-stacked method at redshifts 0.5 < z < 1.5, but the

stacking method had erratic results at the lowest redshift bin used in this study,

0.3 < z < 0.5, presumably due to the substantial changes in both survey population

(dN/dz) and cosmological effects from z = 0.3 to z = 0.5. In all further discussions

in this dissertation, I employ the non-stacked method.

Finally, for purposes of clarity I note that, as with the SPICES study, a

correlation function calculated in this way for a given galaxy is based upon the full

sample of galaxies located around it (within 0.1 z), not solely on galaxies of the

same SED-type as it.

3.7.2 Photometric Redshifts and SED Classifications

Another important difference between the FLAMEX and SPICES stud-

ies lies in the methods of determining photometric redshifts and SED-types.

While Andrew Connolly's code provided redshifts for the SPICES data (see

Section 2.3.3), Mark Brodwin contributed the redshifts for the combined NDWF-

S/FLAMEX/IRACSS surv-,- and a few words about his technique are in order.

His primary approach used template-fitting based upon the Coleman et al. (1980)

galaxy SEDs along with Kinney et al. (1996) starburst SEDs, with extensions into









the far-UV and mid-IR based on Bruzual and C'!I lot (2003) models. With linear

interpolations between the basic templates, the total number of SED classes rose

to 19. Each galaxy was simultaneously fit for redshift and SED-type; they were as-

signed SED values of 0-18, where the original templates were 0=E, 7 Sbc, 13 Scd,

16 Im, 17 SB3, and 18 SB2. Comparisons of the photometric redshifts with the

AGES spectroscopic redshifts (primarily galaxies with z < 0.8) demonstrated a

dispersion of a, = 0.230 and a,/(1 + z) = 0.170, while a 95'. clipping to remove

the effects of catastrophic errors results in a, = 0.079 and a7/(1 + z) = 0.061.

For a smaller in-house sample of ~ 500 spectroscopic redshifts that is more rep-

resentative of the full redshift range of the survey, the unclipped dispersion was

a, = 0.498 and a,/(1 + z) = 0.253 and the clipped dispersion was a = 0.127 and

a,/(1 + z) = 0.081. Brodwin went on to supplement these results with those from a

neural network algorithm (ANNz; Collister and Lahav 2004) which was very effec-

tive within the AGES redshift limits, particularly for strong PAH-emitting galaxies

and AGN which are not fit well by the SED template set; however, these values

were not incorporated into this project. For further details about the photometric

redshifts and SED classifications, see Brodwin et al. (2006).

3.7.3 The Final Catalog: catalog' i. e.c

Only a fraction of the sources listed in the full catalog were useful for this

project, and so I wrote a program called catalogparse. c (see Appendix A) to cull

through it and output a greatly streamlined catalog. In the code, I implemented

the following procedure.

First, I imported two files of useful information. The first file contained K*

magnitude values and 4.5/m K color values vs. redshift. (K* is the absolute

K-band magnitude of the turnoff for the Schechter luminosity function for galaxies;

high-luminosity galaxies and low-luminosity galaxies follow different frequency

distribution laws, with high-luminosity galaxies at brighter magnitudes than K*









and low-luminosity at fainter magnitudes.) An important issue for high-redshift

galaxies is that the light emanating from them has been stretched to longer

wavelengths, so that the part of the spectrum in which we observe the light is not

the part from which it originated. The adjustments that must be made for this

effect are called K-corrections; P. -._.i i ,li (1997) has a good overview. Additionally,

evolutionary corrections must be made to account for the differences in galaxies'

spectra/colors earlier in the universe's history, when brighter, bluer stars pl i, d

a larger role. These corrections can be calculated with one of several publicly-

available stellar population synthesis codes; we used GALAXEV (Bruzual &

C'!i i lot 2003). Our input parameters were for a passively-evolving single-burst

galaxy which formed at zf = 3; we used solar metalicity, Padova 1994 evolutionary

tracks, and a Salpeter (1955) IMF from 0.1 to 100 solar masses (see Figure 3

1). (Standard alternatives would have little effect in the redshift range in which

I am interested, z < 1.5.) The objective of all this is to estimate the absolute

magnitudes of the galaxies in my sample and to employ an absolute magnitude

cutoff. This prevents the inclusion of faint, low-redshift galaxies in my galaxy

density calculations that would not have been observed at high-redshifts. According

to the modelled corrections, the faintest apparent 4.5/m magnitude that an L*

galaxy would have at z < 1.5 would be 17.23. (I use the Vega magnitude system

throughout.) The 4.5/m magnitude limit of the IRACSS data is 17.8. Therefore, I

discarded all galaxies which were fainter than L* + 0.57 1 1.- using the corrections

for each galaxy's redshift to identify the galaxy's absolute magnitude and the value

of L* at that redshift.

The second file imported into my program contained cosmological angular

diameter distances (DA) versus redshift in intervals of Az = .001. DA is a

represention of the physical distance that corresponds to a given angular distance

in the sky. I calculated these values following Hogg (2000), using the following










































Figure 3-1: IRAC ch2 a: :. :-ent magnitude versus [i i :::, for an L* galaxy. T.
Sis based on the stellar pc :1 :: synthesis code of Bruzual and ( :: t ( .)
and ,.i.1. I K and evolutionary corrections for a pa i 1 evolving L* galaxy with
zform, 3. i : dashed line shows the :i:AC.'' 50- depth using tures (17.8
and the dotted line shows the faintest -:.. .rude that an L* galaxy would
have at : : redshift less than 1.5 (17.23 nmag).









cosmological parameters from the 1st-year Wilkinson Microwave Anisotropy Probe

(WMAP) observations: QM = 0.27, QA = 0.73, k = 0, and Ho = 71 km/s/\!pc

(Spergel et al, 2003).

My program then read and analyzed the information for each of the 225,746

objects in the IRACSS 4.5/m-selected catalog. I output information only for

those objects which met certain strict conditions. First, they had to fall within

the FLAMEX Bo6tes region, and specifically within three subregions which

represented 3.55 deg2 of the 4.7 deg2 Bo6tes area, excluding areas close to the

survey boundaries and also a section of the FLAMEX survey which extended

outside the NDWFS and IRACSS surv-v- Only 93,907 objects met this condition.

Table 3-1 presents the sky coverage of the three subregions.
Table 3-1: FLAMEX Subregions
Name RA Bounds Dec. Bounds Area (deg )
Subregion 1 216.329167 < a < 218.820833 33.062500 < 6 < 33.641667 1.205
Subregion 2 216.291667 < a < 219.529167 33.641667 < 6 < 34.350000 1.901
Subregion 3 217.729167 < a < 219.333333 34.350000 < 6 < 34.686944 0.445


Next, the objects had to pass Mark Brodwin's galaxy/star separation pro-

cedure. The primary criterion was SExtractor's STAR_CLASS parameter in the

best-seeing NDWFS optical band. Only 77,075 objects met this standard, which

was a conservative cut reliable down to R ~ 23, designed to err on the side of

retaining stars rather than removing galaxies. Some bright, unresolved, star-like ob-

jects were also retained if they were robustly in the "AGN-v. I;, according to the

mid-IR color criteria defined by Stern et al. (2005), as these are almost certainly

quasars. A secondary cut relied on IRAC shape information and was effective only

at bright magnitudes, but it ruled out an additional 169 objects, leaving 76,906.

Finally, I automatically discarded those objects with z < 0.01. These were generally

objects (stars in many cases) whose photometric redshift probability distribution

from Brodwin's code was flat, contributing no clear information. This procedure

left 74,577 galaxies.









The following cuts were of a more subjective nature. I removed galaxies with

z > 2. Above this value, the redshift uncertainties were large, the sample sizes

were small, and the galaxies were faint. I therefore decided that they would not

reasonably be useful in my study. This reduced the total to 60,592 galaxies. An

additional 197 galaxies were discarded, leaving 60,395, if they were in a masked

region for any of the optical NDWFS bands (Bw, R, and I) or chi (3.6/m) or ch2

(4.5/pm) of the IRACSS data, since this rendered their photometric redshifts less

certain and since I would later use a combined mask image for all five bands when

making corrections for undetectable galaxies. I then used information from my

first imported file (discussed above) to remove galaxies which were fainter than the

constant luminosity threshold, which left 45,461 galaxies. This cut took a large toll

on galaxies at z < 0.5, as many of these were intrinsically faint galaxies that would

not have been observed at higher redshifts.

The remaining galaxies were all potentially useful for my study, and I exported

their information into a final catalog file. However, only 37,494 of them could be

used as "reference" galaxies, meaning galaxies for which calculations of A were

made. The other galaxies were within 2 Mpc of the region edges; although I could

have corrected for this, I chose not to for the sake of simplicity, and so these

galaxies were used only in estimating the densities around reference galaxies.

I output the following information for each of these 45,461 galaxies: Galaxy

ID, right ascension, declination, SED type, and Zphot. I also included a binary

flag to indicate whether the galaxy could be a reference galaxy, as well as a flag

indicating whether it matched our criteria for extremely red objects (EROs,

discussed in Section 3.8). Finally, I used the first imported file (discussed above) to

output the angle corresponding to 2 Mpc at that galaxy's redshift.

In practice, fewer than 45,461 galaxies were used in this study, as I decided to

restrict the final version to a redshift range of 0.3 < z < 1.5, which meant that









only galaxies within this range could be reference galaxies and only galaxies within

0.2 < z < 1.6 were potential neighbors for purposes of calculating A values. This

resulted in the use of 41,837 galaxies, including 32,650 reference galaxies, for all

results in Section 3.8.

3.7.4 Masking Information: maskfrac.pro

After using catalogparse. c to establish a final catalog with only the galaxies

that were important to my project, I ran a second preparatory program called

maskfrac .pro, written in IDL. The purpose of the code was to determine the

extent to which masking affected the neighborhood of each galaxy, and to correct

for it as much as possible. The masking information was taken from a large full-

survey FITS file which superimposed the individual mask files for the optical

NDWFS bands (Bw, R, and I) or chi (3.6/m) or ch2 (4.5/m) of the IRACSS data,

indicating areas which fell within masked regions for any of them due to bright

stars, bad pixels, etc. The maskfrac .pro program ran in two stages. The first

stage involved a complete sampling of the Bootes subregions used in my project

(see Table 3-1, checking a grid of test points with 4" spacing to determine what

overall fraction of the area is unmasked (89.7' .). The main program corrbrod. c

(described below) used the unmasked survey area, 0.897 3.55 deg2 = 3.19 deg2,

to calculate galaxy surface densities. The second stage of maskfrac .pro created a

grid of test points around each reference galaxy in the final catalog, testing them

to see if they are in masked regions or not. It then determined their distances from

the reference galaxy, sorted them by those distances, and binned them according to

the number of annuli used in corrbrod. c. Finally, it output the fraction of masked

points in each annulus. The grid points had 4" -1' ii.- with double-sampling

in the innermost 7'. of the annuli. This was the most computationally-intensive

portion of my project's calculations, and so the code was written to be easily









adapted for use on multiple machines simultaneously, and it only needed to be

rerun if the final catalog was changed. The basic code is included in Appendix B.

3.7.5 A and ro Calculations: corrbrod.c

I will now describe the algorithm for my main program corrbrod. c in some

detail, showing how I took my final catalog (described in Section 3.7.3) and

determined the relation at different redshifts between galaxies' SED-types and their

spatial correlation lengths. (The program code is available in Appendix C.)

I began by reading my full catalog info into large arrays. During this process,

I kept track of the number of galaxies in each Az = 0.1 redshift bin, which

was necessary for the next step. I then calculated the Limber inversion factor

for every redshift in my range of interest (0.3 < z < 1.5) in intervals of Az

0.1. The Limber inversion is the process by which the amplitude of the angular

correlation function (which is actually observed) is converted to the expected

spatial correlation length by a geometrical deprojection; Section 3.7.1 provides

additional details.

With the preliminary work done, corrbrod. c then calculated A for each

galaxy individually. First, the galaxy's flags (see Section 3.7.3) were checked to

determine whether it qualified as a reference galaxy; if not, then all remaining

steps were skipped, and the code proceeded to the next galaxy. If so, then the

program identified all i, i,1iiI in; galaxies within 2 Mpc and Az = 0.1 and

stored the information for these galaxies in a separate array, which was then sorted

according to their distances from the reference galaxy. During this search, I also

counted up all galaxies within Az =0.1 (even if they were not within 2 Mpc) and

divided this quantity by the total image area (with masked regions subtracted;

see Section 3.7.4) to determine the average surface density of galaxies within that

redshift range for calculations of A.









The next stage involved setting up a linear least-squares fit to find the A

coefficient. I created two arrays of 100 elements each. The first consisted of 100

equally-spaced radii, representing the distances to concentric annuli around the

reference galaxy out to 2 Mpc. The second consisted of the number of galaxies

found within each of the 100 annuli. It was necessary to correct these values for

regions with poor data using the output of maskfrac.pro (Section 3.7.4), which

included an estimate of the fractional unmasked area within each annulus around

each galaxy. If, for example, 95'. of the region comprising a certain annulus of the

reference galaxy was unmasked, then the number of observed, unmasked galaxies

within that annulus were multiplied by 1.0/0.95 to produce a "true ,I 1::;

estimate for the X2 fit of A. The program would also assign the reference galaxy a

"data quality" value of .95, which was used in later mean A calculations to signify

that it only possesses 95' of the information content that a galaxy with no masked

regions nearby would have; it would then be weighted accordingly. However, for

purposes of fitting for an individual galaxy's A, I weighted the annuli equally.

All of the reference galaxies' A values were determined individually; corrbrod. c

then exported info for each galaxy into an output file, including the galaxy ID, the

number of neighboring galaxies, the galaxy's A value, an estimate of the data qual-

ity based upon the fractional masking in the neighborhood, the galaxy's SED-type

and photometric redshift, and a flag carried over from the original catalog that

indicated whether the galaxy was an ::l i i. ly red object" (ERO). Finally, the

code read the information back in for purposes of inning it by redshift intervals

(generally with Az = 0.2 width), which were further divided into SED bins. The

SED bins could either be flexible, where galaxies in adjoining SED bins were au-

tomatically binned together in such a way as to make every bin of equal size, or

fixed, where the same predetermined SED ranges were used for inning throughout,

regardless of bin size. (A separate procedure was used for analysis of EROs.) All of









the A values for a given redshift+SED bin were averaged together, and the result

was then multiplied by the appropriate Limber inversion factor for the mean of the

galaxy redshifts to obtain a single spatial correlation length (ro) for the bin. (See

Section 3.7.1 for further discussion.) The raw data for analyzing the density-SED

relation was thus available for plotting and analysis.

3.8 Results

3.8.1 Evolution of the SED-Density Relation

The results of the primary density-SED study are shown in Figure 3-2. The

standard form of the local-Universe relation, in which early-type SEDs are more

highly clustered than late-type SEDs, is clearly visible at all redshifts. The errors

are determined using a bootstrap technique, in which the set of A values for a given

bin is used as the sampling pool for 1000 randomly-generated sets of A values (with

replacement). For each random set, I then convert the mean A to ro through the

Limber inversion, as usual. I use the standard deviation of the 1000 ro values to

establish an error estimate. There is no consistent change with redshift in the slope

of the density-SED relation, although it is interesting that the highest redshift

range appears to have the flattest results.

It is also interesting to note that, at intermediate redshifts (0.9 < z < 1.3),

the absolute correlation lengths are consistently higher than they are at z < 0.9

or at z > 1.3 (see Figure 3-3). One plausible explanation for this is that the

4.5pm L* model evolution depicted in Figure 3-1 deviates from the true evolution,

presumably due to its assumption of passive evolution. If my fixed-luminosity

selection criteria (see Section 3.7.3) are in fact removing slightly higher-mass

galaxies at z = 1 than at z = 0.5, then this would cause the observed rise in ro.

In Figure 3-4, the data is replotted after renormalizing to a mean ro of 4.69

Mpc, consistent with the lowest redshift bin. The plot again sl.;-.- -1- a slight





















6 i


-0.7 (954,


9!




111


] T I


Figure 3-2: FLAMEX density-SED results (flexible bins). The bins in this fig-
ure are all tuned to have equal numbers of galaxies for a given redshift range and
roughly equal numbers of galaxies across redshift ranges, in this case around 1000
(the exact numbers are included in parentheses in the legends). Error bars are
based on bootstrap sampling as described in the text. It is important to bear in
mind that the SED types are based on non-evolved models.


bLU VS. ro, z I I.)
z=1.1 1.3 (990)
z 1.3-1.5 (1057)












6


5
4


2





Redshift


Figure 33: Overall ro vs. redshift. This figure shows the combined ro for all SED
values in each redshift bin, with standard bootstrap errors, and the increase in ro
at 0.9 < z < 1.3 is clearly visible. For simplicity, the datapoints are plotted at the
bins' midpoints rather than using the mean redshift; however, this has an effect of
less than Az = 0.01.

amount of flattening in the slope at higher redshifts, though the effect is not a

strong one.

Figure 3-2 has flexible bin boundaries in an effort to equalize the galaxy

populations in the bins as much as possible. Conversely, Figure 3-5 has fixed bin

boundaries that correspond to specific ranges of Brodwin's SED classifications. The

bins now have unequal quantities of galaxies, and this is reflected in the larger error

bars for less-populated bins. There is no significant change in the overall trends,

however.

A natural question is whether bright galaxies follow the same general trends

as the overall population. Figure 3-6 is comparable to Figure 3-2, but shows only

galaxies with L > L*, rather than the main study's L > 0.6L*. It is difficult to

identify any clear differences between the two figures, although the L > L* density-

SED relation shows the same evidence, perhaps slightly stronger, of flattening in

















d'i'


II 4


Figure 3-4: N.i i, i. .1 FLAMEX density-SED results (flexible bins). This figure
is similar to Figure 3-2, with the exception that every redshift bin has been renor-
malized so that their mean ro values are equal to that of the lowest redshift bin, i.e.
5.98 Mpc.













I
I

ii I


Figure 3-5: FLAMEX density-SED results (fixed bins). The bins in this figure
cover fixed ranges of Brodwin's SED classification values, namely 0-2, 3-6, 7-10,
and 11-18. The exact x-axis value is still determined by the mean SED class within
each bin, however, so slight offsets may be seen.


I


i











z-0.3-0.5 (706) z-0.7-0.9 (815) z 1.1-1.3 (844)
z-0.5-0.7 (726) z 0.9-1.1 (832) z-1.3-1.5 (772)







-I 4 I
6 6 6

61T IT







2 2 2 -
0 I LPi







E SO Sbc Scd E SO Sbc Scd E SO Sbc Scd
SED type SED type SED type

Figure 3-6: L > L* density-SED results. This plot uses flexible inning, like Fig-
ure 3-2.

the highest redshift bin. An effort at a L > 2L* luminosity cut was abandoned due

to insufficient candidates for meaningful inning on these fine scales.

3.8.2 Evolution of the ERO-Density Relation

Another question is how the clustering of EROs changes with redshift, and

how it compares to the clustering of non-EROs. I identify EROs according to

the criteria in Elston et al. (2006), namely R Ks > 5 (within 6" apertures),

J Ks > 1.2, and Ks < 19.5, resulting in few matches for z < 0.9. EROs are

commonly considered to represent two separate types of galaxies: passive, evolved

systems at z = 0.8 2.0 and (d,-li- starbursts at comparable redshifts. At the Ks

limit that we use, the EROs are predominantly passive galaxies. In any event, as

there is no SED template for the d(t-li- starburst galaxies, they are also generally

registered by Brodwin's code as early-type galaxies. Figure 3-7 indicates how

the EROs as a whole are distributed among our SED-types. In order to compare









the density-SED relation of EROs with non-EROs, I restricted our non-ERO

sample to those galaxies which are detected in Ks, and specifically to those with

Ks < 19.5, so as to acquire a similarly-selected set. The results for these are

plotted in Figure 3-8. EROs are substantially more clustered than non-EROs at

0.9 < z < 1.3, as expected, although the clustering at 1.3 < z < 1.5 appears to be

comparable for both classes of objects and markedly lower in the case of the EROs.

ERO-ERO spatial correlation lengths are also plotted, showing how they correlate

with each other, since it is the most common diagnostic in other studies. The plot

also contains a theoretical prediction for early-type galaxies with stellar masses

greater than 3 x 10'"'\! from Kauffmann et al. (1999), based on a ACDM universe.

Table 3-2 presents a comparison with other ERO studies that use R K > 5

or R Ks > 5 for selection; it is based on Table 1 from Brown et al. (2005).

The survey names refer to the following studies: FLAMEX, this study; NDWFS,

Brown et al. (2003); NTT-WHT, Daddi et al. (2001); Subaru 1 and 2, Miyazaki et

al. (2003) for dl-i- starburst and passive evolved SEDs respectively; and ELAIS

N2, Roche et al. (2002) for the no-evolution model. Values of ro are adjusted to

assume Ho = 71, in accordance with my plots. This study includes substantially

more EROs than any other to date. The measured ro values are smaller than those

reported in other studies. In the case of Brown et al. (2003), this may be due

to the different magnitude cuts; only brighter galaxies are included there, and a

strong relation between spatial correlation and luminosity has been identified by

N. .i. ig et al. (2002). A secondary cause may be the added selection by absolute

magnitude, based upon L > 0.6 L* at 4.5/m, used in my project. The spatial

correlation lengths for the other surveys cannot be reconciled with my findings; if

verified, the present results would require significant modifications to current model

predictions of the present-day descendants of the ERO population.






























Figure 3-7: Histogram of EROs versus Brodwin's SED types. 0=E, 7 Sbc, 13 Scd






10 --- -
ERO-ERO r,


'630


U.2 U.4 U.b U0. I .U 1.2 1 .4
Redshift


Figure 3-8: ERO and non-ERO correlation lengths versus redshift. The bins in this
figure are each Az =0.2 wide. Note that the ERO ro values are based on all sur-
rounding galaxies; these are ERO-galaxy correlations, not ERO-ERO correlations
(as are commonly shown in studies). For simplicity, the datapoints are plotted at
the bins' midpoints rather than using the mean redshift; however, this has an ef-
fect of less than Az = 0.01. The numerical values indicate the number of galaxies
represented by each datapoint. The dotted line is a theoretical prediction from
Kauffmann et al. (1999) for early-type galaxies.









Table 3-2: ERO Spatial Clustering Studies
Survey Redshift Range Galaxies Magnitude ro (Mpc)
FLAMEX 0.9 < z < 1.1 1145 Ks < 19.5 8.6 0.4
FLAMEX 1.1 < z < 1.3 1753 Ks < 19.5 8.2 0.3
FLAMEX 1.3 < z < 1.5 1148 Ks < 19.5 4.7 0.6
FLAMEX 0.9 < z < 1.5 4046 Ks < 19.5 7.7 0.3
NDWFS 0.8 < z < 3.0 671 K < 18.4 13.7 1.4
NTT-WHT 0.8 < z < 2.0 400 K < 19.2 19.4 2.1
Subaru 1 0.0 < z < 4.3 134 K < 20.2 17 3
Subaru 2 0.0 < z < 4.3 143 K < 20.2 15.5 1.5
ELAIS N2 1.0 < z < 3.0 158 K < 20.25 14.5 1.7


3.8.3 Galaxy Clusters

As an additional investigation, I applied my procedure to galaxy clusters,

computing the cluster-galaxy spatial correlation lengths, ro. Similar studies (e.g.,

Yee & L6pez-Cruz, 1999; Yee & Ellingson, 2003) have calculated the amplitude of

the cluster-galaxy spatial correlation function, Beg, by adapting the B calculations

originally made by Longair & Seldner (1979) for the neighborhoods of radio

galaxies. Their objective was to quantify cluster richness and to use Be as a proxy

for cluster mass. As noted in Section 3.7.1, B and ro are simply variants of one

another, where ro = B1/ and ro(z) = (1 + z) x f(z)1/7 x B1/7. After correcting for

Ho, the range of Bcg values found by these studies is roughly 250 to 1000 Mpc177,

which corresponds to ro = 20 50.

The FLAMEX clusters were identified by collaborator Anthony Gonzalez.

His code convolves the galaxy distribution with a wavelet smoothing kernel for

a series of redshift slices, then uses bootstrap simulations to define the threshold

corresponding to one false detection in the Bootes field per redshift bin, and objects

which supercede the threshold are detected and assigned a rating > 1 representing

the strength of detection. Using coordinates approximating the cluster centers, I

obtained A and ro values based on the surrounding galaxies. Figure 3-9 presents

ro versus redshift for the clusters. In general, our ro values are lower than those

indicated by the above-mentioned studies, presumably due to different selection


















10 10



8 -

0.4 0.6 0.8 1.0 1.2 1.4
Redshift


Figure 3-9: Cluster ro values versus redshift. Each datapoint represents a set of
combined ro values from galaxy clusters within a given redshift bin. The numerical
values represent the number of clusters represented by each datapoint, and the bins
in this figure are each Az =0.2 wide. For simplicity, the datapoints are plotted at
the bins' midpoints rather than using the mean redshift.


criteria. The flatness of the slope indicates that the cluster mass limit is not

changing quickly within our redshift regime, although the average richness of the

systems may possibly be diminishing at z > 1.

Figure 3-10 compares the individual cluster ro values with the detection

ratings assigned by Gonzalez to assess the scatter between the two quantities.

There is a visible correlation, but with a high degree of scatter for the lower-

significance detections. Negative ro values indicate that the A value was negative,

i.e. the neighborhood looks less dense than average. This apparent discrepancy

probably results from a stronger luminosity cutoff than that used by Gonzalez,

from clusters whose centers are not well-defined, or from marginal clusters whose

external surroundings are unusually under-dense. There is no apparent difference in

the scatter at high versus low redshifts.















20 +o.+ o++ $ + +

Fu 1 ( au+ w+ +s+s d r
++ +
++
= >++ + +

O + o + z<1.0
# 14 0+ 0 z>1.0
-10 f + +

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Detection Level


Figure 3-10: .. :- -. ro values versus detection rating. Each datapoint represents
an individual galaxy cluster, comparing its ro value to the detection rating assigned
G" Conzalez' code. A detection rating of 1 signifies a threshold detection, while
higher values represent stronger detections.


3.9 Discussion and Conclusions

The results shown above offer useful insights into galaxy evolution. First and

foremost, the density-SED relation is established by z = 1.5, with no substantive

evolution between that epoch and the present. At the latter redshift, there should

be less than 1 cluster with M > 1014 solar masses in the entire FLAMEX Bootes

region. Hence, the SED-density relation is in place prior to cluster assembly. This

is consistent with the idea that the key parameter in determining the SED (and

morphological) fraction is local density rather than the rich cluster environment.

Another important result is that the spatial correlation lengths are not strongly

evolving across the redshift range, -i-.-I -I ii- stable clustering for a fixed luminos-

ity threshold.

This program offers two important benefits to the overall study of the density-

SED relation. By using a 4.5/m selection, we are able to select a sample with a

roughly constant intrinsic luminosity over the entire redshift regime. No previous









such studies with a 4.5/m-selected sample exist. In addition, while the study lacks

spectroscopic redshifts, the use of photometric redshifts allows us to cover a much

larger area, which is necessary to probe a sufficient volume of space to include a

representative sample of massive galaxies and to minimize the unpredictable effects

of cosmic variance. Moreover, because of the extended wavelength baseline used

to generate the photometric redshifts, the redshift uncertainties are only weakly

dependent upon SED-type and redshift out to z=1.5.

The ERO results showed the expected augmentation in clustering for EROs

compared to normal galaxies at 0.9 < z < 1.3 and established values for the spatial

correlation length which showed little change between the 0.9 < z < 1.1 and

1.1 < z < 1.3 ranges. At 1.3 < z < 1.5, however, this study found no significant

difference between EROs and non-EROs, which could be due to an insufficient

sample or could indicate that the population of galaxies that meet my ERO criteria

is different past z ~ 1.3. The di-I v starburst population may begin to dominate

the sample, for example, although studies such as Miyazaki et al. (2003) did not

find a strong difference in the ro values for dusty starburst and passive EROs.

The cluster-galaxy spatial correlation lengths showed little evolution with

redshift, indicating that the mass limit for the FLAMEX cluster survey is only

a weak function of redshift from 0.3 < z < 1.5. The ro values were not highly

correlated with Gonzalez' detection ratings, however, so it is not clear which is

more useful as a proxy for cluster mass.

3.10 Future Work

The most obvious extension of this work is to the Cetus region of the survey

when the NDWFS optical data is released and accurate photometric redshifts

can be calculated. Some of the issues studied above had ambiguous results due

to insufficient sample sizes per bin (e.g., the SED-density relation for bright

luminosity cuts), and the Cetus region would add roughly 50'U. more data. There









is also room for more detailed work beyond what the FLAMEX survey is capable

of achieving. For example, followup spectroscopy of selected regions can measure

the success of our photometric redshifts at high z and look for systematic errors in

much the same way as I used the SPICES spectroscopy. Similarly, we could benefit

from replicating the survey photometry in regions imaged by the Hubble Space

Telescope's Advanced Camera for Surveys to assess the morphological connections

to our SED-types in a variety of cluster and field environments. Finally, pushing a

subset of the survey region to greater depths could provide dividends, as we could

establish whether the apparent flattening of the density-SED relationship at z > 1.3

is a real phenomenon.

There are also separate but related projects that merit investigation. Although

the focus of this work was not specifically upon the evolution of ( ,1-l. i i:- there

is a great deal of ongoing work in this area that is attempting to establish the

extent to which clustering parameters change with redshift, and the FLAMEX

survey is well-suited for contributing to this. An analysis of the evolution of the

luminosity function with redshift will also help to develop the larger picture of

galaxy evolution over the past nine billion years.















CHAPTER 4
AGE DISTRIBUTION OF OPEN CLUSTERS

4.1 Introduction

Open clusters are born in the midst of giant molecular clouds, but they do

not stay there for long. The stars depart the clouds within a few million years

and travel through space together for a time. Unlike OB associations, there is a

significant degree of gravitational binding for open clusters, but there are potential

disruptive forces that will unbind them in the end. Many clusters dissipate within

ten million years of their birth, and although a few are known with ages of billions

of years, they represent only a tiny fraction of the total. Gas removal by O and B

stars, concentration of angular momentum in a central binary, and galactic tidal

disruption have all been cited as causes of cluster dissipation. The primary goal of

this project is to investigate these causes and assess their relative importance.

4.2 Comparison of Cluster Catalogs

Statistical studies of the ages of clusters are a 1 ii' 'r observational means

of achieving this goal, and they require as complete a catalog of clusters as is

currently attainable. The most recent comprehensive published catalog is that of

Lynga (5th ed., 1987), listing all 1162 open clusters known at that time along with

a wide array of their properties (when available). However, many additional obser-

vations have been made in the past nineteen years, both revising and supplement-

ing these values, so that the Lynga catalog is now out of date. One current source

for cluster information is the WEDBA database (http://obswww.unige.ch/webda),

compiled and actively maintained by Dr. Jean-Claude Mermilliod and Dr. Ernst

Paunzen. It encompasses a v ,i I I, i of recent observations (esp. Loktin, Gerasi-

menko, & Malisheva, 2000; Dambis, 1998; Malysheva, 1997; Dutra & Bica, 2000;









and Kharchenko et al. 2005). More recently, Dias et al. (2002) established a second

web-based catalog of open clusters at www.astro.iag.usp.br/~wilton (DAML02).

The primary motivation for DAML02 was to present up-to-date information, par-

ticularly with regards to the proper motions and radial velocities of clusters. Both

catalogs are substantial improvements over the Lynga catalog; WEBDA (as of this

writing, May 2006) has 1746 clusters and DAML02 has 1756 clusters. Many do not

yet have determined ages, but the web-based catalogs have increased the number

from 403 (Lynga) to 960 (WEBDA) and 861 (DAML02); most of the improvement

here has come from studies performed in the last five years. Kharchenko et al.

(2005) is particularly worthy of note, as they published a consistent set of observa-

tions and parameters for 520 clusters (of which 109 were new discoveries) based on

the All-Sky Compiled Catalog of 2.5 Million Stars (ASCC-2.5, Kharchenko 2001).

The question that naturally arises is whether WEBDA or DAML02 is consis-

tently "b' I I i than the other; unfortunately, there is no straightforward answer.

Both catalogs receive updates based on current literature, but DAML02 uses some

sources that WEBDA does not and vice versa. Even their naming conventions for

clusters are slightly different; for 21 of the ASCC clusters listed in WEDBA (10,

22, 32, 41, 42, 44, 47, 49, 50, 68, 86, 89, 92, 96, 97, 103, 106, 112, 118, 124, and

129), DAML02 instead uses the names from their original discoveries by Alessi,

Alessi-Teutsch, Ferrero, Herschel, and Teutsch. Lists of cross-identifications can be

found on both websites, though a little digging may be required. Regarding the

cluster parameters, such as age, a complete analysis of the catalogs to determine

the best information would be a formidable project in its entirety. In lieu of this, I

studied a subset of the catalogs, those clusters (with listed age parameters) whose

identifiers began with 'A' or 'B'. I looked for basic patterns in the catalogs' use of

sources in hopes of identifying a "superior" catalog or an easy way of combining

the best information from both. The investigation comprised 252 and 229 clusters









with ages in the WEBDA catalog and DAML02 catalog, respectively. A detailed

report, broken down by cluster name, is located in Appendix D.

The comparison of WEDBA and DAML02 subsets finds a number of differ-

ences between them, but neither catalog is clearly superior. Both are subject to

sporadic typos (I found two for each and reported them all), and information about

their references is occasionally difficult to locate. I find no simple algorithm for

determining which age value the catalogs use when multiple studies are available.

When the two catalogs list different ages for a cluster, WEBDA uses more recent

sources than DAML02 in some cases (I identified 7), while the opposite is true in

other cases (I identified 4). More commonly, a cluster will have an age listing in

WEDBA but not DAML02 (22) or in DAML02 but not WEBDA (8). In particular,

WEBDA is more likely to include the ages determined by Kharchenko et al. (2005).

DAML02's naming conventions are preferred, since their identifiers are consistently

based on the original discoveries. DAML02's list of removed clusters contains

some valuable information that is not reflected in the WEDBA catalog. Finally,

DAML02 includes flags for the various clusters, such as I ..--I li. globular cluster"

or "dubious cluster," which can be used to cull questionable candidates from a

dataset.

4.3 Sample Construction

There is currently no clear strategy for using the two catalogs to construct a

"b, -I collection of cluster ages. A detailed investigation looking at the full set of

listings in the catalogs and assessing the quality of the age determination methods

used in the various studies that they reference would be a formidable under' l.ii

although a valuable one, worthy of future work. The simplest alternative is to

select a large, self-consistent study such as Kharchenko et al. (2005), which also

eliminates inhomogeneities in the methods of age determination between various

groups. However, in this study, I accepted greater systematic uncertainties in









exchange for a larger sample size, namely all the open clusters whose ages we have

a reasonable estimate of. Accordingly, I constructed my initial sample as follows.

I started with the WEBDA clusters with age values as a base and added all (49)

non-duplicate DAML02 clusters (taking care to identify cases where the naming

conventions were different). Next, all clusters found in DAML02's list of removed

clusters (9) were taken out of the sample. I chose to retain clusters fl .-.-B d as

"dubious" in DAML02, but I could equally well have removed them. The resulting

sample contained 997 clusters.

4.4 Sample Overview: Ages and Locations

A brief overview of the clusters is presented in Figure 4 1 (showing the number

count vs. age), while Figures 4-2 and 4-3 show the spatial distribution of clusters

in the Milky Way. In Figure 4-1, there is an extremely sharp dropoff of clusters

within the first 50 million years, after which they continue to decline, but more

and more slowly. The graph cuts off at the two billion year mark, but a handful

of clusters are seen as old as 8-10 billion years! The rise between the 0-10 million

year bin and the 10-20 million year bin is probably attributable to the youngest,

embedded clusters being more difficult to see; -' of the first bin's members are in

the 5-10 million year range. Consequently, later statistical treatments in this paper

assume the bin's value to be double what is actually observed.















































bi








0 0
Cme










0

SDo
1 1 V




T)


0

Tr












.5
l-J <
* ^ L









Figure 4-2 shows the distribution of the clusters in the Milky Way, from a top-

down vantage point. Not surprisingly, the greatest concentration is near the Sun

at 0,8500. It is also worth noting that older clusters dominate the sample in the

outer regions of the Galaxy, compared to the regions inside the solar circle, where

there are relatively few of them (discussed below). Also, there are significantly

more clusters (61 .) on the positive side of the X=0 axis, which is rather puzzling,

as there is no obvious reason why they would be preferentially seen in front of

or behind the solar revolution path. The hypothesis that young open clusters

trace spiral structure is now out of favor (e.g., Janes & Adler, 1982). Figure 4-3

is another positional map, plotting the clusters' radial distance from the Galactic

center against their z heights out of the Galactic plane. Here, the effects of age

are quite dramatic; virtually all of the clusters 500+ pc from the plane are older

than 400 million years, reinforcing the idea that clusters form in the midst of the

thin disk, and giving an indication of their rate of dispersion. Note also that the

dispersion is unambiguously greater in the outer regions of the Milky Way, as any

high latitude clusters near the solar circle would easily have been identified.

4.5 Selection Effects

Unfortunately, not all of these clusters are created equal: there are a number

of potential selection effects that must be considered. The v--i- in which various

authors treat this produce substantial variations in their results. The first selection

effect is the straightforward prediction that younger clusters, with their brighter,

bluer stars, will be more readily detected at large distances than older clusters.

Another problem is the potential for observer selection. Observers interested in

star formation may specifically seek out young clusters for age determination.

C'!L-I, i at low declinations (< -30 degrees S) may be undersampled, affecting

how many are seen toward the Galactic center (dominated by younger clusters) and

how many are seen toward the periphery (where older clusters are comparatively




















































Figure 4-2: Top-down galactic view of clusters


















































+
+ ++



























Galactic C nter


Z height (pc)



Figure 4-3: Edge-on galactic view









prevalent-see Figure 4-2). Janes and Adler (1982) believe this longitude effect

to be negligible, but it represents the most likely cause for the aforementioned

disparity in Figure 4-2's Y-axis distribution.

Determining the maximum radius from the Sun of a complete sample (or at

least a representative one) can be attempted by statistical tests, particularly the

Kolmogoroff-Smirnov test (Wielen, 1971). Wielen investigated the age distributions

for clusters in two regimes, 0 < r < 500pc and 500 < r < 1000pc, and found them

to be identical with a high probability (~ 95'.). Extending his sample to 2000pc,

however, he found a substantial excess of young clusters, having only a 5'. chance

of being a random permutation of the nearby distribution. Using this and other

arguments, Wielen employ, -1 a 1 kpc cutoff.

Other papers followed this lead, but Battinelli and Capuzzo-Dolcetta (1991)

pointed out that using the Kolmogoroff-Smirnov test to identify the limits of

the solar vicinity age distribution was creating its own bias. Seeking identical

distributions works well if the distribution is expected to be constant over the

entire visible region of the Milky Way, but in fact we expect a preponderance of

young clusters in the spiral arm regions, which are better sampled in the 1-2 kpc

distance regime. So the excess of young clusters seen therein, which Wielen (1971)

and Janes and Adler (1982) had attributed to a selection effect due to their better

visibility, was actually due, at least in part, to the younger spiral arm populations.

Somewhat contrary to expectation, the oldest clusters (> 400 million years)

greatly dominate the detected populations at 2+ kpc (see Figure 4-1). This is

largely due to their greater z dispersion out of the Galactic disk, so that observa-

tions of them are easier, and possibly also due to their tendency to be more massive

than average (hence better able to survive).

The net result is that distance-based selection effects are difficult to parame-

terize, and to some extent balance one another out. This study assumes that they









are not producing substantial effects and retains all of the clusters for its statis-

tics. Battinelli and Capuzzo-Dolcetta's contention raises the question, however,

of whether we are seeking an all-inclusive cluster age distribution, or whether it

would be more appropriate to derive different ones for the active and inactive

star forming regions of our Galaxy. Binning by Galactic radius, i.e. breaking the

project into several mini-studies, would be feasible, as would inning by the other

1 i ri parameter that affects age distributions, namely clusters' mass/density/star

counts (e.g., Janes & Tilley, 1988). Unfortunately, although these do provide useful

qualitative information, the statistics suffer from small sample sizes. As the main

intent of this work is to investigate global properties of the age distribution over

the entire lifetime of the Galaxy, I treat all the clusters as a single population.

4.6 Fitting the Age Distribution

A common assumption for the age distribution is that it fits an inverse ex-

ponential curve, with the number of surviving clusters being halved at regular

intervals. Figure 4-4 presents a plot of the age distribution up to 2 billion years,

in bins of 10 million years (similar to Figure 4-1), with the best fit inverse expo-

nential included (solid line). Some of the bin sizes are zero, which the exponential

regression algorithm is unable to handle. One option was to use larger bins, so that

every bin would have at least one member. The concern with this approach would

be the loss of resolution at younger ages, where the statistics are otherwise most

reliable. Instead, a "smoothiing of the bins was employ, l1 so that bins of zero size

shared the populations of their neighboring non-zero bins, producing many bins of

fractional size. This is easily justified, as much of the clumpiness in the distribution

for large ages is due to studies which expressed ages in round figures such as 1000

Myr or log(age) = 8.9. The smoothing was done by hand rather than using a

filter function, as the clumpiness did not lend itself to an automatic procedure. I




































0 500 1000 1500 200
Cluster Aqe (Myrs)

Figure 4-4: Number of clusters versus age, with fit

repeatedly checked the results by applying larger bins, ensuring that the smoothed

results were broadly consistent with the observations over large spans of time.

For exponential distributions, the number of clusters in each bin will be

N = Noect, where No is the original number of clusters. The constant c is a

measure of the rate of decline, and the distribution's half-life is measured by

t1/2 = 106 .693/c. Taking the natural logarithm of the equation for N yields

InN = InNo ct. Figure 4-5 plots this latter function, now using linear regression

(solid line) to find its slope (-c) and its y-intercept (InNo).

It is apparent from these figures that the fit is an extremely poor one for the

first 200 million years or so. There are several possible contributing factors to this.