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The Formation of Cluster Galaxies

Permanent Link: http://ufdc.ufl.edu/UFE0044851/00001

Material Information

Title: The Formation of Cluster Galaxies
Physical Description: 1 online resource (158 p.)
Language: english
Creator: Mancone, Conor Lamb
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

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

Notes

Abstract: In this work I sought to understand the formation and evolution of galaxies.  Specifically, I studied three key aspects of galaxy formation: star formation, mass assembly, and structural evolution. Past research has shown that the formation of a galaxy is strongly coupled to its local environment (i.e. the local galaxy density).  Therefore, I studied the evolution of cluster galaxies because clusters are the highest density environments that exist in the universe.  In turn, the observational results found herein form a foundation upon which to test theories of galaxy formation in the densest environments.  I used the latest sample of galaxy clusters from the Bootes region to measure the near-infrared luminosity function (NIR LF) of cluster galaxies from 0 1.3.  I used deeper IRAC imaging to study the NIR LF of high redshift cluster galaxies (1 < z < 1.5) with focus on the properties of faint (i.e. low mass) galaxies.  I found no evidence for evolution of the LF for low mass cluster galaxies out to the highest redshifts studied, which suggested that that the cluster galaxy population was in place at high redshift.  Finally, I calculated the evolution of the size-mass relationship (SMR) of cluster galaxies as a function of morphology for the high redshift cluster sample.  I found that apparent evolution of the SMR can be partially explained by the progenitor bias, but that there was a missing population of large, massive cluster galaxies.  These galaxies were either be accreted by clusters at lower redshifts, or the cluster galaxy population underwent size-evolution to account for their presence at low redshift.  I developed two new programs to aid in my research as well as future research in this field.  I created EzGal, a program which extracts observables (magnitudes, k-corrections, stellar masses, mass-to-light ratios, etc...) from standard stellar population synthesis (SPS) models.  This simplified comparisons of observations to many different model sets, and simplified comparison of different model sets to each other.  I used EzGal to quantitatively compare various model sets and estimate SPS model uncertainty, and recovered the well known result that SPS models agree best in the optical for old stellar populations, but disagree substantially for intermediate age stellar populations in the NIR.  The latter uncertainty was caused by the presence of thermally pulsating AGB stars, which are poorly understood observationally but contribute substantially to the NIR light of a stellar population.  I also created the Python Galaxy Fitter (PyGFit), a program which measures PSF matched photometry from crowded imaging with disparate PSFs and resolutions.  This enabled accurate measurement of spectral energy distributions (SEDs) in crowded cluster fields.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Conor Lamb Mancone.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Gonzalez, Anthony.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044851:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044851/00001

Material Information

Title: The Formation of Cluster Galaxies
Physical Description: 1 online resource (158 p.)
Language: english
Creator: Mancone, Conor Lamb
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

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

Notes

Abstract: In this work I sought to understand the formation and evolution of galaxies.  Specifically, I studied three key aspects of galaxy formation: star formation, mass assembly, and structural evolution. Past research has shown that the formation of a galaxy is strongly coupled to its local environment (i.e. the local galaxy density).  Therefore, I studied the evolution of cluster galaxies because clusters are the highest density environments that exist in the universe.  In turn, the observational results found herein form a foundation upon which to test theories of galaxy formation in the densest environments.  I used the latest sample of galaxy clusters from the Bootes region to measure the near-infrared luminosity function (NIR LF) of cluster galaxies from 0 1.3.  I used deeper IRAC imaging to study the NIR LF of high redshift cluster galaxies (1 < z < 1.5) with focus on the properties of faint (i.e. low mass) galaxies.  I found no evidence for evolution of the LF for low mass cluster galaxies out to the highest redshifts studied, which suggested that that the cluster galaxy population was in place at high redshift.  Finally, I calculated the evolution of the size-mass relationship (SMR) of cluster galaxies as a function of morphology for the high redshift cluster sample.  I found that apparent evolution of the SMR can be partially explained by the progenitor bias, but that there was a missing population of large, massive cluster galaxies.  These galaxies were either be accreted by clusters at lower redshifts, or the cluster galaxy population underwent size-evolution to account for their presence at low redshift.  I developed two new programs to aid in my research as well as future research in this field.  I created EzGal, a program which extracts observables (magnitudes, k-corrections, stellar masses, mass-to-light ratios, etc...) from standard stellar population synthesis (SPS) models.  This simplified comparisons of observations to many different model sets, and simplified comparison of different model sets to each other.  I used EzGal to quantitatively compare various model sets and estimate SPS model uncertainty, and recovered the well known result that SPS models agree best in the optical for old stellar populations, but disagree substantially for intermediate age stellar populations in the NIR.  The latter uncertainty was caused by the presence of thermally pulsating AGB stars, which are poorly understood observationally but contribute substantially to the NIR light of a stellar population.  I also created the Python Galaxy Fitter (PyGFit), a program which measures PSF matched photometry from crowded imaging with disparate PSFs and resolutions.  This enabled accurate measurement of spectral energy distributions (SEDs) in crowded cluster fields.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Conor Lamb Mancone.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Gonzalez, Anthony.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044851:00001


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FirstandforemostIthankmyGodandLordformakingthispossibleandbringingmethisfar.ItseemsparticularlyappropriatetothankHimbecauseHeistheGodofgods,theLordofkings,andarevealerofsecrets,andbecausewithHimarewisdomandstrength,Hehascounselandunderstanding.SoIthankHimforsharingHiswisdom,strength,andsomeofthesecretsabouthowthisuniverseofHisworks.Iespeciallythankmyadviser,AnthonyGonzalez,forgivingmetheprivilegeofworkingwithhim,formakingavailabletomethewealthofdataandinformationthathehascollectedovertheyears(withoutwhichnoneofthiswouldbepossible),forsharinghisextensiveexperienceandknowledgeinthiseld,andforbeingpatient,kind,andapleasuretoworkwith.Notonlyhashemademytimehereproductive,buthehasmadeitaneasyandenjoyableexperienceaswell.IwouldliketothankAtaSarajediniforallowingmetoworkwithhimforayearafternishingmyundergraduatedegree.TheexperienceIgainedworkingwithhimwasundoubtedlyabigreasonwhyIwasacceptedintograduateschoolintherstplace.Iwouldliketothankhimandhiswife,VickiSarajedini,fortheirkindnessandfriendshipforthemanyyearsthatIhaveknownthem.IthankAtaSarajedini,VickiSarajedini,andRafaelGuzmanforsharingtheirknowledgeandloveofAstronomywithmewhenItooktheirclasses,foragreeingtobeonmythesiscommittee,andformanyenjoyableconversationsaboutlife,theuniverse,andeverythinginbetween.IthankTarekSaabfortakingthetimeoutofhisbusyscheduletobeonmycommitteeandaddhisexpertisetothisendeavor.Finally,Iwouldliketothankmymanycollaboratorsandotherswhohaveshareddataandresults,givenimportantinsightsintothisresearch,beenpatientwithmeasIhavelearned,andwithwhomIhavesharedmanyenjoyableconversationswhiletraveling.InparticularIthankDanGettings,TroyBaker,MarkBrodwin,AdamStanford, 3

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page ACKNOWLEDGMENTS .................................. 3 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTION ................................... 13 2EZGAL:AFLEXIBLEINTERFACEFORSTELLARPOPULATIONSYNTHESISMODELS ....................................... 16 2.1Background ................................... 16 2.2ProgramProcedure .............................. 19 2.2.1CalculatingMagnitudes ........................ 19 2.2.2CalculatingCompositeStellarPopulations .............. 20 2.2.3CalculatingMass-to-LightRatiosandMasses ............ 22 2.3ModelComparison ............................... 23 2.3.1ModelSetOverview .......................... 23 2.3.2FilterSetOverview ........................... 24 2.3.3Comparison ............................... 24 2.3.4APracticalExample .......................... 32 2.4EzGalWebResources ............................. 35 2.5Conclusions ................................... 36 3PYGFIT:PYTHONGALAXYFITTER ....................... 38 3.1Background ................................... 38 3.2Procedure .................................... 39 3.2.1Overview ................................ 39 3.2.2ObjectDetectionandSegmentation ................. 42 3.2.3CatalogAlignment ........................... 44 3.2.4Fitting .................................. 45 3.2.4.1Cutouts ............................ 45 3.2.4.2ModelGeneration ...................... 45 3.2.4.3Fitting ............................. 47 3.2.5FinalCatalogOutput .......................... 48 3.3ApplyingPyGFittoRealData ......................... 49 3.4Simulations ................................... 53 3.4.1SimulationResults ........................... 54 3.5Conclusions ................................... 57 5

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............. 60 4.1Background ................................... 60 4.2Data ....................................... 63 4.2.1GalaxyCatalog ............................. 63 4.2.2ClusterCatalog ............................. 64 4.3ObservedLuminosityFunction ........................ 64 4.3.1GeneralProcedure ........................... 64 4.3.2FittingDetails .............................. 65 4.3.3StatisticalBackgroundSubtraction .................. 68 4.3.4Results ................................. 69 4.3.5FittingErrors .............................. 69 4.4ModelsforPassivelyEvolvingStellarPopulations .............. 73 4.4.1ModelDescription ........................... 73 4.4.2ModelComparisontoClusterLF ................... 76 4.4.3SystematicUncertainties ........................ 79 4.4.3.1Modelnormalization(M3.6) ................. 79 4.4.3.2Faintendslope() ...................... 86 4.4.3.3Stellarpopulationsynthesismodeling(SPS) ....... 87 4.4.3.4Fittingerrors ......................... 91 4.5MassAssembly ................................. 92 4.5.1LowRedshift .............................. 92 4.5.2HighRedshift .............................. 94 4.6SummaryandConclusions .......................... 98 5THEFAINTENDOFTHECLUSTERGALAXYLUMINOSITYFUNCTIONATHIGHREDSHIFT ................................... 100 5.1Background ................................... 100 5.2Data ....................................... 102 5.2.1ClusterSample ............................. 102 5.2.2ComparisonFields ........................... 103 5.2.3DataReductionandProcessing .................... 103 5.3ObservedLuminosityFunction ........................ 105 5.3.1OpticalNIRColorCut ......................... 105 5.3.2LFFittingProcedure .......................... 106 5.3.3Results ................................. 108 5.4Discussion ................................... 110 5.4.1High-RedshiftComparison ....................... 110 5.4.2Low-RedshiftComparison ....................... 111 5.4.3ComparisontotheFieldLF ...................... 114 5.4.4ImplicationsforGalaxyFormation ................... 114 5.5Conclusions ................................... 116 6

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118 6.1Background ................................... 118 6.2Data ....................................... 120 6.2.1ClusterSample ............................. 120 6.2.2Imaging ................................. 121 6.2.2.1Ground-basedopticalimaging ............... 121 6.2.2.2SpitzerIRACimaging .................... 121 6.2.2.3HSTimaging ......................... 122 6.2.2.4Ground-basedNIRimaging ................. 122 6.2.3Spectroscopy .............................. 123 6.2.4MemberSelection ........................... 124 6.3GalaxyParameters ............................... 125 6.3.1GalaxySizes:GALFIT ......................... 125 6.3.2SEDs:PyGFit .............................. 127 6.3.3Masses ................................. 130 6.3.4Morphologies .............................. 130 6.4Results ..................................... 131 6.4.1GalaxyClassication .......................... 131 6.4.2TheSMRandMorphology ....................... 132 6.4.3TheSMRandQuiescence ....................... 133 6.5Discussion ................................... 136 6.5.1Morphology,TheEvolutionoftheSMR,andProgenitorBias .... 136 6.5.2Quiescence,TheEvolutionoftheSMR,andProgenitorBias .... 136 6.5.3TheEvolutionoftheSMR ....................... 137 6.5.4ImplicationsofSMREvolution ..................... 143 6.5.5Implicationsfortheeld ........................ 144 6.6Conclusions ................................... 145 REFERENCES ....................................... 147 BIOGRAPHICALSKETCH ................................ 155 7

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Table page 2-1ModelSetProperties ................................ 24 2-2FilterData ....................................... 25 4-1SchechterFitParamatersPhoto-zSelection .................... 72 4-2SchechterFitParamatersStatisticalBackgroundSubtraction .......... 73 4-3Modelnormalizationsfromtheliterature. ...................... 81 4-4ImpactofFittingSystematics. ............................ 86 4-5ImpactofModelChoice. ............................... 88 5-1ClusterMemberSummary .............................. 102 5-2BinnedLFs ...................................... 109 5-3BestFittingSchechterParameters ......................... 110 5-4ValuesFromtheLiterature ............................ 112 6-1ClusterMemberSummary .............................. 123 6-2TheSMRofEarly/LateTypeGalaxies ....................... 132 6-3TheSMRofQuiescent/StarFormingGalaxies .................. 134 8

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Figure page 2-1AsimplemodelcomparisonwithEzGal 26 2-2Modeluncertaintyintheopticalasafunctionofage,wavelength,metallicity,andSFH ....................................... 28 2-3ModeluncertaintyintheNIRasafunctionofage,wavelength,metallicity,andSFH .......................................... 29 2-4Modeldifferences .................................. 31 2-5ModeluncertaintyasafunctionofredshiftforarealisticSFH .......... 33 3-1PyGFitFlowChart .................................. 43 3-2APyGFitexample .................................. 50 3-3ExamplesofPyGFitfailures ............................. 52 3-4PyGFitsimulationresults .............................. 55 3-5PyGFitlimitations ................................... 57 3-6PyGFitsimulationresults:postcuts ........................ 58 3-7PyGFitreliabilityasafunctionofenvironment ................... 59 4-1Observedandtted3.6mLFfrom0
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92 4-13TheimpactofsystematicuncertaintiesonM3.6 93 4-14Theimpactofongoingmassassembly ....................... 95 5-150%completenessin3.6and4.5m ........................ 105 5-2HighRedshiftClusterLFandBestFit ....................... 108 5-3CondenceRegionsforOurHigh-zLFFit ..................... 109 5-4Evolutionof 113 6-1Galaxysizesandmassesasafunctionofmorphology .............. 133 6-2Galaxysizesandmassesasafunctionofquiescence .............. 134 6-3Galaxysizesandmassesasafunctionofage .................. 135 6-4Mediangalaxysizesasafunctionofageselection ................ 138 6-5zfandageversuscompactness .......................... 139 6-6MeasuredSMRevolution .............................. 141 10

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Lewisetal. 2002 ; Gomezetal. 2003 ; Weinmannetal. 2010 ; Pengetal. 2010b ; Chungetal. 2011 ; Muzzinetal. 2012 ; Grutzbauchetal. 2012 ).Itisexpectedthatthistrendreversesathighredshifts,asgalaxyformationisexpectedtohappenearlierindenserenvironments( DeLuciaetal. 2004 ).Therstevidenceofthishasonlyrecentlybeenfoundinindividualclustersatz&1.4( Tranetal. 2010 ; Hiltonetal. 2010 ).Galaxymorphologyisalsoseentodependuponenvironment.Thefractionofearly-typegalaxiesincreaseswithlocaldensityouttothehighestredshiftsstudied( Dressler 1980 ; Postmanetal. 2005 ; Smithetal. 2005 ; Poggiantietal. 2009 ; Meietal. 2012 ).Observationssuchastheseprovideastartingpointforunderstandingtherolethatenvironmentplaysingalaxyformation.Inthiscontext,galaxyclustersareapromisingtoolastheycontainthehighestdensityenvironmentsintheuniverse.Therefore,studyingthestarformation,massassembly,andstructuralevolutionofclustergalaxiescanprovideadditionalconstraintsontheprocessesimportantingalaxyevolution.However,ourunderstandingofthepropertiesofclustergalaxiesisrelativelyincompletecomparedtogalaxiesinlowerdensityenvironments.Sincegalaxyclustersonlyforminthedensestregionsoftheuniverse,theyareararephenomenon.Findingastatisticallyusefulnumberofgalaxyclustersrequiressurveyinglargeareasofthesky(manysquaredegrees).Evenwithsuchasurveyinhand,ndingclustersinanunbiasedfashionisnon-trivial.Foropticalwavelengthstheonlytrulyunbiasedmethodforndingclustersisbysearchingfor3-D 13

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Stanfordetal. 2005a Elstonetal. 2006a Brodwinetal. 2006a Eisenhardtetal. 2008a ).TheISCScombineddatafromtheNOAODeep,Wide-FieldSurvey(NDWFS; Jannuzietal. 1999 )andtheIRACShallowSurvey(ISS; Eisenhardtetal. 2004 )togeneratephotometricredshiftsfornearly2105galaxiesandthendetectclustersas3-Doverdensitiesofgalaxies.ThedepthoftheIRACimaginginthisregionwasincreasedbyafactoroffouraspartoftheSpitzerDeep,Wide-FieldSurvey(SDWFS; Ashbyetal. 2009a ),whichhasenabledamorerobustdetectionofhigh-redshiftclustercandidates(theIRACDistantClusterSurvey,IDCS).Followupworkhassoughttondconrmthehighestredshiftcandidates.Todate,morethan20galaxyclustersintheBooteseldwithz>1havebeenspectroscopicallyconrmed( Stanfordetal. 2005a ; Elstonetal. 2006a ; Brodwinetal. 2006a ; Eisenhardtetal. 2008a ; Brodwinetal. 2011 ; Stanfordetal. 2012 ; Zeimannetal. 2012 ).Ofthese,thetwohighestredshiftclustersareatz=1.75(IDCSJ1426.5+3508)andz=1.89(IDCSJ1433.2+3306),makingthemtwoofthehighestredshiftclustersdiscoveredtodate.Thisclustersample,combinedwithsubstantialspectroscopicandphotometricdata,formsthebasisofthiswork.Webeginwithadescriptionoftwotoolsdevelopedtoaidthisandotherresearch.EzGalisaprogramdesignedtoextractobservables(magnitudes,mass-to-lightratios,masses,etc...)fromstellarpopulationsynthesis(SPS)modelsasafunctionofredshiftandformationredshift.EzGalsimpliescomparisons 14

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2 andispublishedas Mancone&Gonzalez ( 2012 ).PythonGalaxyFitter(PyGFit)isaprogramthatmeasuresPSFmatchedphotometryfromdatasetswithdisparatePSFsandresolutions,andisdesignedtoworkincrowdedelds.MeasuringPSFmatchedphotometryminimizesuncertaintiesinspectralenergydistributions(SEDs)measuredfromdisparatebroad-bandimaging.PyGFitisdescribedinChapter 3 .InChapter 4 (publishedas Manconeetal. 2010 )wemeasurethenear-infrared(NIR)luminosityfunction(LF)ofclustergalaxieswith0.3
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Conroyetal. ( 2009a )and Conroy&Gunn ( 2010 ).ThenetresultisthatthechoiceofmodelsetisitselfasourceofuncertaintywhenusingSPSmodels.TheuseofSPSmodelsisacentralingredientforawiderangeofactiveresearchprograms,asisevidentevenfromasimpleliteraturesearch.SPSmodelsarecommonlyusedtoperformSEDttingandestimateadiversesetofpropertiesforstellarpopulationsincludingages,redshifts,k-corrections,andmasses(seeforexample Blanton&Roweis 2007 ; Tayloretal. 2011 ; Maetal. 2012 ; Fotopoulouetal. 2012 ).Theyareusedtotisochronestocolormagnitudediagramsandmeasureagesandmetallicitiesofresolvedstellarpopulations,tomeasurethestrengthofspectralfeaturesinobservedgalaxies,topredicttheevolutionofastellarpopulationasafunctionofage,andtopredictobservablesfromsimulations(forexample Jonsson 2006 ; Marn-Franchetal. 2009 ; Manconeetal. 2010 ; Krieketal. 2011 ).BecauseoftheutilityandubiquityofSPSmodels,itisimportanttohavesimplifyingmethodsforcomparingthemodelstoobservationsaswellastoeachother.OfthemanySPSmodelsetsthemostcommonlyusedisthatofBruzual&Chalot( BC03 ;2003)whichweuseasareferenceforcomparisonsbecauseofitswideuse. 16

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M05 ;2005)whichincludesadetailedtreatmentofthermallypulsatingAGB(TP-AGB)stars,whichcandominatetheinfraredlightofayoungstellarpopulation.AnupdatedtreatmentoftheTP-AGBphaseisalsoincorporatedintothelatestversionofthe BC03 models( Charlot&Bruzual privatecommunication ,commonlyreferredtoasCB07).MorerecentmodelsincludetheworkofPercivaletal.( BaSTI ;2009)whichincludenotonlyarangeofmetallicitiesbutalsoenhancedmodels.TheFSPSmodels( C09 )from Conroyetal. ( 2009a )and Conroy&Gunn ( 2010 )areuniqueintheirabilitytotreatthemostimportantSPSinputs(suchasIMForvariousuncertainphasesofstellarevolution)asfreeparametersallowingtheuncertaintiesintroducedbyvariousSPSinputstobequantitativelymeasured.AllofthesemodelspredicttheevolutionoftheSEDofastellarpopulationasafunctionofage,givenastarformationhistory,initialmassfunction(IMF),andmetallicity.HowevertheeasiesttomeasureobservablesarenottheSEDorage,butratherthemagnitudeandredshift.Thereforeallofthesemodelsetsaremostusefulwhentheycanbeeasilytranslatedintopredictionsofmagnitudeevolutionasafunctionofredshift.Thistransformationinvolvesassumingaformationredshift(theredshiftatwhichstarformationstarts),calculatingacosmology-dependentluminositydistance,andprojectingtheSEDsthroughlterresponsecurvestocalculatemagnitudes,e-corrections,andk-corrections.Thee-correctionsspecifytheamountofobservedmagnitudeevolutionthatisduetotheagingofastellarpopulation,whilethek-correctionsspecifytheamountofevolutionduetoobservingadifferentpartoftheSEDatdifferentredshifts.Togetherthee-corrections,k-corrections,anddistancemodulispecifythemagnitudeevolutionofastellarpopulationasafunctionofredshift.Whilethesestepsarestraight-forward,inthepasttherehasnotbeenasimpleandconsistenttooltodothisforallmodelsets. BC03 and C09 bothcomewithcodeforcalculatingmagnitudeevolutionasafunctionofredshiftandbothcomewithanumberof 17

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BaSTI and M05 calculateanddistributetheabsolutemagnitudeevolutionofthestellarpopulationsforaxedsetoflters.ThislackofdirectlycomparableoutputsbetweendifferentmodelsetsisthereasonwhywehavedevelopedEzGal,apythonprogramthatcalculatesmagnitudeevolutionasafunctionofredshiftfrommodelsoftheevolutionofanSEDasafunctionofage.EzGalcomeswithanumberofthemostcommonlyusedlterresponsecurves,andmorecanbeeasilyaddedbytheuser.ItincludesthelatestVegaspectrumfromSTScI1sothatmagnitudescanbecalculatedonboththeVegaandABsystems.ByusingthestellarmassinformationthatcomeswithallofthesemodelsetsEzGalcanalsocalculatemass-to-lightratiosinanylter.ThisrequirescalculatingtheabsolutemagnitudeoftheSuninanylterandsothelatestsolarspectrumfromSTScI2isalsoincludedwithEzGal.EzGalcaninterpolatebetweenmodels,whichisusefulforgeneratingmodelswiththesamemetallicityfromdifferentmodelsets.ItcanalsogenerateCSPswitharbitraryinputstarformationhistoriesordustreddeninglaws.Finally,EzGalcanreadinSEDsinASCIIformatorinthebinaryisedformatthatthe BC03 and CB07 modelsaredistributedin.Inprinciplethisallowsittoworkwithanymodel,enablingeasycomparisonwithanynewcodesinthefuture.EzGalisdesignedtobeaneasy-to-usetoolforpredictingobservablesfromSPSmodelsandgreatlysimplifyingthetaskofcomparingdifferentSPSmodelsets.ThispaperexplainshowEzGalworksandgivesadetailedcomparisonbetweencommonlyusedmodelsets.Section 2.2 describesdetailsofhowEzGalworksanddiscussescalculatingmagnitudes(Section 2.2.1 ),generatingcompositestellarpopulations(Section 2.2.2 ),andcalculatingmassesandmass-to-lightratios(Section 2.2.3 ).InSection 2.3 wepresentadetailedcomparisonbetweenthemodelsets. 18

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Section 2.4 listsEzGalresourcescurrentlyavailablefromtheinternetsuchasthewebinterface.OurconclusionsarefoundinSection 2.5 2.2.1CalculatingMagnitudesEzGalcalculatesapparentmagnitudes,absolutemagnitudes,e-corrections,andk-correctionsfromthemodelsetsasafunctionofredshift.Conceptually,thesequantitiesarealleasytocalculateandarederivedfromtherest-frameandobserved-frameabsolutemagnitudesasafunctionofageandredshift.EzGalusesEquation 2 tocalculateobserved-frameabsolutemagnitudesasafunctionofredshift(z)andformationredshift(zf).ThisequationcalculatestheabsoluteABmagnitudeasafunctionofredshiftandage,MAB[z,t(z,zf)],foranSPSmodelbyprojectingtheredshiftedSED,F[(1+z),t(z,zf)],atthegivenage,t(z,zf)(withtheagedeterminedbyredshiftandformationredshift),throughthelterresponsecurve,R(),andcomparingthistotheuxofazeromagABsource.ForthepurposesofthisequationtheSEDshouldhaveunitsofergs1Hz1cm2andshouldbetheobserveduxforagalaxyatadistanceof10pc.Theageofthegalaxy,t(z,zf),isgivenbyt(z,zf)=TU(z)TU(zf)whereTU(z)istheageoftheuniverseasafunctionofredshiftgiventhecosmology.BydefaultEzGalassumesaWMAP7cosmology( Komatsuetal. 2011 ,m=0.272,=0.728,h=0.704),althoughanycosmologycanbeused.Tocalculatetherest-frameabsolutemagnitude,EzGalcalculatesMAB[0,t(z,zf)].EzGalalsocalculatesanumberoflterpropertiesusingstandardSTScIdenitions,includingmeanwavelength,pivotwavelength,averagewavelength,effectivedimensionless 19

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Bohlin&Gilliland ( 2004 )andcomesfromIUEspectrophotometryfrom0.12-0.17m,HSTSTISspectroscopyfrom0.17-1.01m,andaKuruczmodelatmosphereatlongerwavelengths.Finally,theabsolutemagnitudeoftheSunisalsocalculatedbyprojectingthesolarspectrumthroughthelterresponsecurveinthesamewayaseverythingelse.ThesolarspectrumusedbyEzGalisanobservedspectrumoftheSunfrom0.12-2.5m( Colinaetal. 1996 )whichwehaveextendedusingaKuruczmodelatmosphereatlongerwavelengths.Specically,wetakeamodelatmospherewithsolarmetallicity,Te=5777K,andlogg=4.44,normalizeittomatchtheobservedsolarspectrumfrom1.5-2.5m,andthenuseitwheretheobservedspectrumends. 2 tocalculatetheevolutionoftheSEDofaCSPasafunctionoftime. exposuretime2.html#4802213http://www.stsci.edu/hst/wfc3/documents/handbooks/currentIHB/c06 uvis06.html#57 20

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Charlot&Fall ( 2000 )dustlawwith()=e(t)(=5500A)0.7where(t)=1.0fort107yrand(t)=0.5fort>107yr.Equation 2 representsthesamegeneralmethodologyusedby BC03 and C09 togenerateCSPs. M05 usesadifferentnormalizationandinsteaddividesbyRt0(t0)dt0sothattheCSPshaveonesolarmassofstarsatallages. BaSTI doesnotprovideanyCSPswiththeirmodels.InpracticeEzGalusesSimpson'sruletonumericallyevaluatethetopintegralinEquation 2 .Whenperformingnumericintegrationitisoftennecessarytosub-sampletheagegridoftheSSPstoproperlysampleanysharpfeaturesinthestarformationhistoryorintheevolutionoftheSEDs.Inordertominimizeexecutiontimeandstillensurehighdelityinthenumericintegration,EzGalusesaniterativealgorithmtodecidehownelytosub-sampletheagegrid.EzGalperformstheintegralinEquation 2 atwavelengthsof3000,8000,and12000Awithincreasinglynerlevelsofagesub-samplinguntilthedifferencebetweentwosubsequentintegralsdropsbelowsometuneablethreshold(inmagnitudes).WeverifyourprocedureforgeneratingCSPsbycomparingmagnitudepredictionsforCSPsgeneratedwithEzGalfrom BC03 and C09 modelstomagnitudepredictionsforCSPsgeneratedbythecodedistributedwith BC03 and C09 .Wenddifferencesthataresmallandnegligible:for BC03 thedifferencesinmagnitudeare<0.005magsforshort(=0.1Gyr)andlong(=1.0Gyr)dust-freeexponentially-decayingbursts,andfor C09 thedifferencesare<0.01magsforshortburstsand<0.005magsforlongbursts. 21

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Komatsuetal. 2011 ,m=0.272,=0.728,h=0.704).Therest-framemass-to-lightratioinagivenlterasafunctionofredshiftandfromationredshiftisthengivenby: 100.4fMF[t(z,zf)]M,Fg(2)EzGalusesEquation 2 tocalculaterest-framemass-to-lightratios.Itusesitsowncalculationoftheabsolutemagnitudeevolutionofastellarpopulationasafunctionofage,calculatestheabsolutemagnitudeoftheSunusingthesolarspectrumfromSTScI,andgetsstellarmassesdirectlyfromthemodelsets(whichtypicallydistributestellarmassasafunctionofagealongwiththeSED).Theresultingmass-to-lightratiosdependonthechosenmodelset,starformationhistory,andinitialmassfunction.EzGalalsocalculatesanobserved-framemass-to-lightratioasafunctionofredshiftusingtheobserved-frameabsolutemagnitudeofthemodelandtheobserved-frameabsolutemagnitudeoftheSun.Thelatteriscalculatedbyredshiftingthesolarspectrumtothegivenredshiftandprojectingitthroughthebandpassnormally. 22

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2.3.1ModelSetOverviewInthispaperwecompareresultsfromvedifferentSPSmodelsets: BC03 M05 CB07 BaSTI ,and C09 .ThesemodelsetsincludeavaryingrangeofmetallicitiesandIMFs,andhavedifferentspectralresolutionsandagegrids. M05 hasthehighestmetallicitymodel(Z=3.5Z)while BC03 CB07 ,and BaSTI havethelowest(Z=Z/200). C09 hasthenestgridinmetallicityspacewith22metallicitiesfromZ=0.01Z1.5ZandistheonlymodelsetthatdistributesmodelswithallthreecommonIMFs:Salpeter,Chabrier,andKroupa.Finally, BaSTI istheonlymodelsethereintopublishmodelswithalphaenhancedmetallicities.ThisinformationisprovidedasaquickreferenceforcomparingmodelsetsandissummarizedinTable 4-5 whichincludesthenumberofagesineachmodelset,thenumberofmetallicitiesprovided,andtheIMFsprovided.Tofacilitatedirectcomparisonsbetweenmodelsetsweinterpolatebetweenthemodelstogenerateanewsetofmodelsforeachmodelsetwiththesamemetallicities. 23

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ModelSetProperties Name#AgesMetallicity(Z=Z)#MetallicitiesIMFs BC03 2210.005-2.56Salpeter,Chabrier M05 680.05-3.55Salpeter,Kroupa CB07 2210.005-2.56Salpeter,Chabrier BaSTI 560.005-210Kroupa C09 1890.01-1.522Salpeter,Chabrier,Kroupa OurnewmodelshavemetallicitiesofZ=0.05,0.1,0.2,0.4,0.8,1.0,and1.5timesZorZ=0.001,0.002,0.004,0.008,0.016,0.02,and0.03.Forallofourcomparisonsbelowweusetheseinterpolatedmodels.WealsochoosetorestrictourcomparisonstomodelswiththesameIMF.AsthereisnoIMFthatiscoveredbyallvemodelsetswedoallcomparisonsusingaSalpeterIMF,andthereforeinthecomparisonsbelowthemodelsfrom BaSTI arenotincluded.ForeachofourinterpolatedmodelsweuseEzGaltogeneratefourCSPmodels.TheCSPsaredust-free,exponentiallydecayingburstswithe-foldingtimescalesof0.1,0.5,1.0,and10.0Gyrs. 2-2 whichhasthepivotwavelengthandrectangularwidthforeachlteraswellastheabsoluteABmagnitudeoftheSunthrougheachlterandthecalculatedABtoVegaconversion.ThelatterisinmagnitudessuchthattheVegamagnitudeofagalaxyisitsABmagnitudeplusthelistedconversion.ThisTableisalsoreproducedonthewebforquickreference. 24

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FilterData NamePivot(A)Width(A)M(AB)Vega-AB GALEXFUV153624617.20-2.093GALEXNUV230073010.04-1.659Sloanu35565586.37-0.916ACSWFCF435W43188455.370.102WFC3F438W43256165.340.152Sloang470211585.120.100ACSWFCF475W474613595.100.096WFC3F475W477313435.080.096WFC3F555W530815634.860.023ACSWFCF555W536011244.840.005WFC3F606W588721834.73-0.085ACSWFCF606W592119924.72-0.088Sloanr617511114.64-0.144WFC3F625W624114614.64-0.150ACSWFCF625W631113084.63-0.165Sloani748910454.53-0.357WFC3F775W764711704.53-0.382ACSWFCF775W769113204.53-0.389WFC3F814W802615384.52-0.419ACSWFCF814W805517334.52-0.425Sloanz894611254.51-0.518ACSWFCF850lp901312394.51-0.521WFC3F850lp916711814.52-0.522WFC3F105W1055026494.53-0.647WFC3F110W1153444304.54-0.761J1246920884.56-0.901WFC3F125W1248628454.56-0.903WFC3F140W1392238404.60-1.078WFC3F160W1537026834.65-1.254H1644825384.70-1.365Ks2162326425.13-1.838WISE3.4m3368268245.95-2.668IRAC3.6m3556968446.07-2.787IRAC4.5m4502087076.57-3.260WISE4.6m46179105086.62-3.307IRAC5.8m57450124417.05-3.753IRAC8m79156255927.67-4.394 25

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Acomparisonbetweenthepredictedibandrest-frameabsolutemagnitudes(top)andg-icolors(bottom)asafunctionofageforsolarmetallicitySSPswithaSalpeterIMF.Thesolid,dotted,dashdotted,anddashedlinescorrespondtothe BC03 M05 CB07 ,and C09 models,respectively.MagnitudesandcolorsareontheABsystem. 26

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2-1 showsthepredictedibandrest-frameabsolutemagnitude(top)andg-icolorasafunctionofageforSSPmodelswithasolarmetallicityandSalpeterIMF.AscanbeseenfromthisFigure,differencesaretypically0.1-0.2magnitudes.Tobetterexplorehowthescatterdependsonageandwavelength,weplotthescatterbetweenmodelsasafunctionofage,wavelength,metallicityandstarformationhistoryinFigure 2-2 .ThetopleftpanelofthisFigureillustratesthescatterbetweenthepredictedmagnitudesofthemodels( BC03 M05 CB07 ,and C09 )fortheSloanltersu,g,r,i,zasafunctionofageforanSSPwithaSalpeterIMFandametallicityofZ=0.001.ThepanelstotherightshowthesamethingbutforZ=0.008,Z=0.02,andZ=0.03.Thebottomrowofpanelsshowstheimpactofchangingstarformationhistories.Allthemodelsinthebottompanelhavesolarmetallicity(Z=0.02)andaSalpeterIMF.TherstplotonthebottomrowsshowsthescatterbetweenthemodelsetsforanSSP,thenextforadust-freeexponentiallydecayingburstofstarformationwithane-foldingtime()of1.0Gyrs,andthelastforadust-freeexponentialburstwith=10.0Gyrs.Scatterinthiscasereferstothestandarddeviationofthemagnitudespredictedbythedifferentmodelsatagivenageandthroughaparticularlter.AnumberofconclusionscanbedrawnfromFigure 2-2 .First,thebest-casecomparisonisforsolarmetallicitiesandintermediatetooldages(&4Gyrs),forwhichdifferencesbetweenthemodelsareatmost0.1magsanddropto0.05magsattheoldestages.FortheSloaniandSloanzltersthescatterincreasesbyafactorof2foryoungerages(.2Gyrs).Thisisparticularlytrueforsub-solarmetallicities,andthescatterinSloaniandSloanzincreasessystematicallyattheseyoungageswhengoingfrommetallicitiesofZ=0.02toZ=0.008andZ=0.001,reachingdifferencesaslarge 27

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ScatterbetweenthepredictedmagnitudesofthemodelsfortheSloanltersasafunctionofage.Thesolid,dashed,dash-dotted,dotted,andsolidlinesrepresenttheSloanu,g,r,i,andzlters,respectively.Inallpanelsthestandarddeviationbetweenthemagnitudepredictionsoffourmodelsets( BC03 ; M05 ; CB07 ; C09 )througheachlterisplottedversusage.InthetopseriesofpanelsallthemodelsareforaSSPwithaSalpeterIMFandvariousmetallicities:Z=0.001(farleft),Z=0.008(left),Z=0.02(right),andZ=0.03(farright).ThebottomseriesofpanelsareforstellarpopulationswithaSalpeterIMFandsolarmetallicity,butforvaryingstarformationhistories.AnSSP(left),adust-freeexponentiallydecayingburstwith=1.0Gyr(right),andadust-freeexponentiallydecayingburstwith=10.0Gyr(farright). as0.4mags.ForthethreebluestSloanltersthescatteris.0.1magsforallagesandmetallicities.Thebottomseriesofpanelshighlightstheimpactofanextendedstarformationhistory,theeffectofwhichistosmoothoutthescatterbetweenmodelsasafunctionofage.Atlongerwavelengthswhenthemodelsdiffermoreatyoungerages,thissmoothinghasatendencytoincreaseerrorsatlattertimesanddecreaseerrorsat 28

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2-3 isthesameasFigure 2-2 butnowvariousnear-IRbandsareplotted:J,H,Ks,andSpitzer/IRAC3.6and4.5m.Therstthingtonoteisthatforanolder(&3Gyr)solarmetallicitySSPthedifferencesinJHKsarecomparabletothedifferencesintheSloanbands(i.e.Figure 2-2 ),whiletheSpitzer/IRACbandstypicallyhavelargererrorsinthissameregime.Thescatterbetweenthemodelsnowhasastrongeragedependency,andforages.2Gyrsthemodeluncertaintyincreasesto0.3mags(J)and0.6mags(3.6m).MetallicityhastheoppositeimpactonthescatterbetweenmodelsintheNIRforyoung(.3Gyrs)andintermediatetoold(&3Gyrs)stellarpopulations.Foryoungeragesthescatterincreasessystematicallywhilegoingtolowermetallicities.ThiseffectisparticularlypronouncedintheKsbandwhichhasamaximumscatterof0.35magsforyoungstellarpopulationswithsolarmetallicity,butamaximumscatterof0.7magsforyoungstellarpopulationswithZ=0.001.Forolderstellarpopulationsthescatterisroughlyconstantorevendecreasing(IRAC3.6and4.5m)asthemetallicitydecreases.ThegeneraltrendofincreasingscattertowardsyoungeragesisbynomeansanewdiscoverybutisstronglyinuencedbyuncertaintieswiththethermallypulsatingAGB(TP-AGB)phase( M05 Marigoetal. 2008 C09 ).Thisshortlivedphaseinstellarevolutionispoorlyunderstoodobservationallyandtheoretically;observationallyduetoitsrarityandtheoreticallybecausethepropertiesofaTP-AGBstararestronglydependentuponmassloss,whichisnotpredictedtheoretically( Conroyetal. 2009a ).Unfortunatelyforstellarmodeling,TP-AGBstarscandominatethelightofastellarpopulationatlongwavelengths(&1m)forages&108yrs.WhileitismostimportantintheNIR,itcanalsoimpactredopticallterstoasmallerextent( C09 ),andsocanreadilyexplainthesystematictrendtohigherscattersseenasafunctionofwavelength 29

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SameasFigure 2-2 ,butfor2MASSJ,H,KsandSpitzer/IRAC3.6and4.5m(solid,dashed,dash-dotted,dotted,andsolid,repsectively). andageinFigures 2-2 and 2-3 .Moreover,itcanexacerbatedifferencesformodelswithdifferentmetallicitiesbecausetheTP-AGBstarsusedtocalibratethemodelstypicallyhaveunknownmetallicities( Conroyetal. 2009a ),creatinganadditionalsourceofuncertainty.Thislikelyexplainsthesubstantiallyhigherscatterseenforyoungages,sub-solarmetallicities,andlongwavelengths.ThedifferencesseeninFigures 2-2 and 2-3 arebestviewedaslowerlimitsfortheuncertaintiesintroducedbySPSmodeling.Thisisbecauseagreementbetweenthemodelscansimplybecausedbysimilarmethodologiesusedbythevariousmodelinggroups,anddoesnotnecessarilyimplythatthemodelsaredoingabetterjobofagreeingwithactualstellarpopulations.Forinstance,wenotedabovethatforoldstellarpopulationsthescatterbetweenmodelsistypicallythesameorsmallerforsub-solarmetallicitiesthanforsolarmetallicities.Thisfactisnotsurprisingsinceallthe 30

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Figure2-4. Differencesbetweenmodelsforsolar(left,Z=0.02)andsubsolarright,Z=0.001)metallicities.ModelsareforaSSPwithaSalpeterIMF.Solid,dashed,dash-dotted,anddottedlinesrepresentthedifferencebetweenthepredictedrest-frameabsolutemagnitudesof BC03 C09 CB07 ,and M05 (respectively)minusthepredictionsofthe BC03 modelsetasafunctionoflterwavelength.Eachpanelisdividedupintofourdifferentplotsrepresentingthedifferencesbetweenmodelpredictionsatfourdifferentages:1Gyr(topleft),2Gyrs(topright),6Gyrs(bottomleft),and10Gyrs(bottomright). Figure 2-4 demonstratesthatthescattersseeninFigures 2-2 and 2-3 arenotdrivenbyjustonemodelset.ThisFigureshowsthedifferencesbetweenthepredictedmagnitudesofthesefourmodelsthroughtheSloanandNIRltersforfourdifferentagesandtwometallicities.AllthemodelsinthisFigureareSSPswithaSalpeterIMF.TheleftpanelinFigure 2-4 isformodelswithsolarmetallicityandtherightpanelisformodelswithametallicityofZ=0.001.Eachpanelisdividedupintofourplotscorrespondingtofourdifferentages:1Gyr(topleft),2Gyrs(topright),6Gyrs(bottomleft),and10Gyrs(bottomright).Thelinesineachplotrepresentthedifferencesbetweenthe 31

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BC03 ; M05 ; CB07 ; C09 )minusthepredictedabsolutemagnitudeof BC03 .Ingeneral,themodelsaredistributedthroughoutthefullrangeofmagnitudescoveredbythemodels.ThisshowsthatapparentdisagreementsinFigures 2-2 and 2-3 arenotcausedbyonediscrepantmodelset.Therefore,thescatterseeninFigures 2-2 and 2-3 isrepresentativeofthegeneraluncertaintiesbetweentheSPSmodels.Finally,wenotethatourresultsarerobustagainstthechoiceofmodelsetsusedforourcomparison.Forinstanceitmightseemexpedienttoexcludethe BC03 modelsfromtheaboveanalysisbecausesubstantialefforthasbeenputforthtounderstandtheTP-AGBphasesince BC03 waspublished.However,excludingthismodelsetfromtheanalaysismakesnoappreciabledifferencesinourresults,whichsimplyreectsthefactthatthe BC03 modelsarerarelyanoutlierinFigure 2-4 .Ourconclusionsalsoremainunchangedifweinsteadcomparethe BaSTI M05 ,and C09 modelsetswithaKroupaIMF.ThisonceagainemphasizesthatthedifferencesnotedinthispaperreectgeneraluncertaintiesinSPSmodelingandarenotcausedbyonediscrepantmodelset. Gonzalezetal. ( 2010 )whichincludesdatafrom Reddy&Steidel ( 2009 ), Bouwensetal. ( 2008 ), Bouwensetal. ( 2007 ),and Schiminovichetal. ( 2005 ).Thisgivestherelativestarformationrateintheuniverseasafunctionofredshiftfromz=0.3toz=8.5.Wefurthersetthestarformationratetozeroatz=0andz>10topreventourstarformationhistoryfromhavinganydiscontinuities.Whilethestarformationrateisunlikelytoturnonsuddenlyatz=10orturnoffatz=0,inpracticethisassumptionmakeslittledifferenceanddoesnotimpactourexample. 32

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BC03 M05 CB07 ,and C09 ).WethenuseEzGaltogenerateapparentmagnitudepredictionsforeachCSPmodelthroughtheSloanr,2MASSH,andIRAC3.6mltersasafunctionofredshift,assumingaformationredshiftofzf=10.0.Finallywecalculatethescatterbetweenthepredictedmagnitudesofthemodelsinthesamewayasinourpreviouscomparisons.WeshowthescatterbetweenmodelsasafunctionoflterandredshiftinFigure 2-5 ,aswellasthestarformationhistoryusedtogeneratetheCSPmodels.ThetrendsseeninFigure 2-5 arecausedprimarilybytwoeffects:increasingmodeluncertaintyforyoungerstellarpopulationsandthechangingrest-framewavelengthstracedbyeachlterasafunctionofredshift.For3.6mthemodelscatterpeaksinthe1.z.3range.Athigherredshiftsthe3.6mltertracestherest-frameopticalwherethemodelsagreewell.Strongstarformationfrom2.z.5guaranteesthatthereisasubstantialpresenceofyoungstarsoverthisredshiftrange,andthereforetheincreasingimportanceofTP-AGBstarsleadstoincreaseduncertainty,asdoesthefactthatthe3.6mltertraceslongerwavelengthswhereTP-AGBstarsareagainmoreimportant.Forz.2thestarformationratebeginstodropandthestellarpopulationsbecomesteadilyolder.Sincethemodelsagreewellforoldages,thiscausesthemodelscattertopeakshortlyafterthestarformationratepeaksandthensteadilydeclinetoz=0.IntheH-bandthescatterbetweenmodelsisrelativelyconstantandtypically.0.1mags.ThislowscatteroccursbecausetheH-bandlteralwaystracesregionsofparameterspaceforwhichthemodelsagreewell.AthighredshiftwhenthestellarpopulationsareyoungandtheimpactofTP-AGBstarsisimportant,theH-bandtracestherest-frameopticalwhichisunaffectedbyTP-AGBstars.Atlowredshiftthesteadilydroppingstarformationrateleadstoanincreasingmeanage,onceagainminimizingtheimpactofTP-AGBstarsandleadingtolowuncertainties. 33

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Scatterbetweenmodelsasafunctionofredshift.Thedashed,dotted,anddot-dashedlinesshowthescatterbetweenpredictedapparentmagnitudesintheSloanr,2MASSH,andIRAC3.6mltersrespectivelyasafunctionofredshiftfor BC03 M05 CB07 ,and C09 modelswithsolarmetallicity,aSalpeterIMF,andwithaSFHgivenbytheglobalstarformationhistoryoftheuniverse.ThesolidlineshowstheglobalSFHused(inarbitraryunits),whichcomesfrom Gonzalezetal. ( 2010 ).Scatterreferstothestandarddeviationofthepredictedmagnitudesfromall4bandsatagivenredshiftandforagivenlter.ThescatterinSloanrcutsoffatz6whereitistracingrest-framewavelengthsbluewardoftheLymanlimitandisthereforeunobservable. SimilarlyforSloanrthescatterbetweenmodelsistypically.0.1magsatlowandhighredshift.However,thereisastrongandsuddenpeakinthemodelscatteratz2.ThissamefeatureisalsopresentatpreciselythesameredshiftandsignicanceinalltheSloanltersandtheJband,althoughweonlyshowSloanrinFigure 2-5 .Thefactthatthispeakshowsupinavarietyofltersatthesameredshiftmeansthattheunderlyinguncertaintydependsprimarilyonage,notwavelength.AtthisredshifttheSloanltersandtheJbandarealltracingrest-framewavelengthsbluewardofthe 34

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2-5 illustratesonemorereasonwhyitisimportanttousequantitativemethodstoestimatetheimpactofSPSmodeluncertainties.Observationsofgalaxiesatvariousredshiftsthroughagivenlterwilltracestellarpopulationswithavarietyofagesandwavelengths.Moreover,theuncertaintiesinSPSmodelingdependsensitivelyonwavelengthandage.Theresultofthesefactsisthat,inpractice,SPSmodeluncertaintyoftendependsonredshiftinhardtopredictways.Therefore,forstudiesthatinvestigatehowstellarpopulationsevolveasafunctionofredshiftitisvitaltoverifythatthisredshiftdependentmodeluncertaintyisnotcausingspuriousresults.Thisisbestdonethroughquantitativecomparisonofthemodelstoeachotheroroftheobservationstomanydifferentmodels,tasksthatEzGalisdesignedfor. server 35

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2-2 ismaintainedontheEzGalwebsitewithbasiclterinformation,solarmagnitudes,andcalculatedABtoVegaconversionslistedforallltersavailablethroughthewebsite.Alsodistributedwiththistableisaplotofmagnitude,mass-to-lightratio,andk-correctionevolutionasafunctionofredshiftforeachlter,aplotofthelterresponsecurve,andadatalegivingthelterresponsecurveusedbyEzGal.AdownloadpageisprovidedwherethesourcecodeforEzGalcanbedownloaded,aswellasEzGal-readymodelles.ThisincludestheoriginalSSPmodelsdistributedwithallthemodelsetsdiscussedinthispaper,aswellastheinterpolatedSSPsandgeneratedCSPsthatweuseforourcomparison.FinallywedistributeamanualfortheEzGalAPIdescribinghowtouseEzGalfromwithinpython. BC03 M05 CB07 C09 BaSTI )asafunctionofage,lter,metallicity,andstarformationhistory.Wecomparethepredictionsbetweenthemodelsandnotesubstantialuncertainty(0.3-0.7mags)foryoungstellarpopulations(ages.2Gyrs)atlongwavelengths(&1m),aregionofwell-knownuncertaintycausedbythecontributionofthermallypulsatingAGBstars.Wenotethatforoldages,opticallters,andsolarmetallicitiesthemodelsagreeatthe0.1maglevel.Foroldagesatallwavelengthsthemodelsagreeaswellifnotbetteratsub-solarmetallicitiesthanatsolarmetallicities,whichlikelyreectsthefactthatthemodelsareallcomparedto 36

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Dressel 2011 ).However,obtainingancillarydatatomatchcanbeachallenge,anditisoftennecessarytoworkwithmixedresolutiondatasets.Thiscanhappenwhenlowerresolutionground-baseddataareusedinconjunctionwithhighresolutionspace-basedimaging,orwhenworkingatwavelengthswherehigher-resolutionimagingissimplynotavailableorfeasible.Insuchcases,crowdingcanvarysubstantiallyfromltertolter,andthenaldatasetislimitedbythereliabilityofmagnitudesextractedfromthemostcrowdedimages.Solongassourcesremainunresolved,PSFttingprovidesaviablemethodforextractingmagnitudesincrowdedelds.However,adifferentprocedureisneededtomeasuremagnitudesofresolvedormarginally-resolvedsourcesincrowdedelds.Withmixed-resolutiondatasets,suchaproceduremustmeasuremagnitudesinaconsistentwaydespitedifferencesinPSF,resolution,andcrowding.Wepresentanewprogram,PythonGalaxyFITter(PyGFit)aimedatsolvingtheseproblems.PyGFitisnottherstprogramtoaddresstheseissues(seeforexample Fernandez-Sotoetal. 1999 Labbeetal. 2005 Laidleretal. 2007 ,and deSantisetal. 2007 ).Indeed,PyGFitandTFIT( Laidleretal. 2007 )areconceptuallysimilar.UnlikeTFIT,PyGFitperformsmodeltting.Itworksonthebasisofahigh-resolutioncatalog(HRC)whichgivestheparametersofamodelt(i.e.aSersicprole)foreveryobjectintheHRI.PyGFittsthosemodelstotheLRI,simultaneouslyttingblendedsources.Theuseofmodelsminimizestheimpactofshot-noiseintheHRI,especiallyforobjectswithlowS/Nratio.Surveyswithhighresolutionimagingroutinelytmodelprolestoallvisiblesources,whichmeansthatPyGFitcanoftenbuildoffofalreadyexistingcatalogs. 38

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3.2 describesPyGFit'sttingprocedure.Section 3.3 demonstratesPyGFit'susageonrealdataanddiscussessomerelevantlimitations.Section 3.4 describesthesimulationsbuiltintoPyGFitandusesthemtomeasurethedelityofPyGFit.Finally,Section 3.5 givesourconclusions.AllmagnitudesareontheVegasystem,andweassumeaWMAP7cosmology( Komatsuetal. 2011 ;m=0.272,=0.728,h=0.704)throughout. 39

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3.2.1OverviewThefundamentalgoalofPyGFitistoenablematchedphotometryinmixed-resolutiondatasetsthatisrobusttotheeffectsofcrowdinginthelowerresolutionimages.Inthelimitingcasewhereasourceiseffectivelyapointsourceinthelowerresolutiondataset,thisproblemhaslongbeensolved(seee.g.theMOPEXsoftwareforMIPSphotometry; Makovoz&Marleau 2005 ).OptimaldeblendinghoweverbecomesmorechallengingandcomputationallyintensivewhensourcesaremarginallyresolvedandtheconvolutionofthePSFandunderlyinggalaxyprolemustbeconsidered.WithPyGFitwepresentanapproachthatisdesignedtobefast,exible,andreliable.Thiscodewasoriginallydesignedtoenablesuchrobustphotometryinthecrowdedcoresofhigh-redshiftclustergalaxiesusingthecombinationofHSTandSpitzerdata,butisgenerallyapplicabletoanysituationinwhichonedesiresprole-matchedphotometrybetweenmixedresolutiondatasets.Asdescribedbelow,PyGFitcansuccessfullydeblendthephotometryoftwosourcesaslongastheirintrinsicseparationismorethanapproximately60%oftheFWHMofthePSFinthelowresolutiondata.ItisalsoworthappreciatingthatPyGFitmakestheimplicitassumptionthattheshapeoftheunderlyingproleisthesameatallwavelengthseffectivelyanassumptionthatmorphologicalkcorrectionsaresmall.Incaseswherethemorphologychangesstronglywithwavelength,suchasastarburstgalaxywithanunderlyingoldstellarpopulation,theresultsfromPyGFitshouldbetreatedwithcare.Atitscore,PyGFitusespositionandshapeinformationofobjectsinahigh-resolutionimage(HRI)todeterminehowtodividetheluminosityofblendsinalow-resolutionimage(LRI)amongtheconstituentobjects.Assuch,theprimaryinputintoPyGFitisahigh-resolutioncatalog(HRC)thatgivespositionsandshapesofallobjectsintheHRI.Currently,PyGFitsupportstwomodels:pointspreadfunction(PSF)modelsandSersicmodels.PyGFit'sprocedurecanbebroadlyseparatedintofoursteps:objectdetection 40

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Pengetal. 2002 2010a ).ThismeansthatwhenGALFITisusedinconjunctionwithPyGFit,theoutputfromGALFITcanbefeddirectlyintoPyGFit.Therefore,thesimplestwaytobuildtheHRCisbyusingaprogram(forexampleGALAPAGOS, Hauleretal. 2011 )whichcanrunGALFITandtaSersicproletoeveryobjectintheimage.TherststepPyGFitexecutes,objectdetectionandsegmentation,isperformedbyrunningSourceExtractor( Bertin&Arnouts 1996a )ontheLRI.TheprimarygoalofthisstepistogenerateasegmentationmapoftheLRI.ThisprovidesaconvenientmethodfordeterminingwhichobjectsintheHRCareblendedtogetherandhencemustbemodeledtogether,anditalsodividestheprocessintomanageablechunks.SourceExtractoralsocreatesalow-resolutioncatalog(LRC)andabackgroundmap.PyGFitstorestheLRCandincludesanydesiredinformationfromitinthenaloutputcatalog.Thebackgroundmapisusedtoestimatetheskyforallobjects,andissubtractedfromtheLRIbeforetting.ThisisfollowedbyanalignmentstepbetweentheHRCandtheLRIwhichservestwopurposes.First,itaccountsforanyzerothorderoffsetsbetweentheWCSoftheHRCandtheLRI.Next,itaccountsforanymiscenteringofthelow-resolutionPSFimage.PyGFitperformsthisglobalalignmentbyndingisolatedobjectsandcalculating 41

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3-1 givesahighleveloverviewofPyGFit'sprocedure,showingtheprimaryinputsrequiredbyPyGFitonthetop,themainstepsitexecutes,andhowthevariousinputsfeedintoeachstep. 42

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AowchartofPyGFit'sprocedure.RectanglesdenotecomputationalprocessesexecutedbyPyGFitwhilethepagesymbolsdenotedataproductscreatedbyorusedbyPyGFit.ThevedataproductsalongthetopareinputswhichmustbeprovidedtoPyGFit. 43

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3.2.4 )butwithalargerallowedpositionshiftthanduringnormaltting.Theprecisesizeoftheallowedpositionoffsetiscongurablebytheuser,andshouldbelargeenoughtoaccountforanypotentialoffsetbetweentheHRCandLRI.SincethereareonlythreefreeparametersbeingttothecutoutfromtheLRI(x,y,andmagnitude),thereisnodegeneracyandPyGFiteasilyrecoversthepositionofthehighresolutionobjectintheLRI.ItisthenasimplemattertomeasurethemediandifferencebetweentheobjectpositionsintheHRCandtheLRIandcorrecttheHRCaccordingly.ThisalsoaccountsforanymiscenteringofthePSF.IfthePSFisnotproperlycenteredthenthegalaxymodelswillalsobemiscenteredafterPSFconvolution.ThettingprocesswillnaturallyaccountforthisoffsetandsothenalobjectpositionswillbeshiftedbythePSFoffset.ThereforewhenPyGFitperformsthealignmentstep,itautomaticallycorrectstheHRCinsuchawaythatthePSF-convolvedgalaxymodelswillbeproperlyalignedwiththeLRI. 3.2.4.1CutoutsTherststepinthettingprocessistoidentifyalllowresolutionsourceswhichhavematchingobjectsfromthealignedHRC.ObjectsfromtheHRCarematchedwithalowresolutionsourceiftheobjectfallsononeofthepixelsidentiedbySourceExtractorasbelongingtothesegmentationregion.Lowresolutionsourceswithoutanyoverlappingobjectsareignored.Fittingisdonewiththebackground-subtractedLRI,andttingproceedsfromthebrightestlowresolutionsourcestothefaintest.AftereachsourceistthebestttingmodelissubtractedfromtheLRItoremoveitscontributiontoanynearbysources.PyGFitgeneratesacutoutoftheblendfromtheLRIandextractsamatchingcutoutfromtheRMSmap.Theextractedcutoutissquareandislargeenoughtoenclosethefullsegmentationregionofthelowresolutionsource.Thecutoutisfurtherextendedineverydirectionbythesizeoftheallowedpositionshiftduringthettingprocess,andan 45

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3.2.4.3 ).Shiftingisaccomplishedwiththird-ordersplineinterpolation,andbeforeshiftingthemodelispadded(theprecisepaddinglengthiscongurable)tominimizetheimpactofedgeeffects.Sersicmodelgenerationbeginsbycalculatingtheaveragesurfacebrightness()oftheSersicmodelineachpixelofthecutout.TheSersicproledependsupontheeffectiveradius(re),Sersicindex(n),axisratio(q),positionangle(P.A.),totalux(Ftot),aboxinessparameter(c),andtheprolecenter(xcent,ycent).FromtheseeightparametersPyGFitderivestwomoreparameters:thesurfacebrightnessattheeffectiveradius(e)andacouplingfactor()thatensuresthattheeffectiveradiusisalsothehalf-lightradius.Thesurfacebrightnessasafunctionofradiusisthengivenby: 3.2.4.3 ).(2n)isthegammafunctionandR(c)isgivenby: 46

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Pengetal. 2002 2010a ),whichisdoneintentionallyforeaseofuse.IfGALFITisusedtotSersicprolestotheHRI,thentheoutputfromGALFITcanbepasseddirectlyintoPyGFitwithoutmodication.PyGFitmustcalculatetheuxineachpixelofthemodelimage.ThemoststraightforwardwaytodothisistointegratetheSersicfunctionovereachpixel.However,theintegrationtimeoftheSersicfunctioncanbecomputationallyprohibitive,andPyGFitwouldbedramaticallyslowerifitattemptedtointegratetheSersicfunctionovereverypixel.InsteadPyGFitperformsanumericintegrationbysplittingeachpixelintosubpixels,evaluatingtheSersicfunctionateachsubpixel,andaveragingtheirvaluestogether.Thelevelofresamplingisnertowardsthecenterofthemodel,withdifferentlevelsofresamplingforr>2re,r<2re,andthecentralpixel.FortheseregionsPyGFitresamplesthemodelimagesuchthatthesizeofeachsubpixelisatmostre=2,re=20,andre=200,respectively.Extensivetestinghasshownthatthismethodologyprovidesareasonableexecutiontimewithoutcompromisingtheresults.TheonlyexceptionisforgalaxieswithsmallradiiandhighSersicindexes(n8),wherewendthattheonlywaytoreliablycalculatetheuxatthecenteroftheSersicproleisbydirectlycalculatingitsintegral.However,thesecasesareeasytodetectand,ifdesired,PyGFitcanautomaticallyswitchfromitsdefaulttreatmenttoafullintegrationtoguaranteethatallgalaxiesareproperlymodeled.AswithPSFmodels,PyGFitpadsthemodelimageduringSersicmodelgenerationtominimizetheimpactofedgeeffects.AftergeneratingtheSersicmodelPyGFitthenconvolvesitwiththelow-resolutionPSF.AttheendofthemodelgenerationprocessPyGFithasamodelimageforeveryhigh-resolutionobjectassociatedwithagivenlowresolutionsource.Thegeneratedmodelimagematchesthecutoutfortheblend.Thetotaluxofthemodelhasbeennormalizedtomatchtherstguessthatgoesintothe2minimization(Section 3.2.4.3 ), 47

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48

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6 .Insummary,wehad13galaxyclusterswith1
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Figure3-2. Originalimages(toprow)andresiduals(bottomrow)fromourGALFITandPyGFitrunsinthecoreofahighredshift(z=1.243)galaxycluster.FromlefttorighttheimagescorrespondtoWFC3/F160W,R,H,and4.5m.TheWFC3/F160WimagewastwithGALFIT,whileallotherbandsweretwithPyGFit.Allpanelsshowthesameeldofview,andthescaleinthetopleftpanelis1000long. At4.5m(farrightofFigure 3-2 )therearesmallresidualsvisibleintheverycentersofmanyobjects.Theseresidualsarecommontobothour3.6mand4.5mltersbutarenotvisibleinthe5.8and8.0mlters.TheprimarydifferencebetweentheourIRACimagesisthesizeofthePSF,whichvariesfrom1.6600to1.9800( Fazioetal. 2004 ).OurIRACimageshavebeenditheredandresampledtohaveapixelscaleof0.86500=pixel,whichmeansthatthePSFisproperlysampledonlyifitislargerthan1.7300.The4.5mimagingfallsjustshortofthisrequirementwithameanPSFsizeof1.7200,whilethe5.8mimaginghasameanPSFsizeof1.8800.Therefore,thePSFisresolvedforour5.8and8.0mimagesbutissub-optimallysampledforour3.6and4.5mimaging.WithoutafullyresolvedPSFinterpolation(whichPyGFitdoesduringmodelgenerationandtting)canintroduceartifacts,andthisislikelythesourceofthesmallresidualsobservedinourblueIRACbands.However,oursimulations(Section 50

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)conclusivelydemonstratethatPyGFitcanreliablyextractmagnitudesanduxesfromtheobservations,andthattheprimarysourceofuncertaintyissimplyskynoise.AnexaminationofourresidualsimagesrevealsafewclassesofproblemswhichcanresultinPyGFitfailures.WeshowafewexamplesofthesecasesinFigure 3-3 .OnesourceofdifcultyiswhenagalaxyisnotwellrepresentedbyaSersicfunction.IntheexampleinFigure 3-3 (farleft)agalaxyhasextendedfeatureswhichcannotbemodeledbyaSersicprole.Asaresult,thecentralregionofthegalaxyisover-subtracted,whiletheouterregionisunder-subtracted.Aslongasthegalaxydoesnothaveasubstantialamountofuxoutsideofthemodelradius,PyGFitcanstillreturnanapproximatelycorrecttotalux.Ifthegalaxydoeshavesubstantialuxoutsideofthemodelradius,PyGFitwillunderestimatethetotaluxofthegalaxy.However,anyerrorintroducedbyamismatchedmodelwillbethesameforalllters.Therefore,whenusingPyGFittomeasureSEDs,thisclassofproblemcanleadtoanunderestimatedSEDnormalizationbutwillnotintroduceanyadditionallter-to-lteruncertaintyintheSED.PyGFitcanfailcatastrophicallywhenobjectsintheLRIaremissingfromtheHRC.If,intheLRI,anobjectintheHRCisblendedwithanotherobjectwhichisnotintheHRC,thenPyGFitwillassignuxfromthesecondobjecttotherst,overestimatingitsux.Thiscanhappeninanumberofways,twoofwhichareillustratedinFigure 3-3 .ThetopcentralpanelofFigure 3-3 showsafaintgalaxy.Thecenterpanelshowsthat,inthe4.5mimage,thereappearstobeasignicantelongationtowardsthebottomright,whichcannotbeaccountedforfromtheF160Wimage.Aftersubtraction(bottomcenter)thereappearstobeanobjectleftoverbelowandtotherightoftheF160Wsource.Theonlywaytoexplainthisiswiththepresenceofanobjectwhichisbrightin4.5mbutnearlyinvisibleinF160W,andwhichhappenstobeblendedwiththeobjectvisibleinF160W.Asaresult,theobjectfromtheHRCisoverttoaccountfortheuxfromtheadditionallow-resolutionobject,andthereforeitstisunreliable. 51

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ThreeexamplesofcaseswherePyGFitcanfail.ThetoprowofpanelsshowstheF160WimagesusedtocreatetheHRC.ThecenterrowofpanelsshowstheLRIwiththesameeldofview,whilethebottomrowofpanelsshowstheresidualsoftheLRIaftertting.TheLRIfortheleftusesground-basedRbandimaging,whiletheexampleinthecenteristakenfromthe4.5mimagingandtheexampleontherightistakenfromtheIRAC3.6mimaging.TheleftcolumnshowsagalaxywithextendedfeatureswhichcannotbedescribedbyaSersicprole.ThecentercolumnshowsagalaxywhichisisolatedinF160Wbutwhichisblendedwithanothersourcein4.5m.TherightcolumnshowsagalaxyneartheedgeoftheF160WimagewhichisblendedwithabrightsourcewhichisoutsideoftheF160Wimage.Furtherdetailsareinthetext. 52

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3-3 showthesameclassofprobleminanothercontext.ThisshowswhatcanhappenwhentheLRIextendspasttheHRC.ThetoprightpanelshowsanobjectwhichisneartheedgeoftheF160Wimage.Inthe3.6mimage(centerright)abrightobjecthappenstobenearbybutisjustoutsideoftheF160Weldofview,andisthereforemissingfromtheHRC.AlthoughthissecondobjectisoutsideoftheF160Weldofview,itisbrightenoughtocontributesubstantiallytotheuxneartheobjectofinterest.Asaresult,PyGFitoverestimatesthe3.6muxoftheobjectwhichisintheHRC.Whilethisparticularproblemcanlikelyoccurforanyimage,weseeitmostcommonlyinourIRACimages.ThisisbecauseourIRACimageshavethehighestsourcedensitiesandthelargestPSFofallofourimages,andthiscombinationincreasesthelikelihoodofhavingsuchablend.Obviously,PyGFitcannotaccountforobjectswhicharemissingfromtheHRC.ThisfactshouldbekeptinmindwhenusingPyGFitandcaremustbetakentoincludeallsourceswhichwillbevisibleintheLRI,ortorejectsourcesthatareblendedwithobjectsmissingfromtheHRC. 53

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3.2.5 ).Thisincludesinformationonthenumberofobjectsthesimulatedgalaxywasblendedwith,howcloseandbrightthenearestneighboris,andotherenvironmentalindicators. 3-4 .ThetoprowofpanelsinthisFigureshowstheinputandoutputmagnitudeofeachsimulatedgalaxy.Thebottomrowofpanelsshowsthecorrespondingerrorasafunctionofmagnitudewhichiscalculatedbybinningthesimulatedgalaxiesinmagnitudespaceandmeasuringthestandarddeviationineachbin.Errorbarsarecalculatedwithbootstrapresampling.Thesolidcurveinthebottomrowofpanelsshowsanestimateof 54

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Figure3-4. (Top)InputmagnitudeversusinputmagnitudeminusoutputmagnitudeasmeasuredbyPyGFitsimulationsforthreelters:R(left),J(center),and3.6m(right).(Bottom)Magnitudeerrorasafunctionofmagnitude.ThesolidcirclesshowtheerrorofPyGFit'smagnitudeestimatesinmagnitudebins.Forcomparisontheopencirclesshowtheresultingerrorwhena400diameteraperture-magnitudeisusedinsteadofPyGFit.Thesolidlineshowstheuncertaintyintroducedbyskynoiseforanaperturewitha400diameter. FortheRandJbandsthereisexcellentagreementbetweenthemagnitudeerrorsthatresultfromPyGFitandtheerrorthatresultsfromskynoisefora400diameteraperture-magnitude.WhilethemagnitudesreturnedbyPyGFitarenotanaperturemagnitude(theyareinsteadamodelt),thisstillprovidesagoodreferencepointforcomparison.ThefactthatthemagnitudeerrorsfromPyGFitareverysimilartotheplottedsky-noiselimitsuggestthatfortheRandJbandsPyGFit'sperformanceisprimarilylimitedbyskynoise,whichsetsafundamentallimitforanymethodthatmeasurestheuxofanobject.WenotethatPyGFitdoessubstantiallybetterthana 55

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3-4 .Thisisnotsurprising,asaperturemagnitudesarenotrobustincrowdedenvironments.However,PyGFitdoesnotreachthesky-noiselimitfora400aperturemagnitudeinour3.6mdata.AcloseexaminationofthetoprightpanelofFigure 3-4 showsthattherearepoorlytgalaxies(jMagInMagOutj>0.75)drivingthisscatter.OursimulationsrevealthatPyGFitbeginstobreakdownwhentwogalaxiesareveryclosetogetherorwhenagalaxyisblendedwithamuchbrighterone.Toshowthisweperformanothersimulationwhereweinsertpairsofgalaxiesintoanimagewiththesamenoiseproperties,pixelscale,andPSFasthe3.6mimage.Thesesimulatedpairshaveseparationsbetween0.200and300,magnitudedifferencesbetween0and3(i.e.uxratiosbetween1and15),andthebrightergalaxyinthepairhasamagnitudebetween15and17.WedropthesepairsintoanotherwiseblankimageandmeasurePyGFit'sdelityasafunctionofuxratioandseparationforclosepairs.Figure 3-5 illustratestheresult.Theleftpanelshowsthemagnitudeerrorforsimulatedgalaxiesasafunctionoftheuxratioofagalaxyanditsneighbors.Toisolatetheinuenceoftheuxratio,thispanelexcludesgalaxiesseparatedbylessthantheFWHMofthePSF(1.6600in3.6m).TherightpanelshowsthemagnitudeerrorforsimulatedgalaxiesasafunctionoftheseparationbetweenthepairrelativetotheFWHMofthePSF.Thispanelonlyshowsgalaxieswhicharethebrightestgalaxyinthepair.Wendthatour3.6mPyGFitresultsbecomeunreliableforgalaxieswithuxratios<0.25orseparations.60%(.100)ofthePSFradius.Testsshowthatourotherltersencounterasimilarissueforsuchpairs.However,sourcedensityisbyfarthehighestinourIRACimages.Becausethecrowdingislessofanissueinourotherbands,theselimitshaveasmallerimpactinourrealandsimulateddataforournon-IRACbands.WethereforeremovethesesimulatedgalaxiesfromoursampleandplotinFigure 3-6 thedelityofPyGFit'sresultsfortheremaininggalaxies. 56

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Differencebetweeninputandoutputmagnitudeforsimulatedgalaxiesasafunctionofuxratio(left)andseparationrelativetothesizeofthePSF(right).Tocleanlyseparatethetwocompetingeffectstheleftpanelonlyincludesgalaxiesseparatedbyatleast1PSFFWHM,andtherightpanelonlyincludesgalaxieswhicharethebrightestgalaxyinthepair. Figure 3-6 showsthatafterremovingthisproblematiccaseofgalaxiesfromoursample,thequalityoftheIRACresultsismuchbetter.Wenotethatnoalgorithmcandeblendobjectswhicharearbitrarilyclosetogether,orwhichhavebeenblendedwithanarbitrarilybrighterobject.Indeed,aclosepairisonlyconsideredresolvedwhenitsmembersareseparatedbyatleastonePSFradius.However,PyGFitisreliablyttinggalaxiesseparatedby60%ofthePSFradius,whichshowsthatitisaviableoptionforcrowdedelds.WeexaminehowPyGFitperformsasafunctionofenvironmentaldiagnostics.InFigure 3-7 weshowthedelityofPyGFit'sresultsasafunctionofthenumberofobjectsblendedtogether,thedistancetothenearestobject,theuxratiobetweenanobjectanditsnearestneighbor,andthefractionoftheblendaccountedforbythesimulated 57

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SameasFigure 3-4 ,exceptsimulatedgalaxieswithseparations<60%ofthePSFradiusoruxratios<0.25havebeencutfromthesample. object.Weonlyplotsimulatedgalaxiesinthisgureiftheyhave[3.6]<19.0andpassthecutsdiscussedabove(i.e.uxratio>0.25andseparation>100).TherearenostrongcorrelationsinFigure 3-7 ,demonstratingthatthequalityofPyGFit'sresultsareindependentofthedegreeofcrowdingorotherenvironmentalfactors.Similarly,wealsondthatthereisnorelationshipbetweentheuncertaintyofPyGFit'sresultsandanyoftheSersicparameters.Otherthanmagnitude,PyGFit'sdelityisindependentofre,n,B=A,andP.A. 58

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PyGFiterrorsasmeasuredwithoursimulationsforour3.6mgalaxieswith[3.6]<19.0versusthenumberofobjectsintheblend(topleft),thedistancetothenearestblendedobject(topright),theuxratiobetweentheobjectanditsnearestneighbor(bottomright),andthefractionoftheblenduxaccountedforbythesimulatedobject(bottomleft). subtractgalaxiesfromtheLRI.Especiallyintheground-basedimageswherethePSFiswellresolved,thereappearstobenothingleftintheresidualimagesbutskynoise.SimulationsshowthattheuncertaintyinPyGFit'smagnitudesareconsistentwithbeinglimitedbyskynoise.OursimulationsidentifyafewclassesofproblemswhichcanintroduceerrorsintothePyGFitresults.Mostimportantarecatalogproblems,i.e.incorrectormissinghighresolutiondata.Primaryexamplesofcatalogproblemsincludettinggalaxymodelsin 59

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60

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Trageretal. 2008 )itisausefulsimplicationandworkssurprisinglywell,especiallyformassiveclustergalaxies.Anumberofdifferenttechniqueshavebeenusedtomeasurethemeanageofthestellarpopulationsingalaxyclusters.Themoststraight-forwardtechniqueistousespectralindicesormodelcomparisonstogalaxyspectratomeasureagesdirectly. Thomasetal. ( 2005 )studyearlytypegalaxiesindenseenvironmentsusingsuchamethodandndthatthemajorityofthestarformationinmassivegalaxiesoccurredbetweenz35,withvigorousstarformationepisodesfromz25.Ageestimatesforclustergalaxiescanalsocomefromtheclusterredsequenceinvariousways. Kurketal. ( 2009 )usesthecoloroftheredsequenceinasinglez=1.6assemblingclustertoestimateaformationepochofzf3. Tranetal. ( 2007 )examinethesmallscatterofabsorptionlinegalaxiesabouttheredsequenceofaz=0.83galaxycluster,andconcludethatallstarformationceasedbyz1.2andthatmostofthemembersformed 61

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vanDokkum&vanderMarel ( 2007 )estimatealuminosity-weightedmeanformationredshiftfortheirgalaxiesof2.01+0.220.17.Forsurveysthathavemanyclustersdistributedoverarangeofredshifts,itispossibletoexaminethecolororluminosityevolutionofclustergalaxiesovertimetoconstraintheprimarystarformationepoch. Eisenhardtetal. ( 2008b )exploreasampleofclusterswithphotometricredshiftsbetween01clusters). Muzzinetal. ( 2008a ,hereafterM08)ndaclustersamplewithphotometricredshiftsbetween0.11.5.Itisimportanttonotethatluminosity-weightedmeasuresofstellarpopulationageswillgenerallyreturnlaterformationredshifts(andyoungerages)thanmass-weightedmeasurements,sinceyoungstellarpopulationscontributemoreluminosityperunitmassthanoldstellarpopulations.Wenotethatofthepapersquotedabove, Thomasetal. ( 2005 )istheonlyonethatprovidesamass-weightedagemeasurement,andsoitisnotsurprisingthatitpointstotheearliestformationredshifts.Itishardtosaywhethertheobservedvariationbetweentheluminosity-weightedageestimatesrepresentsgenuinedifferencesinthestellarpopulations,differencesinthemethods,orsignsofsystematicerrors.OnerecognizeduncertaintythatfactorsintomanyofthesestudiesistheslopeoftheIMF(inparticularnear1M)athighredshift.SincetherateofluminosityevolutionisstronglydependentupontheslopeoftheIMF( Conroyetal. 2009b ),anyoftheabovestudiesthatestimateformationepochsbasedontheevolutionofgalaxyluminosities 62

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vanDokkum&vanderMarel 2007 M08 )arestronglydependentupontheslopeoftheIMF.IngeneralatterIMFsatearlierepochswouldpushthesestudiestoearlierformationredshifts.Thereisstillmuchworkneededonourpictureofmassassemblyinthemostmassiveclustergalaxies.Pastworkontheluminosityevolutioninclustergalaxieshastypicallysearchedfordeviationsofthegalaxiesrelativetomodelsforpassivelyevolvinggalaxies.Findingnone,studieshaveconcludedthatthereislittleornomassassemblyinmassiveclustergalaxies,outtothefarthestredshiftsstudied,z.1.3(see Strazzulloetal. 2006a DeProprisetal. 2007a M08 ).Howeveritisnotclearjusthowmuchmassassemblyisruledoutbysuchstudies.Agreementwithpassiveevolutionmodelsrepresents,atbest,anupperlimitontheamountofmassassemblyallowed,butthislimithasnotbeenexplicitlycalculated.Anothermethodofconstrainingmassassemblyistolookatthebuild-upoftheredsequence.Theredsequencehastheadvantageofbeingrelativelyeasytoidentify,evenathighredshift.Indeed, Kodamaetal. ( 2007 )ndevidencethatthemassiveendoftheredsequencebeginstobuildupasearlyas2.z.3,and Zirmetal. ( 2008 )ndaredsequencearoundaz=2.16protocluster.Thissuggeststhatthebrightendoftheclusterredsequenceisestablishedveryearly,afactveriedbywelldenedredsequencesfoundintwoassemblingclusters,oneatz=1.6( Kurketal. 2009 )andanotheratz=1.62( Papovichetal. 2010 ; Tanakaetal. 2010 ).Inthischapterweextendtheworkofpreviousresearcherswhohavestudiedtheevolutionoftheluminosityfunctionofmassiveclustergalaxies( Strazzulloetal. 2006a DeProprisetal. 2007a Muzzinetal. 2007 M08 ).WemakeuseoftheSpitzerDeep,Wide-FieldSurvey(SDWFS, Ashbyetal. 2009b ),an8.5deg2surveywithalimitingmagnitudeof18.8(5)at4.5m(ontheVega-magsystem).Thissurveyhassufcientmultiwavelengthdatatocalculateaccuratephotometricredshiftsandreliablyidentifyclustersandlikelymembers.Becauseofthesizeofoursurveyareawehavealarger 63

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4.2 describesthedataweareworkingwith,Section 4.3 presentsourluminosityfunctions,andinSection 4.4 wecomparethemtomodelsforpassivelyevolvingstellarpopulations.InSection 4.5 wediscusstheevidenceformassassemblyinourresults,andSection 4.6 containsoursummaryandconclusions.ThroughoutthisworkweassumeaWMAP5cosmology,0=0.279,=0.721,andH0=70.1kms1Mpc1( Hinshawetal. 2009 ).AllmagnitudesareontheVegamagnitudesystem. 4.2.1GalaxyCatalogOurgalaxycatalogforthisworkcomesfromSDWFS,whichisareimagingoftheIRACShallowClusterSurvey(ISCS, Eisenhardtetal. 2004 ).TheISCShad90secondsofintegrationtimeacross8.5deg2intheBooteseld,andSDWFSadded3more90secondexposuresateverypointing. Ashbyetal. ( 2009b )describesthedatareductionforSDWFS.Thesourcecatalogreachesdepthsof19.77and18.83magsin3.6and4.5mandcontains670,446detectedsourcesat3.6mand528,232sourcesat4.5m(5,4aperturecorrectedtototal).Weuse4aperturemagnitudescorrectedtototaltoderivephotometricredshiftprobabilitydistributionfunctionsfromcombinedSDWFS(3.6,4.5,5.8,and8.0m)imagingandBwRIdatafromtheNOAODeepWide-FieldSurvey(NDWFS).WeworkwithasubsampleoftheSDWFScatalogconsistingofsourceswhicharebrighterthan18.8magsin4.5mandhaveopticaldata.Oursubsampleconsistsof454,418sourcesforwhichweassignredshiftprobabilitydistributionsusingthemethodologyof Brodwinetal. ( 2006b ).Comparingto15,052galaxieswithspectroscopicredshifts, Brodwinetal. ( 2006b )ndthattheirphotometricredshiftsaregoodtoz=0.06(1+z)for95%oftheirgalaxiesat0
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Stanfordetal. 2005b ; Elstonetal. 2006b ; Brodwinetal. 2006b ; Eisenhardtetal. 2008b ; Sternetal. 2010 ).Theidenticationoftheclustersampleisdescribedin Eisenhardtetal. ( 2008b ),andwesummarizethemajorfeatureshere.Thisclusterlistwasgeneratedbyusingtheredshiftprobabilitydistributionsfrom Brodwinetal. ( 2006b )toperformawaveletanalysisandidentifyclustersintheISCS.Withthismethodprobabilitymapsaregeneratedforxedredshiftslices,andsignalisaddedtotheprobabilitymapsatthelocationofthegalaxiesinproportiontotheintegratedprobabilityofeachgalaxybeingfoundintheredshiftslice.Clustersarethenidentiedbysearchingforstatisticallysignicantpeaksintheseprobabilitymaps.Ofthe335clustersinthissurvey25%areconrmed,including15atz>1( Stanfordetal. 2005b ; Eisenhardtetal. 2008b ).Werestrictouranalysisto0.3
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4.3.1GeneralProcedureWhileusingphotometricredshiftsallowsustoconstructalargegalaxycatalogouttohighredshifts,itisnotwithoutitsdisadvantages.Withoutspectroscopicredshiftswecanonlyndclustermembersinastatisticalfashion.Insteadofmeasuringtheluminosityfunctionofclustergalaxiesdirectly,wemustmeasuretheluminosityfunctionofgalaxiesneareachclusterandcorrectforthepresenceofeldgalaxies.Toaccomplishthiswerstndphoto-zclustermembersandeldgalaxiesforeachcluster.Galaxieswithin1.5Mpc(physicaldistance)andneartheclusterredshiftareconsideredphoto-zclustermembers,andgalaxieswith4Mpc
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4.3.5 and 4.4.3.4 ).Ourchoiceofcutprobabilityhasonlyaminorimpactonourresults.Usingaxedcutatallredshiftswillremovealargerfractionofgalaxiesathighredshift,becausetheirphotometricredshiftprobabilitydistributionsarebroader.Toaccountforthiswexthecutprobabilityatz=0andallowittodecreaseasafunctionofclusterredshifttoaccountforthebroadeningofthephotometricredshiftstohighredshift.Thecutdecreasessuchthatagalaxythatisattheclusterredshiftandmakesthecutatz=0willnotbeexcludedifitisattheredshiftofahigher-zcluster.Also,thisprobabilitycutdisproportionatelyremovesfaintgalaxiesbecausetheyhavethelargestphoto-zerrorsatagivenredshift.WecorrectforthiseffectbyperformingasimpleMonteCarlosimulationusingtheredshiftprobabilitydistributionsforthegalaxiestoestimatethefractionofgalaxieslostasafunctionofmagnitude,duetothisprobabilitycut.Wethenweightthegalaxiesappropriatelyinourtstoaccountforthisincompleteness.Wemustaccountforanypotentialoverlapbetweenclusters.Wesearchforanyclustersthatfallwithin10Mpcandz=0.06(1+z)ofagivencluster,andremoveanyphoto-zclustermembersoreldgalaxiesthatarewithin2Mpcofacontaminatingcluster.Wealsocalculatetherelativesizeoftheeldandmemberregionsforeachcluster,accountingforanymissingareasduetocontaminatingclusters,badpixels,brightstars,ortheedgeofthesurvey.Theclustersaredividedintoredshiftbinswithawidthofz=0.15startingatz=0.3.Insteadofconsideringthecenterofeachbintobethebinlocation,weusethemedianredshiftoftheclustersineachbinasthebinlocation.Wecombinehighredshiftbinstoincreasesignaltonoise,soourtwohighestredshiftbinsgofromz=1.351.63andz=1.632.00.Weremoveapproximately12%oftheclustersinoursample 67

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Ashbyetal. 2009b ).Forreferencethecompleteness 68

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Marshalletal. ( 1983 ).Ourdataareonlydeepenoughtoreliablyconstraininthelowestredshiftbin,forwhichwend=0.60.2.Previousworkintheliteraturehascommonlyfound( Linetal. 2004 ,hereafterL04)orassumed( M08 )0.8forclusters.Thisisconsistentwiththevaluefromourlowestredshiftbin,sowealsoassumeandx=0.8inourtsforallredshiftbins.InSection 4.4.3.2 weexplorethesensitivityofourresultstodifferentvaluesof.Weuseadownhillsimplexalgorithm( Pressetal. 2007 )tomaximizethelikelihoodasafunctionofmand.Therelationshipbetweenthelikelihood,m,andissmoothwithonlyonemaximum,soourresultsareindependentofthestartingguess.Finally,weestimateerrorsinmforeachredshiftbinusingbootstrapresampling.WegeneraterealizationsofeachredshiftbinbyrandomlyselectingNclustersfromthebinwithreplacement,whereNisequaltothenumberofclustersinthebin.ThisnumberofrealizationsforeachbinissuchthateveryredshiftbinwillhaveatleastNlog(N)2realizations,whichhasbeenshowntobeasufcientnumberforaccuratelyestimatingerrors( Babu&Singh 1983 ).Weteachrealizationinthesamefashionasbefore.Errorestimatescomefromthedistributionofttedmvaluestotherealizations.Wendthemvaluesthatcontain68%ofthetteddistribution,andusetheseasourerrors. 69

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4-1 (3.6m)and 4-2 (4.5m).ForclarityweplotinFigures 4-1 and 4-2 the(binned)differencebetweentheluminosityfunctionofgalaxiesneartheclusterandtheeldluminosityfunctioninunitsofgalaxiespermagnitude.Thisisrepresentedbysolidcircles.ThesolidcurvedenotestheSchechterfunctionwith=0.8ttedtotheclusterluminosityfunction,andthesolidverticallineshowsthettedvalueofm.ThedottedlineshowsthettedSchechterfunctionwith=1.0,andthedashedverticallineistheapparentmagnitudelimitoftheredshiftbin.Figures 4-1 and 4-2 showthatourttedvaluesofmare2.5magsbrighterthantheapparentmagnitudelimitofthesurveyatlowredshift.Athighredshiftthe4.5mdataare1magbrighterthantheapparentmagnitudelimit,whilethe3.6mdataareonly0.5magsbrighter.Table 4-1 liststhebestttingmvaluesanderrorsfor=0.6,0.8,1.0,and1.12asafunctionofredshift.Table 4-2 liststheresultscalculatedwithourstatisticalbackgroundsubtraction. 70

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ThesameasFigure 4-1 ,butfor4.5m. 72

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SchechterFitParamatersPhoto-zSelection

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SchechterFitParamatersStatisticalBackgroundSubtraction 4.3.2 werejectgalaxieswhichhaveatotalprobability<30%ofbeingwithinz=0.06(1+z)oftheclusterredshift.Usingaprobabilitycutof20%movesourresultsbrighterby0.05mags,andcuttingat40%movesourresultsfainterby0.05mags.Acutof50%scattersourresultsrandomlyby0.1mags.Secondistheluminosityfunctioncompletenesscorrectionwhichwehaveappliedtoaccountforthelossoffaintgalaxiesduetoourprobabilitycut.Ifwedonotincludethiscorrection,ourttedmvaluesmovesystematicallybrighterby0.05mags.Third,ourchoiceofisanimportantsourceofttinguncertaintyinthisstudy.Fornowwenotethatadjustingproducesalargelysystematicshiftinourresults.Ingeneralifbecomessteeperby0.1thenourttedmvaluesmovebrighterby0.1mags.WediscusstheimpactofourchoiceofinmoredetailinSection 4.4.3.2 becausecomparisontoourmodelsforpassivegalaxyevolutionprovidesthebestwaytoinvestigatetheimpactofonourresults. 4.4.1ModelDescriptionTomeasuretheprimarystarformationepochforgalaxiesinthisworkwecompareourmeasuredmvaluesagainstmodelpredictionsforapassivelyevolvingstellar 74

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Bruzual&Charlot ( 2003a ,hereafterBC03),anupdatedversionof BC03 withdetailedtreatmentofthermally-pulsingasymptoticgiantbranch(TP-AGB)stars( Charlot&Bruzual privatecommunication ,hereafterCB07),andthemodelsfrom Maraston ( 2005 ,hereafterM05).Figure 4-3 comparesthepredictionsofthesethreemodelsetsat3.6m(top),and4.5m(bottom).InthisgureallthemodelsarenormalizedtohavethesameMvalueatz=0.05in3.6m(M3.6),whichwediscussinmoredetailbelow. CB07 and BC03 usea Chabrier ( 2003a )IMFand M05 usesaKroupaIMF.Forallthreemodelsetsweassumesolarmetallicity,andinSection 4.4.3.3 weinvestigatetheresultsofchangingIMFormetallicity.Wecharacterizethestarformationhistoryasanexponentiallydecliningburstofstarformationwithacharacteristictimescaleof0.1Gyr,effectivelyasingleburstmodel.Sinceourgoalistocompareourresultsagainstmodelsforpassivelyevolvingstellarpopulations,weconcentrateonthisoneburstingmodelofstarformationanddonotattempttomodelmorecomplicatedstarformationhistories.WecompareallthreemodelsetsinFigure 4-3 ,whichshowsthepredictedevolutionin3.6mwhenstarformationturnsonatz=2.5.The BC03 and CB07 modelsagreewellatlowredshift,butstarttodivergeathigherredshifts.The CB07 modelsarebrighterthanthe BC03 modelsathigherredshift,dueprimarilytoamoreimprovedtreatmentofTP-AGBstarsinthe CB07 models. M05 ,whichalsoincludesanupdatedtreatmentofTP-AGBstars,isbrighterthan CB07 atz0.6,andlacksthedipatz1.8thatboth CB07 and BC03 have.Fortheremainderofthispaperwefocusupon M05 butalsocompareourresultswith BC03 and CB07 (Section 4.4.3.3 )todeterminethesystematicerrorsintroducedbyourchoiceofmodel.Withallthreemodelsetswebuildarangeofmodelswhichdifferonlybytheirpeakstarformationepoch.Weusepeakstarformationredshiftsthatspantherangeofzf=1.0tozf=9.95inredshiftincrementsofz=0.05.Previousstudieshaveusedmeasurementsofthegalaxyluminosityfunctionatlowredshifttonormalizesuch 75

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Acomparisonbetweenthemodelsof BC03 (dottedline), CB07 (dashedline),and M05 (solidline).Thestarformationepochisassumedtobez=2.5forallmodels.Redshiftisonthex-axis.Toppanelis3.6m,bottompanelis4.5m.Allthreemodelsetsarenormalizedtomatchtheresultsof L04 atlowredshift. 76

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4-3 )weshowmodelswithouthavingperformedattothedata.Forsimplicityinthesecases,wexthemodelnormalizationusingtheresultsfrom L04 forwhichwecalculateM3.6=24.32forgalaxiesatameanredshiftofz=0.05.Thiscomesfromtakingtheoriginalresultfoundby L04 inKsband(MKs=24.02)andusingourmodelstoconvertfromrest-frameKstoobserved3.6m. 4-4 .Asmallsubsampleofthepassiveevolutionmodelsareoverplotted(withthenormalizationxedaccordingto L04 ).Figure 4-4 includestheresultsof M08 .Ourerrorbarsaresmallerasexpectedbecauseofouruseofphotometricredshiftstoselectgalaxies(asopposedtothestatisticalbackgroundsubtractionusedby M08 ),andbecauseofthelargerareaandgreaterdepthoftheSDWFSsurvey. M08 useddatafromtheSpitzerFirstLookSurvey( Lacyetal. 2005 ),a3.8deg2eldwith1/6thofourintegrationtime.InFigure 4-4 wealsoincludetheresultsofourstatisticalbackgroundsubtractionandndexcellentagreementbetweenourphoto-zselectionmethodandourstatisticalbackgroundsubtraction.Forthisreasonwewillconcentrateontheresultsfromourphoto-zselectionmethodandonlyreturntoourstatisticalbackgroundsubtractionwheninvestigatingtheimpactofsystematicuncertainties(Section 4.4.3.4 ).Figure 4-5 comparesourresultswiththepredictedcolorevolution.Thecolorevolutionisnotusefulforconstrainingtheformationepochbecausethereislittledifferencebetweenthemodels.Insteadwenotethatthecolorevolutionweobserveisconsistentwiththemodelpredictionsandhenceservesasausefulcheckofourresults. 77

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Measuredevolutionofm3.6(top)andm4.5(bottom)versusredshiftcomparedwith M05 modelpredictions.Weshowourresultsfrombothourphoto-zselectionmethodandstatisticalbackgroundsubtraction.Themodelsarenormalizedtomatchtheresultsof L04 atlowredshift.Alsoincludedinthetopplotaretheresultsof M08 whomeasuredm3.6asafunctionofredshift. 78

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Measuredevolutionofm3.6-m4.5versusredshiftcomparedwith M05 modelpredictions. Tomeasuretheactualformationredshiftweperformasimple2minimizationbetweenthedataandthemodels,allowingthemodelnormalizationtooat.Thebesttmodelhaszf=9.95,whichistheearliestformationredshiftweattemptedtot.2forthisbesttis4.63,whichexcludesthebestttingmodelforpassiveevolutionat>5.Thereasonforthisdiscrepancyisillustratedbycomparingourobservedevolutionwiththebestttingmodel,showninFigure 4-6 .Thetopleftandtoprightplotsshowtheobservedevolutionandbestttingmodelwithzf=9.95for3.6and4.5m,respectively.Thelowerleftandlowerrightpanelsshowtheresidualsofthet.Thelarge2isclearlycausedbecausethez>1.4datapointsarefaintrelativetotherestofthedata,andsothemodelsmissboththelowredshift(z<1.3)andhighredshift(z>1.3)data.AcloseinspectionofFigure 4-4 showsthatnocombinationofformationredshiftandmodelnormalizationcanmatchboththelowredshiftandhighredshiftdata. 79

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Bestttingmodelusingtheentireclustersampleouttoz=1.86.Redshiftisplottedversusm3.6(topleft)andm4.5(topright).Thesolidlineisthebestttingmodelforpassivelyevolvingstellarpopulationswithzf=9.95.ThemodelsarenormalizedtohaveM3.6=24.71atz=0.05,asdeterminedfromthettingprocess.Thecirclescorrespondtothemeasuredevolutionofmwithxedto0.8.Differencesbetweenthedataandthemodelsareplottedfor3.6m(bottomleft)and4.5m(bottomright). Forthisreasonweredothe2twithoutthetwohighestredshiftdatapoints.TheresultingtisplottedinFigure 4-7 .Thepreferredformationredshiftisnowzf=2.4+0.160.18.Thequalityofthetissubstantiallyimproved(2=1.5).Ananalysisof2residualsrevealsthatboththehighredshift3.6mdataandthe4.5mdatarejectthebestttingzf=2.40modelatveryhighcondence(>5).Therearetwoplausiblereasonsforthisdiscrepancyathighredshifts.First,thereisalwaysthepossibilitythatsomesystematic 80

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4.5.2 .Eitherwaywewillexcludethehighestredshiftdatapointsfromallfurtheranalysisinvolvingourmodelsforpassivestellarevolution. Figure4-7. SameasFigure 4-6 exceptthetwohighestredshiftbins(opencircles)havebeenexcludedfromthet.Thenewbesttmodelhaszf=2.40andM3.6=24.47. 81

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L04 ,allowingustocomparedirectlytotheirresultssolongasweusethesamevalueof.Wehavealsosearchedtheliteratureforothermeasurementsofthegalaxyluminosityfunctionatlowredshift.InTable 4-3 welistresultsfrom Belletal. ( 2003 ), L04 Babbedgeetal. ( 2006 ),and Daietal. ( 2009 ,hereafterD09)whichcoverarangeofvaluesof,arangeofredshifts,anduseboth3.6mandKs-band.WeuseourmodelstoconvertfromKs-bandto3.6masnecessary,tocorrectforthepredictedpassiveevolutionfromthesurveyredshifttoz=0.05,andtomovetheresultsfromrestframe3.6mtoobserved3.6m.WethereforecalculateobservedM3.6atz=0.05forallthepapersinTable 4-3 ,allowingustocomparemoredirectlytootherresults. Table4-3. Modelnormalizationsfromtheliterature. ReferenceBandzMM3.6@z=0.05 3.6m0.235-1.12-25.060.18-24.99 Babbedgeetal. ( 2006 )3.6m0.13-0.9-24.670.10-24.72 Babbedgeetal. ( 2006 )3.6m0.38-1.0-25.070.10-24.85 L04 L04 Belletal. ( 2003 )Ks0.08-0.77-24.06-24.32 Webeginthecomparisonofourttedmodelnormalizationstotheliteraturebylookingatthetstoour=1.12data.Whilethisisnotourducialvaluefor(0.8)webeginherebecauseboth D09 and L04 haveresultsfor1.12,andbecausethedifferencesbetween D09 L04 ,andourworkareinstructive. D09 lookedateldgalaxies 82

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L04 examinedclustergalaxiesinKsband.Sowhilethegalaxies L04 examinesareinasimilarenvironmenttothegalaxieswestudy,thegalaxiesin D09 wereobservedatthesamewavelengths,withthesameinstrument,andsomeofthemareeventhesamegalaxiesasours.GiventhesefactsweillustrateinFigure 4-8 theimpactofthemodelnormalizationonourresults.InthisFigureweshow1,2,and3condenceregionsinM3.6versuszfspace,withthebestttothelowredshiftdata(z<1.3,zf=2.80,M3.6=24.91)markedwithalledcircle.Therearetwosetsofsolidanddashedverticallines,representingthepredictedvaluesofM3.6atz=0.05for L04 and D09 (seeTable 4-3 fortheprecisevalues).Clearlyourmodelnormalizationisinexcellentagreementwithpredictionsfor D09 ,anditissystematicallybrighterthan L04 .Theagreementwith D09 isencouragingand,sincetheyusedthesameinstrumentandlookedatthesameeld,notsurprising.SimilartoFigure 4-8 ,weshowinFigure 4-9 the1,2,and3condenceregionsinM3.6versuszfspaceforthettoourresultswith=0.8,forwhichwendzf=2.40andM3.6=24.47.WealsoshowthepredictedM3.6valuefor L04 fortheirtwith=0.84.Wenotethat Belletal. ( 2003 )alsomeasuredMinthelocaluniversending=0.77.For Belletal. ( 2003 )wecalculateM3.6=24.32,thesameaswhatwendfor L04 Belletal. ( 2003 )examinedgalaxiesinthesamebandas L04 (Ks),sothestudieswithKsdatainTable 4-3 areinternallyconsistent.Similartoourresultsforthe=1.12data,thecalculatedM3.6valuefor L04 isfainterthanourt,thistimeby0.15mags.Wenotethatbecausewehavetforthemodelnormalizationourformationredshiftisrobustagainstanysystematicerrorsinm.Thus,evenifthisdisagreementmeansthatthereissomeunaccountedforsystematicerrorsinm,ourbestttingformationredshiftwillremainunchanged.Ontheotherhand,ifwehadxedourmodelnormalizationtomatch L04 thiswouldhavearticiallyforcedourttolaterformationredshifts. 83

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Condenceregionsfortheformationepochversusmodelnormalizationexcludingthetwohighestredshiftbins,usingourresultswith=1.12.ThesolidcircledenotesthebesttofM3.6=24.91,zf=2.80.Thecontoursrepresent1,2and3condenceintervalsforourdataset.Thesolidverticalanddottedlinesrepresentthenormalizationanderrorsfrom L04 and D09 (seeTable 4-3 fortheprecisevalues). 84

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SameasFigure 4-8 exceptwehavettedourdatawith=0.8.ThesolidcircledenotesthebesttofM3.6=24.47,zf=2.40.Theverticallinesrepresentthenormalizationanderrorfrom Linetal. ( 2004 )with24.320.02and=0.84.OurttedmodelnormalizationisconsistentwiththeresultsfromD09,butdisagreeswithL04. 85

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4-9 demonstratesthatwecanplacetightconstraintsontheformationredshifteventhoughwehaveleftthemodelnormalizationasafreeparameter.Weconstrainthestarformationepochtobewithin2.0.zf.3.0at3givenourchoiceofmodelsetand.ForcomparisonweincludeFigure 4-10 whichshowstheconstraintsonmodelnormalizationandformationredshiftthatresultfromourstatisticalbackgroundsubtraction(Section 4.3.3 ).Thebestttingformationredshift,zf=2.10+0.060.10,isconsistentwiththeresultfromourphoto-zselectionmethod.AcomparisonofFigures 4-9 and 4-10 showsthatwhilethe1condenceregionforthestatisticalbackgroundsubtractionisactuallysmallerthanforourphoto-zselectionmethod,thephoto-zselectionprocessplacestighterconstraintsoverall.Wealsonotethat,unlikethephoto-zselectionmethod,thestatisticalbackgroundsubtractiondoesinfactmatchthenormalizationof L04 .Thisdifferenceiscausedbecausethestatisticalbackgroundsubtractionismissingthelowestredshiftdatapoint,whichplacesthebestconstraintsonthemodelnormalization.Therefore,thestatisticalbackgroundsubtractioncanhaveadifferentbestttingmodelnormalization,despitethefactthatthereisgoodagreementbetweentheresultsofourstatisticalbackgroundsubtractionandphoto-zselectionmethod(seeFigure 4-4 ). 4-3 andcommonlyfoundintheliterature.AscanbeseeninTable 4-1 thebehaviorofmasafunctionofiswellbehavedandsmooth.Ingeneralachangeinof0.1correspondstoasystematicchangeinmof0.1mags.Thechangeinmislargelyconstantasafunctionofredshift,andsotheobservedshapeoftheevolutionintheluminosityfunctionchangesonlyslightlyasafunctionof. 86

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SameasFigure 4-9 exceptthemodelshavebeenttoourresultsusingastatisticalbackgroundsubtraction.ThesolidcircledenotesthebesttofM3.6=24.33,zf=2.10. 87

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4-4 .Themostimportantfactisthatthebestttingformationredshiftisfairlyrobustagainstchangesof.Changinghasonlyasmallimpactontheobservedevolutionofm,andasaresultchangingprimarilychangesthettedmodelnormalization.Thebestttingformationredshiftvariesfromzf=2.80for=1.12tozf=2.40for=0.6whileatthesametimeourttedmvaluessystematicallyshiftby0.6magsoverthissamerangeof. Table4-4. ImpactofFittingSystematics. SystematicUncertaintyzfM3.62 WealreadymentionedinSection 4.4.3 thatourttedmodelnormalizationfor=1.12isingoodagreementwith D09 ,butdisagreeswith L04 .Wenotenowthatwealsohavegoodagreementwith Babbedgeetal. ( 2006 ).FortheirresultswecalculateM3.6=24.720.1andM3.6=24.850.1fortheirz=0.13andz=0.38datapoints,whichhave=0.9and=1.0.For=1.0wendM3.6=24.750.04,whichiswithintheerrorsforboth.Thismeansthatourttedmodelnormalizationsagreewithboth3.6msurveys( D09 and Babbedgeetal. 2006 )butdisagreewithbothKssurveys( L04 and Belletal. 2003 )overarangeofvaluesof.Weusethettedformationredshiftsacrosstherangeofstudiedinthispaperasanestimateforthesystematicerrorintroducedby.Thereforewendthatuncertaintiesinintroduceanuncertaintyintoourbestttingformationredshiftofzf=+0.400.05. 88

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BC03 and CB07 .For BC03 wendzf=1.95+0.210.07,M3.6=24.57+0.040.05andfor CB07 wendzf=2.70+0.190.19,M3.6=24.570.04(comparedtoourducialtofzf=2.40+0.160.18,M3.6=24.470.04).TheseresultsarealsosummarizedinTable 4-5 wherewelistbothbestttingformationredshift,modelnormalization,and2forallthreemodelsets.Weusethedifferencesbetweentheseresultstoestimatethesystematicerrorintroducedbyourchoiceofmodel(zf=+0.300.45). Table4-5. ImpactofModelChoice. ModelSetIMFMetallicityzfM3.62height M05 KroupaSolar2.40+0.160.1824.47+0.040.041.50 M05 SalpeterSolar2.15+0.310.0824.45+0.030.081.57 M05 Salpeter0.5*Solar3.00+0.100.0924.63+0.030.031.75 M05 Salpeter2*Solar2.80+0.150.1624.54+0.030.031.66 CB07 ChabrierSolar2.70+0.190.1924.57+0.040.040.95 BC03 ChabrierSolar1.95+0.210.0724.57+0.040.050.60 Wealsoinvestigatetheeffectofcommonsourcesofsystematicbiasesinthemodels,suchastheparameterizationoftheIMFandmetallicity.IfweuseaSalpeterIMFinsteadofKroupathebestttingformationredshiftmovestozf=2.15.Usingboth 89

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4-5 .Recently Conroyetal. ( 2009b )performedathoroughinvestigationofpotentialsystematicuncertaintiesinSPSmodeling.ForourpurposesthemostimportantuncertaintytheyfoundwasthelogarithmicslopeoftheIMFaround1M.Foroldstellarpopulationsthemassofthemainsequenceturnoff(MSTO)isabout1M,andtheslopeoftheIMFattheMSTOisanimportantfactorfordeterminingtheevolutionoftheluminosityofastellarpopulation. Conroyetal. ( 2009b )estimatestheimpactthattheuncertaintyinslopeoftheIMFnear1MhasonSPSmodelingandconcludesthatthelevelofsystematicbiasinthepredictedevolutionoftheluminosityfunctioninthecurrentgenerationofstellarmodelscouldbeaslargeas0.4magsperunitredshift.Toaccountforthisweaddtoourmodelsasimpleprescription(Conroy,privatecommunication)todescribetherelationshipbetweentheslopeoftheIMFat1Mandtheevolutionofthemodels(dmag/dz)in3.6and4.5m,andtforzfasafunctionoftheIMFslope.Forthetweuseourdatawithxedat0.8andxthemodelnormalizationtoM3.6=24.47.TheresultisshowninFigure 4-11 whichplots1,2,and3condenceintervalsaroundthebestttingcombinationofIMFslopeandzf.ASalpeterslopeintheseunitsis2.35.ClearlythereisastrongdegeneracybetweentheslopeoftheIMFandthebestttingformationredshift.IftheslopeoftheIMFnear1Misatterathighredshift,thentheactualformationredshiftcanbesubstantiallyearlier.Inthiscontextitisimportanttoconsidertheworkof vanDokkum ( 2008 )whoexaminedtheevolutionofboththecolorandmass-to-lightratioofclustergalaxies.BecausetheluminosityevolutionofgalaxiesisstronglydependentupontheIMFandthecolorevolutionisnot, vanDokkum ( 2008 )wasabletoplacejointconstraintsontheIMFandtheformationredshiftoftheclustergalaxiesinhissample.Lookingatjusttheevolutionofthemass-to-lightratioandassumingaSalpeterIMFhefoundgoodagreementtomodelswithzf=2.0,similartowhatwehavefoundfromtheluminosity 90

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1,2,and3condenceregionsfortheformationepochversusthelogarithmicslopeoftheIMF,excludingthetwohighestredshiftbins.Forthesetswehaveusedthedatawithxedto0.8andhavexedthemodelnormalizationtoM3.6=24.47,takenfromourducialttothedata.IntheseunitsaSalpeterslopeis2.35. evolutionofoursample.Howeverthissamemodelcouldnottthecolorevolutioninhissampleforwhichanearlierformationredshift,zf=6.0,wasnecessary. vanDokkum ( 2008 )foundthatthecolorandmass-to-lightevolutioncouldonlybesimultaneouslytbyaatIMFandanearlyformationredshift(zf=6.0).TheyconcludethattheslopeoftheIMFathighredshiftismuchatterthanaSalpeterIMF,whichiftruemeansthatourttedformationredshift(zf=2.4)isreallyonlyalowerlimitontheformationredshift,asperFigure 4-11 .Asnotedin Conroyetal. ( 2009b ),thisdegeneracybetweentheIMF 91

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Eisenhardtetal. ( 2008b )wholookedatthecolorevolutionofthissamesampleofclusters. Eisenhardtetal. ( 2008b )ndzf=3withatrendtowardsearlierformationredshiftsforhigherredshiftclusters(z>1).IftheIMFisatterathigherredshifts,thenthecolorevolutionoftheclustersshouldpointtoanearlierformationredshiftthantheluminosityevolution.Aswith vanDokkum ( 2008 )wecanusethisfacttoplacejointconstraintsontheformationredshiftandtheIMFbycombiningboththeluminosityandcolorevolutionofourclusters.Thiswillbeanimportantgoalforourfuturework. 4.3.5 .Weapplythesame2minimizationprocesstoeachvariationofourttingprocedureusingthe M05 modelswithxedat0.8andcalculatethebestttingformationredshifts,modelnormalizations,anderrors.WelisttheresultsinTable 4-4 alongwith2foreacht.Figures 4-12 and 4-13 directlycomparealloursystematicbiasesgraphicallybyshowingtheresultsfromTables 4-4 and 4-5 .WeplotthebestttingformationredshiftanderrorsforbothttingsystematicsandmodelsystematicsinFigure 4-12 .ThebestttingnormalizationsanderrorsareshowninFigure 4-13 .Consideringthevariety 92

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4-12 wasnotaforegoneconclusion.Allofourbesttsfallintherangeof1.930%datapointrepresentthesamettothesamedata(ourducialt).Ithasbeenincludedtwicetoillustratethedependenceofourresultsonbothandthecutprobability. Couldthegoodagreementbetweenthevarioussystematicbiasesbeanartifactofourchoicetoletthenormalizationoat?Anysignsofadiscrepancymightshowupinthemodelnormalizationinsteadoftheformationredshift.HoweverFigure 4-13 ,whichcomparesthettedmodelnormalizationsinthesamewayasFigure 4-12 ,demonstratesthatthisisnotthecase.Thelargestoutlierscorrespondtochangesin.Asdiscussed 93

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ThesameasFigure 4-12 exceptforthebesttmodelnormalizations(M3.6)anderrorsforthevariousmodelsystematics.Thesolidanddashedlinesrepresentourchosenducialtwith24.470.04.Wenotethatboththe=0.8datapointandtheP>30%datapointrepresentthesamettothesamedata(ourducialt).Ithasbeenincludedtwicetoillustratethedependenceofourresultsonbothandthecutprobability. inSection 4.4.3.2 weexpectlargechangesinthenormalizationfordifferentvaluesofbecauseofthestrongcorrelationbetweenandm.Ourconsistencycheckwithresultsfromtheliterature(seeSections 4.4.3.1 and 4.4.3.2 )showsthatthesenormalizationsareconsistentwiththeirexpectedvaluesfromother3.6mstudies,andsothereisnoevidenceofaproblem.OveralltheconsistencyfoundinFigures 4-12 and 4-13 isquiteremarkable,andisatestimonytotherobustnessofourresultsandthequalityofourdata.AtthispointthemostimportantsystematicuncertaintiesaretheslopeoftheIMFnear1Mand 94

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4.5.1LowRedshiftWealsoexaminetheimpactofongoingmassassemblyinourlowredshiftbins.Whileourresultsarewelltbymodelsforpassivelyevolvingstellarpopulations,thisdoesnotruleoutthepossibilityofgalaxyassembly.Totestforthepresenceofmassassemblyinourlowredshiftgalaxies,wecreateasimplemodelforluminosityevolutioninwhichthesamemodelsforpassiveevolutionareusedbutanadditionaldimmingfactorof(1+z)isintroducedtoaccountforthebreakupofgalaxiesathigherredshift.Wettothez<1.3redshiftbins,usethedatawith=0.8,andxthemodelnormalizationtoM3.6=24.47.Wendthebestttingcombinationofformationredshiftand(zf=2.40,=0)andshowthe1,2,and3contoursforthistinFigure 4-14 .Ourbesttdemonstratesclearlythatwehavenoneedforadditionalmassassembly(atleastforthistoymodel),inagreementwithpastwork( Strazzulloetal. 2006a ; DeProprisetal. 2007a ).Howeveritisalsoclearthatourresultscantasmallamountofmassassembly.0.2isconsistentat1,and0.35isconsistentat3.Thesecorrespondto90%and75%ofthenalgalaxymassbeingassembledbyz=1.0.Consideringthatwehaveconstructedonlyaverysimpletoymodelformassassemblyatlowredshifts,thesenumbersshouldnotbeconsideredauthoritative.Howeverthisshouldmakeitclearthatthereisroomforgrowthofmassivegalaxiesatlowredshift,albeitnotmuch.Itisalsoimportanttoconsiderthatasmallamountofmassgrowthdoesn'timplyanequallysmallnumberofmergers.Assuggestedby Monacoetal. ( 2006 )itispossiblethatmergersinvolvingmassivegalaxiescanunbindasubstantialfractionofthestars,lesseningtheimportanceofmergersinthemassassemblyofgalaxies. 95

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1,2,and3condenceregionsfortheformationepochversus,whichparameterizestherateofmassassemblyinlowredshiftgalaxies.Inthismodelgalaxiesareassumedtolosemassattherateof(1+z)outtohigherredshifts.Thebottomaxisshowsthevaluesoftted,andthetopaxisshowsthefractionofthenalgalaxymassthatisassembledatz=1.0foragivenvalueof.Thesolidcircleshowsourbesttofzf=2.40,=0. 96

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4-14 ourdataandtoymodelcouldallowforformationredshiftsaslateaszf2.1at1,orzf1.9at3. 4.4.2 thatourbesttmodeldeviates(inastatisticallysignicantway)fromthetwohighestredshiftdatapoints.Therearetwopossibleexplanationsforthisphenomenon:eitherasystematicerrorisimpactingthehighredshiftdataorthisisasignatureofgalaxyassembly.Wehavealreadydiscussedanumberofpossiblesystematicerrorsinboththettingprocess(Section 4.3.5 )andinourmodels(Section 4.4.3 ).WendthatthedisagreementbetweenthemodelsanddataathighredshiftisaconsistentfeaturefoundforallthevariationsofmodelandttingparameterslistedinTables 4-4 and 4-5 .MoreoverwendthatthisdisagreementremainsforallofthevariationsoftheIMFslopediscussedinSection 4.4.3.3 ,andisrobustagainstchangesinredshiftbinsizesandlocations.Evolutioninisalsounlikelytoexplainthisresult,asitwouldrequiretheLFtobesignicantlysteeperathighredshift.Amoresubtlesystematicuncertaintycouldbethecauseofthishighredshiftdeviation.Forinstance,ourphotometricredshiftsbegintodegradeatz1.5,wherethemodelsanddatabegintodisagree.Also,themostdistantspectroscopicallyconrmedclusterisatz=1.48,whichisnearthepointwherethemodelsnolongermatchthedata.Itispossiblethatthefalsepositiverateforourclustersearchgrowsrapidlyathighredshift,attoohighofaredshiftfortheproblemtobedetectedwithourdata.Howeveritisnotclearhoweitherofthesetwopossibilitieswouldcausethedatatogrowsystematicallyfainterby1magnitude.Wehaveperformedasimpletestusing 97

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4-5 ),sincethereislittlecolorevolutioninthemodelsforz&1.5.Howeverinordertoexplainthe1magoffset,thegalaxiesinthez=1.5binwouldhavetohaveameanredshiftofz&2.0.Suchalargeerrorseemsunlikely,especiallysincethereisnoevidenceofz=1.5galaxiesendingupinthez=1.24redshiftbin.Similarly,weseenoreasonwhyanincreasingfalsepositiveratewouldcauseasystematicshifttofaintermagnitudesforourdata.FinallywenotethatinFigure 4-4 theresultsofourstatisticalbackgroundsubtractionalsoshowevidenceforthissamedisagreementathighredshift.Thisisparticularlysignicantbecausephotometricredshiftsdonotfactorintothestatisticalbackgroundsubtraction,andbecauseitshouldingeneralbelesspronetosystematicerrorsthanourphoto-zselectionmethod.Weconcludethatthereisnostrongevidencethatsystematicerrorscausethedisagreementbetweendataandmodelsathighredshift.FurtherworkisrequiredtoinvestigatetheclusterLFindetailathighredshift,andfornowwewilldiscusstheimplicationsofourresultifthesedeviationsarereal. 98

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4-5 ,thecolorofanmgalaxymatchesthemodelsovertheentireredshiftrangeofoursample,despitea1magdeviationinapparentmagnitudeathighredshift.Aslongasthegalaxyassemblyprocessdoesn'tappreciablychangetheluminosityweightedmeanageofthestellarpopulationsthecoloroftheclusterswillcontinuetomatchthemodels,evenwhiletheluminosityincreasesduetotheincreaseofmass.Ifweassumethatallofthedeviationathighredshiftscomesfromgalaxyassemblyandthatthereisnosignicantassemblyinthelowredshiftbins,thenwecanestimatethefractionofthenalgalaxymassthatisassembledinourlasttwobins.Wesimplyassumethatthefractionaldecreaseinluminosityrelativetothemodelscorrelatesdirectlywiththefractionofmasslosttoassembly.Thisimpliesthatthegalaxiesgrowbyafactorof24from1.3
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CB07 and BC03 relativeto M05 .3)TheuncertaintyintheslopeoftheIMFnear1Mintroducesabiasintotheevolutionoftheluminosityfunctionontheorderof0.4magsperunitredshift.ThisbiasislargeenoughthatasufcientlyatIMFcanresultinarbitrarilyearlyformationredshifts.Giventhat vanDokkum ( 2008 )ndsevidenceforaatIMFbasedonjointconstraintsfromthecolorandmass-to-lightevolutionoftheirclustergalaxies,aatterIMFiscertainlyplausible.ThisdegeneracybetweentheformationredshiftandIMFisbestbrokenbyacombinationofcolorandluminosityevolution(aswasdoneby vanDokkum 2008 ),apossibilitywhichweintendtoinvestigatewiththisclustersampleinfuturework. 100

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Cowieetal. ( 1996 )rstrecognizedthatstarformationhappensprimarilyinhigh-masssystemsathighredshiftandlow-masssystemsatlowredshift,afactwhichhasbeenstudiedextensivelysince(see,forexample, Panteretal. 2007 ; Mobasheretal. 2009 ; Chenetal. 2009 ; Villaretal. 2011 ).Moreover,itiswellknownthatclustergalaxiesundergomorphologicaltransformationatlowredshift,withmanyclustermemberstransformingtolenticulargalaxiesatlowredshift( Dressleretal. 1997 ; Desaietal. 2007 ; Wilmanetal. 2009 ).Thereisalsosubstantialevidencethatthelow-luminosityred-sequencegalaxypopulationgrowssubstantiallyinclusterssinceatleastz1( Stottetal. 2007 ; Luetal. 2009 ; Rudnicketal. 2009 ; Lemauxetal. 2012 ).Takentogether,thesefactsdemonstratethatthelow-massclustergalaxiesareactivelyevolvingandformingsincez1.Therefore,bycomparinglowmass,z=0galaxieswiththeirhigh-redshiftprogenitorswecanpotentiallyconstraintheprocessesimportantingalaxyformationandevolution.Thiscanbedonebystudyingindividualgalaxies(throughtheirstarformationrates,stellarmasses,morphologicaltypes,andstructuralproperties)orbystudyinggalaxypopulations(throughtheirluminosityandmassfunctions).Inparticular,thenear-infraredluminosityfunction(NIRLF)canbeusedtostudythestellarmassgrowthofagalaxypopulation,astherest-frameNIRisagoodproxyforstellarmass( Muzzinetal. 2008b ).Inclusters,theNIRLFhasbeenusedextensivelytostudytheassemblyofthemostmassiveclustergalaxies.SuchstudieshavefoundthatthemassiveendoftheNIRLFevolvespassivelyouttoz1.3,suggestingthatthebulkofthestellarmassofthesegalaxiesisinplaceathighredshift( Andreon 2006 ; 102

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, 2006b ; DeProprisetal. 2007b ; Muzzinetal. 2008b ; Manconeetal. 2010 ).Inaddition,in Manconeetal. ( 2010 )wefoundstatisticallysignicantdeviationsfrompassiveevolutionatz>1.3whichwecouldonlyexplainwithongoingstellarmassassemblyattheseredshifts.Mostattemptstoprobethefaintendoftheclusterluminosityfunction(LF)athighredshifthavebeenlimitedtostudyingtheredsequence.Suchstudieshavefoundadecitoffaintandredclustermembersathighredshiftwhencomparedtotheirlow-redshiftcounterparts( DeLuciaetal. 2004 ; Stottetal. 2007 ; Luetal. 2009 ; Rudnicketal. 2009 ; Lemauxetal. 2012 ).Thiscouldmeanthatlow-massclustergalaxiesundergosubstantialmassgrowthatlowredshift,orsimplythatlow-massclustergalaxiesarestillblueathighredshiftandhavenotnishedtransitioningontotheredsequence( Lemauxetal. 2012 ).DifferentiatingbetweenthesetwocasesrequiresmeasuringtheLFofallfaintclustermembers.Previously, Strazzulloetal. ( 2010 )wastheonlystudytodothis,ndingafaint-endslopeconsistentwithat.However,theydidnotcomparetheirresultstolow-redshiftclusterstodeterminetheimplicationsforthestellarmassgrowthoflow-massclustergalaxies.Inthischapterwemeasurethe3.6and4.5mLFofhighredshift(1
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Komatsuetal. 2011 ;m=0.272,=0.728,h=0.704)throughout.AllSPSmodelpredictionsaregeneratedusingEzGal( Mancone&Gonzalez 2012 ). 5.2.1ClusterSampleTheclustersfromthisstudyarepartoftheIRACShallowClusterSurvey(ISCS)( Stanfordetal. 2005a ; Elstonetal. 2006a ; Brodwinetal. 2006a ; Eisenhardtetal. 2008a ),acatalogofclustersidentiedas3-Doverdensitiesusingphotometricredshiftsinthe8.5deg2Booteseld.Furtherworkwiththehigh-redshift(1
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ClusterMemberSummary ClusterRADecz#Members ISCSJ1432.4+333214:32:29.1833:32:36.01.11226ISCSJ1434.5+342714:34:30.4434:27:12.31.23819ISCSJ1429.3+343714:29:18.5134:37:25.81.26118ISCSJ1432.6+343614:32:38.3834:36:49.01.35112ISCSJ1433.8+332514:33:51.1333:25:51.11.3696ISCSJ1434.7+351914:34:46.3335:19:33.51.37410ISCSJ1438.1+341414:38:08.7134:14:19.21.41416 fromthenumbercountsofgalaxiesnearthecluster.Thistechniquehasbeenusedsuccessfullyby deProprisetal. ( 1998 ), Linetal. ( 2004 ), Muzzinetal. ( 2008b ),and Manconeetal. ( 2010 ).ThisrequiresasurveywithIRACimagingofatleastthesamedepthasourclusterimagesaswellasACSF775Wimaging.ForthispurposeweselecttheGOODSNorthandSouth( Dickinsonetal. 2003 )elds.Wedownloadedthelatestfullyreduced3.6and4.5mSpitzerIRACimagestakenoftheGOODSelds.WealsoretrievedthelatestHSTACSF775WcatalogsfromtheGOODSsurvey.ThroughoutthispaperwerefertotheGOODSeldsasourcontrolelds. Ashbyetal. ( 2009a ).ThisincludedthemannerinwhichoutlierswererejectedandinthewaytheindividualIRACframeswerepreparedformosaicingbyrstremovingtheresidualimagesarisingfromearlierexposuretobrightsources.Wegeneratedcatalogsbyrunningourfullyreduced3.6and4.5mIRACimages(fortheclustersandthecontrolelds)throughSourceExtractor( Bertin&Arnouts 1996a )insingle-imagemode.Weused400diameteraperturemagsthatwereaperture-correctedtototalmagsbycomparing400and2400diameteraperturemagnitudesforbright,unsaturatedstarsinourimages.WeusedstarstomeasuretheaperturecorrectionsbecausegalaxiesattheseredshiftsaretypicallyunresolvedinIRACimaging.Thisgaveaperturecorrectionsof0.32(0.34)magnitudesin3.6(4.5)mforourclusterimages 105

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Reachetal. 2005 ).Toverifyourcalculatedaperturecorrectionswecomparedour400aperturecorrectedmagnitudestothe400aperturecorrectedmagnitudesfromSDWFS,andfoundverysmallsystematicoffsets(<0.03mags).TheACSimagingforourclusterswasobtainedaspartoftheHSTClusterSupernovaSurvey,andthereductionoftheimagesisdescribedindetailin Suzukietal. ( 2012 ).WeranthereducedACSF775WimagesthroughSourceExtractorandusedMAG AUTOtocalculatetheF775Wmagnitudeofourgalaxies.WeusedOurF775WphotometrytoperformanopticalNIRcolorcuttoremovecontaminantsfromourLF(Section 5.3.1 ).ForourcontrolweusedtheACSF775WMAG AUTOvaluesfromtheGOODScatalogs,whichwerealsogeneratedwithSourceExtractor.Nextwecalculatedcompletenessasafunctionofmagnitudeat3.6and4.5mforeachclusterimageandeachcontrolimageseparately.WeapproximatedourgalaxiesaspointsourcesduetothecoarseIRACpointspreadfunction(PSF).Wegenerated24,000articialpointsourcesforeachimage,uniformlydistributedbetween13and25mags.OurarticialpointsourcesweresimplycopiesofthePSFforeachimage,whichwegeneratedbymediancombiningunsaturatedstarstakendirectlyfromeachimage.Weaddedthesesourcestotheoriginalimagestenatatime,ranSourceExtractoragainforeachnewimage,andnallycalculatedtherecoveryrateasafunctionofmagnitudeforagivenimageandlter.Figure 5-1 showsahistogramofthemeasured50%pointsourcecompletenesslimitsforeachofourclusterimagesandcontrolimagesat3.6(left)and4.5m(right).Forcomparisontheverticalblacklinedenotesthe50%completenesslimitineachbandfromtheSDWFSsurvey.WeonlywanttotfortheclustergalaxyLFwhenthecompletenessofallgalaxiesinallclustersisatleast50%.ThereforewelimitourLF 106

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Figure5-1. Measured50%completenesslimitsforourimagesin3.6(left)and4.5m(right).Inbothpanelsthesolidhistogramsshowthecompletenesslimitsforourclusterelds,andopenhistogramsshowcompletenessforourcontrolelds.Theverticaldashedlinedenotesthe50%completenesslimitsfromtheSDWFSsurvey( Ashbyetal. 2009a ). 5.3.1OpticalNIRColorCutWeuseasimplecolorcuttoremovestarsandlow-redshiftgalaxiesfromourcatalogsandincreasethesignal-to-noiseratioofourhigh-redshiftclustergalaxies.Ourcolorcutisdesignedtoincludethebluecloud,asexcludingpartofitwouldinduceasystematicbiasinourmeasurementofthefaint-endslope.Wechooseourcolorcutbyusingthe Bruzual&Charlot ( 2003b )stellarmodelstocreateamodelofastar-forminggalaxywithacoloronthebluesideofthebluecloud,consistentwith Lemauxetal. ( 2012 ).Wethenusethissamemodeltoestimatethecoloroftheblueststarforminggalaxiesinourclusters,ndingF775W[3.6]3.5andF775W[4.5]3.75.Weusethesevaluesforourcolorcut,andnotethatournalresultsarenotsensitivetoour 107

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Bonattoetal. 2004 ; Girardietal. 2008 ; Marigoetal. 2008 ; Girardietal. 2010 ).Foralowmetallicity(Z=0.008)model,whichisrelevanttotheGalactichalo,nostarofanyagehasF775W[3.6]&4.SolarmetallicitystarshaveF775W[3.6]5,atthereddest.Therefore,onlythetipoftheRGBandAGBforoldstarsextendredderthanthecolorcut.Assuch,onlyasmallfractionofstarsmightremainafterthecut,meaningthatstellarcontaminationisnotanissue.ThisisconrmedbythefactthatourresultsdonotchangeevenwhenusingcolorcutsasredasF775W[4.5]=5,whichremovesallstellarcontamination.WeadditionallyremovefromourcatalogsallobjectswithCLASS STAR>0.8intheACScatalogs.Wendthatthishasanegligibleimpactonourresults,againshowingthatstellarcontaminationisnotanissueforoursample. 108

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5.3.1 ),arewithin1.5Mpcoftheclustercenter,andareoutsideoftheheavilyblendedclustercores(typically100kpc).ThelatterrestrictionalsoremovestheBCGsfromoursample,whichareknowntonotfollowaSchechterdistribution.Foreachclusterweusea Bruzual&Charlot ( 2003b )SPSmodeltocalculatethek-correctionanddistancemoduluscorrectionneededtomoveapassivelyevolvinggalaxy(zf=3,ChabrierIMF,solarmetallicity)fromtheclusterredshifttothemedianredshiftofourclustersample(z=1.35).Wethenapplythisk-correctionanddistancemoduluscorrectiontoallgalaxiesintheclusterLF.NextwebuildacontrolLFforeachclusterinasimilarfashion.Weselectallgalaxiesinthecontrolimageswhichpassourcuts,weightthemaccordingtotherelativeareaoftheclusterandeldimages,andapplytheexactsamek-correctionanddistancemoduluscorrectionthatweappliedtotheclusterLFtoallthegalaxiesinthecontrolLF.Wedothissothatthesametransformationhasbeenappliedinthesamewaytotheclusterandcontrolgalaxies,andthereforewhenwesubtractthecontrolLFfromtheclusterLFthesubtractioniseffectivelydoneinobservedspace.ThisproceduregivesusanunbinnedclusterandcontrolLFforeachcluster.WethencombinetheindividualclusterandcontrolLFsintoacompositeclusterandcompositecontrolLF,whichweusetomeasuretheLFofclustermembers.Weparameterizetheluminosityfunctionofclustermembersasa Schechter ( 1976 )luminosityfunctionandmeasurethebestttingSchechterparameterswithmaximumlikelihoodtting,similartotheprocedureusedin Manconeetal. ( 2010 ).ThisprocedurerequiresananalyticalrepresentationforthecontributionfromthecontrolregionsowebinourcompositecontrolLFbymagnitude,correctforphotometricincompleteness,andtathirdorderpolynomialtoitinlogspace.WethenusemaximumlikelihoodttingtotthesumofaSchechterluminosityfunction(theclustermemberLF)andthettedcompositecontrolLFtothecompositeclusterLF.Weuseadownhillsimplexalgorithm 109

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Pressetal. 2007 )tomaximizethelikelihoodasafunctionof,m,and,andtallgalaxiesbrighterthanthe50%completenesslimitfortheclusters(Section 5.2.3 ). 5-2 showsthecontrol-subtractedclusterLFandtheSchechterttotheclustermemberLFfor3.6m(left)and4.5m(right).MaximumlikelihoodttinggivesattotheLFwithoutbinning,butforplottingpurposesweshowthebinnedandcontrol-subtractedclusterLFinFigure 5-2 ,whichisthebinneddifferencebetweenthecompositeclusterLFandthecompositecontrolLF.Ineachpanelthesolidcurveshowsthebesttwhilethedashedverticallineillustratesthemagnitudelimitusedforthet.Figure 5-3 showsthe1,2,and3contoursinMvs.spacederivedfromourmeasuredlikelihoods.WealsoreportthebinnedLFvaluesinTable 5-2 ,althoughwenotethatourtwastotheunbinneddata. Figure5-2. Binnedandbackground-subtractedluminosityfunctionsfor3.6(left)and4.5m(right).MedianclusterredshiftandbestttingSchechterparametersaredisplayedinthetopleft.Thesolidcurveshowsthebestt.Thedashedverticallineillustratesthemagnitudelimitforthet,whichisdeterminedbythe50%completenesslimitoftheshallowestclusterimage. Wealsomeasureuncertaintiesusingbootstrapresampling,assuchanerrorestimateismoresensitivetosystematicuncertaintiescausedbycluster-to-clustervariations.WegeneraterealizationsoftheLFbyrandomlyselectingsevenclusters 110

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CondenceregionsfortheSchechtertstoour3.6m(lled)and4.5m(dashed)clusterLFs.Contoursrepresentthe1,2,and3condenceregionsinvsMspace.FilledcirclesdenotethebesttSchechterparameters Table5-2. BinnedLFs Mag#[3.6]#[4.5] 15.251.320.507.097.0215.7510.649.103.3110.1216.250.8713.9724.3420.7616.7532.8623.1288.9430.7617.2595.6132.39114.7137.0017.75128.2937.82118.1141.7218.25136.1341.68143.1845.3718.75181.9848.57214.3954.0919.25145.1151.32182.1359.0619.75270.4062.5020.25253.2571.37

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5-3 .WenotethatourmeasuredbootstrapuncertaintiesagreewellwiththecontoursinFigure 5-3 Table5-3. BestFittingSchechterParameters 5.4.1High-RedshiftComparisonForabasicconsistencycheckwecomparetoourresultsfrom Manconeetal. ( 2010 ).In Manconeetal. ( 2010 )wemeasuredM3.6mandM4.5mouttoz=1.8usingtheslightlyshallowerSDWFSdataandastatisticalbackgroundsubtraction.Assuchthemethodologyisverysimilar,theltersarethesame,andthesevenclustersstudiedhereinwerealsoincludedin Manconeetal. ( 2010 ).Duetoourshallowerdatain Manconeetal. ( 2010 )wexedandreportedttedMvaluesfor=0.6,0.8, 112

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Manconeetal. ( 2010 ).ThereforewecompareourttedMvaluestotheaverageoftheMvaluesforthez=1.24and1.46binswith=1.0,whichgivesM3.6m=17.420.1andM4.5m=16.920.1,ingoodagreementwiththevaluesofMmeasuredherein.WenotethatourrandomerrorsforMinthispaperarelargerthanthequotederrorsin Manconeetal. ( 2010 ).Thisisasimpleresultofnumberstatistics.Whileweonlyhavesevenclustersinthisstudy,wehad25(22)clustersinourz=1.24(1.46)binsin Manconeetal. ( 2010 ).ThisleadstoalargerrandomuncertaintyinMforthiscurrentwork,althoughwehavelowersystematicuncertaintyforMinthispaperbecausetherequirementofxingin Manconeetal. ( 2010 )introducedasystematicuncertaintyof0.2magsintoM.Wealsocompareto Strazzulloetal. ( 2010 )whomeasuretheH-bandLFofaz=1.39galaxyclustertoM+4.TheyndH=1.2+0.20.15,alsoconsistentwithourresults.Whilethereisadifferenceinpassbandbetweenourstudies,bothtracerest-framewavelengthsredwardofthe4000Abreaksoweexpectthedifferenceinpassbandtohaveaminimalaffectonourttedvaluesof.Recentstudieshavefoundadecitoflow-luminosityred-sequencegalaxiesinhigh-redshiftclusters( DeLuciaetal. 2004 ; Rudnicketal. 2009 ; Lemauxetal. 2012 ).Atfacevaluethisseemsincontradictionwiththeatvaluesfoundinthisstudyaswellas Strazzulloetal. ( 2010 ).However,neitherourresultsnortheresultsfrom Strazzulloetal. ( 2010 )arelimitedtored-sequencegalaxies,andthereforethisapparentdifferencecansimplybeasignthatlow-luminositygalaxiesareinplaceintheclusterenvironmentattheseredshiftsbuthavenotyetnishedtransitioningontotheredsequence,aswassuggestedin Lemauxetal. ( 2012 ). 113

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5-4 .Wenotethat deProprisetal. ( 1998 ), Andreon ( 2001 ),and DePropris&Christlein ( 2009 )didnotpresentaformalerrorforbutdidplotcondenceregionsfortheirt,soweestimatedtheerroronfromtheplotsoftheircondenceregions.Specically,wederivedtheerrorfromthefullrangeofvaluescoveredbytheir1condencecontours.WesplitTable 5-4 upintotwosections:studieswhichtracetherest-frameopticalandstudieswhichtracetherest-frameNIR(suchasthiswork).Starformationcanbeanimportantcontributortotherest-frameopticalLF,andassuchisnotnecessarilydirectlycomparablebetweenthetwosetsofstudies. Table5-4. ReferenceBand#ClustersBandhzi ( 1998 )NIR1H0.0230.780.3 ( 2001 )NIR1Ks0.31.180.15 ( 2004 )NIR93Ks0.0430.840.02 ( 2007 )NIR13.6m0.0231.250.05 ( 2007 )NIR15K0.2960.840.08 ( 2009 )NIR1Ks0.0161.260.1 ( 2009 )NIR10K0.070.980.2 ( 2010 )NIR353.6m0.370.600.2ThisWorkNIR73.6m1.350.970.14ThisWorkNIR74.5m1.350.910.28 ( 2003 )Opt.1R0.0231.18+0.040.02 ( 2003 )Opt.60Bj<0.111.280.03 ( 2006 )Opt.1V0.01141.4+0.10.18 ( 2010 )Opt.1H1.391.2+0.20.15 5-4 arepresentedgraphicallyinFigure 5-4 .InthisFigurethettedvaluesanderrorsareplottedforalltherest-frameNIRresultsinTable 5-4 .Thereissubstantialstudy-to-studyscatteratlowredshift,andlargeerrorbarsathighredshift, 114

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5-4 showsnoobviousevidenceforevolutioninfromz=0toz1.4,representingnearly70%ofcosmichistory. Figure5-4. Best-ttingvaluesoftotheclusterluminosityfunctionversusredshift.Datapointscomefromtherest-frameNIRstudiesfromTable 5-4 andincludeavarietyofliteratureresults.Theresultsfromthisworkareshownasredcircleswhilepreviousresultsareshownasblacktriangles.Thedashedhorizontallinedenotes=1.0,correspondingtoaatLFforfaintgalaxies. PastworkonclusterLFshaveprimarilycharacterizedtheevolutionofM,andshallowimaginghasrequiredassumingavalueforandxingitasafunctionofredshift(see,e.g., Muzzinetal. 2008b and Manconeetal. 2010 ).Fixinghasbeenapotentialsourceofsystematicuncertainty,asthestrongcouplingbetweenMandmeansthatifisimproperlyheldxedthenthettedvaluesofMwillalsobewrong.ThiscanbeparticularlyimportantforstudiesoftheevolutionofMbecauseifisevolvingbutassumedtobexedthenthisfalseassumptioncancreatespuriousevolutioninM.Thispotentialsourceofsystematicuncertaintywasdiscussedindetail 115

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Manconeetal. ( 2010 )becausewefoundthatforz&1.3thettedvaluesofMtotheclusterLFdeviatedstronglyfrompassiveevolution.Weconcludedthatwhileevolutionincouldcontributetothemeasureddeviationsfrompassiveevolution,itwasunlikelytobetheunderlyingcausebecausethedirectionofthedeviationwouldrequiretobecomesteeperathigherredshift.Havingnowmeasuredathighredshiftwecanconcludethatevolutioninwasnotthecauseofourobserveddeviationsfrompassiveevolutionasdoesnotevolvesignicantlywithredshiftouttoz1.4. Saraccoetal. ( 2006 )measuredintherest-frameJ-bandforeldgalaxies,nding=0.94+0.160.15inaredshiftbincenteredatz1.2. Cirasuoloetal. ( 2007 )found=0.920.18forgalaxieswith1.25
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Fontanotetal. 2009 andreferencestherein)suggeststhatstarformationwillbepreferentiallyfoundinlowermassgalaxiesatlowredshift.Suchamassdependenceforgalaxystarformationhistorieswillnecessarilyimplyevolutioninthefaint-endslopeoftheLF.Theamplitudeofthiseffecthoweverdependsuponthetotalamountofongoingstarformation,whichwillvarybetweenclustersandmaydependuponthetotalmassofthehostclusterhalo.Thereisevidencethatsubstantialstarformationisstillongoinginourclustersample( Snyderetal. 2012 ),aswellasotherclustersatsimilarredshifts( Hiltonetal. 2010 ; Tranetal. 2010 ; Fassbenderetal. 2011 ).Incontrast, Muzzinetal. ( 2012 )ndthatstarformationhasalreadybeenstronglyquenchedintheirclusteratz=1.2.Mergerscanalsobuildupthestellarmassofclustergalaxies,althoughmergersareexpectedtobesuppressedintheclusterenvironmentduetothehighrelativevelocitiesofclustergalaxies( Alonsoetal. 2012 ).Recenttheoreticalstudies( Muranteetal. 2007 ; Conroyetal. 2007 ; Puchweinetal. 2010 )suggestthatformassivegalaxiesgrowthbymergersbecomesveryinefcient(butsee Rudnicketal. 2012 ),anditispossible 117

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Mooreetal. 1996 ; Boselli&Gavazzi 2006 ; Muranteetal. 2007 )andthereforecausetogrowatterorturnoverwithtime.Anotherprocessforconsiderationistheinfallofnewgalaxiesintothecluster,theeffectofwhichdependsontheshapeoftheLFfortheinfallinggalaxypopulation.Sincewendthattheclusterandeldgalaxypopulationshaveasimilarfaintendslope(Section 5.4.3 ),weexpectthattheinfallofnewgalaxiesintotheclusterwillprimarilyacttomitigateanypotentialevolutionoftheclusterLFbydrivingtheclusterLFbacktowardsaatfaint-endslope.Instead,theinfallofnewgalaxieswillleadtoanincreasein,thenormalizationoftheLF,whichwehavenotconstrainedFinally,amass-dependentgalacticinitialmassfunction(IMF)cancausetheshapeoftheLFtochangerelativetotheunderlyingstellarmassfunction.ThisisbecausetherateofluminosityevolutionforastellarpopulationdependssensitivelyontheIMF( Conroyetal. 2009c ).Recentwork( Cappellarietal. 2012 )hassuggestedthattheIMFdoesindeeddependongalaxymass,suchthatlowermassgalaxieshaveaatterIMF(i.e.,ahigherfractionofhigh-massstars).AatterIMFleadstoafasterfadingoftheunderlyingstellarpopulation( Conroyetal. 2009c )andtherefore,iftrue,theresultsof Cappellarietal. ( 2012 )suggestthatlow-massgalaxiesshouldfadefasterthanhighmassgalaxieswhenthestellarmassesofbothremainsxed.Thiswillcausetogrowatterorturnoverwithtime,effectivelyactingagainstprocesseswhichbuildupthestellarmassofgalaxiesbutwithoutimpactingtheunderlyingmassfunction.Clearly,therearemanyprocesseswhichcouldpotentiallycauseevolutionoftheNIRclusterLFatz<1.5.Therefore,thelackofevolutioninobservedherein, 118

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Manconeetal. 2010 ),placesanimportantconstraintontheseprocesses.Innet,theycannotcauseanylargeevolutionintheshapeoftheNIRclusterLF.Thiscouldbebecausebothlowmassandhighmassclustergalaxiesarelargelyassembledathighredshift,orbecausethedifferingeffectsoftheseprocessescauseslittleevolutioninnet.Thelattermightimplyanuncomfortabledegreeofnetuning.Ingeneralthough,theabilityofinfallinggalaxiestodiluteanyevolutionintheclusterLFallowsformoreexibilityinthestrengthofotherprocesses. 1. WecomparetostudiesoftheNIRLFoflow-redshiftclustersandndnostatisticallysignicantevidenceforevolutionofthefaint-endslopeoftheclusterLF.ThereforeweconcludethatthefaintendoftheclusterLFhasnotevolvedsignicantlyover70%ofcosmichistory. 2. Havingmeasuredanon-evolvingfaint-endslopewehaveremovedonesourceofsystematicuncertaintyfromstudiesoftheevolutionofMasafunctionofredshift.Thisisparticularlyrelevantforourrecentdetectionofdeviationsfrompassiveevolutionathighredshift( Manconeetal. 2010 ).Shallowimagingin Manconeetal. ( 2010 )necessitatedxing,whichcouldhaveleadtospuriousevolutioninMifwasevolving. 3. Wecomparetothefaintendslopeforeldgalaxiesatsimilarredshiftsandndgoodagreement.Fieldstudies( Saraccoetal. 2006 ; Cirasuoloetal. 2007 ; Stefanon&Marchesini 2011 )ndafaint-endslopeconsistentwithatathighredshift,andthemostrecentresults( Stefanon&Marchesini 2011 )ndnoevidenceforevolutionouttoz=3.5. 4. Givenrecentstudies( Muzzinetal. 2008b ; Manconeetal. 2010 )whichhavefoundthattheevolutionofthebrightendoftheclusterLFisconsistentwithpassiveevolutionouttoz1.3,weconcludethattheshapeoftheclusterLFhas 119

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Daddietal. 2005 Papovichetal. 2005 Trujilloetal. 2006 Trujilloetal. 2007 Longhettietal. 2007 Toftetal. 2007 vanderWeletal. 2008 vanDokkumetal. 2008 Damjanovetal. 2009 ,and Saraccoetal. 2010 ),ourunderstandingofsizeevolutioningalaxyclustersisinitsinfancy.Todate,onlyahandfulofstudieshaveattemptedtoconstraintthesizeevolutionofclustergalaxies(e.g. Valentinuzzietal. 2010a b Papovichetal. 2012 ,and Raichooretal. 2012 ).Suchstudiestypicallylimitthemselvestoawell-denedsubsampleofthegalaxypopulation.Thisisespeciallytrueforclustersasasimpleredsequence(RS)orcolorselectioncaneasilyselectasampleofgalaxieswithacommonredshift,andwhicharepreferentiallyearly-types( Lintottetal. 2008 ).Forinstance, Valentinuzzietal. ( 2010a ), Valentinuzzietal. ( 2010b ),and Raichooretal. ( 2012 )allinvestigatedthestructuralpropertiesofETGsinclusterswhile Papovichetal. ( 2012 )studiedthesizeevolutionofpassiveclustergalaxies.Finally, Retturaetal. ( 2010 )and Strazzulloetal. ( 2010 )examinedthepropertiesofhigh-redshiftclustergalaxieswhichwereselectedtobebothpassiveandearlytype.Itisnecessarytoverifythatthissampleselectiondoesnotintroduceanysystematicerrorthroughtheprogenitorbias.Thisprogenitorbiasoccurswhenaselectioncriteriaexcludessomeofthehigh-redshiftprogenitorsoflow-redshiftgalaxiesinawaythatbiasesthesample(see vanDokkum&Franx 2001 foranexampleinasimilarcontext).Thisisparticularlyimportantingalaxyclustersbecausetheclusterenvironmentisveryeffectiveattransformingstarforminggalaxiesintopassivegalaxies( Lewisetal. 2002 ; 121

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, 2003 ; Weinmannetal. 2010 ; Pengetal. 2010b ; Chungetal. 2011 ; Muzzinetal. 2012 )andlate-typegalaxies(LTGs)intoETGs( Dressler 1980 ; Postmanetal. 2005 ; Smithetal. 2005 ; Poggiantietal. 2009 ; Meietal. 2012 ).ThereforetheprogenitorsofclusterETGswerenotallETGsathighredshift.Similarly,theprogenitorsofquiescent-clustergalaxieswerenotallquiescentathighredshift. Valentinuzzietal. ( 2010a b )investigatedthisindetailandfoundthatETGsinhighredshift(z0.7)galaxyclustersweresmallerthanatlowredshift,butthatthisapparentsizeevolutioncouldbeexplainedbytheprogenitorbias.TheyfoundthatathighredshiftbothETGsandpassiveclustermembersweremorecompactthantheoverallclusterpopulation.Therefore,amorphologicalselectionandapassiveselectionarebiasedtracersofthehigh-redshiftclusterpopulation.Clearly,akeyissueforunderstandingsizeevolutioninclustergalaxiesistoproperlyaccountforthisbiaswhenestimatingthesizeevolutionoftheclusterpopulation.Ignoringthisbiaswillleadtooverestimatedsizeevolution,andwithoutaccountingforitthereisnowaytomeasuretheactualevolutionofthegalaxyclusterpopulation.Todate, Valentinuzzietal. ( 2010a ,z=0)and Valentinuzzietal. ( 2010b ,z0.7)aretheonlystudiestoattempttocorrectforthisbiaswhenmeasuringthesizeevolutionoftheclusterpopulation.Onedifcultyincorrectingforthisbiasistheneedtosamplethefullcluster-galaxypopulationathighredshift.ThisrequiresidentifyingclustermemberswithmorethanjustaRSselection.Inthispaperweutilizeasampleofthirteenhighredshift(1
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6.2 describesourdata,whichincludesourclustersample(Section 6.2.1 ),imaging(Section 6.2.2 ),spectroscopy(Section 6.2.3 ),andmemberselection(Section 6.2.4 ).Section 6.3 explainshowwemeasuredgalaxyparametersincludingsizes(Section 6.3.1 ),SEDs(Section 6.3.2 ),masses(Section 6.3.3 ),andmorphologies(Section 6.3.4 ).InSection 6.4 wepresentthesize-massrelationshipwendforourclusters,andcompareourresultstotheliterature.WediscusstheimplicationsofourresultsinSection 6.5 ,andourconclusionsarepresentedinSection 6.6 .AllmagnitudesareontheVegasystem,andweassumeaWMAP7cosmology( Komatsuetal. 2011 ;m=0.272,=0.728,h=0.704)throughout. 6.2.1ClusterSampleTheclustersfromthisstudycomeprimarilyfromtheIRACShallowClusterSurvey(ISCS; Stanfordetal. 2005a Elstonetal. 2006a Brodwinetal. 2006a Eisenhardtetal. 2008a ).TheISCSisacatalogof335clustersidentiedas3-Doverdensitiesusingphotometricredshiftsinthe8.5deg2Booteseld.PhotometricredshiftsintheISCScamefromaSpitzerIRAC4.5mselectedcatalog.Therefore,thegalaxyclustersintheISCSareprimarilystellarmass-selected,anddonotrelyuponassumptionssuchastheexistenceofaredsequence.AspartoftheSpitzerDeep,Wide-FieldSurvey(SDWFS, Ashbyetal. 2009a )theBooteseldwasrevisitedandreimagedinallfourIRACbandstoincreasethetotalexposuretimebyafactorof4.Thisenabledanewclusterdetectionwithincreasedsensitivitytohighredshiftclusters.WorkonclusterdetectionsfromtheSDWFSdatacontinues,andtodatetwohighredshiftclustershavebeenpublishedasaresultoftheadditionalimaging:IDCSJ1426+3508atz=1.75( Stanfordetal. 2012 )andIDCSJ1433.2+3306atz=1.89( Zeimannetal. 2012 ). 123

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Stanfordetal. 2005a ; Elstonetal. 2006a ; Brodwinetal. 2006a ; Eisenhardtetal. 2008a ; Brodwinetal. 2011 ; Stanfordetal. 2012 ; Zeimannetal. 2012 ).Ofthese,13haveacombinationofHSTWFC3/F160WimagingandHSTopticalimagingwhichallowsforred-sequencememberselection.Thissubsetformstheclustersamplestudiedherein. 6.2.2.1Ground-basedopticalimagingTheBooteseldhasbeenobservedbyanumberofsurveys,providingawealthofbroad-bandphotometricdata.ThiseldwasrsttargetedbytheNOAODeep,Wide-FieldSurvey(NDWFS, Jannuzietal. 1999 )whichprovidedopticalobservationsintheBW,R,andIbands.Theobservationshave5point-sourcedepthsofapproximately27.1,26.1,and25.0magsinBW,R,I,respectively.Seeingtypicallyvariedbetween0.700and1.500. A.Deyetal. ( inpreparation )and B.Jannuzietal. ( inpreparation )describeimagereductiontechniques. Eisenhardtetal. 2004 2008a ).ItwasthenrevisitedfortheSDWFSwhichbroughtthetotalIRACexposuretimeintheBoteselduptoatleast360s,withamedianexposuretimeof420s.Whiletheimagedepthdoesvaryacrosstheeldofviewduetotileoverlaps,theaverage5,400aperturedepthis19.77,18.83,16.50,and15.82magsin3.6,4.5,5.8,and8.0m,respectively. Ashbyetal. ( 2009a )describesindetailthereductionoftheSDWFSimaging.WeobtainedfurtherSpitzerIRACimagingfortheelevenclustersinthissamplefromtheISCS,with1000secondsofintegrationtimeobtainedinallfourIRACbands.Fortheseobservationswecarriedoutdatareductionusingstandardprocedures.WeprocessedtheBasicCalibratedData(BCD)frameswiththeSpitzerScienceCenter 124

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6-1 .WereducedalltheHSTimagingfollowingstandardprocedureswiththeMultiDrizzlesoftware( Koekemoeretal. 2002 ; Fruchteretal. 2009 ).WedrizzledthereducedWFC3imagesdowntoapixelsizeof0.06500tobetterrecovertheundersampledWFC3point-spreadfunctionandtomorecloselymatchthenativepixelscaleoftheACS/WFPC2opticalimages.WedrizzledtheACSandWFPC2imagestopixelsizesof0.0500and0.0600,respectively.FurtherdetailsoftheHSTimagesandreduction,includingobservationstrategies,canbefoundin Snyderetal. ( 2012 )fortheISCSclusters, Stanfordetal. ( 2012 )forIDCSJ1426.5+3508,and Zeimannetal. ( 2012 )forIDCSJ1433.2+3306.AsanalstepweusedScamp( Bertin 2006 )andSwarp( Bertinetal. 2002 )totietheastrometricsystemofalltheHSTimagestotheSDWFSandresamplethemtoanalpixelsizeof0.06500.ThiswasdonetoallowforaccuratecolorestimationbyusingSourceExtractor( Bertin&Arnouts 1996b )indualimagemode. 125

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ClusterMemberSummary ISCSJ1429.2+335714:29:15.1633:57:08.51.059WFPC2/F814W2511ISCSJ1432.4+333214:32:29.1833:32:36.01.112ACS/F775W116ISCSJ1426.1+340314:26:09.5134:03:41.11.136WFPC2/F814W5017ISCSJ1426.5+333914:26:30.4233:39:33.21.163WFPC2/F814W6123ISCSJ1434.5+342714:34:30.4434:27:12.31.243ACS/F775W4111ISCSJ1429.3+343714:29:18.5134:37:25.81.262ACS/F850LP7116ISCSJ1432.6+343614:32:38.3834:36:49.01.349ACS/F850LP538ISCSJ1433.8+332514:33:51.1333:25:51.11.369ACS/F850LP309ISCSJ1434.7+351914:34:46.3335:19:33.51.372ACS/F850LP5113ISCSJ1438.1+341414:38:08.7134:14:19.21.413ACS/F850LP4219ISCSJ1432.4+325014:32:24.1632:50:03.71.487ACS/F814W4022IDCSJ1426.5+350814:26:32.9535:08:23.61.75ACS/F814W306IDCSJ1433.2+330614:33:16.4733:07:01.91.89ACS/F814W017TotalMembers4916168 Stanfordetal. ( 2005a ), Elstonetal. ( 2006a ), Brodwinetal. ( 2006a ), Eisenhardtetal. ( 2008a ), Brodwinetal. ( 2011 ), Stanfordetal. ( 2012 ), Zeimannetal. ( 2012 ),and Zeimannetal. ( inpreparation ).WehavetargetedallbutISCSJ1432.4+3250(z=1.487)andIDCSJ1433.2+3306(z=1.89)withground-basedspectroscopy.Ourground-basedspectroscopyidentiedbothabsorption-linemembersaswellasemission-linemembers.WealsotargetedalltheclustersinthissamplewithWFC3slitlessspectroscopy(GOproposalsIDs11597and12203)whichprimarilydetectedemission-linemembers.Thegrismspectroscopyreliablydetectedonlyfourabsorption-linemembers:twoinIDCSJ1426.5+3508(z=1.75)andtwoinIDCSJ1433.2+3306(z=1.89).Ourgrismprogramisthelargestsinglesourceofspectroscopicconrmationsfortheseclusters.Almostalloftheemission-linemembersinournalsamplehaveameasured 126

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Kummeletal. 2009 ).Usingthebestavailablecalibrationles1,spectrawereextractedfollowingthestepsfoundintheWFC3GrismCookbook2.Amoredetaileddescriptionofthegrismdataanalysisforthez>1clusterswillbepresentedin Zeimannetal. ( inpreparation ). Snyderetal. ( 2012 ),whileIDCSJ1426.5+3508andIDCSJ1433.2+3306aredescribedin Stanfordetal. ( 2012 )and Zeimannetal. obs/calibrations/2http://www.stsci.edu/hst/wfc3/analysis/grism obscookbook.html 127

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2012 ),respectively.Wealsosummarizethedetailshere,whicharethesameforallourclusters.OurredsequenceselectionisbaseduponourHSToptical-NIRcolorsmeasuredwithSourceExtractorindualimagemode.TheopticallterusedvariesfromclustertoclusterandisgiveninTable 6-1 .WeusedourWFC3/F160WimagingastheredbandinourRSselectionforallourclusters.WeselectgalaxiesasRSmembersiftheyarewithintwostandarddeviationsoftheclusterRS(asdenedin Snyderetal. 2012 )andarebrighterthanH(z)+1.5,whereH(z)iscalculatedbyevolvingthecharacteristicbrightnessforComa( deProprisetal. 1998 )tothecluster'sobservedredshiftassumingthegalaxiesformedinasingleshortburstatzf=3.WepresentaclustermembersummaryinTable 6-1 .Thistablelistsalltheclustersincludedinthisstudyalongwiththeirredshifts,numberofmembers,andthebandsusedforRSselection.Wenotethatthistabledoesnotreectthetotalnumberofspectroscopically-conrmedmembersineachcluster.Insteaditliststhenumberofmembersineachclusterwhichareincludedinournalsample,whichissubjecttoavarietyofselectioncriteriadiscussedinSection 6.3 6.3.1GalaxySizes:GALFITWemeasuresizesforourgalaxiesbyusingGALAPAGOS( Hauleretal. 2011 )andGALFITv3.0( Pengetal. 2010a )onourF160Wimages.GALAPAGOSautomatesthetaskofrunningGALFIT.OurGALAPAGOScatalogsformthebasisofourSEDttingandmassttingprocedures.GALFIT,whichdoestheactualtting,performsa2Dmodelttoimagesusing2minimization.WetourgalaxieswithasingleSersicprole.Themostimportantquantitiesreturnedbythetarethetotalmagnitude(mF160W),Sersicindex(n),theeffectiveradiusalongthesemi-majoraxis(ae,whichcontainshalfthetotalux),andtheaxisratio(B=A).Wethencalculatethecircularizedeffectiveradii,re=aep 128

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GALFIT)andtheAUTOmagnitude(MAG AUTO)fromSourceExtractor.SincetheGALFITmagnitudeisunderestimated,thesegalaxieshavemuchlowerMAG GALFITMAG AUTOvaluesthanproperlytgalaxies.WendthatremovinggalaxiesfromoursamplewithMAG GALFITMAG AUTO<0.5

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3 butwealsodiscusstheimportantdetailshere.PyGFitworksbytakingSersicprolesttedtowell-resolvedanduncrowdedHSTimaging(thehighresolutioncatalog)andttingthemtoblendedobjectsinthelowresolutionimages.PyGFitrstrunsSourceExtractor( Bertin&Arnouts 1996b )todetectobjectsinthelowresolutionimageandbuildasegmentationmapwhichdividestheprocessintomanageablechunks.Itthenrunsanalignmentsteptomeasureanyglobaloffsetsbetweenthehighresolutioncatalogandthelowresolutionimages.Next,PyGFitmatchesupobjectsinthehighresolutioncatalogtothesegmentationregions.Foreach 130

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Moustakasetal. inpreparation ),aBayesianSED-ttingcodethatusespopulationsynthesismodelstoinferthephysicalpropertiesofagalaxygivenitsobservedbroadbandSED.Weadoptthe Bruzual&Charlot ( 2003b )populationsynthesismodelsbasedonthePadovaisochrones,thestelibstellarlibrary,andthe Chabrier ( 2003b )IMF.Forourmasstsweuseourbroadbandphotometryfromnineofourlters:BWRI,JHKs,WFC3/F160W,andIRAC3.6and4.5m.Werequireallgalaxiesinoursampletohaveareliablemeasurementin4.5mandtobedetectedinatleastoneopticalband.Wecompareourmeasuredmassestoanumberofresultsfromtheliterature.InallcasesweadjustthecomparisondatasetstomatchourchoiceofIMFandmodelset.Inparticular,weincreasethemassesfrom Valentinuzzietal. ( 2010a )by0.15dex(assuggestedby Cimattietal. 2008 )toaccountforsystematicdifferencesforyoungstellarpopulationsoriginatingfromadifferingtreatmentofthethermally-pulsatingAGBstars. Valentinuzzietal. ( 2010a )madethissamecorrectiontotheirhigh-redshiftcomparisonsamples.Wenotethatthiscorrectiondoesnotchangeanyofournalconclusions. 133

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Valentinuzzietal. ( 2010a )andtheirresultsformthebaselinefromwhichwemeasureSMRevolution. 6.4.1GalaxyClassicationPreviousstudiesoftheevolutionoftheSMRinclustershaveoftensub-dividedgalaxiesaccordingtomorphologicaltypeorquiescence. Valentinuzzietal. ( 2010a ), Valentinuzzietal. ( 2010b ),and Raichooretal. ( 2012 )dividedtheirgalaxiesaccordingtomorphologicaltype(allusingvisualclassications). Papovichetal. 2012 lookedatsamplesofquiescentgalaxies.Finally, Retturaetal. ( 2010 )selectgalaxieswhichwerebothquiescentandearlytype.Forcompleteness,weclassifyourgalaxiesbybothmorphologyandquiescence.Morphologicalclassicationisdoneusingourvisualclassications(Section 6.3.4 )forbothourspec-zandRSselectedgalaxies.Classifyingourgalaxiesasquiescent/star-formingisstraightforwardforourspec-zmembers,whichweclassifyasstar-formingifemissionlinesarepresentintheirspectrum,andquiescentotherwise.ClassifyingourRSselectedgalaxiesismoredifcult.Ourclustersareathighredshift,wherethereisongoingstarformationintheclustercores( Tranetal. 2010 )andasubstantialpopulationofyounggalaxiesenteringtheredsequence( Snyderetal. 2012 ).ThissuggeststhatsomeoftheRSgalaxiesmightnotbequiescentgalaxiesbutsimplydustyorrecentlystarforminggalaxies.Therefore,wedonotattempttoclassifyourRSselectedgalaxiesasquiescent/star-formingbutwillinsteadinvestigatehowtheirstructuralpropertiesdependonthepropertiesoftheirstellarpopulations(asdeterminedbyourSEDts). 134

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6-1 weshowthemeasuredsizesandmassesforourgalaxies,dividedaccordingtomorphology.Wecompareourresultstosizesandmassesofearly-typegalaxiesintwoz=1.26clusters( Raichooretal. 2012 ).WealsocomparetothemedianSMRfortwolowredshiftsamples:early-typeeldgalaxiesfrom Shenetal. ( 2003 )andearly-typeclustergalaxiesfrom Valentinuzzietal. ( 2010a ).Thereseemstobeasmalloffsetforthegalaxiesfrom Raichooretal. ( 2012 )eithertowardslowermassesorlargerradii.InthisFigurewecomparedourresultstothosefrom Raichooretal. ( 2012 )usinga Bruzual&Charlot ( 2003b )modelset,andscaledtheirresultstoaChabrierIMF.Moreover,webothusedGALFITtomeasureciruclarizedradii,sothesourceofthisoffsetisunclear.OurETGsappeartobesmalleronaveragethanourLTGs,aswasalsofoundwiththe0.4
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Sizeversusmassforourearly(lledcircles)andlate-type(opencircles)clustermembers.Forreferenceweincludethesizesandmassesofhighredshift(z=1.26)early-typeclustergalaxiesfrom Raichooretal. ( 2012 )(stars),themedianSMRforsloanearly-typegalaxiesfrom Shenetal. ( 2003 )(solidline),andthebinnedSMRforWINGSearly-typeclustergalaxies(opencircles,dashedline)atlowredshiftfrom Valentinuzzietal. ( 2010a ). 6-2 weplotthesizesandmassesofourgalaxies,dividedaccordingtoquiescence.ThisFigureonlyincludesourspec-zconrmedgalaxies,whichareeasilyclassiedasquiescent/star-forming(Section 6.4.1 ).WealsoincludeinthisFigurethequiescentclustergalaxiesfrom Retturaetal. ( 2010 )atz=1.237and Papovichetal. ( 2012 )atz=1.62.Thequiescentgalaxiesfrom Retturaetal. ( 2010 ), Papovichetal. ( 2012 ),andthisworkalloccupythesameregioninparameterspace.SimilartoFigure 6-1 wendthatourquiescentgalaxiesappeartobesmaller,onaverage,thanourstar-formingones.Finally,wenotethatourstar-forminggalaxiesgotomuchlowermassesandaremorenumerousthanourquiescentones.Thisisasimpleselection 136

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6-3 themedianSMRinfourlogarithmicmassbinsforourspectroscopically-conrmedquiescentandstar-forminggalaxies.Thequotederrorsrepresenttherangeoftheinnerquartiles. Figure6-2. Sizeversusmassforourspec-zconrmedquiescent(lledcircles)andstarforming(opencircles)clustermembers.Forreferenceweincludethequiescentearly-typegalaxiesfromRDCS1252.9-2927( Retturaetal. 2010 )atz=1.237(triangles)andthequiescentgalaxiesfromXMM-LSSJ02182-05102( Papovichetal. 2012 )atz=1.62(squares). Table6-3. TheSMRofQuiescent/StarFormingGalaxies QuiescentStarFormingMassBinNMedianreNMedianre ByincludingourRSselectedmemberswecanincreaseournumberstatistics.However,asdiscussedinSection 6.4.1 ,classifyingourRSmembersasquiescent/star-forming 137

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6-3 colorcodedaccordingtotheirageasdeterminedfromourSEDts. Figure6-3. SizeversusmassforallourgalaxiescolorcodedaccordingtotheiragefromtheSEDts.RSselectedgalaxiesareplottedassquares,whilespec-zconrmedmembersareplottedasstars. AstrikingfeatureofthisFigureistheconnectionbetweenage,size,andmass.Atxedsize,oldergalaxiesarepreferentiallymoremassive.Atxedmass,oldergalaxiesareonaveragesmaller.Wenotethatthistrendbetweenage,size,andmassisasprominentforourspec-zmembersasitisforourRSselectedmembers.ThisrulesoutthepossibilitythatthistrendisdrivenbythepresenceofinterlopersontheRS. 138

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Valentinuzzietal. ( 2010a )foundthesametrendintheirlowredshiftcluster-galaxysample. 6.5.1Morphology,TheEvolutionoftheSMR,andProgenitorBiasWendthattheSMRofETGsathighredshiftissmallerthantheSMRofETGSatlowredshift.Thisisingoodagreementwithrecentworkfromtheliterature( Papovichetal. 2012 ; Raichooretal. 2012 ).Conversely,theSMRofourlate-typegalaxiesisverysimilartothatfrom Valentinuzzietal. ( 2010a )atz=0,exceptinourhighestmassesbin.Atfacevalue,thiswouldimplythattheSMRofETGsevolvestowardsthepresentday.However,theimpactoftheprogenitorbiasneedstobecarefullyconsidered( Valentinuzzietal. 2010a b ).ItiswellestablishedthattheclusterenvironmentiseffectiveattransformingLTGsintoETGs( Dressler 1980 Postmanetal. 2005 Smithetal. 2005 Poggiantietal. 2009 ,and Meietal. 2012 butsee Justetal. 2010 ).Therefore,theprogenitorsoflowredshiftETGsarecomposedofbothETGsandLTGsathighredshift.AscanbeseeninFigure 6-1 ,ourhigh-redshiftLTGsarelargeronaveragethantheirearly-typecounterparts,ashasbeenfoundinpastwork( Shankar&Bernardi 2009 ; Saraccoetal. 2009 ; Valentinuzzietal. 2010a b ).Thus,selectingETGsatbothlowredshiftandhighredshiftpreferentiallyexcludesthelargestprogenitorsofthelow-redshiftETGs.ThisbiasesmeasurementsoftheevolutionoftheSMRandintroducesspuriousevolutionoftheSMR.Thisisthesamescenarioproposedin Valentinuzzietal. ( 2010a )and Valentinuzzietal. ( 2010b ),whichwecannowconrmathigherredshift. Lewisetal. 2002 ; Gomezetal. 2003 ; Weinmannetal. 139

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; Chungetal. 2011 )andhighredshift( Pengetal. 2010b ; Muzzinetal. 2012 )meansthatmanyofourstar-formingmemberswillbequiescentatlowredshift(butsee Verdugoetal. 2008 ).Therefore,aquiescentselectionmightexcludeourstar-formingmembersathighredshift,butincludethematlowredshift.Moreover,athighredshifttheseyounggalaxiesarelargeronaveragethanoldones(seeFigure 6-3 aswellas Toftetal. 2007 Valentinuzzietal. 2010a ,and Valentinuzzietal. 2010b ).Thusimposingaquiescentselectionatlowandhighredshiftcanexcludethelargestprogenitorsofthelowredshiftgalaxies,leadingtoaspuriousmeasurementofsizeevolution.WecaninvestigatetheimportanceofthisbiasquantitativelybyseeinghowourmedianSMRchangesasafunctionofourselectioncriteria.WeshowinFigure 6-4 howourhigh-redshiftSMRchangeswhenweonlyincludegalaxiesolderthanaparticularage.Allofourgalaxies(spec-zconrmedandRSselected)areincludedinthisFigure.Figure 6-4 showsthat,withtheexceptionofourhighestmassbin,placingamorerestrictiveagecutonoursample(i.e.removingyoungergalaxies)leadstoasmalleraveragegalaxysize.TheprecisechoiceofagecutcanbiasthemeasuredSMRsmallerbyafactorof2.WeemphasizethatthiscanleadtospuriousevolutionoftheSMRifcareisnottakentoaccountforthiseffect.Tofurtherillustratethispoint,weplotthecompactnessofourgalaxies(relativetothemedianETGSMRatz=0)asafunctionofformationredshift(zf)andageinFigure 6-5 .ThisFiguredemonstratesthatwhilenotallcompactgalaxiesareold,alloldgalaxiesarecompact.Thereforeselectingold(i.e.quiescent)galaxiesathighredshiftpreferentiallyselectsthemostcompactgalaxies,leadingtospuriouslylargesizeevolution. Valentinuzzietal. ( 2010b )dealtwiththisissuebycomparingtheSMRofETGs+LTGsathighredshifttotheSMRofETGsatlowredshift.ThisisasimplewaytoestimatetheevolutionoftheSMRandaccountfortheprogenitorbias.Itimplicitly 140

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Themediansizeofgalaxiesinfourmassbinswhengalaxiesyoungerthanthegivenagearecutfromthesample. assumesthatalltheLTGsinthehighredshiftsampletransformintoETGsbyz=0.Italsoassumesthatthez=0sampleisdescendedfromtheclustergalaxypopulationathighredshift,whichmeansthatgalaxyinfallfromtheeldhasonlyaminimaleffect.AnalternativeapproachistomeasuretheevolutionoftheSMRoftheclustergalaxypopulationasawhole,ratherthantheevolutionofjusttheETGpopulation.Thisremovesonepotentialsourceofbias,astheevolutionofallclustergalaxiescanbemeasuredwithoutknowingtheefciencywithwhichtheclustertransformsLTGsintoETGs.Instead,wemustsimplyknowthemorphologicaldistributionofclustergalaxiesatlowandhighredshift.Wecanthenextractamatchingdistributionfromourhigh-redshiftsampleaswellasfromacomparisonsampleatlowredshiftandcomparethetwo 141

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ThesizeofourgalaxiesrelativetothemeanSMRrelationshipatz=0from Valentinuzzietal. ( 2010a )asafunctionofzf(left)andage(right).Starsdenotespec-zconrmedgalaxies,whilesquaresshowRSselectedgalaxies. directly.Theonlyremainingassumptionisthatgalaxyinfallfromtheeldisminimal,apossibilitywediscussinSection 6.5.4 .Athighredshift, Meietal. ( 2012 )measuredthemorphologicalfractionofclustergalaxiesasafunctionofenvironmentinaz=1.26supercluster,andfoundthatinthedensestenvironmentstheETGfractionis50%.Atlowredshift, Poggiantietal. ( 2009 )and Fasanoetal. ( 2012 )foundanETGfractionof77%intheWINGSclusters.Therefore,wewilluseourhighredshiftsampletoconstructaclustergalaxypopulationwithanETGfractionof50%,usetheWINGSgalaxies( Valentinuzzietal. 2010a )to 142

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6-6 andsummarizetheminTable 6.5.3 .ThetoppanelofFigure 6-6 showsthemedianSMRofETGsandLTGsathighredshift(thiswork)andlowredshift( Valentinuzzietal. 2010a )forreference.ThebottompanelshowstheresultsofourMonteCarlosimulations,plottingtherelativesizeofthehigh-redshiftgalaxypopulationcomparedtothelow-redshiftgalaxypopulationforourtwosimulations.ThisFigureshowsthatifwesimplycomparetheSMRofhigh-redshiftETGstotheSMRoflow-redshiftETGs(i.e.ouruncorrectedETGevolutionsimulation),wewouldndthathigh-redshiftgalaxiesare60%smallerthantheirlow-redshiftcounterparts.Thisisverysimilartowhatotherstudieshavefoundattheseredshifts( Papovichetal. 2012 ; Raichooretal. 2012 ).Againthough,thisdoesnotimplythatsize 143

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Figure6-6. Toppanel:MedianSMRforETGs(triangles)andLTGs(circles)athigh(solidsymbols)andlow(opensymbols)redshift.Bottompanel:Mediansizeofhigh-redshiftgalaxiescomparedtolow-redshiftgalaxiesinfourmassbins.OpencirclesshowtheresultsfromouruncorrectedETGevolutionsimulation,andsolidcirclesshowtheresultsfromourclusterSMRevolutionsimulation. SMREvolution ClusterSMREvolutionUncorrectedETGEvolutionMassBinre=re,z=0re=re,z=0

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6-1 showsthesourceoftheSMRevolutionathighmasses.AtM>1011M,wehaveveryfewgalaxieslargerthantheSMRoflow-redshiftETGs.Infact,wedonothaveanygalaxiesinoursamplelargerthan8kpc.Thislackoflarge,high-redshiftgalaxiesisthedrivingfactorbehindourmeasuredevolution.Thisabsenceoflargegalaxiescouldconceivablybecausedbyincompleteness,becauseatxedmasslargergalaxieswillhavelowersurfacebrightnessesandwillbehardertodetectthansmallergalaxies.Wethereforeruncompletenesssimulationstoassessourincompletenessasafunctionofgalaxyradiusforourmassive(M>1011M)galaxies.ForourRSselectedgalaxieswendthatwecaneasilydetectETGs(n=4)outtothelargestsizessimulated,30kpc.OursimulationsshowthatLTGs(n=1)arehardertodetect,andourselectionreachesthe50%completenesslimitatre16kpc.ForLTGsourcompletenessis>95%outtore=10kpc.Therefore,thelackofgalaxieswithre>8kpcisnotlikelycausedbyincompletenessfromourRSselection.However,thesituationismorecomplicatedforourspec-zselectedgalaxies.Foremission-linegalaxies,ourabilitytospectroscopicallyconrmthemdependsontheirmassandstarformationrate.ForsimulatedLTGswithre=10kpc,n=1,andM>1011Mwendthatthe50%completenesslimitofourgrismobservationsisreachedforgalaxieswithstarformationratesof78Myr1.Forthesamegalaxieswithre=16kpc,the50%completenesslimitis15Myr1.Wehavesevenemission-linegalaxiesinthismassrangewithmeasuredstarformationrates.ThesegalaxieshaveSersicindexesof1.5.n.3.5.Fourhavestarformationrates>8Myr1andwouldthereforebedetectablewithre>10kpc. 145

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Retturaetal. ( 2010 )comparedETGsinaz=1.2clustertoETGsintheeldatthesameredshift,andconcludedthatthetwosamplesofgalaxieshadthesameSMR. Raichooretal. ( 2012 )studiedETGsinaz1.3superclusterwhichincludedcluster,group,andeldenvironments.TheyfoundthateldETGsarelargerthanclusterandgroupETGsatz1.3.Finally, Papovichetal. ( 2012 )comparedquiescentgalaxiesfromaz=1.62clustersampletoaz=1.6eldsample,ndingthathigh-redshiftquiescentclustergalaxiesarelargerthantheircounterpartsintheeld. 146

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Smithetal. 2005 ).Therefore,itispossiblethattheinfalloflargeLTGsfromtheeldcoulddriveSMRevolutionforclustergalaxies.Totestthistheory,weselectLTGs(n<2.5)atlowerredshifts(z<1)from Trujilloetal. ( 2007 ),addthemtoourhigh-redshiftsample,andrepeatourSMRevolutionsimulation.WendthatallofourobservedSMRevolutioncanbeaccountedforbyaninuxofeldgalaxiesiftheclusteraccretestwiceasmanygalaxiesatz<1thanitcurrentlycontains.Ifinsteadthehigh-redshiftclusterpopulationisonlydilutedby50%,thenwendnoevidenceofSMRevolutioninoursecond-highestmassbin,andtheSMRinourhighest-massbinisonly20%10%smallerthanatz=0.Oneadvantageofthiscurrentworkisthatitincludesthestructuralpropertiesofgalaxiesofallmorphologiesinhighredshiftclusters.Therefore,weestablishforthersttimethattheSMRofmassive(log(M=M)>10.75)clustergalaxiesdoesevolve,independentofmorphologyorquiescence.MoreworkisneededtodeterminetowhatextentthisSMRevolutioniscausedbysizeevolutionoftheclusterpopulation.Weemphasizethatathoroughunderstandingofthestructuralpropertiesofgalaxiesasafunctionofenvironment,morphology,andredshiftisneeded.Otherwise,itisimpossibletodifferentiatebetweenSMRevolutioncausedbytheinfallofgroup/eldgalaxiesorbyactualsizeevolutionofclustergalaxies.OnepossiblewaytodothiswouldbetomeasuretheSMRofallgalaxiesintheinfallregionouttoatleastafewtimesr200. 147

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Daddietal. 2005 Trujilloetal. 2007 vanderWeletal. 2008 vanDokkumetal. 2008 Damjanovetal. 2009 ,and Saraccoetal. 2010 ).Itisthereforeworthconsideringwhetherornotsucheldstudiesmightalsobesensitivetothissamebias.Inthiscontext,wenotethatthemorphologicaltransformationseeninclustersisnotasstrongintheeld( Smithetal. 2005 ).Therefore,comparingETGsintheeldathighandlowredshiftisnotassensitivetothesourceofprogenitorbiasthatwediscussinthispaper.Caremuststillbetakenwhenselectingandcomparingeldgalaxiesbyageorquiescence,asthecosmicstarformationratedensitydependsuponredshift(seeforexample Gonzalezetal. 2010 andreferencestherein).Thiscanpotentiallycausebiasforstudiesofquiescenteldgalaxies,similartoourdiscussioninSection 6.5.2 .However,noneofourndingsinthispapergivereasontoquestionthemanystudieswhichhavemeasuredevolutionoftheSMRforETGsintheeld. 148

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1. TheSMRofourlow-mass(10
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ConorManconegraduatedwithaBachelorofScienceinastronomyandaBachelorofArtsinphysicsfromtheUniversityofFloridain2006.HespentayeardoingresearchwithProfessorSarajediniattheUFAstronomyDepartmentbeforebeginninggraduateschoolin2007.HecontinuedtoworkwithProfessorSarajediniforthenextyear,expandingourknowledgeofgalaxyformationbystudyinggalaxiesinthelocalgroup.AfterthathebeganworkwithProfessorGonzaleztounderstandgalaxyformationbystudyinggalaxiesinhigh-redshiftgalaxyclusters.HereceivedaMasterofScienceinastronomyin2009andaDoctorofPhilosophyinastronomyinDecemberof2012. 158