MULTI-WAVELENGTHOBSERVATIONSOFGALAXYCLUSTERS:POPULATIONEVOLUTIONANDSCALINGRELATIONSFORINTERMEDIATE-REDSHIFTCLUSTERSByThomasPatrickConnorADISSERTATIONSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeofAstrophysicsandAstronomy-DoctorofPhilosophy2016ABSTRACTMULTI-WAVELENGTHOBSERVATIONSOFGALAXYCLUSTERS:POPULATIONEVOLUTIONANDSCALINGRELATIONSFORINTERMEDIATE-REDSHIFTCLUSTERSByThomasPatrickConnorGalaxyclustersarekeysignaturesoftheformationofstructureintheUniverseduetotheirpositionsatthenodesofthecosmicweb.However,theseprivilegedpositionsfeaturetamountsofactivityasaconsequenceoffrequentaccretionandcollisionswithothergalaxiesandclustersofgalaxies.Thus,arigorousunderstandingofclusterevolutionconstrainsnotonlycosmologicalstructureformationbutalsogalaxydynamicsinthemostextremeenvironments.Here,weexaminetheevolutionofclustersintwosituations:howthepropertiesofthehotintraclustergaschangeswiththetotalmassesoftheclustersattheobservationalfrontiersofmassandredshift;andhowclustergalaxiesevolvewithredshiftinsomeofthemostmassiveclustersintheUniverse.InChapter2weexamineapopulationofmoderate-luminosityclustersatintermediateredshiftsusingtheXMM-Newtontelescopewithwell-determinedmassesfromHubbleSpaceTelescope(HST)observations.Wethatthesesystemsdonotdeviatefromscalingrelationsbetweenmass,luminosity,andtemperaturederivedfrommoremassiveclusters,implyingthat,evenattheredshiftsandmassesprobedhere,gravitationalenergeticsstilldominateoversupernovae.InChapter3weutilizenewtechniquestomaximizeamulti-wavelengthdatasetfromHSTof25massivegalaxyclusters.Wepresentnewmethodsfordetectionandphotometryofgalaxiesinthepresenceofinconsistent,background.Usingthesetechniques,weconstructaphotometriccatalogdowntoM*+4-5forclustersatredshiftz˘0:2toz˘0:9,whichwevalidatewithcomparisonstospectralobservationsandasimilarcatalog.Wealsoconsidertheluminosityfunctionfortheseclusters;wedainthefaint-endslopewhenonlyselectingredsequencegalaxies.Finally,inChapter4,weexploitournewphotometriccatalogstostudytheevolutionoftheredgalaxies,the\redsequenceofgalaxies,"inthesemassiveclustersofgalaxies.Withthecombinationofresolution,depth,andspectralcoverageavailableinthiswork,weareabletousespectraltoexaminetheofmetallicityandageinshapingthephotometricpropertiesofclustergalaxies.Weseeevidenceofametallicitygradientalongtheredsequenceandminimalevolutionintheslopewithredshift,implyingitisaconsequenceofthemass-metallicityrelationinplaceatz˘2.However,wealsoseesecondaryindicatorsthattheredsequenceisbeingsteadilypopulatedatthefainterendafteritsinitialformation.CopyrightbyTHOMASPATRICKCONNOR2016Tomymother;letthescienrecordshowthatIamyourfavoriteson.vACKNOWLEDGMENTSAftermyself,noonehashadabiggerpartinthecompletionofthisthesisthanMeganDonahue.Notonlydidsheprovidethefundingthatletmecontinuetoworkonresearch,shealsohelpedguidemethroughtheproblemsofresearch.Furthermore,sheprovidedmefreetimeonSOARandaccesstotheCLASHcollaboration,withoutwhichthisdissertationwouldbentlyshorter.AlongwithMegan,Iwouldliketothankmyothercollaborators.AndishehMahdaviandHenkHoekstrawereinstrumentalinthesuccessofmyX-rayanalysis.DanCoe,DanKelson,andMarcPostmanprovidedmonetary,scienandtechnicalsupportandguidancetohelpmeshapetheCLASHportionofthisthesis.JohnMoustakashasbeenvitalinthesuccessofthatanalysis.NorbertWerner,KevinFogarty,andGrantTremblaywerenotinvolvedinanythesiswork,buttheyhavebeenexcellentcollaborators.Finally,MarkVoitandMingSunhavebothbeenexceptionallyhelpfulandencouraging.IwouldnotbeherewereitforChrisMihos,VeronicaStrazzullo,MaurilioPannella,PaulHarding,ColinSlater,TimAtherton,antSjouwerman,EarleLuck,HeatherMorrison,andAgnesTorontali.Theirguidanceandsupportbothgavemetheabilitytobeacceptedintoagraduateprogramandthefoundationtosucceedthere.AtMSU,Aaronwasanexcellentmentorwhotaughtmehowtoobserve.Lookingforward,IextendmythankstoJohnMulchaeyforgivingmeanimmovabledeadlinetomotivatemywriting.FiveyearsinLansingwouldnothavebeenpossiblewithoutallofthefriendsandcol-vileaguesIhavesharedthattimewith.Therearetoomanypeopletoname,butIwouldliketothankAlexDeibel,TomHettinger,RyanConnolly,andBrianCrosby,inparticular,forbridgingthegapbetweencoworkerandfriend,andAubreyThompsonforgivingmeareasontolookforwardtoweekends.Finally,manythankstomyfamily.Mybrothers,AndrewandMatthew,whopavedthewayformetomovepastafouryeardegree,inspiredmetoaimforaPhDbeforeIhadevenhighschool.Mygrandmothersupportedmethroughoutmychildhood,butwillnotbeabletoseemeearnonelastdegree.And,withoutdebatingnaturevs.nurture,IamtthatIwouldnothaveaccomplishedhalfofwhatIhavewithouttheparentsIhave.Thankyou.viiTABLEOFCONTENTSLISTOFTABLES....................................xLISTOFFIGURES...................................xiKEYTOSYMBOLSANDABBREVIATIONS.................xviiiChapter1Introduction...............................11.1TheGrandDichotomy..............................11.2TheRedSequenceinGalaxyClusters......................51.3CLASH:TheClusterLensingandSupernovaSurveywithHubble......81.4X-rayScalingRelations..............................13Chapter2X-RayScalingRelationsforModerateLuminosityGalaxyClus-tersatIntermediateRedshift.....................222.1Introduction....................................232.2DataandAnalysis................................272.3Analysis......................................362.4Results.......................................382.4.1Flux....................................382.4.2X-ray...............................412.4.3ScalingRelations.............................422.5Discussion.....................................522.5.1ComparisonwithPreviousX-rayObservations.............522.5.2ComparisonwithOtherScalingRelations...............532.5.3ComparisontoLow-RedshiftGroups..................562.5.4ComparisonbetweenGroupsandClusters...............572.6Conclusions....................................57Chapter3OptimizedPhotometryofClusterGalaxiesinCLASH.....613.1Introduction....................................623.1.1StatisticalBackgroundLightEstimators................643.2DataSet......................................673.2.1DetectionImages.............................693.2.2SourceDetection.............................703.3Photometry....................................743.3.1UVSystematicUncertainties.......................773.3.2PhotometricRedshifts..........................793.4ComparisontoSimilarWorks..........................81viii3.5OpticalScalingRelations.............................883.5.1Mass-RichnessRelation..........................903.5.2LuminosityFunction...........................913.5.3StellarMass................................973.6Summary.....................................101Chapter4GalaxyProperties,Membership,andRedSequenceEvolutioninCLASHClusters...........................1044.1Introduction....................................1044.2Data........................................1084.2.1SEDFitting................................1104.3ClusterMembership...............................1154.3.1AlternativeSelections...........................1174.4RedSequenceFitting...............................1194.5IndividualGalaxies................................1254.6Mass-to-LightRatios...............................1294.7Discussion.....................................1314.8Summary.....................................137Chapter5Summary.................................1395.1RevisitingtheLuminosityFunction.......................1415.2WhichRedSequence...............................1435.3BringtheBackgroundtotheForeground....................1445.4PublicRelease...................................144APPENDICES.................................146AppendixAAppendicesforChapter2.......................147AppendixBAppendicesforChapters3and4..................152REFERENCES.....................................168ixLISTOFTABLESTable1.1PropertiesofCLASHClusters.....................8Table2.1SampleProperties............................26Table2.2ObservationsofClusters........................27Table2.3MaskedSources.............................31Table2.4SpectralFittingPropertiesWithinr2500................37Table2.5ScalingRelations............................44Table2.6CCCPClusterPropertiesWithinr2500................46Table3.1SourceExtractorDetectionParameters................71Table3.2CLASHScalingProperties.......................88Table3.3CLASHLuminosityFunctionFit....................91Table3.4CLASHr2500values...........................98Table4.1CLASHRedshiftedFilterAnalogs...................109Table4.2RedSequenceFits............................122TableB.1ACSDataProperties{Exposuretime(s),Zeropoint(ABMag),andA(Mag).................................156TableB.2WFC3(UVIS/IR)DataProperties{Exposuretime(s),Zeropoint(ABMag),andA(Mag)........................158TableB.3MaskedStarsinCLASH(R>200)................162xLISTOFFIGURESFigure1.1grcolor-magnitudediagramfor500000extendedgalaxiescatalogedfromtheSloanDigitalSkySurvey.Thesegalaxiesarethe500000inthe13thDataReleasewithgandrmagnitudesbrighterthan25andwithnoconstraintsonposition.Twogalaxypopulationsarevisible:thebluecloudandtheredsequence.Incolor-magnitudediagramspresentedinthisdissertation,bluercolorsareloweronthey-axis,whilebrightergalaxiesaretotheleftoffaintergalaxies....2Figure1.2Fractionalthroughputsofthe17usedbyCLASH.Theyare,frombluetored,F225W,F275W,F336W,F390W(allUVIS);F435W,F475W,F555WF606W,F625W,F775W,F814W,F850LP(allACS);F105W,F110W,F125W,F140W,F160W(allWFC3-IR)......9Figure1.3DistributionofphotometricredshiftsfromCLASHclusterphotom-etryforMACS1423.Datafromtheoriginalcatalogspublishedby(Postmanetal.,2012b)isshowninorange,whiledatafromthepho-tometrywepresentinthisworkareshownindarkblue.Thespectro-scopicredshiftoftheclusterisindicatedbythepurplebar.WeonlyconsiderthosegalaxieswithF814Wmagnitudesbrighterthan25.5.12Figure1.4X-rayscalingbetweenX-raytemperatureandX-rayluminosityforasampleofclusters(purple,Wuetal.,1999)andgroups(orange,Xue&Wu,2000).Bothsamplesshowself-similarscalingcharacterizedbyapower-law,butthetslopesofthatscalingbetweengroupsandclustersisevidenceofapossiblebreakinself-similarity......14Figure2.1Gaussian-smoothedX-rayemissioncontoursoverlaidonHubbleSpaceTelescopeimagesofthefourclustersweobservedinthiswork.Con-toursarespacedatintervalsof106counts1arcsec2,withthemin-imumlevelforeachclusterdescribedinSection2.2..........29Figure2.2ComparisonbetweenourmeasuredusingXMM-NewtonandthosereportedbyVikhlininetal.(1998)usingROSAT.ROSATwereadjustedtocorrespondtotheinner300h170kpcofthecluster,asdescribedinthetext.Thesolidlineistheidentityline,whiletheshadedbandindicatesagreementtowithin10%.......39xiFigure2.3DistributionoftoBCGpositionsmeasuredbyHoekstraetal.(2011)fromX-raycentroidmeasurementsusingXMM-Newton(thiswork,hashesrisingtotheright)andROSAT(Vikhlininetal.,1998,hashesloweringtotheright).Dataarebinnedtoincrementsof5arcseconds.................................41Figure2.4Plotofweak-lensingmassMWLasafunctionofbolometricX-rayluminositywithinr2500.MassesandluminositieshavebeenrescaledbyE(z)toaccountfortherangeofredshiftcoveredbythesamples.Dataanalyzedinthisworkareshownascircles,whileclusterproper-tiesfromtheCCCPareshownassquares.RXJ0826.1+2625wasnotincludedinthisOurbesttoEquation(2.2)fortheM-Lrela-tionisshownbythesolidline.Ourbestwhenincludingintrinsicscatterisshownbythedashedline.Botharetothecombinedsampleof160SDandCCCPclusters..................45Figure2.5PlotofX-raytemperatureasafunctionofbolometricluminositywithinr2500.LuminositieshavebeenrescaledbyE(z)toaccountfortherangeofredshiftcoveredbythesamples.Dataanalyzedinthisworkareshownascircles,whileclusterpropertiesfromtheCCCPareshownassquares.OurbesttoEquation(2.2)fortheT-Lrelationisshownbythesolidline.........................50Figure2.6PlotofMasafunctionofX-raytemperaturewithinr2500.MasseshavebeenrescaledbyE(z)toaccountfortherangeofredshiftcoveredbythesamples.Dataanalyzedinthisworkareshownascircles,whileclusterpropertiesfromtheCCCPareshownassquares;botharederivedfromweaklensing.RXJ0826.1+2625wasnotincludedinthisWealsoincludeasampleofnearbygalaxygroupsfromSunetal.(2009)asdiamonds,wheremassesarederivedfromhydrostaticequilibrium.OurbesttoEquation(2.2)fortheM-TrelationfromtheclustersanalyzedinthisworkandfromtheCCCPisshownbythesolidline.OurbesttotheM-Trelationusingthepropertieswithinr2500ofthegroupsfromSunetal.isshownasadashedline.51Figure3.1ThecentralregionofAbell383aftersubtractingalocalbackgroundfoundusingthePearsonapproximationforthemode.Backgroundregionsusedare:left:4pixels(0.2600);middle:16pixels(1.0400);andright:128pixels(8.3200).Largerstructuresarevisiblewhenalargerbackgroundradiusisused,whilesmallerobjectsaremoreclearlyresolvedwithamorelocalizedbackgroundregion...........69xiiFigure3.2AportionoftheMACSJ0717seeninF125W(red),F814W(green),andF555W(blue).Detectedobjectsareoutlinedinwhiteellipsescorrespondingtotheregionusedforphotometry.Alsoshownareobjectsasstarsinthiswork,whicharemarkedbyblueellipses.Thisimageisapproximately4500wide.............73Figure3.3Aschematicrepresentationofthephotometrytechnique.Ontheleft,thegalaxyofinterestisshowninred,withasuperimposedgridrep-resentingthepixelsoftheimage.Startingwithapixelontheoutsideofthegalaxy{markedhereinred{weidentifyacircularbackgroundregion.Pixelscontaininggalaxylight(blue)arerejected,whilethosewithonlybackground(yellow)createourbackgroundsample.Inthemiddleframe,weshowthedistributionofsanduncertaintiesforthosepixels.ByconvolvingeachmeasurementwithaGaus-siankernel(sizedaccordingtotheuncertaintyofeachpoint'sandsumming,wecreateahistogramofvalues,suchasshownontheright.Thepeakofthatdistributionisconsideredthemode;thewidthofthebackgrounddistributionisfoundbytracingdownfromthepeakuntilreachingavaluewithafrequencyofˇ0:608timesthepeakfrequency............................75Figure3.4TheofourbackgroundmodelingandsubtractiontechniqueforAbell209.ImagesarefromtheF814Wter:theoriginal(left),aftereverygalaxyhasbeenphotometered(center),andafterthesub-tractedimagehasbeenresampledright.................77Figure3.5Comparisonofphotometricredshiftsmeasuredinthisworktospec-troscopicredshifts.Thethinbandtracestheregionwherej(zpzs)=(1+z)j<0:05.Thefullredshiftcoveragefromz=0toz=3.0isshownontheleftpanel;azoom-intojustz=0toz=1.0isshownontheright.Pointsarebinnedintohexagons,withthetotalden-sityofpointsscaledlogarithmicallyfrom1to100countsperhex,asindicatedbythecolorbar.........................80Figure3.6Comparisontospectroscopicredshiftsbetweenthephotometricred-shiftsmeasuredinthiswork(orange)andthosefromthepreviouslyreleasedCLASHphotometriccatalogs(purple).Onlygalaxieswithspectroscopicredshiftswithinjzspeczclusterj<0:05areshown.Alloutlierswithjzphotzspecj>0:2areshownatjzphotzspecj=0:2.Theoverlapbetweenbothhistogramsisshowninpink.Ourtech-niquebettermatchesmeasuredspectroscopicredshiftsandhasasig-tlyreduced(˘65%)fractionofoutliers.............81xiiiFigure3.7ComparisonbetweenF814WmagnitudesmeasuredbytheASTRODEEPCollaborationandthisworkforMACS0416.Pointsarebinnedintohexagons,withthetotaldensityofpointsscaledlogarithmicallyfrom1to30countsperhex.Detailsoftheareprovidedinthetext.Acomparisonoftheisprovidedinthelowerpanel........84Figure3.8ComparisonbetweenmeasuredcolorsforMACS0416intheASTRODEEPcatalogandthiswork.Pointsarecoloredaccordingtothedeviationofthephotometricredshiftmeasuredinthisworkandtheclusterredshift,asindicatedbythecolorbarontheright...........85Figure3.9ComparisonbetweenredshiftsmeasuredbytheASTRODEEPCol-laborationandthisworkforMACS0416.Pointsarebinnedintohexagons,withthetotaldensityofpointsscaledlogarithmicallyfrom1to30countsperhex,asindicatedbythecolorbar.Detailsoftheareprovidedinthetext.Azoom-intojustmatchesbelowredshift1.0isprovidedontherightpanel.Theclusterredshiftisindicatedbytheverticalandhorizontallines;thediagonallineistheidentityline.....................................87Figure3.10ComparisonbetweenmeasuredvaluesofE(z)N2500andE(z)M2500fromthiswork(purple)and(Hoekstraetal.,2011,orange).Wealsoshowourblineinblack,andabesttoourdataaloneinpink.DetailsoftheselectionofN2500areprovidedinthetext....89Figure3.11Thek-correctedi-magnitudeluminosityfunctionsforall25CLASHclusters.Galaxiesareshownbinnedinhalf-magnitudeintervals.ThebSchechterluminosityfunctionisshowninorange(purple)forX-rayselected(highclusters.Galaxiesareplottedinorderofincreasingredshift.Best-valuesof,M*,and˚areprovidedinthatorderoneachplot.Detailsoftheareprovidedinthetext.................................92Figure3.12Themeasuredslopesoftheluminosityfunctionsforall25CLASHclusters.Weshowtheresultsforallclustermembersinpurpleandforonlythosealongtheredsequenceinorange.Asaslope"inmagnitude-spaceisgivenby=1,valuesgreaterthanthatshowaluminosityfunctionwithfewerfaintgalaxiesthangalaxiesatM*.Weseeacleartrendforasteepeninginthefaintendslopewhenonlyincludingredsequencemembers.....................95xivFigure3.13ThemeasuredvaluesofM*fori-bandluminosityfunctionsofCLASHclusters.Showninpinkandorangearefori-bandM*valuesforall(orange)andonlyred(pink)galaxies,withevolutionparametersfromLovedayetal.(2012),althoughassumingthevaluesofM*foradouble-power-lawasdiscussedinthetext............95Figure3.14Comparisonbetweenstellarmassesandtotalmasseswithinr2500.Clustersarecolor-codedbyredshift.TotalmassesaremostlydrawnfromlensingmeasurementsbyMertenetal.(2015)andUmetsuetal.(2016),butalsoincludeX-raymassesfromDonahueetal.(2014).Stellarmassesarederivedfromtotalclusterluminositymeasure-ments,asdescribedinthetext,adjustedasneededtoaccountforapertureShownarelinescorrespondingtoM=0:01MTot(solid),M=0:02MTot(dot-dashed),andM=0:04MTot(dotted).100Figure4.1ModeledSEDtoagalaxyintheofMACS1423(z=0:545).Inthisparticularrun,theredshiftwasallowedtovary.Upperlimitsaremarkedwithdownwardpointingarrows.TheemptyboxcorrespondstotheF555Wnodataweretakenusingthatforthiscluster.Theparametersoftheshownbspectrumarelistedontheleft..................................110Figure4.2Bestparameters(orange)anduncertainties(purple)fromourSEDtformistheageoftheUniverseatthecluster'sredshiftminustheSFR-weightedage.Onlygalaxiesasclustermembersareshownhere.Derivationoftheseparametersisexplainedinthetext.114Figure4.3TheanaloggrCMDforall25clusters.Shownontheleftarethosegalaxieswecallmembers,whilethosedasnon-membersareplottedontheright.Hexbinsarescaledlogarithmicallywiththenumberofgalaxiescontainedinside...................117Figure4.4Thek-correctedgrCMDforall25clusters.Shownontheleftarethosegalaxieswecallmembers,whilethosedasnon-membersareplottedontheright.Apotentialredsequenceselectionregionisshownasashadedbox.Hexbinsarescaledlogarithmicallywiththenumberofgalaxiescontainedinside...................118Figure4.5Thegrvs.rcolormagnitudediagramsforgalaxiesascolormembersusinganalogmagnitudesideninTable4.1.Clustersareplottedinincreasingredshiftorder,startingintheupperleftandinthelowerright;thesecond-lowest-redshiftclusteristhesecondframeinthetoprow.Clusternamesforallclustersex-ceptCLJ1226.9+3332aredisplayedfollowingtheconventioninTable1.1.....................................120xvFigure4.6Thegrvs.rcolormagnitudediagramsforgalaxiesascolormembersusingk-correctedmagnitudes.ThedetailsofthisplotareotherwisethesameasforFigure4.5................121Figure4.7Measuredredsequenceslopesforthe25CLASHclustersasafunc-tionofredshift.K-correctedvaluesareshowninorange;observedvaluesareinpurple.Theeclusterschosenfortheironpropertiesaremarkedwithboxes,whilethe20X-rayselectedclustersaredenotedwithcircles.AbestofjusttheX-rayselectedclustersforbothsetsofmagnitudesisshownwithsolidlines;thosesamewhenincludingthestronglenssourcesareshownbydashedlines..123Figure4.8Measuredredsequenceinterceptsforthe25CLASHclustersasafunctionofredshift.Theeclusterschosenfortheirpropertiesaremarkedwithorangeboxes,whilethe20X-rayselectedclustersaredenotedwithpurplecircles.AbestofjusttheX-rayselectedclustersisshownwithasolidline;thesamewhenincludingthestronglensingsourcesisshownbyadashedline.TheexpectedbehaviorofapopulationwithmetallicityZˇ0:5Zformedatz=2isshownbythedottedblackline................124Figure4.9Themetallicityfunctionofclustermembers,givenbyfromandpositionalongtheredsequence.Hexbinsarecoloredaccordingtotheirmedianmetallicity,asindicatedbythecolorbar.Forlegibility,onlythosebinswithatleasttwocountsareshown.gandrmagni-tudesarek-corrected.Themedianmetallicityinonemagnitude-widebinsisshownatthebottomoftheplot,whilethemedianmetallicityin0.05magnitude-widecolorbinsisshownontheleft.........126Figure4.10TheSFR-weightedformationagefunctionofclustermembers.Hexbinsarecoloredaccordingtotheirmediantform,whichisdescribedinthetext,asindicatedbythecolorbar.Forlegibility,onlythosebinswithatleasttwocountsareshown.gandrmagnitudesarek-corrected.Themedianagein9colorbandsareshownontheleftoftheandin6magnitudebinsatthetop............127Figure4.11Stellarmasstoi-bandlightratiosforallclustermembers.Inthebottompanel,weshowthedistributionofmass-to-lightratioswithrespecttooverallluminosity,inSolarunits.Onlyhexbinswithatleastonecountareshown.Intheupperpanel,weshowthedistri-butionofmass-to-lightratios;purpleisallgalaxies,fuchsiaisthosegalaxiesgrcolorswithin0.1magnitudesoftheredsequence,andorangeisthosegalaxieswithgrcolorswithin0.05magnitudesoftheredsequence.Thedistributionoflowmass-to-lightratiogalaxiesisdominatedbylow-luminositygalaxiesoftheredsequence....130xviFigure4.12Measuredslopesofthegrredsequenceforthe25CLASHclustersasafunctionofredshift.Measuredslopesareshowninpurple.Weshowtwotoymodels:ametal-drivenslopemodel(orange)andanage-drivenslopemodel(pink),bothofwhicharedescribedinthetext.Neitherisabletocompletelymodelthebehavioroftheredsequence..................................134Figure4.13Color-colorplotsshowinghowgalaxiesoftmetallicitiesandagesoccupysimilarspacesincolor-colorplotsthatcanbebrokenapartbyfurtherphotometricinformation.Inthetoppanel,tracksshowlinesofconstantmetallicity,whilethebottompanelshowsisochrones.ColorsarefromJohnson/CousinInthetop(bot-tom)panel,linesarecoloredbyincreasingmetallicity(age),withthebluestlinesbeingthemostmetal-poor(youngest).Squaresdenotetheyoungest(mostmetal-poor)partofeachtrack,whilecirclesde-notetheoldest(mostmetal-rich).ThesetracksaretakenfromtheMILESstellarlibrary...........................136Figure5.1Luminosityfunctionsforthe25CLASHclustergalaxies,takingonlythosewithinjgr)j<0:2ofthemeasuredredsequence.ThisisotherwisethesameasFigure3.11..............140Figure5.2Thegivs.icolormagnitudediagramsforgalaxiesascolormembersusingk-correctedmagnitudes.ThedetailsofthisplotareotherwisethesameasforFigure4.6.Thevalueofthegrslopeisstillshowntoillustratethechangebetweensets........142xviiKEYTOSYMBOLSANDABBREVIATIONS2000.......................RightAscensioninJ2000CoordinatesA..............................Angstrom,1A=1108cmACS................AdvancedCameraforSurveys,anHSTinstrumentAGN.........................ActiveGalacticNucleus/NucleiBCG..............................BrightestClusterGalaxy2000.........................DeclinationinJ2000CoordinatesE(z)EvolutionFactorfortheHubbleExpansionParameter,E(z)=pM(1+z)3+H0..........CurrentValueoftheHubbleConstant,H0˘70kms1Mpc1G................GravitationalConstant,G=6:67108ergcmg2HST.............................TheHubbleSpaceTelescopeICM.....IntraclusterMedium,hotintergalacticgasboundbygravityinaclusterkB..................BoltzmannConstant,kB=1:3811016Ergs1keV...........KiloelectronVolt,1keV=1:6109erg=1:16107Kk1B......Cosmologywithanon-zerocosmologicalconstantanddarkmatterL..................LuminosityoftheSun,L=3:831033ergs1M2500............................MassEnclosedInsideR2500M.........................MassoftheSun,M=1:9891033g.....RatioofDensityofDarkEnergytotheCriticalDensityc2,˘0:7M...........RatioofDensityofMattertotheCriticalDensity,M˘0:3pc.............................Parsec,1pc=3:091018cmxviiiR2500...........RadiusInsideWhichAverageMatterDensityis2500ˆcˆc.................CriticalDensityoftheUniverse,ˆc˘1029gcm3SED.............................SpectralEnergyDistributionTX..................................X-RayTemperatureWFC3....................WideFieldCamera3,anHSTinstrumentXMM.........X-rayMulti-mirrorMission,XMM-Newton,anX-rayTelescopez..........................................RedshiftxixChapter1Introduction1.1TheGrandDichotomyIndividualgalaxies,whetherinagalaxyclusterorinthemakeuptwoseparatepopu-lations,bycolorasbeingineithera\bluecloud"ora\redsequence"(Baldryetal.,2004;Belletal.,2004;Wyderetal.,2007).Theseclascationsalsohavemorphologicalbasis,asredsequencegalaxiespreferentiallyshowearly-typemorphology(ellipticalgalaxies)whilebluecloudmembersaredominatedbylate-type(spiral)morphology(Stratevaetal.,2001),althoughcolordoesnotalwaysactasaproxyformorphology(Lintottetal.,2008).Thispopulationbimodalityextendeventolargeredshifts(Belletal.,2004).Weshowthecolorsofapproximately250,000galaxiesselectedfromtheSloanDigitalSkySurvey(SDSS)inFigure1.1;thetwopopulationsarevisibleinthisimage.Analysisofthephysicalpropertiesofindividualgalaxiesshowsthattheredsequenceandbluecloudcorrespondtoquiescent(undergoingverylittletonegligiblestarformation)andstar-formingpopulations,respectively(Schiminovichetal.,2007).Thiscolordistinctionisaconsequenceofongoingstarformationcausingastellarpopulationtobeblue.Whenitisactivelyformingstars,brightblueOandBstarsdominatethelightofagalaxy,makingitappearblue.However,theirshortlifespans(ontheorderof10'sto100'sofmillionsofyears,Hansenetal.,2004)meansthat,withoutconstantreplenishmentoftheOandBstarpop-1Figure1.1grcolor-magnitudediagramfor500000extendedgalaxiescatalogedfromtheSloanDigitalSkySurvey.Thesegalaxiesarethe500000inthe13thDataReleasewithgandrmagnitudesbrighterthan25andwithnoconstraintsonposition.Twogalaxypopulationsarevisible:thebluecloudandtheredsequence.Incolor-magnitudediagramspresentedinthisdissertation,bluercolorsareloweronthey-axis,whilebrightergalaxiesaretotheleftoffaintergalaxies.2ulation,galaxieswillbecomeredfairlysoonaftertheirmostrecentburstofstarformation.Theredsequenceisnedbyatightbunchingincolorspace(Baum,1959;Visvanathan&Sandage,1977),yetitextendsacrossarangeofluminosity,suchthatitappearsasaridgelineinFigure1.1.Redsequencegalaxieshavearangeofluminosities,frombrighttofaint(e.g.,Gelleretal.,2012),sothatthelengthoftheredsequenceimpliesthatbothlargeandsmallgalaxiesarehavingtheirstarformationshutAlthoughtheredsequenceistightlydistributedincolor,itisnotcenteredonauniformcoloracrossallluminosities;instead,theredsequenceexhibitsaslope,suchthatlowerlumi-nositygalaxiesarebluerthantheirbrightercounterparts.Onepossibleoriginforthisslopeisthatitiscausedbymetallicity,wherebylessmassiveobjectsaremoremetal-poorthanbrighterredsequencemembers(Kodama&Arimoto,1997;Stanfordetal.,1998;Ferrerasetal.,1999;Gallazzietal.,2006).Metalscanmakeastellarpopulationredderintwoways:lineblanketingandswelling.Metalswillcreateabsorptionlinesinastar;whentheyareathigherenergies,theywillabsorbbluelight(andthenre-emititatredderwavelengths),therebyreddeningthestar(Milne,1928;Chandrasekhar,1935;Sandage&Eggen,1959).Also,anenhancementinmetallicitycausesabuildupofradiationpressure,swellingastarandtherebyreducingitsetemperatureandmakingitredder(Conroy,2013).Duetohowmetallicitythecolorsofastellarpopulation,ametal-richgalaxywillberedderthanametal-poorgalaxy(Faber,1973;Worthey,1994;Bruzual&Charlot,2003;Maraston,2005).Iftheredsequenceslopeiscausedbymetallicitys,thenthemassivegalaxiesarethereforemoremetal-richthanlessmassivegalaxies.Aqualitative3originforthisrelationisthatsupernovae-drivenwindejectmetalsfromgalaxies,andtheenessofthisprocessisinverselycorrelatedwiththedepthofthepotentialwellofthegalaxy(Larson,1974;Arimoto&Yoshii,1987;Matteucci&Tornambe,1987;Lillyetal.,2013;Voitetal.,2015).Becausetheyhavelessgravitationalpull,lessmassivegalaxiesmayhavehadmoremetalsejected,andarethereforelessmetal-enrichedthanmassivegalaxies,whichcanretainmetalsinspiteofsupernovawinds.Matchingthisbehaviorwithsimula-tions,however,hasproventobeatask(DeLuciaetal.,2004a;deRossietal.,2007;Mouhcineetal.,2008).Antoriginoftheredsequenceslopecouldcomefromfaintergalaxieshavingtheirstarformationquenchedatalatertime.Evenafterseveralbillionyears,oldergalaxiesarestillsomewhatredderthantheiryoungercounterpartswithsimilarmetallicity.Asageandmetallicitybothobservedcolorsofgalaxies(thisiscalledthe\age-metallicitydegeneracy,"Worthey,1994,1999),disentanglingtheoriginoftheslopecannotbedonebycoloralone.Theorigincanbeeasilytested,however,byinvestigatingtheredshiftevolutionoftheredsequence;wereitcausedbyage,theslopewouldbecomemorepronouncedastherelativeagediscrepancybetweenmassiveandlessmassivegalaxiesbecamemoret.Observationsoftheredsequenceexistingbeyondevenmoderateredshifts(zˇ0:3)showsthatthetrendmustbedrivenbymetallicity(Kodama&Arimoto,1997;&Char-lot,1998;Kodamaetal.,1998).Nevertheless,whilemetallicityappearstobetheprimarycomponenttotheredsequenceslope,agevariationscanstillhavean(Ferrerasetal.,1999;Terlevichetal.,1999;Trageretal.,2000;Poggiantietal.,2001;Rakos&Schombert,2004).4Onefurtherclueabouttheoriginoftheredsequencecomesfromtheintrinsicscatter,thedispersionaboutthenominalredsequencelinebeyondthatcausedbyphotometricmea-surementuncertainties.Zeroscattermeansthatallgalaxiesofagivenluminositystoppedformingstarsatthesametime,whilealargescattermeansthatstar-formationceasedoverarangeoftimesforgalaxiesofthesamesize.Whileearlyworksontheredsequencefoundatightscatter(Boweretal.,1992;Ellisetal.,1997;Stanfordetal.,1998;Boweretal.,1998;Andreon,2003;McIntoshetal.,2005),whichimpliesthattheshtimewasconsistentforgalaxiesofagivensize,recentstudieshaveseenthatthemeasuredscattergrowsandevolveswithredshift(Hiltonetal.,2009;Papovichetal.,2010;Foltzetal.,2015).Asthecolorbetweentwostellarpopulationsoftagesdecreasewithtime,relativetothesizeoftheiragegap,themeasurementofscatteranditsevolutionconstrainsbothwhenandoverhowlonggalaxiesofacertainsizestoppedformingstars.Otherworkshaveshownthattheintrinsicscatterislargeratthefaintendoftheredsequence(Conseliceetal.,2002;Gallazzietal.,2006),implyingthatfaintergalaxiesareeitherquenching(ceasingstarformation)lateroroveralargerdistributionoftime.1.2TheRedSequenceinGalaxyClustersWhileredgalaxies{andtheredsequence{occurinthetheyaretlymorecommonindenseenvironmentssuchasgalaxyclusters(Baloghetal.,2004;anchez-Janssenetal.,2008).Clustersarethereforethebestwaytostudytheformationmechanismsoftheredsequence;notonlyisaclustergalaxymorelikelytobered,buttheenhancedgalaxydensitymeanswecanobservemoregalaxies.5Hubble&Humason(1931)notedthetendencyforellipticalgalaxiestobemorecom-moninclustersthaninthe(seealsoMorgan,1961),whichwasstatisticallybyDressler(1980).Spitzer&Baade(1951)consideredtheimplicationofthisdiscrepancyanditsrelationtoclusterformationandevolution;aclusterenvironmentispronetogalaxycollisions,whichwouldconvertspiralstoellipticals.Onecomplicatingfactoristhatclustersarenotstaticobjects,butgrowandmergeovertime.Infallinggalaxiesexperienceaburstofstarformationastheycrossthecluster'svirialradius(Porteretal.,2008),whichappearstobesustainedforˇ0:52:0billionyears(Hainesetal.,2015).Baheetal.(2013)showedthatgalaxiesfallingthroughtsareshowingsignsofhotgasstrippingouttoaroundetimesthevirialradius,asopposedtothoseequidistantfromclustercentersbutfallinginthroughvoids.Asclustersarecontinuallyaccretinggalaxiesthroughoutcosmichistory(Berrieretal.,2009),thesewillhaveamajorimpactontheobservablepropertiesofthebulkpopulationofclustergalaxies.Despitetheseconcerns,galaxyclustersstillactasafantasticlaboratoryforstudyingtheredsequence.Hoggetal.(2004)foundthatforbrightellipticalgalaxies(withi-bandabso-lutemagnitudesMi<20),galaxycolorsweremostlyindependentofthedensityoftheirenvironments.However,Tanakaetal.(2005)showedthatthefaintendoftheredsequenceisnotasdistinctforgalaxiesasitisforclustergalaxies,implyinga\downsizing"scenarioinwhichmoremassivegalaxiesandgalaxiesindenserregionsquenchtheirstarformationearlier.6Iffaintergalaxiesaremovingontotheredsequenceatalatertime,buttheoverallslopeoftheredsequenceiscausedbymetallicity,then,tostudytheredsequence,wewillneedawaytomeasuretheagesandmetallicitiesofindividualgalaxies.Thepreviously-mentionedage-metallicitydegeneracymeansthatindividualcolorsalonecannotconstrainonepropertywithoutassumingtheother.However,whileolderpopulationsandmoremetal-enrichedgalaxiesarebothredderthantheiryoungerormetal-poorcounterparts,theydonotreddeninthesameway.Bysamplingmultiplecolors,wecanbreaktheage-metallicitydegeneracyforindividualgalaxies.Intheastronomicalcontext,colorsaretheinmagnitudesmeasuredintwoSincemagnitudesarelogarithmicmeasureoftheinmagnitudesisauxratio.Conventionally,thebluererisplacedinthece,sothelargerthecolor,thereddertheobject.Additionally,tostudythefaintgalaxypopulation,werequireasamplewithbothexcel-lentangularresolution(toresolvegalaxiessmallerinsize)andtdepthtoobservefaintgalaxies.Toobtainsuchobservations,previousstudieshavemostlyusednearbyclus-ters,whichareaccessibletoground-basedobservations(e.g.,Edwards&Fadda,2011;Liuetal.,2011;Zhangetal.,2011;Tianetal.,2012;Ferrareseetal.,2016).However,tostudytheevolutionoftheredsequence,wealsoneedtemporalcoverage.Basedonthesecon-straints,theidealsurveyisahighresolutionsurveyofmultipleclustersspanningalargerangeofredshiftswithtcoveragetobreaktheage-metallicitydegeneracy.Wedescribesuchasurveyinthenextsection.7Table1.1.PropertiesofCLASHClustersFullNameCluster2000120002z3TX4LX4;5M25006(keV)(1044ergs1)(1014h170M)X-raySelected:Abell209A20901:31:52.5413:36:40.40.2067:30:5412:70:32:490:36Abell383A38302:48:03.4003:31:44.90.1876:50:246:70:21:420:07MACSJ0329.60211m032903:29:41.5602:11:46.10.4508:00:5017:00:62:240:24MACSJ0429.60253m042904:29:36.0502:53:06.10.3996:00:4411:20:52:490:57MACSJ0744.9+3927m074407:44:52.82+39:27:26.90.6868:90:8029:11:22:340:24Abell611A61108:00:56.82+36:03:23.60.2887:90:3511:70:23:200:35MACSJ1115.8+0129m111511:15:51.90+01:29:55.10.3558:00:4021:10:43:300:42Abell1423A142311:57:17.36+33:36:37.50.2137:10:657:80:21:820:17MACSJ1206.20847m120612:06:12.0908:48:04.40.43910:80:6043:01:04:590:68WARP1226.9+3332c122612:26:58.25+33:32:48.60.89013:82:8034:43:013:62:90MACSJ1311.00311m131113:11:01.8003:10:39.80.4945:90:409:40:41:800:30RXJ1347.51145r134713:47:30.6211:45:09.40.45115:50:6090:81:09:140:45MACSJ1423.8+2404m142314:23:47.88+24:04:42.50.5456:50:2414:50:42:700:50MACSJ1532.8+3021r153215:32:53.78+30:20:59.40.3625:50:4020:50:93:000:15MACSJ1720.2+3536m172017:20:16.78+35:36:26.50.3876:60:4013:30:52:400:29Abell2261A226117:22:27.18+32:07:57.30.2247:60:3018:00:23:240:23MACSJ1931.82635m193119:31:49.6226:34:32.90.3526:70:4020:90:62:740:12RXJ2129.6+0005r212921:29:39.96+00:05:21.20.2345:80:4011:42:02:670:25MS2137.32353ms213721:40:15.1723:39:40.20.3135:90:309:90:31:780:12AbellS1063r224822:48:43.9644:31:51.30.34812:40:6069:50:17:190:79HighMagnif.:MACSJ0416.12403m041604:16:08.3824:04:20.80.3977:50:8016:00:93:81:4MACSJ0647.8+7015m064706:47:50.27+70:14:55.00.58413:31:8032:52:16:53:2MACSJ0717+3745m071707:17:32.63+37:44:59.70.54812:50:7055:81:15:40:5MACSJ1149.6+2223m114911:49:35.69+22:23:54.60.5448:70:9030:21:23:10:8MACSJ21290741m212921:29:26.0607:41:28.80.5709:01:2022:61:54:71:71Rightascension.2Declination.3RedshiftsarefromPostmanetal.(2012b),exceptm0416,whichwasupdatedbyEbelingetal.(2014).4FromPostmanetal.(2012b).5Bolometricluminosity(from0.1-100keV).6ChandraHSEmassesfromDonahueetal.(2014).1.3CLASH:TheClusterLensingandSupernovaSur-veywithHubbleMuchofthisworkisbasedonobservationsconductedaspartoftheClusterLensingandSupernovasurveywithHubble(CLASH),aHubbleSpaceTelescope(HST)Multi-CycleTrea-suryprogram(foranoverviewofthesurvey,seePostmanetal.,2012b).TheCLASHsampleconsistsof25galaxyclusters:20(16fromAllenetal.,2008)selectedduetotheirdynami-8Figure1.2Fractionalthroughputsofthe17usedbyCLASH.Theyare,frombluetored,F225W,F275W,F336W,F390W(allUVIS);F435W,F475W,F555WF606W,F625W,F775W,F814W,F850LP(allACS);F105W,F110W,F125W,F140W,F160W(allWFC3-IR).callyrelaxedX-raymorphology,inordertoquantifythedistributionofdarkmatterwithinclusters,and5selectedduetotheirstrengthasstronggravitationallenses,forexploringthehighredshiftUniverse.These25systemswerechosenfromtheMassiveClusterSurvey(MACS,Ebelingetal.,2001,2007,2010)andtheAbellcatalog(Abell,1958;Abelletal.,1989).AllCLASHclustershaveX-raytemperatureskT5:0keV.Coordinatesandob-servedpropertiesofthe25clustersareprovidedinTable1.1.CLASHobservationsconsistof524orbitsofHubbletimedividedamongthe25clustersusing16(withanadditionalusedinarchivalobservations).TheseshowninFigure1.2,spanˇ2000Atoˇ1:7micronsandtheWFC3/UVIS,ACS,andWFC3/IRinstruments.Filterswerechosentomaximizephotometricredshiftresults,basedonthe9resultsofasimulatedre-observationofspectralenergydistribution(SED)templateswiththeHSTset.Thisselectionwasmadesothat80%ofobjectswithABMag<26intheF775Wbandwouldhaveaccuratephotometricredshifts<0:02(1+z)).Inaddition,forallACSandWFC3/IRthe5˙detectionthresholdwasasfaintorfainterthanABMag=26.7foracircularaperture0:400indiameter.Foreacheachclusterwasobservedforˇ1toˇ2orbits,withthetotalobserva-tionsforeachclustertotaling20orbits.Only476orbitsofnewobservationswererequiredforthis,asarchivalimageswerealsoused.Asanadditionalreserve,50orbitsoffollowupobservationswereallottedtosupernovaesearches,drawnfromapoolof200additionalorbitssharedwiththeCosmicAssemblyNear-IRDeepExtragalacticLegacySurvey(CANDELS;Groginetal.,2011;Koekemoeretal.,2011).Combiningthreetinstrumentspresentstheproblemofofview.Thelargestdetector,ACS,has220484096pixeldetectors,providingacoverageareaof2020020200.WFC3/IR,however,hasonlya10141014pixeldetectorandanangularcoverageof1360012300.Finally,WFC3/UVIShas220514096CCDsandaofviewof1620016200.Theseareasareexpandedbythetwoseparatepointingsbeingturned30apart,butthiscomesatreduceddepthforobjectsonlyintheofviewforonepointing.ObservationsarereducedbytheMosaicDrizzlepipeline(Koekemoeretal.2011,basedonFruchter&Hook2002;Koekemoeretal.2003).ACS/WFCdataarecorrectedforbiasstripingandchargetransferdegradation(Anderson&Bedin,2010).Thepipelinethenalignseveryvisitandeveryontothesamegrid,providingastrometric10accuracyontheorderofonemilliarcsecond.Badpixelsandcosmicraysarerejected,which,alongwithreadnoise,statisticaluncertainty,andaccumulateddarkcurrent,areusedtopro-duceaninversevariancemapforeachandcluster.Theoutputimagesarebinnedtoseveralscales,butthroughoutthisworkweonlyusethoseimagesbinnedto0.065"perpixel.Sinceobservationsbegan,theCLASHdatahavebeenwidelystudied.Coeetal.(2013),Bradleyetal.(2014),Bouwensetal.(2014),andMcLeodetal.(2016)havefoundextremely-highredshiftgalaxiesinthelensedbackgroundsoftheseclusters.Numerousstudieshavebeenmadeofthelensingofgalaxyclusters(Zitrinetal.,2011;Limousinetal.,2012;Umetsuetal.,2012;Zitrinetal.,2012b;Gruenetal.,2013;Medezinskietal.,2013;Zitrinetal.,2013;Umetsuetal.,2014;Zitrinetal.,2015;Umetsuetal.,2016).Meneghettietal.(2014),Mertenetal.(2015),andSerenoetal.(2015)haveusedtheCLASHdatatotheconcentration-massrelationforgalaxyclusters.Individualgalaxieshavebeenstudiedataphotometric(Jouveletal.,2014)andspectroscopic(Bivianoetal.,2013;Annunziatellaetal.,2014;Girardietal.,2015;Fogartyetal.,2015)level.Donahueetal.(2014)andDonahueetal.(2016)exploredtheX-raypropertiesofthe25clusters.CLASHclustersarebeingfurtherstudiedbytheHubbleFrontierFields(Coeetal.,2015)andtheGrismSurveyfromSpace(Schmidtetal.,2014).PhotometriccatalogsoftheCLASHclustergalaxieswerepublishedbyPostmanetal.(2012b),butthesewerenotsuitabletostudytheclusterpopulations.Weshowthedistribu-tionofphotometricredshiftsderivedfromthiscatalogforoneoftheclusters,MACS1423,inorangeinFigure1.3.Notonlyistheclusternotapparentinthedistribution,butmuchofthedetectedgalaxypopulationappearstonotbeassociatedwiththecluster,contraryto11Figure1.3DistributionofphotometricredshiftsfromCLASHclusterphotometryforMACS1423.Datafromtheoriginalcatalogspublishedby(Postmanetal.,2012b)isshowninorange,whiledatafromthephotometrywepresentinthisworkareshownindarkblue.Thespectroscopicredshiftoftheclusterisindicatedbythepurplebar.WeonlyconsiderthosegalaxieswithF814Wmagnitudesbrighterthan25.5.12whatavisualinspectionoftheHubbleimagewouldindicate.TostudytheCLASHclusterpopulation,wethereforeneededtoperformourowndetectionandphotometryinawaythatavoidstheissuesoftheoriginalcatalog.AstheCLASHclustersarecrowdedweusemode-basedbackgroundsubtractiontodetectgalaxiesofallsizeswithonlyaminimalamountofsourcedecomposition;usingasimilartechnique,weestimatethebackgroundsofallthegalaxiestophotometerthemindividually.Thistechnique,aswellasourphotometricresults,arepresentedinChapter3.TheimprovementinphotometryisseeninFigure1.3,wherethenewdataareshownindarkblue.WecharacterizeourdetectionlimitasatleastM*+5formostoftheclusters.InChapter4,weuseourmeasuredphotometrytoinvestigatetheredsequence.StartingwithSEDtomeasureagesandmetallicitiesforeachgalaxy,weobserveametallicitygradientalongtheredsequence.Furtherinvestigation,however,showsevidenceforapop-ulationevolvingontotheredsequenceatfaintmagnitudes.1.4X-rayScalingRelationsGalaxyclustersareassumed,atleasttotobeself-similar;thatis,smallerclustersarejustscaled-downversionsoflargerclusters.Statistically,thismeansthattherelationshipbetweenmassandotherparametersisoftenrepresentedbypower-laws(Giodinietal.,2013),which,inturn,meansthoseotherparametershavetheirownself-similarscaling.Weshowanexampleofself-similarscalingforclusterX-raypropertiesinpurpleinFigure1.4;the13Figure1.4X-rayscalingbetweenX-raytemperatureandX-rayluminosityforasampleofclusters(purple,Wuetal.,1999)andgroups(orange,Xue&Wu,2000).Bothsamplesshowself-similarscalingcharacterizedbyapower-law,buttheentslopesofthatscalingbetweengroupsandclustersisevidenceofapossiblebreakinself-similarity.dataforthispartofthearefromWuetal.(1999).Inscience,weseektocomparenaturewithourmodelsfornature.Forclusters,thefundamentalpropertiespredictedbyourcosmologicalmodelsaretotalgravitatingmasses(otherwiseknownasvirialmasses),or,lesscommonly,velocitydispersion(whichisrelatedtothedepthofthegravitationalpotentialM/R).Intheeraoflargesurveys,well-calibratedscalingrelationsareavitallinkinconnectingeasily-observedquantities(suchasLXorYSZ)withmoreeasily-predictedbuttougher-to-measureparameterssuchasvirialmass.Clusterofgalaxiesareextendedastronomicalsources,madeupofanaggregateofindi-vidualgalaxies,or,intheX-rayregime,agiantcloudofhotgaswithnow14edge.Evenassigningsomethingassimpleasaluminosityrequirescarefulofthesizeoftheregionoverwhichthemeasurementismade.Scalingrelationscanassistinsuchregions(usuallysomefractionofavirialradiusoraradiusinsidewhichthetotalmassrepresentssomescaledoverdensitycomparedtothecriticaldensity)byallowinganestimateofthevirialmassandthevirialradiuswithoutdirectlymeasuringeither.Anumberofstudiesusescalingrelationstomaximizetheutilityoftheirdatasets,evenwhenthederivedparametersarenottheendgoal.ohringeretal.(2013)usedtheX-rayluminosity-massscalingrelationtoiterativelyluminositymeasurementsbycorrectingforinderivedr500apertures.ohringer&Chon(2015)usedscalingrelationstoconvertamatterdensityation-derivedclustermassfunctionintoanX-rayluminosityfunction.ToruleoutastatisticalinSunyaev-Zeldovich(SZE)datafromacatalogofdetectedclusters,vanderBurgetal.(2016)usedascalingrelation.Forthesereasons,amorethoroughunderstandingofscalingrelationsallowsformoreaccurateestimationoftheseparameters.Anotheruseforstudyingscalingrelationsistoseewheretheydeviatefromexpectations.Deviationsfrombehaviorpredictedbyasimplemodelcanbeusedtoadjustthatmodel(e.g.,Kaiser,1991),and,byextension,furtherunderstandthebehaviorofgalaxyclusters.Addi-tionally,breaksfromscalingrelationsattheextremesofclusterenvironments(particularlyatthetransitionbetweenclusterandgroup,e.g.,Ponmanetal.,1996;Helsdon&Ponman,2000;Mulchaey,2000;Osmond&Ponman,2004;Sunetal.,2009;Eckmilleretal.,2011;Kettulaetal.,2013;Connoretal.,2014)revealthescaleatwhichtprocesses{suchasAGNheating(Puchweinetal.,2008;Fabjanetal.,2010;McCarthyetal.,2010;Gasparietal.,2014)andsupernovafeedback(Baloghetal.,1999;Loewenstein,2000;Kay,2004){15dominateinacluster;howpropertiesscalebelowthisthresholdisalsousedtoquantifytheoftheseevents.WhileasimplemodelpredictsthatLX/T2E(z),whereE(z)isacorrectionforcos-mologicalevolution,numerousstudieshaveobservedaluminosity-temperature(L-T)rela-tionshipbetterbyLX/T3E(z)(Mushotzky,1984;Edge&Stewart,1991;Davidetal.,1993;Maughanetal.,2012).Theimplicationofthisdiscrepancyisthatsomethingotherthangravitationalcollapsealoneisheatingclusterbaryons.OnemechanismtoproducetheobservedL-Tscalingistoincreasethecentralgasentropyofclusters(Evrard&Henry,1991;Kaiser,1991;Ponmanetal.,1999;Tozzi&Norman,2001),whichcanbeaccomplishedthroughenergeticevents,heating,and,indirectly,throughcooling(andthereforethere-movaloflow-entropygastomakestarsornon-X-rayemitting\cold"gas;Baloghetal.,1999;Bryan,2000;Boweretal.,2001;Voit&Bryan,2001;Voitetal.,2002;Muanwongetal.,2006).Thiscentralentropyormakesittoughertocompressgas,therebyimposinganupperlimitoncentraldensity.AsX-rayluminosityisproportionaltodensitysquared(seeEquation1.8),thisdensitylimitreducestheclusterluminosity,suchthatthehigherthebaselineentropyor,thelowertheX-rayluminosity.Alongwiththeluminosity-temperaturerelation,wealsoconsiderthemass-temperature(M-T)andluminosity-mass(L-M)relations.TheM-Trelationsteepensslightlyforlow-massclustersandgroups(Arnaudetal.,2005),butotherwisedisplayssmallintrinsicscatter(e.g.,Mantzetal.,2010a),whichisbelievedtoappearasaconsequenceofsubstructure(O'Haraetal.,2006;Yangetal.,2009).MuchliketheL-Trelation,theL-Mrelationissteeperthanthatpredictedbygravityalone(e.g.,Reiprich&ohringer,2002;Eckmilleretal.,2011),16andpreviousstudieshaveseenlargeintrinsicscatter(Prattetal.,2009;Vikhlininetal.,2009).Notonlydoclusterscalingrelationsfollowaslopetfromwhatisexpectedbypredictionsbasedsolelyongravity,butanumberofpreviousstudieshavefoundevidencefor\breaks"inthepowerlawrelations,suchthatlow-massgroupsfollowarentpowerlawthanmassiveclusters(Ponmanetal.,1996;Xue&Wu,2000;Eckmilleretal.,2011;Stottetal.,2012).WeshowanexampleofsuchabreakinFigure1.4;groupobservations(orange)fromXue&Wu(2000)arebbyatpower-lawthanclusterobser-vations(purple)fromWuetal.(1999).Thesebreaksinself-similaritycanbetiedtothemechanismthatraisestheclusterentropy;if,e.g.,supernovaeandactivegalacticnuclei(AGN)areraisingtheclusterentropy,theseeventswillhavealargerongroups,whichhaveshallowergravitationalpotentialwells.Characterizingthelocationandmagnitudeofbreaksfromself-similarity,aswellasthedeviationfromgravity-onlyscaling,isimportanttoconstraintheastrophysicsofclusters.Breakscanalsobecausedbyinconsistentchoicesfortheregionsoverwhichluminosity,temperature,andmassaremeasured.Finally,breakscanalsobecausedbybiasesinthesampleselectionandchangesintheintrinsicscatterasafunctionofclustersize(soa\break"inapower-lawrelationmightnotbeabreakatall).Therefore,inthisworkwehavetobecarefulinourof\luminosity,"\tempera-ture,"and\mass,"inthesensethatthevolumeoverwhichthosequantitiesaremeasuredmustbespandconsistentfromclustertocluster.Tothepredictedbehaviorofscalingrelations,webeginwithawaytorelatemass17toradius.Ifr1(suchasr2500)istobetheradiusinwhichtheaveragedensityofasystemisˆc,whereˆcisthecriticaldensity,thenM=4ˇ3ˆcr3:(1.1)WecanthensubstitutethecriticaldensitywithE(z)usingˆc=3(H0E(z))28ˇG/E(z)2;(1.2)whereH0istheHubbleconstantandGisthegravitationalconstant.RearrangingEquations1.1and1.2,wehaveanexpressionfortheradiusR/E(z)2=3M1=3:(1.3)Withthisexpression,wecansubstitutetheradiusoutofanyexpressionandreplaceitwithobservablequantities.Next,weconsidertheequationofhydrostaticequilibrium,dPdr=GM(r)ˆ(r)r2:(1.4)Weassumethatthemassinhydrostaticequilibriumcanberepresentedbyanidealgas,sothatthepressureisgivenbyP=ˆmkBT;(1.5)1Throughoutthiswork,wedenotevalueswithsubscripts\2500"and\500";thesecorrespondtovaluesmeasuredwithinradiigivenbythisformula,ortotheradiithemselves.18wheremisthemassofaparticle,notofthesystem.BymultiplyingEquation1.4byr/P,usingEquation1.3tosetM=r/(ME(z))2=3,andusingEquation1.5tosetˆ=P/T1,wedlnPdlnr=G(M(r)=r)(ˆ(r)=P)/(ME(z))2=3T1:(1.6)Wethereforecomeuponascalingrelationbetweenmassandtemperature:M/T3=2=E(z):(1.7)Undertheassumptionthatthehotclustergasisinhydrostaticequilibriumandfollowstheidealgaslaw,thismodelallowsustoconvertobservedgastemperaturestomassesandviceversa.ToextendtheserelationstoX-rayluminosity,weassumethatalloftheemissionofthehotgascomesfrombremsstrahlung.Inthatcase,weuseaversionoftheequationofbremsstrahlungemission,LX/MˆT1=2X:(1.8)WeconvertthedensitytermtoanevolutiontermwithEquation1.2andreducethisex-pressiontotemperaturealoneusingourconversionfrommasstotemperature,Equation1.7.ThisleavesuswithascalingrelationbetweentheX-rayluminosityandgastemperature,LX/T2E(z):(1.9)19BycompletingthetrianglecreatedbyEquations1.7and1.9,wehaveLX=E(z)/M2=3E2=3(z);(1.10)awaytoconnecteasily-obtainedredshiftandluminositymeasurementsofclusterstoesti-matesoftheirmass.Oneoftheimportantpredictionsofthegravity-onlymodelisthattheserelationshipshaveadependenceonredshift,causedbytheevolutionofthecriticaldensityoftheUni-verse(Equation1.2).Incontrast,non-gravitationalshouldhaveamoretredshiftdependenceiftheydependontheevolutionoftheastrophysicalprocesses,suchastheAGNluminosityfunction(Georgakakisetal.,2015;Fotopoulouetal.,2016).Duetotheyinobtaininggoodmeasurementsforhigher-redshiftclusters,previousstudieshavebeeninconclusiveaboutthecharacterizationofevolution(e.g.,Ettorietal.,2004;Kotov&Vikhlinin,2005;O'Haraetal.,2006;Pacaudetal.,2007;Reichertetal.,2011).InChapter2weinvestigateasampleof15galaxyclusterswithweak-lensingmassesde-rivedfromHSTdata;weusenewandarchivalobservationsfromXMM-NewtontomeasureX-rayluminositiesandtemperaturesforthesesystems.Duetohowtheseclusterswereran-domlyselectedforsnapshotHSTobservationsfromacomplete,X-rayx-limitedsampleofclustersofgalaxies(Vikhlininetal.,1998;Mullisetal.,2003),theyareelyanX-raysample,withX-raypropertiesconsistentwithbeingattheboundarybetweengroupsandclustersandwithredshiftscovering0:3<z<0:6.20Tomaximizetheutilityofoursample,wealsoinclude50moremassivegalaxyclustersinthesameredshiftregimefromMahdavietal.(2013,2014)aswellasasampleoflow-redshiftgroupsfromSunetal.(2009).BothsampleswereselectedbasedontheirX-raycharacter-istics.Wenoevidenceforabreakinthethreescalingrelationsbetweenluminosity,temperature,andmassforthesesamples.Incomparisonwiththelow-redshiftgroups,wealsoaweakstatisticalpreferencefortheexpectedself-similarevolution.21Chapter2X-RayScalingRelationsforModerateLuminosityGalaxyClustersatIntermediateRedshift1WepresentnewX-raytemperaturesandimprovedX-rayluminosityestimatesfor15newandarchivalXMM-Newtonobservationsofgalaxyclustersatintermediateredshiftwithmassandluminositiesnearthegalaxygroup/clusterdivision(M2500<2:41014h170M,L<21044ergs1,0:3<z<0:6).Theseclustershaveweak-lensingmassmeasurementsbasedonHubbleSpaceTelescopeobservationsofclustersrepresentativeofanX-rayselectedsample(theROSAT160SDsurvey).TheangularresolutionofXMM-Newtonallowsustodisentangletheemissionofthesegalaxyclustersfromnearbypointsources,whichcantlycontaminatedpreviousX-rayluminosityestimatesforsixofthenclusters.WeextendclusterscalingrelationsbetweenX-rayluminosity,temperature,andweak-lensingmassforlow-mass,X-ray-selectedclustersouttoredshift˘0:45.Theserelationsareim-portantforcosmologyandtheastrophysicsoffeedbackingalaxygroupsandclusters.Ourjointanalysiswithasampleof50clustersinasimilarredshiftrangebutwithlargermasses(M500<21:91014M,0:15z0:55)fromtheCanadianClusterComparisonProject1Thischapteristakenmostlyword-for-wordfromConnoretal.(2014),aspublishedintheAstrophysicalJournal22thatwithinr2500,M/L0:440:05,T/L0:230:02,andM/T1:90:2.TheestimatedintrinsicscatterintheM-Lrelationforthecombinedsampleisreducedto˙log(MjL)=0:10,from˙log(MjL)=0:26withtheoriginalROSATmeasurements.WealsoanintrinsicscatterfortheT-Lrelation,˙log(TjL)=0:070:01:2.1IntroductionSimulationsofcosmologicalstructureformationshowclustersandtsofdarkmattergrowingfromasetofrandominitialperturbationsintoacosmicweb(e.g.,Springeletal.,2005;Boylan-Kolchinetal.,2009;Klypinetal.,2011).Thestatisticalpropertiesofthiscosmicwebareextremelysensitivetothevaluesofcertaincosmologicalparameters,partic-ularlyMand˙8,theamplitudeoftheinitialperturbationspectrum(e.g.,Ekeetal.,1996;Bahcall&Fan,1998;Holderetal.,2001;Allenetal.,2011).Thiscosmicwebofdarkmatteriseasiesttoinvestigatebystudyingitsmostmassivesystems,whichareclustersofgalaxies.About85%ofacluster'smassiscomposedofdarkmatter,whilenearlyalloftherestisintergalactichotgas,withatraceamountcontributedbystars(Rosatietal.,2002;Voit,2005;LaRoqueetal.,2006).Thehotgasisedbythecluster'sgravitationalpotentialandradiatesX-rays,providingpowerfuldiagnosticsforpropertiesofthehostcluster,includingitsmass,baryoniccontent,anddynamicstatus.Accuratemeasurementsofgalaxyclustermassesareusefulformorethanjustdescribingindividualsystems;galaxyclustermassesareneededtoverifymodelsoflarge-scalestructureformation(Jenkinsetal.,2001;Grossietal.,2007;Vikhlininetal.,2009)andtoconstrain23cosmologicalparameters(Tinkeretal.,2008;Rozoetal.,2010;Mantzetal.,2010b;Bhat-tacharyaetal.,2011).Onewaytoaccuratelymeasuretheprojectedmassofaclusteristhroughmeasurementsofgravitationallensing(Hoekstraetal.,2013).However,perform-ingsuchmeasurementsisprohibitivelyexpensiveforlargesamplesofclustersandforlowredshiftclusters.Tothisend,scalingrelationshavebeenempiricallycalibratedtoconnectobservedpropertiestomasses.ExamplesofthisincludeLXMX,MXTX,andMXYXrelations.EarlyworkbyKaiser(1986)showedthattheserelationscanbecastanalyticallyforthecasewherecoldgasfallsintopreexistingdarkmatterstructures.Thoseearlyrelationspre-dictedclustersthatwereoverluminousforagiventemperaturecomparedtoobservations.SoKaiser(1991)andEvrard&Henry(1991)showedthatpreheatingcouldincreasetheentropyofintergalacticgas.Sucha\preheating"modelelevatestheentropyofthegas,preventingthegasfromgettingtoodense.ThesepredictedLXMXandTXMXrelationswereroughlyconsistentwithobservations.ThisexpectationthatclusterswouldfollowsuchlawsoveralargerangeofMX,withstandardevolutionaryfactors,isknownasself-similarity(Navarroetal.,1997;Bower,1997;Bryan&Norman,1998).Thescale-freenatureofthisbehaviorarisesbecausethegravitationalpotentialdominatesoverotherenergysources,andgravityisscale-free.Previousworkhasshownpossibledeviationsfromself-similarityatmassesapproachingthoseofgalaxygroups(e.g.,Ponmanetal.,1996;Xue&Wu,2000;Eckmilleretal.,2011;Stottetal.,2012),possiblyduetotheincreasingfractionalcontributionoflocalfeedbackprocessestotheclusterenergybudgetcomparedtothegravitationalpotential.Theexact24magnitudeandbehaviorofthisdeviationisnotyetbutithasbeenqualitativelyreproducedinnumericalwork(Puchweinetal.,2008;Fabjanetal.,2010).Afullunderstandingofthedeviationfromself-similaritycanonlycomethroughathor-oughexplorationoftheclusterparameterspace{acrossclustermassrangesandredshifts.Oneunder-sampledregimeisatmoderateredshiftandlowmass.Clusterswiththeseprop-ertiesustheabilitytoanswerthequestionsofhowscalingrelationschangefromhighredshifttolowredshiftandwhetherthereisanyevolutioninthelow-massbehavioroftheserelations.RecentworkbyHoekstraetal.(2011)providedweaklensingmassmeasurementsfromtheHubbleSpaceTelescope(HST)of25galaxyclustersoccupyingthisredshiftregime.Thatworklackedhigh-qualityX-rayobservationsformostoftheobjects,however.Weuseob-servationswiththeXMM-NewtonsatellitetostudytheX-raycharacteristicsofthissampleandtoconstrainX-raypropertyandmassscalingrelationsforthisredshiftandmassregime.Thestructureofthischapterisasfollows.InSection2.2,wedescribethepropertiesofoursample,whileouranalysistechniquesaredescribedinSection2.3.TheresultsofouranalysisarepresentedinSection2.4.Inparticular,wediscussourofthreescalingrela-tionsinvolvingX-rayluminosity,temperature,andweaklensingmass.Finally,wecompareourresultstootherpublishedworksinSection2.5andAppendixA.Throughoutthispaper,weassumeacosmologywithM=0:3,andH0=70kms1Mpc1.2526Table2.1.SamplePropertiesClusterName2000a2000a2000b2000bzcNHdr2500a1020cm2h170MpcRXJ0056.9274000h56m56:98s2740m29:9s00h56m57:9s2740m29:3s0.5631.790.270RXJ0110.3+193801h10m18:22s+1938m19:4s01h10m18:2s+1938m18:7s0.3173.820.293RXJ0522.2362505h22m15:48s3624m56:1s05h22m15:4s3624m55:7s0.4723.630.313RXJ0826.1+262508h26m08:03s+2625m16:7s0.3513.390.157RXJ0847.1+344908h47m11:79s+3448m51:8s08h47m11:7s+3448m51:9s0.5602.920.452RXJ0957.8+653409h57m51:22s+6534m25:1s09h57m51:1s+6534m26:1s0.5305.320.257RXJ1117.4+074311h17m26:04s+0743m38:3s11h17m26:1s+0743m41:0s0.4773.590.280RXJ1354.2022113h54m17:19s0221m59:0s13h54m17:2s0221m59:4s0.5463.220.428RXJ1642.6+393516h42m38:35s+3936m10:4s16h42m38:4s+3936m07:9s0.3551.200.239RXJ2059.9424520h59m54:92s4245m32:1s20h59m54:9s4245m34:8s0.3233.130.280RXJ2108.8051621h08m51:17s0516m58:4s21h08m51:2s0516m57:6s0.3196.300.210RXJ2139.9430521h39m58:22s4305m13:9s21h39m58:3s4305m14:2s0.3761.630.292RXJ2146.0+042321h46m05:52s+0423m14:3s21h46m05:6s+0423m02:6s0.5314.820.436RXJ2202.7190222h02m45:50s1902m21:1s22h02m45:5s1902m20:1s0.4382.440.152RXJ2328.8+145323h28m52:27s+1452m42:8s23h28m52:3s+1452m42:7s0.4973.880.254aCoordinatesandr2500fromHoekstraetal.(2011).bCoordinatesfromXMMcentroid(seeSection2.4.2).cClusterredshiftfromMullisetal.(2003).dColumndensityfromKalberlaetal.(2005).Table2.2.ObservationsofClustersClusterNameOBSIDExposureTimeUsableExposureTime(s)MOS1MOS2pnRXJ0056.9274001112820018876819080174135RXJ0110.3+193805009401013281818883184976973RXJ0522.23625006576020131919313333131726904030258090131110200772028416481RXJ0826.1+26250691670201a487423151631419231350603500301a405091996720463RXJ0847.1+34490107860501914195870858333RXJ0957.8+6534050243020172070447624506230090RXJ1117.4+0743020356040186515810735629302035602018191371366572550082340101632066088943232RXJ1354.202210112250101336462458424000RXJ1642.6+39350603500701a23917171081713311099RXJ2059.942450691670101a57915567945657141238RXJ2108.805160110860101381163463734668RXJ2139.943050603501001a41916367153687519382RXJ2146.0+0423030258070147120240912408118316RXJ2202.7190202034502016411727842260816919RXJ2328.8+14530502430301104910940049424970516aNewdata.2.2DataandAnalysisOursampleisbasedon25galaxyclustersdetectedintheROSAT160SquareDegreeSurvey.Vikhlininetal.(1998)describetheinitialsurvey,andareanalysiswithspectroscopicredshiftscomesfromMullisetal.(2003).These25clusterswerefurtherstudiedwithanHSTsnapshotprogram(PI:Donahue)ofoneorbitperclusterwiththeF814WDuetothenatureofthesnapshotprogram,theclusterswererandomlyselectedfromamasterlistof72clusters.Hoekstraetal.(2011)usedthoseimagestoestimateweak-lensingmassesfortheseclusters.ThefocusofthisworkistoimproveandaugmenttheX-raymeasurementsoftheseclusterswithobservationswithXMM-Newton.Alongwithnewobservations,weusedarchivaldatatosupplementtheclustersamplewithnewuniformmeasurementsofX-rayproperties.27WesearchedthearchiveofXMM-NewtonobservationswiththeXMM-NewtonScienceArchive(XSA)v7.2withina15'radiusoftheclusterpositionsgiveninHoekstraetal.(2011).AsofJune28,2013,wefound27observationsthatincludedoneoftheclusters.Weexcluded9becausetheyweretooshortandexcluded4thatwereunusableduetoexcessiveparticlecontaminationfromleaving14observationsof11clusters.Wesupplementedthesewithenewobservationsoffourclusters.AllobservationsweretakenwiththeEu-ropeanPhotonImagingCamera(EPIC),whichconsistsoftwoMOScameras(Turneretal.,2001)andthepncamera(Struderetal.,2001).ClusterpropertiesdrawnfromearlierworksareprovidedinTable2.1.Hydrogencolumndensity,NH,istakenfromthecompilationbyKalberlaetal.(2005).ThedatasetsusedinthisworkarelistedinTable2.2.OurnewobservationsarepresentedinFigure2.1.OurdataareshownassmoothedX-raycontoursfromcombinedEPICimagesoverlaidonHSTimagesoftheclusterusingtheAdvancedCameraforSurveys/WideFieldChannelF814WCombinedX-rayprod-uctswerecreatedusingtheXMM-NewtonScienceAnalysisSystem(SAS)imagesscriptbinningto200andsmoothingwithaGaussianFWHMof1500intheenergyrangeof0.4-8.0keV.Contoursarelevelsof106counts1arcsec2,withthelowestdisplayedcontourcorrespondingto106counts1arcsec2forRXJ0826.1+2625andRXJ2059.94245and2106counts1arcsec2forRXJ1642.6+3935andRXJ2139.94305.ObservationswerereducedusingtheXMM-NewtonSASversion12.0.1.2Badtimein-tervalswerebasedonthecountrateofhighenergyevents(>10keV)in100-secondbins;timeperiodswherethoseexceeded0.35counts1(MOS)or0.40counts1(pn)2http://xmm.esac.esa.int/sas/28Figure2.1Gaussian-smoothedX-rayemissioncontoursoverlaidonHubbleSpaceTelescopeimagesofthefourclustersweobservedinthiswork.Contoursarespacedatintervalsof106counts1arcsec2,withtheminimumlevelforeachclusterdescribedinSection2.2.29wereexcluded.OneexceptiontothiswastheobservationofRXJ1354.20221,0112250101,whichhadanabnormallyhighhigh-energybackground.Toavoidovthedata,weincreasedthecountratelimitsto0.5counts1(MOS)and0.65countss1(pn)forthisobservationonly.Forallobservationsthelevelswerescrutinizedtoensurethatpe-riodsoftwereentirelyremoved.Whennecessary,wemadethehigh-energycountratethresholdsmorestringent.Pointsourcesweredetectedusingtheindividualtasksthatmakeupedetectchain.Thistaskuseseboxdetecttoperformaslidingboxdetectionofsourceswithalocalback-ground,thenhasesplinemapgenerateasource-correctedglobalbackground,whichasecondrunofeboxdetectusestosourcesagain.Sourceswereselectedfromthesedetectionsbyhandafteravisualinspection.Table2.3liststhecoordinatesandradiiofourmasks.Allidensourceswereexcludedfromthespectralextractionregions.Wethenextractedspectrafromtheobservationsinthreetaperturesusingstan-dardoptions("#XMMEAEM"forMOSdataand"#XMMEAEP"forpn).Forallcamerasweselectedsingleanddoubleevents,with"PATTERN<12"forMOSand"PATTERN<4"forpn.Ouraperturewas300h170kpc,whichwaschosentocompareourmeasuredagainstthoseofVikhlininetal.(1998).Oursecondaperturewasacirclewithradiusequaltothevalueofr2500giveninTable2ofHoekstraetal.(2011).r2500istheradiusinsidewhichtheestimatedmeanmassdensityis2500timesthecriticaldensityattheredshiftofthecluster3.Weaklensingmassmeasurementsusedinthisworkwerederivedforr2500for3Similarly,r500istheradiuswhereaveragedensityis500timesthecriticaldensity.Throughoutthiswork,weusethesubscripts2500and500todenotethatquantitiesaremeasuredinsidetheseradii.30Table2.3:MaskedSources20002000radius(00)0h57m04:704s2740m23:52s21.462100h57m04:103s2741m11:52s21.462100h57m09:219s2739m39:49s20.513700h56m49:649s2740m07:55s25.768000h56m48:444s2740m59:54s12.873001h10m11:496s1938m56:76s26.308201h10m11:448s1940m27:12s22.245701h10m28:704s1938m41:64s23.602901h10m22:008s1939m32:40s21.236401h10m09:960s1936m50:76s23.417701h10m09:048s1938m22:92s23.375801h10m08:640s1938m55:68s27.936201h10m14:287s1935m16:84s19.309401h10m13:831s1936m17:04s19.309405h22m23:736s3625m22:08s26.332105h22m14:424s3624m33:48s19.663805h22m20:328s3622m15:24s24.540405h22m12:792s3623m14:28s23.980205h22m12:168s3621m46:44s21.6200031Table2.3(cont'd)20002000radius(00)5h22m15:216s3623m37:68s22.725605h22m12:978s3625m42:22s10.154608h26m05:760s2627m40:32s24.862008h26m13:920s2626m16:44s20.450408h26m10:320s2626m27:60s20.612208h26m04:080s2626m33:00s21.489508h26m15:120s2625m18:12s22.790608h26m03:360s2622m56:64s19.136108h26m18:823s2624m48:31s16.963308h26m13:824s2627m41:13s16.963308h26m00:960s2623m28:32s16.963308h46m59:280s3448m24:12s22.651608h47m09:840s3449m18:84s17.035208h47m11:520s3447m16:44s23.746608h47m07:622s3449m46:84s14.866708h47m14:376s3446m54:03s14.866708h47m03:209s3447m03:63s21.506008h47m07:622s3447m38:84s19.707909h57m57:360s6535m25:08s17.8906032Table2.3(cont'd)20002000radius(00)11h17m40:080s0744m11:22s24.4514011h17m35:040s0743m35:04s28.2048011h17m32:880s0741m46:57s24.7282011h17m29:280s0746m31:84s25.1226011h17m37:200s0742m44:96s24.5163013h54m14:751s0220m28:26s16.0979016h42m32:640s3934m50:52s18.5573020h59m44:880s4244m57:84s47.3436020h59m57:840s4242m24:12s22.9939020h59m57:600s4242m57:96s18.6188020h59m49:920s4244m53:88s15.6008021h08m40:800s0518m10:51s21.5971021h39m51:286s4307m57:00s19.1551021h40m14:022s4305m11:40s21.8693021h46m08:880s0424m03:92s19.9797021h46m08:160s0424m42:95s19.2458021h46m05:280s0420m22:74s16.2882022h02m39:120s1903m17:28s15.9197022h02m48:240s1903m47:52s21.8367033Table2.3(cont'd)20002000radius(00)22h02m39:600s1900m05:76s22.4937022h02m43:200s1904m33:96s22.5322022h02m48:480s1904m27:84s20.5257022h02m36:720s1903m32:04s26.1011022h02m42:960s1900m28:08s21.2601022h02m52:268s1901m08:05s14.6214023h28m43:680s1453m35:16s18.7016023h28m52:800s1450m02:76s21.4418023h29m03:360s1452m01:20s36.0000023h28m48:372s1454m11:16s18.70160eachcluster.Thisradiuswastypicallybetween40-6000.Forbackgroundregions,weusedannulicenteredontheclusterwithinnerradiiof1.20andouterradiiof1.80.Wechosetousethissizetoobtainaslocalabackgroundonthedetectoraspossiblewithoutanydetectableclusteremissionpresent.Fortypicalrangesofbparameters(Vikhlininetal.,1998)weestimatethatourchoiceofbackgroundannulimayslightlyover-subtracttheat<1%level,wellbelowourstatisticaluncertainties.Thisestimateisconservativebecauseasingle34beta-modeltendstoover-predicttheX-raysurfacebrightnesswhenextrapolatedtolargeradii(e.g.,Ettori&Brighenti,2008).Withoneexception,whenchoosingacenterforourapertures,weusedtheBrightestClusterGalaxy(BCG)coordinatespresentedinHoekstraetal.(2011).Thispositionisthecenteraroundwhichtheyestimater2500andM2500,andadirectcomparisonbetweenthemassandX-raypropertiesofaclustershouldbewithinthesamearea.Theexception,RXJ0826.1+2625,wewillshowinSection2.4.1,isanexamplewheretheROSATcenterisinerrorduetopointsourcecontamination.Hoekstraetal.(2011)idenaBCGwithareported\quality"oftheBCGdetectionof0,implyinganambiguousidenFur-thermore,theirreportedvalueofM2500=0:8+2:12:1impliesapoordeterminationoftheclustermassaroundthatlocation.AsthecenteroftheX-rayemissiondetectedinXMM-Newtonisbarelywithinr2500ofthereportedBCGposition,weinsteadrepositionedouraperturearoundthecenteroftheX-rayemission.ThecoordinatesaroundwhichwelocatedouraperturesareprovidedinTable2.1.Becauseofthecenteringissues,RXJ0826.1+2625wasnotincludedinofweak-lensingmassscalingrelations.SpectrawereextractedusingtheSAStaskevselect,whileredistributionmatrix(RMF)andancillaryresponse(ARF)weregeneratedwithSAStasksrmfgenandarfgen,respectively.Thetaskbackscalewasusedtodeterminetheusablearea(cor-rectingforbadpixelsandCCDedges)foreachspectrum.Photonspectra,RMF,andARFwereallbinnedfrom0.4to8.0keVwithbinsofsize0.038keV.352.3AnalysisOurextractedspectrawereanalyzedusingXSPECversion12.8.0andPyXspecversion1.0.1.Foreachcluster,threeindependentspectrafromMOS1,MOS2,andpnweresimultane-ouslywiththesamemodel.InallthreeobservationsofRXJ1117.4+0743,theclusteraperturewechoseextendedoutsideoftheofviewfortheMOS2camera.Asthiswouldbiasourresultstowardthepropertiesofthecenterofthecluster,wedidnotusethoseMOS2dataforanyofthethreeobservations.Asidefromthespectralbinningperformedinthespectralgeneration,nobinningwasperformed.Becauseofthat{andthelownumberofcountsforourobjects{weusedthemoC-statistic(amaximumlikelihoodfunction;Cash,1979;Wachteretal.,1979)fordeterminingthebestanduncertaintiesforourmodelparameters.Ourspectraweremodeledwithacombinationofemission(APEC,agasemissionspectrum)andabsorption(phabs,aphotoelectricabsorptionmodel)componentsfrom0.7-8.0keV.APECusestheATOMDBv2.0.24codetocomparetheobserveddatatomodelsofcollisionallyionizedgasemissionspectra.Itrequirestheredshift(fromMullisetal.,2003)andmetalabundancestoanormalizationandplasmatemperature.Weusedtheangrabundancetable,whichcomesfromAnders&Grevesse(1989).ForallmodelweusedXSPECtoderivevaluesfrom0.5-2.0keV,thesamerangeusedbyMullisetal.(2003).Wealsocalculatedluminositiesfrom0.1-2.4keV(therangepresentedinHoekstraetal.,2011),0.5-2.0keV(tomatchMullisetal.,2003),and0.1-50keV(a\bolometric"luminosity).4http://atomdb.org/3637Table2.4.SpectralFittingPropertiesWithinr2500NameMassakTAbundanceNorm.FluxbLcLbLdh17010131041014h2701044h2701044h2701044MkeVZAPECeergs1cm2ergs1ergs1ergs1RXJ0056.927405:2+4:23:03:51+0:910:49<1:03f1:97+0:160:194:59+0:260:360:524+0:0440:0320:437+0:0360:0311:05+0:080:10RXJ0110.3+19385:0+3:42:62:95+0:720:620:56+0:500:320:98+0:190:163:64+0:200:080:119+0:0030:0060:102+0:0020:0060:219+0:0160:015RXJ0522.236257:2+4:23:15:32+0:420:370:37+0:130:122:11+0:080:096:11+0:130:100:454+0:0120:0120:371+0:0100:0091:19+0:040:03RXJ0826.1+26250:8+2:12:11:52+0:200:270:13+0:120:080:31+0:060:050:80+0:050:020:035+0:0020:0020:031+0:0010:0020:045+0:0020:003RXJ0847.1+344924:2+8:97:64:17+0:590:400:29+0:180:162:02+0:130:135:20+0:110:100:568+0:0120:0120:467+0:0090:0091:31+0:030:05RXJ0957.8+65344:3+3:22:62:88+0:210:170:23+0:100:081:65+0:090:093:95+0:090:070:393+0:0090:0110:330+0:0090:0090:745+0:0120:019RXJ1117.4+07435:2+3:42:84:31+0:690:390:40+0:190:191:01+0:070:062:90+0:060:040:224+0:0040:0040:184+0:0040:0030:527+0:0120:015RXJ1354.2022120:2+6:45:67:55+1:861:210:38+0:340:272:55+0:180:196:89+0:250:190:679+0:0250:0200:547+0:0210:0242:12+0:090:09RXJ1642.6+39352:8+2:81:83:01+0:410:380:43+0:260:200:95+0:100:103:43+0:160:080:147+0:0050:0060:127+0:0040:0050:264+0:0110:012RXJ2059.942454:4+3:32:42:58+0:100:100:53+0:100:081:93+0:090:097:25+0:120:090:250+0:0030:0050:216+0:0040:0040:424+0:0070:008RXJ2108.805161:8+2:21:42:34+0:900:49<2:67f1:16+0:100:292:89+0:130:320:097+0:0090:0080:082+0:0090:0030:161+0:0180:014RXJ2139.943055:3+3:72:63:06+0:230:220:32+0:120:101:86+0:100:106:13+0:110:160:297+0:0060:0080:255+0:0050:0060:542+0:0100:013RXJ2146.0+042321:0+6:75:75:02+0:410:380:41+0:140:122:98+0:130:137:87+0:180:170:739+0:0170:0210:601+0:0180:0201:97+0:060:04RXJ2202.719020:8+2:00:83:91+0:790:630:77+0:590:390:37+0:060:061:29+0:070:040:084+0:0050:0050:071+0:0040:0050:186+0:0080:012RXJ2328.8+14534:0+3:72:63:12+0:280:230:38+0:160:120:59+0:040:041:58+0:040:020:135+0:0030:0030:113+0:0030:0030:269+0:0070:005aWeaklensingmassesfromHoekstraetal.(2011).b0.5-2.0keV.c0.1-2.4keV.dBolometric.e10144ˇ[DA(1+z)]21RnenHdV:DAhasunitscm.neandnHhaveunitscm3:f3˙upperlimit.2.4ResultsTheresultsofourspectralaresummarizedinTable2.4.Massestimatesbasedonweak-lensinganalysesarethosereportedinHoekstraetal.(2011).Ourreportedluminositiesaretheunabsorbedluminosities.Forallmeasurements,thereportederrorsareatthe1˙level.2.4.1FluxOneofouraimswastoinvestigatehowimprovedXMM-Newtonimagingwouldthemeasurementsofthesefaintclusters.Alongwithimprovedspectralresponseandcalibra-tions,theimprovedresolutionallowedustoidentifyandmaskoutcontaminatingpointsources.Tothisend,wecompareourmeasuredstothosereportedintheinitial160SDpaperofVikhlininetal.(1998),V98hereafter.Intheoriginalwork,V98wereunabletouseawideaperturetointegrateduetothelargestatisticaluncertaintyintroducedbytheROSATbackground.Instead,theyestimatedthefromthenormalizationofa-model(Cavaliere&Fusco-Femiano,1976),I(r;rc)=I0(1+r2=r2c)3+0:5:(2.1)Theyestimatedcoreradiibya=0.67modeltotheirsurfacebrightnessthen,theyextrapolatedtoobtainthebasedonthenormalizationandshapeoftheb-model.Theirreportedwasactually(f0:6+f0:7)=2,wheref0:6andf0:738Figure2.2ComparisonbetweenourmeasuredusingXMM-NewtonandthosereportedbyVikhlininetal.(1998)usingROSAT.ROSATwereadjustedtocorrespondtotheinner300h170kpcofthecluster,asdescribedinthetext.Thesolidlineistheidentityline,whiletheshadedbandindicatesagreementtowithin10%.39aretheobtainedassuming=0:6and=0:7,respectively.Fordirectcomparisonwiththeseresults,weintegratedcountsinsideaaperture.Inordertoavoidbiasingtheseresultsbyoursomewhatuncertainestimationofr2500,weadoptedametricapertureofradius300h170kpc.FortheequivalentweusedthemodelparametersfromV98toinfertheestimatedROSATinside300h170kpc.Theerrorsonthesewerekeptatthesamepercentastheoriginallyreportedvalues.DetailsofthisprocedurearegiveninAppendixA.ThecomparisonbetweenourresultsandV98isshowninFigure2.2.Ourmeasuredagreetowithin1˙withthemoofV98inallbutsixcases.ForRXJ0847.1+3449,includinganXMM-Newtonpointsourceblendedwiththeclus-tercausesthemeasuredtoagreewithintheircombined1˙errors.TomatchourmeasurementofRXJ0056.92740withthatofV98,weonlyneededtocenterourapertureonthesameposition.RXJ2146.0+0423,whichwetobeslightlylowerinthanallowedbyV98'suncertainty,matchesperfectlywhenweshifttotheV98coordinatesandexpandtheaperturetoincludeanearbyXMM-Newtonpointsource.Toaccountforourex-pandedaperture,werederivedanew,correctedV98tocompareinthiscase.Similarly,repositioningouraperturearoundRXJ0522.23625andusingalargeraperturebringsthetwomeasurementsintoagreement.Finally,RXJ0826.1+2625andRXJ2328.8+1453wereoriginallymeasuredatatpositionalfromV98(ˇ3700and4500,respectively).Inbothcases,itappearsasiftheROSATimagesblendedinnearbypointsources.ByrecenteringouraperturearoundtheV98coordinatesandexpandingtheregiontoincludetheneighboringobjects,weagreementbetweenthetwosetsofmeasurements.40Figure2.3DistributionofsetstoBCGpositionsmeasuredbyHoekstraetal.(2011)fromX-raycentroidmeasurementsusingXMM-Newton(thiswork,hashesrisingtotheright)andROSAT(Vikhlininetal.,1998,hashesloweringtotheright).Dataarebinnedtoincrementsof5arcseconds.WehavereproducedtheROSATX-rayestimatesfromV98anddemonstratedthatblendedpointsourcesandteraperturestheestimatesoftheseclustersoverandabovetheuncertaintybasedoncountingstatisticsandbackgroundsubtractionalone.2.4.2X-rayInTable2.1welistcoordinatesforeachclustertwice.ThecoordinatesfromHoekstraetal.(2011)aretheirbestestimateofthepositionofeachcluster'sBCG.ThenewcoordinatesareofanX-raycentroidperformedondatafromtheMOS1cameraaroundeachcluster's41X-rayemission.Centroidswerecomputedineiterationsofcentroidinganaperturewithradius1600,ofimagesbinnedto1.600perpixel.TwelveoftheX-ray-determinedpositionsarewithin500oftheBCGposition,andtheonlypositionmorethan1200fromtheBCGisforRXJ0826.1+2625,wheretheBCGidenmaybequestionable.Weplotourresults,alongwiththeusingX-raypositionsfromROSAT,inFigure2.3.TheseXMM-NewtonobservationsprovideatimprovementintheabilitytoproperlydetecttheclusterpositionovertheoriginalROSATdetectionpositions.2.4.3ScalingRelationsWeourmeasurementsofbolometricluminosity,temperature,andmassinsider2500totherelationlogYY0=logXX0+CX:(2.2)X0andY0arepivotvalues,whichwere1044ergs1,4keV,and1014Mforluminosity,temperature,andmass,respectively.Luminosityandmasswerecorrectedforredshiftevo-lutionbyincludingthefactorE(z);werethereforeofL/E(z)andME(z).Toextendthedynamicrangeofoursampleandtocompareourlowmasssamplewithahighermasssampleatsimilarredshift,wealsoincludeddatafromtheCanadianClusterComparisonProject(Hoekstraetal.,2012;Mahdavietal.,2013,hereafterCCCP).Thissampleof50galaxyclustersspansredshifts0.15<z<0.55,andallclusterswererequiredtohaveatemperaturekBTX>3keV.CCCPdatawasacquiredthroughtheonlinedatabase5.Inanerratum(Mahdavietal.,2014)thesedatahavebeenupdatedsinceoriginalpublicationto5http://sfstar.sfsu.edu/cccp42anerrorinthebolometricluminositycorrectionfactor.WethereforepresentalloftheclusterpropertiesusedforinTable2.6.Individualarediscussedbelow,buttheresultsaregiveninTable2.5.Fitsincludingdatainthisworkarelabeled\160SD,"whilethoseincludingCCCPdataaremarkedassuch.Exceptwherenoted,uncertaintiesinvalueswerederivedthrough50,000bootstrapresamplings.FitswereperformedusingtheWLSandBCESmethodsdescribedbyAkritas&Bershady(1996).WhereluminositywasservingastheXvariable,weusedtheWLSandBCES(YjX)methods,whichminimizedtheresidualsintheotherparameter.Conversely,whenluminositywastheYvariable,weusedtheBCES(XjY)method.Whenthemass-temperaturerelation,weusedtheBCESBisectorandOrthogonalmethods,whichconsiderstheresidualsinbothvariables.Toaccountforasymmetricerrorbars,weestimatedasingle,logarithmicerrorforavalueX+udtobe˙=0:43430:5(u+d)X:(2.3)Forclarity,whendescribingarelationbyEquation(2.2),wecallittheY-Xrelation,whereXistheindependentvariable.Ourwasoftheluminosity-massrelationwithinr2500.Whenthisrelation,wedidnotincludeRXJ0826.1+2625,asitsmasswasnotwelldetermined(asdiscussedinSection2.2).Wethisrelationshipwithoutassumingintrinsicscatter;theresult-ingbslopewas=0:4350:047.Thisresultshowsnotfromtheresultforthe50CCCPclustersalone,butitdoesnotagreewiththeresultfora43Table2.5.ScalingRelationsXYSampleLogSlopeLogInterceptBootstrappedNotesL/E(z)ME(z)CCCP+160SD0:3050:0420:1340:043NOWLS,˙log(MjL)=0:100L/E(z)ME(z)CCCP+160SD0:4350:0470:0390:049YESBCES(YjX)L/E(z)ME(z)CCCP0:2910:0750:1350:082YESWLS,˙log(MjL)=0:1370:028L/E(z)ME(z)CCCP0:3790:0810:0050:091YESBCES(YjX)L/E(z)ME(z)160SD1:020:170:1950:076YESBCES(YjX)ME(z)L/E(z)CCCP+160SD2:330:270:0790:111YESBCES(XjY)ME(z)L/E(z)CCCP2:780:730:0710:311YESBCES(XjY)ME(z)L/E(z)160SD1:010:2250:1860:066YESBCES(XjY)L/E(z)TCCCP+160SD0:2290:0160:0050:015YESWLS,˙log(TjL)=0:0730:009L/E(z)TCCCP+160SD0:2250:0160:0120:015YESBCES(YjX)L/E(z)TCCCP0:2570:0290:0260:029YESWLS,˙log(TjL)=0:0700:009L/E(z)TCCCP0:2610:0290:0280:028YESBCES(YjX)L/E(z)T160SD0:3000:0550:0520:030NOWLS,˙log(TjL)=0:066L/E(z)T160SD0:2930:0640:0630:039YESBCES(YjX)TL/E(z)CCCP+160SD4:470:330:0570:072YESBCES(XjY)TL/E(z)CCCP3:880:450:0980:100YESBCES(XjY)TL/E(z)160SD3:290:570:2250:090NOBCES(XjY)TME(z)CCCP+160SD1:880:210:0580:049YESBCESBisectorTME(z)CCCP+160SD1:930:240:0660:053YESBCESOrthogonalTME(z)CCCP1:650:240:0050:061YESBCESBisectorTME(z)CCCP1:800:330:0290:077YESBCESOrthogonalTME(z)160SD1:980:920:0960:100NOBCESBisectorTME(z)160SD1:790:960:1030:101NOBCESOrthogonalME(z)TCCCP+160SD0:5370:0590:0290:024YESBCESBisectorME(z)TCCCP+160SD0:5250:0650:0320:024YESBCESOrthogonalME(z)TCCCP0:6220:0970:0080:040YESBCESBisectorME(z)TCCCP0:5740:1110:0090:044YESBCESOrthogonalME(z)T160SD0:5060:2350:0490:066NOBCESBisectorME(z)T160SD0:5590:3000:0580:079NOBCESOrthogonal44Figure2.4Plotofweak-lensingmassMWLasafunctionofbolometricX-rayluminositywithinr2500.MassesandluminositieshavebeenrescaledbyE(z)toaccountfortherangeofredshiftcoveredbythesamples.Dataanalyzedinthisworkareshownascircles,whileclusterpropertiesfromtheCCCPareshownassquares.RXJ0826.1+2625wasnotincludedinthisOurbesttoEquation(2.2)fortheM-Lrelationisshownbythesolidline.Ourbestwhenincludingintrinsicscatterisshownbythedashedline.Botharetothecombinedsampleof160SDandCCCPclusters.45Table2.6:CCCPClusterPropertiesWithinr2500NameMassE(z)L/E(z)kBTRedshifth1701014Mh2701045ergs1keV3C2953:300:8600:780:016:430:350.464Abell00682:870:6450:960:027:250:340.255Abell0115N0:680:4600:470:014:840:100.197Abell0115S0:840:5300:320:015:600:240.197Abell02092:050:4300:970:017:140:340.206Abell02221:750:6200:230:014:350:270.207Abell0223S1:110:5300:230:015:550:180.207Abell02672:300:4800:760:016:900:250.231Abell03704:621:0300:940:027:600:460.375Abell03830:790:4500:700:014:240:060.187Abell05202:270:4700:960:018:190:210.199Abell05211:510:7800:530:016:000:350.253Abell05861:330:5300:830:025:700:370.171Abell06112:080:8000:940:026:360:380.288Abell06972:970:6701:910:0510:600:670.282Abell08513:730:5600:410:016:050:360.407Abell09593:650:7200:370:016:980:790.286Abell09631:410:4500:990:016:420:120.206Abell16895:220:7402:830:018:880:140.18346Table2.6(cont'd)NameMassE(z)L/E(z)kBTRedshifth1701014Mh2701045ergs1keVAbell1758E3:170:6000:890:027:780:370.279Abell1758W3:020:5500:690:028:210:530.279Abell17633:300:6001:090:027:590:230.223Abell18353:570:6003:580:017:040:070.253Abell19142:360:3602:110:039:410:160.171Abell19421:920:3700:210:014:870:280.224Abell21042:360:6000:830:016:140:230.153Abell21112:290:4800:570:026:630:570.229Abell21633:230:8203:590:0110:800:160.203Abell22043:460:6402:920:016:530:060.152Abell22182:600:6800:900:016:960:190.176Abell22193:160:7302:620:059:190:390.226Abell22590:750:3100:490:014:690:540.164Abell22614:310:6701:700:027:280:290.224Abell23903:350:5403:040:048:600:210.228Abell25373:770:6200:870:026:420:440.295CL0024.0+16524:150:9400:210:014:840:510.390MACSJ0717.5+37457:701:9803:150:0611:500:770.548MACSJ0913.7+40561:971:0501:420:036:350:180.44247Table2.6(cont'd)NameMassE(z)L/E(z)kBTRedshifth1701014Mh2701045ergs1keVMS0015.9+16096:071:2902:010:058:870:530.541MS0440.5+02041:360:6000:270:013:940:280.190MS0451.603052:330:8601:980:0610:200:930.550MS0906.5+11101:950:4100:530:015:590:230.174MS1008.112242:350:6200:540:026:520:510.301MS1231.3+15420:510:2700:160:014:980:260.233MS1358.1+62452:410:5700:800:016:340:290.328MS1455.0+22321:550:4001:440:014:580:060.258MS1512.4+36470:860:4400:320:013:270:160.372MS1621.5+26402:941:1800:450:024:960:640.426RXJ1347.511453:590:9807:300:1212:200:410.451RXJ1524.6+09571:290:8000:190:014:000:390.520onlyofthelow-masssamplepresentedhere.Wecautionthatthisdiscrepancyisnotnec-essarilyindicativeofabreakinthescalingrelation,forreasonswewilldiscussinSection2.5.Whenallowingforintrinsicscatter,thebvalueofis0:3050:042,withanintrin-sicscatterof˙log(MjL)=0:100.Figure2.4showsbothalongwiththeclusterproperties48forbothsamples.Foradirectcomparisonofthereducedscatter,wetheM-LrelationusingluminositiesfromtheoriginalworkbyHoekstraetal.(2011).Withthese,theintrinsicscatterwas˙log(MjL)=0:262.Nextwethetemperature-luminosityrelationwithinr2500,thistimeusingallnclustersstudiedhere.Wefoundthatthebestfortheentiresamplewas=0:2290:016withanintrinsicscatterof˙log(TjL)=0:0730:009,consistentwiththeforthetwoindividualsamples.ThisisshownalongwiththedatainFigure2.5.Whenwedidnotallowforintrinsicscatter,wefoundthebslopewasrelativelyunchanged,becoming=0:2250:016.Wealsoinvestigatedthescalingbetweenmassandtemperaturewithinr2500.Again,RXJ0826.1+2625wasexcludedfromthisForthecombinedsample,thebwiththeBCESBisectorwas=1:880:21,whichwasconsistentwithforthesub-samplesalone.ThisisshowninFigure2.6.Inaddition,weincludedatatakenfromSunetal.(2009).Massesfromthatstudyarenotbasedonweaklensingmeasurements,butwereinsteadde-rivedfromanassumptionofhydrostaticequilibrium.Thesedatawerenotincludedinourhowever.Inordertomoreeasilycompareourworktootherstudies,wealsotheinverseofthesethreerelations.UsingBCES(XjY),theL-MrelationfortheCCCP+160SDsam-pleis=2:330:27.Incontrast,forBCES(YjX),theinverseoftheM-Lrelationis1=2:30.OurBCES(YjX)ofL-Tis=4:470:33,whilethecorrespondingfromtheT-Lrelationis1=4:36.WhenT-M,thebestfromBCESBisectorwas49Figure2.5PlotofX-raytemperatureasafunctionofbolometricluminositywithinr2500.LuminositieshavebeenrescaledbyE(z)toaccountfortherangeofredshiftcoveredbythesamples.Dataanalyzedinthisworkareshownascircles,whileclusterpropertiesfromtheCCCPareshownassquares.OurbesttoEquation(2.2)fortheT-Lrelationisshownbythesolidline.50Figure2.6PlotofMasafunctionofX-raytemperaturewithinr2500.MasseshavebeenrescaledbyE(z)toaccountfortherangeofredshiftcoveredbythesamples.Dataanalyzedinthisworkareshownascircles,whileclusterpropertiesfromtheCCCPareshownassquares;botharederivedfromweaklensing.RXJ0826.1+2625wasnotincludedinthisWealsoincludeasampleofnearbygalaxygroupsfromSunetal.(2009)asdiamonds,wheremassesarederivedfromhydrostaticequilibrium.OurbesttoEquation(2.2)fortheM-TrelationfromtheclustersanalyzedinthisworkandfromtheCCCPisshownbythesolidline.OurbesttotheM-Trelationusingthepropertieswithinr2500ofthegroupsfromSunetal.isshownasadashedline.51=0:5370:059,whichagreeswiththeBCESBisectorofM-T,1=0:532.2.5Discussion2.5.1ComparisonwithPreviousX-rayObservationsWecomparedourresultstopreviouslypublishedindividualXMM-Newtonresultsforfourclusters(RXJ0110.3+1938,RXJ0847.1+3449,RXJ1117.4+0743,andRXJ1354.20221).Toinvestigatethewereplicatedtheanalysisofpreviousobservations,includingtheiraperturesizesandcosmology.Wewereabletoreasonablyreproducepreviousresults.Thediscrepanciesarisingfromsystematicssuchasinbackgroundchoicesorparticlebackgroundscreeningcriteriaaresmallerthanthestatisticaluncertainty.Wethatanyapparentbetweenourresultsfortheseclusterswithpreviousresultsarisebecauseofrencesinaperturesizes,andrarely,choiceofaperturecenters.ThedetailsofthiscomparisonarereportedinAppendixA.Ourmostobvioussourceofpossiblediscrepancywithpreviousworksisourchoiceofapertures,whichhavearadiusr2500motivatedbyweak-lensingestimatesfromHoekstraetal.(2011)thatwereunavailabletomostoftheotherstudies.AnotherpotentialsourceofX-raytemperaturediscrepancyisthechoiceofbinningspectraldata.Somepreviousworksbinnedspectraldatatoasfewas12countsperspectralbin.WeleaveourspectraunbinnedandwiththeC-statistic.Asthisworkisfocusingonfaintclusters,wearelimitedbylowphotoncounts.Ifdataarebinnedsuchthatonlyafewcountsareineachbin,eachbinwillhavenon-Gaussianbehavior.Sincethe˜2statisticisforGaussian-distributed52data,itwillnotbeavalidgstatisticinthiscase.Alternatively,datacanbebinned,butdoingsopotentiallydegradesspectralresolution.Alongwithproducingbetterforlowcounts(Nousek&Shue,1989;Tozzietal.,2006),useoftheC-statisticcanalsoavoidbiasesinthehigh-countregime(Humphreyetal.,2009).Useofentthermalmodelsforspectradidnotcausemajordeviationsinourresults.AswewereabletoreproducetheearlierresultswhilestillusinganAPECmodel,thisshouldnotthereforebiasourresultstly(seealsoBelsoleetal.,2005;Matsushitaetal.,2007).Wedemonstratedindetail(seeAppendixA)thatwecanrecoverresultsofpreviousworks,whichvtheirresultsandours.HoweverwecautionthatthechoiceofapertureandcenteratheestimateofL,T,andMforanycluster,andthatresultsfromtanalysescannotbeblindlycombined.2.5.2ComparisonwithOtherScalingRelationsWehavemeasuredscalingrelationsbetweenweaklensingmass,X-rayluminosity,andtem-peratureforasampleofclusterswithmassandluminosityaroundthecluster/groupbound-aryandatredshifts0:3<z<0:6.Asweusedweaklensingmassesandbolometricluminosi-tiesandbecauseweonlyinvestigatedX-raypropertieswithinr2500,noexactcomparisonsareavailableforourresults.However,wecancompareourresultstoothersimilarstudies,boththosefocusedonlocalgroupsandthosethatincludeclustersatredshiftssimilartowhatwasstudiedherebutmoremassivethanoursample.OurbestoftheM-Lrelationwithinr2500was,whenneglectingintrinsicscatter,53=0:4350:047.Hoekstraetal.(2011)thisrelationusingalmostthesameclustersstudiedhere,withROSATluminositiestakenfromtheROSATmeasurements,andahighermasssample,reporting=0:680:07.Otherworks(Maughan,2007;Ryketal.,2008;Eckmilleretal.,2011;Reichertetal.,2011)valuesintherange0:5..0:75,consis-tentwithbutsomewhatsteeperthanours.FortheL-Trelationwithinr2500,wefoundabestof=4:470:33,althoughthe160SDgroupsandtheCCCPclusterseachhadshallowerslopeswhenindependently.Pre-viousresults(Maughan,2007;Prattetal.,2009;Bruchetal.,2010;Eckmilleretal.,2011;Reichertetal.,2011;Nastasietal.,2014)havereportedslopesfrom2:5..4:5.Ourresults,particularlyforthetwosub-samplesindividually,areconsistentwiththisrange,albeitonthehighend.Inthiswork,wereportedthebestslopeoftheM-Trelationwithinr2500was=1:880:21.Previousworks(Sunetal.,2009;Eckmilleretal.,2011;Reichertetal.,2011;Kettulaetal.,2013)havereportedslopesintherange1:45..1:85.AswasthecasewiththeT-Lrelation,ourslopeforthecombinedsampleisslightlyhigherthanthisrange,butthegroupandclustersamples,whenindependently,arebothinagreementwiththesestudies.Whilecomparingourscalingrelationshipstoothersisworthwhile,wecautionthatthereareahandfulofissuesthatmakedirectcomparisonproblematic.Asmentionedearlierinthisdiscussion,otherworksusedtradiiwithinwhichtomeasureclusterproperties.Ourchoiceofr2500wasmotivatedbytherequirementsimposedfromourweaklensingmasses,butitmeansweareanalyzingX-raypropertiesindtaperturesfromotherstudies.54Anotherissuethatariseswhencomparingtootherstudiesistheofluminosity.Inthiswork,weusedbolometricluminosities.However,inthethreeworksthatlookedatgroupsthatwediscussinthissection(Ryketal.,2008;Hoekstraetal.,2011;Eckmilleretal.,2011),allscalingrelationswithaluminosityonlywithintheenergybandof0.1-2.4keV.TheimportanceofenergybandswasshownbyMarkevitch(1998),whofoundthatwhenswitchingfromluminositieswithin0.1-2.4keVtobolometricluminositesthemeasuredslopeoftheL-Trelationsteepenedfrom=2:100:24to=2:640:27.Suchalargechangeinthemeansthatweshouldbecarefulcomparingscalingrelationsforluminositiesderivedfromtenergybands.AsatestofthiswetheM-LandT-Lrelationsusingluminositiesmeasuredinthe0.1-2.4keVenergybandforthe160SDclusters.Thepowerlawindicesincreasedwhenusingtheenergylimitedluminositiesfrom1:020:17to=1:190:22andfrom0:2930:064to=0:3340:101forM-LandT-L,respectively.The160SDsampleherehastoosmalladynamicalrangetobeseriouslyconsideredforascalingrelation,buttheofchoosingtobolometricluminositiesoverband-limitedluminositiesisclear.Also,whileoursampleisasubsetofarandomlyselectedsurvey,itisoriginallybasedonX-rayselectedclusters.Hicksetal.(2013)suggestthatX-rayselectionpreferentiallypickscentrallyconcentratedsystems;thesesystemspopulatethehighLXsideoftheT-Lrelation.Similarly,sinceourdataweredrawnfromthefaintendofasample,wewouldexpectpreferentiallyover-luminousclustersfortheirmasstobeselected.552.5.3ComparisontoLow-RedshiftGroupsOneoftheissueswithcomparingthebetweenthegroupsexaminedinthispaperandthoseatlowredshiftistheubiquityofmassesderivedfromhydrostaticequilibrium.Hy-drostaticmassesmaysomewhatunderestimatethemassofgalaxyclusterswhencomparedtoweaklensingmeasurements(Arnaudetal.,2007;Mahdavietal.,2008,2013).However,inordertoallowacomparisonwithworkonlowredshiftgroupsandpoorclustersusinghydrostaticmasses,wemaketheassumptionthatbothmassestimatesareidentical.LookingatFigure2.6,wecanseethatourmoderateredshiftclusters(z=0:444)arealmostallhotterand/orlessmassivethanwhatwouldbepredictedbythelowerredshiftscalingrelationsforgroupspresentedinSunetal.(2009)(z=0:042),althoughelow-temperatureclustersagreeverywell.IfwetestthehypothesiswhetherourdataarebytheSun2009relationshipbetweenmassandtemperature,wea˜2valueof19.09for14clusters(p=0:089).Therefore,towithin2˙weseenobetweenoursampleandthelow-redshiftsample.IfwelimitthisanalysistoonlythoseclusterswithtemperaturekT<4keV,ourvalueof˜2is3.15for9clusters(p=0:87).IfwedonotscalethemassbyE(z),˜2becomes29.53for14clusters(p=0:0033).Thisisjustbelow3˙,constitutingveryweakevidencefortheexpectedself-similarevolutioninthetemperature-massrelationforgroups.562.5.4ComparisonbetweenGroupsandClustersAdirectcomparisonbetweentheCCCPsampleandoursample,whichacomparisonbetweenlow-massandhigh-massclustersatasimilarredshiftrange,isduetothelimitednumberofclustersinbothsets.SotoprovidesomequanofwhetherthetwopopulationsweutilizeFisher'sexacttest,whichlooksathowtwopropertiesaredistributedintwopopulations.Inthiscase,welookathowoursampleandtheCCCPsamplecomparetothescalingrelations.WechoosetouseFisher'sexacttestduetohowfewobjectswehave;inthisdomain,Fisher'sexacttestisthebest,ifnottheonly,testtouse(Wall&Jenkins,2012).Forbothsamples,wecounthowmanyclusterslieabovethelinesofbestforeachscalingrelationandhowmanyliebelow.Ournullhypothesisisthatthesamplesaresimilarandsothenumberofclustersabovetherelationshouldequalthenumberbelow,statisti-cally.Wecomputep-valuesfortheT-L,M-L,andM-Trelationsofp=0:13,p=0:19,andp=0:19,respectively.Wethereforecannotrejectthehypothesisthatgroupsandclustersatintermediateredshiftbehaveidenticallywithrespecttothescalingrelationsderivedinthiswork,soourmeasurementsareconsistentwiththehypothesisthatz˘0.3-0.5X-rayselectedclustersandgroups/poorclustersfollowsimilarX-rayscalinglaws.2.6ConclusionsWehavepresentednewandrevisedX-raypropertiesforasampleof15galaxyclustersorig-inallydrawnfromarandomsampleofthe160SquareDegreeSurvey.Coveringarangeof57redshiftsfrom0:3<z<0:6andlimitedinmasstoM2500.21015M,ournewX-raydatatogetherwithpreviouslypublishedHSTweaklensingmeasurementsprobealargely-unexploredparameterspaceinclustermassandredshift.Byusingarigorousanalysistomatchclusterpropertiesmeasuredwithinthesameradiusasexistingweak-lensingmasses,weinvestigatescalingrelationsbetweenmass,luminosity,andtemperature.Ourprimaryconclusionsaresummarizedbelow.1.WemeasurefainterthanreportedfromearlierROSATmeasurements(Vikhlininetal.,1998)foreoftheclustersstudiedhere(RXJ0522.23625,RXJ0826.1+2625,RXJ0847.1+3449,RXJ2146.0+0423,RXJ2328.8+1453).Duetoacombinationoffaintersourcesblendingintotheextendedclusterlightandmultiplesourcesblendingintoone,wealsofoundthatreportedX-raypositionsfortheseclusterswerenotaccurate.Duetotheoriginalpositionalinaccuracy,RXJ0056.92740wasoriginallyreportedtobefainterthanwemeasured.Useofdetectionsnearthethresholdofobjectssubjecttoblend-ingbecauseoftheangularresolution,suchasROSATclustersurveys,canthereforeleadtoerrorsinbothpositionandthatcanbelargerthanthequotedstatisticaluncertainty.2.Insider2500,forthemassandredshiftrangestudiedhere,thefourteenclusterswithreasonablemassmeasurementsand50clustersfromtheCCCParebestbytherelationME(z)1014M=100:040:05 LE(z)11044ergs1!0:440:05:(2.4)Whenweallowforintrinsicscatter,theexponentofthebestbecomes0:310:04.Ourresultsindicateneitherabreakinthescalingrelationamonggroupsnorincreasedscatter58atlowmass.3.Usinguncontaminatedluminositymeasurementsandr2500valuesfromweaklensing,theintrinsicscatterintheL-Mrelationreducedfrom˙log(MjL)=0:26to˙log(MjL)=0:10.4.Similarly,whendeterminingthescalingrelationbetweenluminosityandtemperaturewithinr2500,wedthatkBT4keV=100:0050:015 LE(z)11044ergs1!0:230:02:(2.5)Weasmallintrinsicscatterof˙log(TjL)=0:070:01.Whenthehigh-andlow-masssamplesareseparately,the50clustersfromtheCCCPsampleandthe15clustersfromthe160SDsamplescalingrelationseachhavesteeperslopes,0:260:03and0:300:06,respectively.Again,wenoevidenceofabreakinthisrelationamonggroups.5.Forscalingbetweenweak-lensingmassesandX-raytemperatureswithinr2500,thecombinedsampleof14clustersfromthisworkwithreasonablemassmeasurementsand50fromtheCCCParebestbytherelationME(z)1014M=100:060:05kBT4keV1:90:2:(2.6)Whenhighandlowmasssubsamplesindependently,theslopebecomes1:70:2and1:81:0,respectively.Theseresultsagreewithotherresultsforbothnearbygroupsand59intermediate-redshiftclusters,alongwiththeself-similarpredictionthatM/T3=2.6.Tothestatisticallimitsofourdata,theintermediateredshiftgroupsarewithin2˙oftheM-Trelationextrapolatedfromalow-redshiftgroupsamplefromSunetal.(2009).Withoutself-similarevolution,thereisadeviationjustbelowthelevelof3˙,indicatingaweakstatisticalpreferencefortheexpectedself-similarevolution.TheauthorswishtothankSethBruchforhisworkplanningthisproject.MeganDonahueandThomasConnoracknowledgepartialsupportfromaNASAADAPawardNNX11AJ60G.AnidishehMahdaviacknowledgessupportfromNASAgrantNNX12AE45G.ThisworkisbasedonobservationsobtainedwithXMM-Newton,anESAsciencemissionwithinstrumentsandcontributionsdirectlyfundedbyESAMemberStatesandNASA.60Chapter3OptimizedPhotometryofClusterGalaxiesinCLASHWepresentanewmethodformeasuringthephotometryofobjectsaroundgalaxyclusters,employinganovelmotechniqueforbothdetectionandphotometry.Withthis,weareabletoinvestigatethegalaxypopulationsinsidethe25massiveclustersobservedbytheClusterLensingandSupernovasurveywithHubble(CLASH).Weproducemulti-wavelengthcatalogscovering16bandpassesfromultraviolet(˘2360A)toinfrared(˘1:54m)includ-ingphotometricredshifts.Acomparisonwithspectroscopicvaluesfromtheliteraturethat˘82%ofourreportedphotometricredshiftsliewithinjzpzsj/(1+zs)<0:05.Thisimprovementinredshiftaccuracy,incombinationwithadetectionschemedesignedtomax-imizepurity,yieldsasubstantialupgradeinclustermemberidenoverthepreviousCLASHgalaxycatalog.Weconsistencybetweenthegalaxymagnitudes,colors,andphotometricredshiftsobtainedhereandfrompreviousstudies,includingadeeperobserva-tionofoneoftheCLASHclusters.Evaluatingtheluminosityfunctionsfortheseclusters,wethatweareabletoobservegalaxiesdowntoM˘M+5,andthevaluesofM*wederiveareconsistentwiththatexpectedfrompublishedclustergalaxyluminosityfunctions.Theseclustersfollowaconsistenttrendinmass-richnessthatagreeswithlow-massclusterobservations.Wemeasureluminosityfunctionsfortheseclusters,whichweusetoderive61totalluminosity,and,fromthat,stellarmasses.Westellarmassfractionsof1:80:7%ofthetotalhalomass,inagreementwithpreviousstudies.NotonlywillthiscatalogenablenewstudiesofthepropertiesofCLASHclusters,butthephotometrictechniquesweusesetthestageforfuturesurveysofgalaxyclusters.3.1IntroductionGalaxyclustersarethelargestvirializedstructuresintheUniverse,althoughmostofthatmassisindarkmatterandhotintraclustergas.Galaxiesthemselvesonlycontributeasmall(ˇ1%)amounttotheclustermassbudget(e.g.Gonzalezetal.,2013).Despitethisfact,individualgalaxiesplayacriticalroleinunderstandingthenatureofclustergrowthandformationofmassivegalaxiesandofgalaxiesinadenseenvironment.Notonlyareindivid-ualgalaxiestracerparticlesforthegravitationalpotentialoftheirhosts,theirevolutionissensitivetotheconditionsoftheirenvironment(Ceruloetal.,2016).Havingformedoutofthesameoverdensityastheclusteritself(seeKravtsov&Borgani,2012,forareview),theinitialconditionsofclustergalaxiesareprobesoftheirhost'sbegin-nings(Voit,2005).Asgalaxiesaccreteontothecluster,theysamplethephysicalpropertiesofinnerandouterregionsofthesystem.Variationsbetweenmore-andless-massivegalax-iescanbeusedtoinvestigatetheenergeticscaleofeventssuchasactivegalacticnucleus(AGN)feedbackandsupernovae(e.g.,Larson,1974;Arimoto&Yoshii,1987;Matteucci&Tornambe,1987).Detailedstudiesofclustermembersaremostlyconductedatlowredshift(e.g.,Edwards62&Fadda,2011;Liuetal.,2011;Zhangetal.,2011;Tianetal.,2012;Ferrareseetal.,2016),astheseclustersarebrighterandmoreaccessibletoground-basedobservations.Distantclusterstheabilitytostudytheevolutionofclusterpopulations,however,byprovidingtemporalconstraints(e.g.,Hiltonetal.,2009;Papovichetal.,2010;Foltzetal.,2015).Duetotheyinobservingtheseclusters,previousworkshavehadlimitedspatialresolu-tion,coverage,and/ordepth(e.g.Muzzinetal.,2013).Inparticular,thestudyofgalaxyclusterluminosityfunctionsrequiresprecisephotome-tryofredshiftedclustermemberstodrawmeaningfulconclusions.Anumberofworkshaveobservedasteepeningofthefaint-endslope(Rudnicketal.,2009;Lanetal.,2016),butevidenceforevolutionisinconclusive(Crawfordetal.,2009;Luetal.,2009).Eveninsideasinglecluster,theparametersoftheluminosityfunctionaresensitivetothegalaxiesincluded(Agullietal.,2016),meaningthataccuratemembershipdeterminationisnecessarytodrawmeaningfulconclusionsaboutanyslopeevolution.Inthiswork,wepresentaphotometriccatalogof25massivegalaxyclusters,usingmode-basedtoselectandphotometergalaxiesdowntoMM˘5(whereM*isthecharacteristicmagnitudeofeachcluster'sluminosityfunction)across16usingtheHubbleSpaceTelescope(HST).WeverifytheaccuracyoftheseresultswithcheckstospectroscopicmeasurementsandanoverlapwithaclusterintheHubbleFrontierFields.Finally,wepresenttotheobservedluminosityfunctionsforthese25clustersinrestframeibandpass.Throughoutthiswork,weassumeacosmology,withM=0:3,=0:7,andH0=70kms1Mpc1.633.1.1StatisticalBackgroundLightEstimatorsObtainingaccuratephotometry{particularlycolorphotometry{forgalaxiesinclustersisalongstandingproblem(e.gButcher&Oemler,1978).Clustersarewithintraclusterlight(ICL,Vomez,1999;Mihosetal.,2005;DeMaioetal.,2015),whichcanimpacttheobservedcolorsofgalaxies(Zibettietal.,2005;DaRocha&MendesdeOliveira,2005;Williamsetal.,2007;Rudicketal.,2010).Inparticular,itistodisentanglethecontributionsofICLfromgalaxyemissionnearthecenterofclusters(Kricketal.,2006).AlongwiththeICL,theestimateoflightfromagivengalaxymaybebyprojectedoverlapsbetweengalaxiesandfore-andbackgroundcontamination.Whilepreviousworkhasmodeledandsubtractedthesurfacebrightnessofmajorgalaxiessuchasthebrightestclustergalaxy(BCG,Postmanetal.,2012a),thisresultdoesnotscalewelltomeasurementsofthehundredsofobjectsvisibleeveninthenarrowWFC3ofview.Andanymethodtoaccountforlightcontaminationneedstobedependent{ICL,galaxybrightness,andPSFsizeallchangewithcolor.Here,wepresentatechniquetodeterminebackgroundpropertiesbystatisticallymodelingthelightofnearbypixels.Oneofthefundamentalassumptionsofthisworkisthat,forapixelcontainingthelightfromagalaxy,theobservedinthatpixelisthesumoflightfromthegalaxyandfromthebackgroundlightdrawnfromsomeunknowndistribution.Lackingacompleteunderstandingofthebackgroundlightduetothelimitationsofourtelescope'sopticsandtheobserva-tiontime,ourbestsolutionistomodelthebackgroundlightdistributionfromnearbypixels.Therearethreechallengesthatmustbecontendedwithtoaccuratelydescribetheback-64ground:determininganominalmeasureoftheexpectedvalueofthebackgroundlight,determiningtherangeofthatdistribution,andperformingthischaracterizationwithalim-itedsampleofpixels,someofwhichmaybeoutliersfromaseparatedistribution(suchasfromthewingsofanearbygalaxy).Theeasieststatistictocomputefromabackgroundsample,themean,isbiasedbyoutliers.Acommonchoiceistoinsteadusethemedian,whichisswayedlessbyskew.However,themedianisstillsensitivetooutliers;additionally,itwillalwaysbethevalueofoneofthemeasurementsinthebackgroundsample(orthemidpointoftwovalueswhenthereisanevennumberofsamplingpoints),whichintroducesanextraleveloferrorinthebackgroundmeasurement.Toavoidtheseissues,weinsteadconsiderthemode.Foragivenprobabilitydistribution,wethemodeasthepointatwhichthefre-quencyisgreatest.Forawell-sampleddistribution,thiswillconvergewiththeclassicalofthemode,whichisthesamplevaluethatappearsmostoften.Themodeisextremelyusefulasabackgroundmeasureas,forasamplingofbackgroundpixelswhereintwodistinctly-resolvedbackgrounddistributionscanbedetected,themodewillthecentralvalueofthedominantbackgrounddistribution.Inthecontextofthiswork,weusetwodeterminationsofthemode:aless-rigorousyetmorecomputationallytestima-tortodetectgalaxiesandamorerobustyetcomputationallyintensivemethodforaccuratemeasurementsofandratios.Wedescribetheformer.Pearson(1895)notedthatthemodeofadistributioncanbeapproximatedthroughtherelationM=3m2(3.1)65whereMisthemode,misthemedian,andisthemean.Thisrelation,whichwewillrefertoasthePearsonapproximationinthiswork,hasanimportantcaveat:thisisanempirically-derivedrelation,anditdoesnotalwaysthecorrectmode,particularlyinthecaseofcomplexbackgrounds.Indeed,inthecaseofabackgroundregioncontaininglightfromtwodistributions(suchasforaregionconsistingmostlyofICL,butwithasmallsub-regioncontaininge.g.theemissionofanearbygalaxy),thisexpressionwillnotgiveanaccuraterepresentationofthemode.Duetotheseconcerns,wewillusethismethodforcomputationalexpediencyinestimatingthebackgroundforpurposesofidentanddetectionofsources,butnotforestimation.Sinceoursciencedoesnotdependonteas-ingoutdetectionsofthefaintest,smallestbackgroundsources,smallerrorsinthemodeforindividualpixelsdonotdetectionandsourcedeforourscienpurposeshere.Oneadditionalinputtoconsiderwhendeterminingthebackgroundisthecontributionofmeasurementuncertainty.Asamplepointwithuncertainuxshouldnotbeweightedashighlyasapointwithmoreaccuracy,yetitshouldalsosupportbackgrounddeterminationoveralargerrange.Toaccountforalloftheseissues,weinsteadcomputethemodeusingakerneldensityestimationtoderiveaccuratecolorswithindapertures.Eachbackgroundpixelisbytwovalues:fiand˙i,theanduncertainty,respectively.ByconvolvingtheineachpixelwithaGaussiankernelofwidth˙i,wecreateaprobabilitydistributionfortheentireofthebackgroundregion.Themodeis66thenfoundasthepeakofthisdistribution,whichisgivenbyP(x)=Xi1˙iexp(xfi)2=(2˙2i):(3.2)Tothemaximumofthisfunctioninacomputationallyexpedientmanneroveralargenumberofpoints,weidentifythezeroesofitsderivative,givenbydP(x)=dx=Xi(xfi)˙3iexp(xfi)2=(2˙2i):(3.3)Afulldescriptionoftheapplicationofthistechniqueisprovidedbelow.Duetothelimitsofcomputational,weonlyemploythemoreaccuratekerneldensityestimationusingEquations3.2and3.3formeasuring3.2DataSetImagingdatainthisworkcomesfromtheClusterLensingandSupernovasurveywithHub-ble(CLASH,Postmanetal.,2012b).ThisHSTMulti-cycleTreasuryProgramimaged25galaxyclusterin16coveringtheultraviolettotheinfrared.Withanaverageof20orbitspercluster,theHSTcomponentofCLASHprovidesuswithanunprecedentedlookintotheenvironmentsofgalaxyclusters.Tocreatethiscatalog,weutilizedallsixteenforeachcluster;however,duetoofviewbetweenHSTinstruments,manyobjectsawayfromtheclustercenterlackIRcoverage.HSTusedinthisworkhavethenamingconventionthataofcentralwavelengthnnnislabeledaseither\FNNNW"or"FNNNLP,"dependingonifitisawideorlong-passrespectively(long-passare67slightlybroaderintheirspectralcoverage;seeFigure1.2fortheusedinthiswork).Forcentralwavelengthslongerthan1micron,nnnislistedinm;below1micron,nnnisinnm(forthesennnisalwaysgreaterthan200).ForsomeclusterswealsousedarchivalF555Wimages.ObservationsarereducedbytheMosaicDrizzlepipeline(Koekemoeretal.2011,basedonFruchter&Hook2002;Koekemoeretal.2003).ACS/WFCdataarecorrectedforbiasstripingandchargetransferdegradation(Anderson&Bedin,2010).Thepipelinethenalignseveryvisitandeveryontothesamegrid,providingastrometricaccuracyontheorderofonemilliarcsecond.Badpixelsandcosmicraysarerejected,which,alongwithreadnoise,accumulateddarkcurrent,andstatisticaluncertaintyineachpixel,areusedtoproduceaninversevariancemapforeachandcluster.TheoutputimagesavailableinthepublicCLASHdatadistributionarebinnedtoseveralscales,butthroughoutthisworkweonlyusethoseimagesbinnedto0.065"perpixel.PhotometricpropertiesoftheseobservationsareprovidedinTableB.1(ACS)andB.2(WFC3)inAppendixB.Aseachprocessedimagewasreducedtoacountrate,exposuretimesdoubleasgainvalues.ZeropointsareinABMagnitudes.AssumedGalacticextinc-tionvaluesaretakenfromtheNASA/IPACExtragalacticDatabase(NED)1,whichusestheSc&Finkbeiner(2011)recalibrationoftheSchlegeletal.(1998)infrared-baseddustmapsutilizingaFitzpatrick(1999)reddeninglawwithRv=3:1.1NEDisoperatedbytheJetPropulsionLaboratory,CaliforniaInstituteofTechnology,undercontractwiththeNationalAeronauticsandSpaceAdministration.68Figure3.1ThecentralregionofAbell383aftersubtractingalocalbackgroundfoundusingthePearsonapproximationforthemode.Backgroundregionsusedare:left:4pixels(0.2600);middle:16pixels(1.0400);andright:128pixels(8.3200).Largerstructuresarevisiblewhenalargerbackgroundradiusisused,whilesmallerobjectsaremoreclearlyresolvedwithamorelocalizedbackgroundregion.3.2.1DetectionImagesTofacilitatethedetectionofsmallerobjectsembeddedinmassivestructure,wecreatedspe-cialdetectionimagesforeachclusterandwiththeexceptionofthefourUVISForeachpixelineachimage,wesubtractedthemodeofnearbypixelsinasurroundingregion.Forspeedofprocessing,weusedthePearsonapproximationofthemode.Wegen-erated7background-subtractedimages,withbackgroundregionslogarithmicallyspacedinsizesfrom4to256pixels.ThreeoftheseforAbell383areshowninFigure3.1.Asthistechniquedestroysstructurethatdoesnotvarywithinthebox,arangeofscalesrevealsbothlargeandsmallgalaxies.Oneissuethathampersdetectionofobjectsinclusterissourceconfusion,wherebytwonearbygalaxiesaredetectedasone,creatingapseudoobjectthatincludesbothofthembutisconcentricwithneither.Tomitigatethisissue,weproducedaseparatesuiteofpaired-scalebackground-subtractedimages;here,background-subtractedimagesproducedateachbackgroundscaleweresubtractedfromthebackground-subtractedimage69withthenext-smallestbackgroundscale(e.g.,theimagewithan8pixelbackgroundscalewassubtractedfromtheimagewitha16pixelbackgroundscale).Thisstrategyremovessmallersourcesfromthedetectionareasoflargergalaxies.Ourmethodofdeterminingthemodeispotentiallybiasedbyitsuseofthemedianandthemean,bothofwhichcanbeskewedbyoutliers.Indeed,somenon-physicalblottingintheinnermostregionsofgalaxiesisseenontheleftpanelofFigure3.1.Here,backgroundestimationislimitedbythecomplexityofmorerobustmodedeterminants;togeneratesevenscalesofbackground-subtractedimagesfor12foreachof25galaxyclusters,aroot-methodformode-basedestimationwouldhavebeenprohibitivelyexpensiveintermsofcomputertime.Becauseofthispotentialsystematicuncertainty,however,thesedetectionimagesareusedonlyfordetectionandnotforphotometry.3.2.2SourceDetectionTodetectobjects,weranSourceExtractor(Bertin&Arnouts,1996)onallsixpaired-scalebackground-subtractedimagesandthesmallestscale(4pixels)background-subtractedimageforeachnon-UVISforeachcluster.Parametersusedforeachdetec-tionaregiveninTable3.1.WeusedanRMSmapbasedontheweightmapproducedbyMosaicDrizzleforeachandclustercombination.Foreachdetection,SourceExtractoroutputgeometricpropertiesofthedetectionellipse,spWCSandpixelcoordinates,semi-majorand-minoraxes,positionangle,andtheKRONRADIUS2.2TheKronradius(Kron,1980)isaradiusselectedtocapturemorethan90%ofagalaxy'sx.SeeGraham&Driver(2005)foradiscussionofitsusageinSourceExtractor.70Table3.1.SourceExtractorDetectionParametersDetectionaCLEANPARAMbDEBLENDMINCONTbDEBLENDNTHRESHbDETECTMINAREAbMax(pix)(pix)0040.20.4050150080040.20.2060160.50160080.30.1060180.80320160.40.1060201.50640320.50.1060201.51280640.60.1060201.52561280.20.1060201.5Stars0.40.106020aNumericaldetectionimagesareeitherthebackgroundsizeofmodering(004)orthebackgoundsizesofthesubtractedimages(e.g.,008-004)bCLEANPARAMistheofcleaningartifactsofbrightsourcesfromthedetectionlist;alowervalueofCLEANPARAMmoreextendedstructuretobrightsources,resultinginamoreaggressivecleaning.DEBLENDMINCONTandDEBLENDNTHRESHdeterminewhetherSourceExtractorseparatesdetectionsintomul-tipleobjects.ForDEBLENDNTHRESHlogarithmically-spacedbins,objectsaredeblendedintotwoobjectsiftheybothhaveDEBLENDMINCONToftheoftheircombinedmeasure.DETECTMINAREAistheminimumrequirednumberofpixelsabovethedetectionthresholdforagalaxytobedetectedbySourceExtractor.Wecombinedthedetectionsacrosseachindividualbyworkingfromthelargerback-groundregionimagesandworkingtothesmallest.Foreveryobjectdetectedinonecatalog,wecheckedtoseeiftherewasamatchinthenext-smallestdetectioncatalogwithinasmallspinTable3.1.Thosethathadmatches,aswellasunmatchedobjectsfromthesmallercatalog,werepassedontothenextstep.Forallbutthelastimageineachtheactualdetectionwasperformedonasubtractionimage;becauseofthis,ourtechniquehastheresultofdetectingthefullextentofallbuttheverylargestgalaxiesandpropagatingthemdowntothesmall-backgroundimages.Aftercollectingallthedetectionsfromeachintoonecatalog,wethencreatedamas-tersourcelistforeachclusterbasedonthemulti-wavelengthdetectionsuite.Master-listcreationwasdoneinasimilarfashion:westartedwiththesourcesdetectedinF160Wand71workedbluewardcombiningobjectswithcenterswithin2pixelsofeachother.Asmoredetectionsanobject,thecenterwastakenasarunningaverageofthosecoordinates.AfterworkingthroughallwereducedthegeometricparametersofeachobjecttothoseofadetectionofthatobjectinoneThewaschosentobewherethesumofsemi-majorandsemi-minoraxeswasatitsmedianforthatobject(foranevennumberofdetections,theobjectwiththelargerofthetwovaluesstraddlingthemedianwasused).WetrimmedthiscatalogtoonlythoseobjectsdetectedinatleastfourToavoiddetectingonspikesfromstars,wealsoonlyincludedthoseobjectswithsemi-majoraxisnomorethan8timesthelengthofthesemi-minoraxisorwithasemi-minoraxisofatleast5pixels.Toremovestarsfromourcatalog,weranSourceExtractorontheoriginalimagesforeachusingtheparametersgiveninTable3.1.Detectionsineachwerecombinedinthesamemannerasbefore;toonlyincludestars,weexcludedanyobjectwithaCLASSSTARvaluebelow0.9.Wematchedthisstarcatalogwithourpreviousdetectioncatalog,andthoseobjectsincludedinbothweremarkedasstars.Wegeneratedamaskapertureusingthegeometricparametersfromouroriginaldetectionimageforeachstar.Aftercreatingthemasterdetectionimagesforeachcluster,weinspectedthembyhand.Wevtheaccuracyofourstarmasks,reclassifyingeasily-idenobjectsthatourpipelinehadidenasstars.Toensurerepeatability,weprovidethecoordinatesandradiiofthestarmasksusedinthisworkwithmaskradiiofr>200inTableB.3.Second,weidenanycatastrophicerrorsinourdetections;theseconsistedofdoubledetectionsofthesameobjectorofover-detectionofspiralgalaxies,particularlyofspiralarms.Thislast72Figure3.2AportionoftheMACSJ0717seeninF125W(red),F814W(green),andF555W(blue).Detectedobjectsareoutlinedinwhiteellipsescorrespondingtotheregionusedforphotometry.Alsoshownareobjectsasstarsinthiswork,whicharemarkedbyblueellipses.Thisimageisapproximately4500wide.73stepwasontheorderofahandfulofsourcesexcisedforeachcluster.ThedetectionregionsforasectionofMACSJ0717areshowninFigure3.2.WhilethistechniquewassuccessfulindetectinggalaxiesofallsizesacrosstheCLASHithastwocharacteristicsthatneedtobeconsideredbeforeapplyingittofutureworks.AscanbeseeninFigure3.2,largegalaxiesarenotdetectedtotheirfullextent;thisisnotice-ableinthisworkduetothecombinationofIRandopticalimaging.Additionally,duetothistechnique'sabilitytodetectsmallstructureembeddedinlargergalaxies,low-redshiftspiralgalaxieswithlargeangularsizecanbeover-dividedintonon-physicalregions.Therefore,tousethesemeasurementstoestimatethetotalamountoflightfromlargergalaxiesortostudyresolvedspiralsinthisadditionalcarefulworkisnecessary.3.3PhotometryForeachweworkedthrougheachdetectedgalaxy,beginningwiththesmallestandworkingtothelargest(asrankedbysemi-majoraxis).Eachgalaxywasphotometeredonapixel-by-pixelbasis,startingfromtheouteredgesandworkingin.Backgroundswerefoundlocally,and,oncephotometered,pixelswerereplacedwiththemeasuredoftheirback-grounds.Notethatforasmallgalaxybeingphotometeredagainsttheprojectedlightfromalargergalaxy,thisprocedurereplacesthesmallergalaxy'simagewithlightestimatesthataredominatedbythelargergalaxy.ThisprocessisshownschematicallyinFigure3.3andexplainedbelow.74Figure3.3Aschematicrepresentationofthephotometrytechnique.Ontheleft,thegalaxyofinterestisshowninred,withasuperimposedgridrepresentingthepixelsoftheimage.Startingwithapixelontheoutsideofthegalaxy{markedhereinred{weidentifyacircularbackgroundregion.Pixelscontaininggalaxylight(blue)arerejected,whilethosewithonlybackground(yellow)createourbackgroundsample.Inthemiddleframe,weshowthedis-tributionofanduncertaintiesforthosepixels.ByconvolvingeachmeasurementwithaGaussiankernel(sizedaccordingtotheuncertaintyofeachpoint'sandsum-ming,wecreateahistogramofvalues,suchasshownontheright.Thepeakofthatdistributionisconsideredthemode;thewidthofthebackgrounddistributionisfoundbytracingdownfromthepeakuntilreachingavaluewithafrequencyofˇ0:608timesthepeakfrequency.Whenphotometeringeachgalaxy,wecreateanellipticalaperturebasedontheSourceExtractordetectionparameters.Thisregionisblocky;pixelsareeitherintheapertureoroutofit,withnopartialassociations.Wethenassignanorderofphotometrybytakingaone-pixel-wideannuluswithouterradiusequaltothegalaxy'ssemi-majoraxis,andallofthegalaxypixelsinsidethatring.Weshrinktheannularradiuspixel-by-pixel,notingtheorderofgalaxypixelstofallwithinit,untilwehavereachedthecenter-mostpixel.Wethenphotometerthegalaxyfollowingthatorder.Tomeasuretheofapixel,wemustcomputethebackgroundvalue.Weconsideracircularaperturearoundthatpixel,withradiusequalto1:5b,wherebisthesemi-minoraxisofthegalaxy.Thisvalueisconstrainedtoliewithin3and12pixels(0:19500and0:7800,respectively);theformertoensureenoughbackgroundpixelscanbefoundandthelattertokeepthebackgroundlocaltothegalaxy.Weexcludefromthisapertureanypixels75containedwithinthegalaxyitselfthathavenotyetbeenphotometered.Fortheremainingpixels,wepasstheirmeasuredanduncertaintiestoourbackgroundmeasuringroutine.ThisroutineconvolveseachmeasurementwithaGaussiankernelthathasastandarddeviationgivenbythatmeasurement'suncertainty(initiallydrawnfromthevariancemapoftheimage,butincreasedforpixelsthathavealreadyhadabackgroundreplacementperformed).Thesedistributionsarethensummedtocreateasingleprobabilityfrequencycurveforthebackgroundx(asgiveninEquation3.2).Thenominallocationofthebackgroundintensityisdeterminedbythepeakofthisdistribution;todothis,weemployarootonthederivative(giveninEquation3.3)toallmaxima.Asthesedistributionscanbemulti-modal,itisimportanttoallmaxima.Wethereforestepthroughtheorderedrangeofmeasurements.Ifthesignofthederivativechangesfrompositivetonegative,weusetheseboundstoaroot.Ifthederivativeiszeroatanymeasurement,weaddittothelistofroots.Weignoreanychangesfromnegativederivativetopositive,asthosemarkminima.Oneimplicitassumptionisthatmaximacannotoccurboundedbytwomeasurementsatwhichthederivativesarethesamesign{thesewouldnotbefoundbyourrootwhichrequiresboundaryvaluesofoppositesigntofunction.Aswehaveboundsofthemaxima,weusedthebrentqalgorithminthescipypack-age,whicharootusingtheBrent(1973)intervalbisectionmethod.Werequiredtherootdetectortoaroottowithinavalueof106countss1(theprecisionofourimages).Intheeventofanerrorinthisprocess,ourcodewillthemodeusingtheNewton-Raphsonmethod;asthismethodisunbounded,weseededitwithaninitialguessofthemedianofthebackgrounddistribution.Inbothcases,theuncertaintyontheback-76Figure3.4TheeofourbackgroundmodelingandsubtractiontechniqueforAbell209.ImagesarefromtheF814Wtheoriginal(left),aftereverygalaxyhasbeenphotome-tered(center),andafterthesubtractedimagehasbeenresampledright.groundvalueisfoundbythevalueinbothdirectionsatwhichtheprobabilitydistributiongivenbyEquation3.2isequalto0:606531,whereisthemeasuredmode.ThisvalueistherelativeheightofaGaussiandistributionat1˙attheprecisionofourimages.Havingdeterminedthebackgroundvalueforapixel,theexcessisassignedtothegalaxy,whilethepixelvalueisreplacedwiththebackgroundvalueandthewidthofthebackgroundprobabilitydistributionisincludedintotheweightmap.Weworkfromtheoutsideofthegalaxyin,sothattheconditionsattheoutsideofthegalaxyarepropagatedinward.Aftertheentirehasbeenphotometered,wealsoproduceresampledimagesusingtheweightmaps;thisstepmaintainsthenoisepropertiesofthegalaxy-subtractedimage.Weshowthebefore,after,andresampledimagesofasectionofAbell209inFigure3.4.3.3.1UVSystematicUncertaintiesUVISphotometry,atleastwithintheCLASHsample,isbothnoisyandsensitivetoscat-teredlight.SincethecountrateoftheUVimagesissolow,thesystematicnoiseacross77theimageoftenexceedsthestatisticalnoisefromaperturephotometry.Inordertoproperlydeterminedetectionthresholds,wehadtoaccountforthesystematicuncertaintiesofeachimage.Donahueetal.(2015)measuredsystematicuncertaintiesofUVphotometryforCLASHBCGsbymeasuringtheinseemingly-blankskyareasaroundtheimageandcomput-ingthedeviationinthosemeasurements.However,thosemeasurementswerelimitedtoapertureswiththesameradiusandannularbackgroundsizeastheapertureusedtopho-tometertheBCG.Inthiswork,wemeasuregalaxiesofarangeofsizes,whichwillallhavetheirownsystematicuncertainty,soourtechniquemustaccountfortheareaoftheaperture.Westmadeamaskimageofeachcluster,blankingoutareasnotcoveredbytheCCD(suchaschipgapsandpixels)andareaswithdetectedsources(asdeterminedbyrunningSourceExtractorontheF390Wimage).Wethenrandomlydistributed1,000pointsacrosstheimage,andmeasuredthephotometryofcircularaperturescenteredoneachofthem,withradiiincreasingfrom0.19500to5.2000.Photometrywascorrectedfortheamountofeachaperturecoveringmaskedpixels.Foreachandclusterpair,wethemeasuredstandarddeviationasafunctionofradiustoanequationoftheformF(r)=k0r2+k1,wherek0andk1arebpoly-nomialcots.Foreachobject,whendeterminingitsUVphotometry,weincludedasystematicerrorbasedonthisresult.Sincetheobjectswereallparameterizedasanellipse,weusedapseudo-radius,p=pab.Whenthiswasgreaterthan20pixels,thesystematicuncertaintywascomputedfromthet.Whenthepseudo-radiuswaslessthan20pixels,78weusedalinearinterpolationbetweenthetwonearestmeasurements,asthewaslessaccurateatsmallradii.3.3.2PhotometricRedshiftsWeusedBPZ3(Ben,2000;Benetal.,2004;Coeetal.,2006)toestimateredshiftprobabilitiesforeachgalaxyinourcatalog.BPZdeterminesredshiftprobabilitiesforeverygalaxyusing˜2minimizationandThiscodehasbeenusedpreviouslyfortheCLASHclusters(Postmanetal.,2012b;Jouveletal.,2014),andisthedefaultredshiftestimationtoolusedintheCLASHpipeline.Ourdeterminationofredshiftprobabilitiescoverstherangeofredshiftsfromz=0:01toz=12:0instepsofz=0:001.Weuse11templatespectra,includingbothellipticalandspiralgalaxies.Fromthese,weinterpolate9additionaltemplatesforeveryintervalbetweenoriginaltemplates,foratotalof101templates.Toaccountforvariationsbetweengalax-iesandzero-pointuncertainties,weenforceaminimumphotometricerrorof0.03magnitudes.Tocharacterizetheaccuracyofourredshifts,wecompareasampleofgalaxieswithspectroscopically-derivedredshiftstoourvalues.ThesevaluescomefromtheCLASH-VLTcollaboration(Bivianoetal.,2013;Balestraetal.,2016;Monnaetal.,2016)aswellasworksbyCohen&Kneib(2002),Mercurioetal.(2008),Guzzoetal.(2009),Holdenetal.(2009),Richardetal.(2010),Sternetal.(2010),Coeetal.(2012),omezetal.(2012),Rinesetal.(2013),andEbelingetal.(2014).Additionally,weuseasampleofunpublishedVLT-VIMOS3http://www.stsci.edu/dcoe/BPZ/79Figure3.5Comparisonofphotometricredshiftsmeasuredinthisworktospectroscopicred-shifts.Thethinbandtracestheregionwherej(zpzs)=(1+z)j<0:05.Thefullredshiftcoveragefromz=0toz=3.0isshownontheleftpanel;azoom-intojustz=0toz=1.0isshownontheright.Pointsarebinnedintohexagons,withthetotaldensityofpointsscaledlogarithmicallyfrom1to100countsperhex,asindicatedbythecolorbar.redshiftsforfourcluster(PieroRosatiandMarioNonino,privatecommunication).Aftercombiningthespectralredshiftcatalogsandremovingduplicates(anytwoobjectswithpositionswithin100ofeachother),wecross-matchedthiscatalogwithourowncatalogofdetectedobjects.Foreachspectroscopicredshift,wematcheditwithanyobjectwithin1.500ofthereportedcoordinates.Intheeventofmultipleobjectswithinthisregion,wematchedwiththebrightestobject;ifmultipleobjectswerewithin0.5magnitudesofthisobject,wematchedtotheobjectclosesttothespectroscopicposition.Fromthismatchedcatalog,wereport1306objectswithspectroscopiccounterparts.54(4.13%)arecatastrophicoutliers(j(zpzs)j=(1+zs)>0:5),41(3.14%)aresubstantialoutliers(0:5j(zpzs)j=(1+zs)>0:15),145(11.10%)areminoroutliers(0:15j(zpzs)j=(1+zs)>0:05),andtheremaining1066(81.62%)arewell-matched(j(zpzs)j=(1+zs)0:05).Acomparisonbetweenour80Figure3.6Comparisontospectroscopicredshiftsbetweenthephotometricredshiftsmeasuredinthiswork(orange)andthosefromthepreviouslyreleasedCLASHphotometriccatalogs(purple).Onlygalaxieswithspectroscopicredshiftswithinjzspeczclusterj<0:05areshown.Alloutlierswithjzphotzspecj>0:2areshownatjzphotzspecj=0:2.Theoverlapbetweenbothhistogramsisshowninpink.Ourtechniquebettermatchesmeasuredspectroscopicredshiftsandhasatlyreduced(˘65%)fractionofoutliers.photometricredshiftsandspectroscopically-derivedmeasurementsisprovidedinFigure3.5.3.4ComparisontoSimilarWorksOnewaytoverifyourtechniqueistocompareourresultstootherphotometricstudiesoftheseclusters.However,theonlypreviousstudyusingCLASHphotometry(Postmanetal.,2012b)wasnottailoredforoptimizingclustergalaxyphotometry;ratheritwasageneral-purposeattempttomeasureeverythingintheincludingbackgroundgalaxies.Nevertheless,itprovidesanimportantcheckofourresults.Wematchthepubliclyavailablephotometricredshiftcatalogs4tospectroscopicredshifts4https://archive.stsci.edu/prepds/clash/81followingthesametechniqueasweusedtomatchournewresults.Usingthesamestan-dardsasinSection3.3.2,ofthe1398totalmatches,77(5.51%)arecatastrophicoutliers,59(4.22%)aresubstantialoutliers,186(13.30%)areminoroutliers,andtheremaining1076(76.97%)arewell-matched,analmost-5%decreasefromourwork.Forgalaxieswithspectroscopicredshiftszs1:0andweightedz=j(zpzs)j=(1+zs)<0:2,thestandarddeviationoftheweightedis˙=0:0531inthisworkand˙=0:0612intheoriginalcatalogs.Inthewell-matchedcasewherez<0:05,˙=0:0438inthisworkand˙=0:0513intheoriginalcatalog.Acomparisonofredshiftforthosegalaxieswithinjzspeczclusterj<0:05oftheirassociatedclusterisshowninFigure3.6.Aswellasmoreaccuratelytheredshiftsofthosegalaxiesinclusters,wealsogreatlyreducetheoutlierrateforclustergalaxies.Incomparisontotheearliercatalog,ourimproveddetectionroutinecombinedwithmoreaccuratephotometricredshiftsshouldproduceamorepuresampleforclusteridenTotestthis,weconsiderthephotometricredshiftsofeveryobjectinthese25Con-sideringonlythoseobjectswithmF814W22,2008of3484(57.6%)objectsinthiscatalogcomparedto2129of6608(32.2%)intheoldcataloghavej(zpzc)j=(1+zc)0:05.Thesenumbersmoveto3772outof10302(36.6%)and3866outof17051(22.7%)formF814W24andto5217outof27694(18.8%)and6287outof46157(13.6%)formF814W26.AnothercomparisonforourworkisthatoftheHubbleFrontierFields(HFF)catalogsproducedbytheASTRODEEPcollaboration(Merlinetal.,2016;Castellanoetal.,2016).TheyanalyzedHSTimagingofMACS-J0416(aswellasAbell2744,whichisoutsidethescopeoftheCLASHobservations)usingHFFHSTdataaswellasground-basedKand82SpitzerIRACobservations.HFFobservationsachieveasubstantialdepth,nominallyˇ2magnitudesfainterthanCLASHdata.TheASTRODEEPcatalogsarecreatedthroughaseriesofstepsinvolvingmaskingbrightobjects,theICL,andtingbrightgalax-ies,withintermediatestepsinvolvingsubtractionofeitherICLorgalaxies.Theymakeanexcellentcomparisonsampleforourwork;theirobservationsaredeeper,theirresultshavebeenrefereed,andtheircatalogiscompiledunderentassumptions(galaxyandICLmodel-basedvs.model-agnostic).TocompareourresultsforMACS0416withthoseofASTRODEEP,wematchourcatalogsgalaxy-by-galaxy.Aftersortingourcatalogfrombrightesttofaintest(usingF814Wmagnitudes),weabestmatchforeachgalaxyusingthefollowingprocess:ifonlyonegalaxyintheASTRODEEPcatalogiswithin0:6500(10pixels)ofourtarget,thatgalaxyismatchedwithours.Ifmorethanonepossiblematchiswithinthatangularradius,wecon-sideronlythosegalaxieswithF814Wmagnitudesmmb+0:5,wherembisthebrightestgalaxyinthatangularrange.Wetakethegalaxywithsmallestangulartothetargetinthatsubsettobethematch.Asacheck,wecompareourmeasuredF814WmagnitudestothosemeasuredforthesamegalaxiesbyASTRODEEPinFigure3.7.Thisvisparticularlyimportant,asitissensitivetowhetherouraperturesareabletowell-sampletheentireofgalaxies.WethatwereportfainterthanASTRODEEPforthebrightestgalaxies,butoth-erwiseareabletoreproducetheirresultsforalmostallofthegalaxiesinthecombinedsample.OurnextvstepistocompareourmeasuredcolorstothoseofASTRODEEP.83Figure3.7ComparisonbetweenF814WmagnitudesmeasuredbytheASTRODEEPCol-laborationandthisworkforMACS0416.Pointsarebinnedintohexagons,withthetotaldensityofpointsscaledlogarithmicallyfrom1to30countsperhex.Detailsoftheareprovidedinthetext.Acomparisonoftheisprovidedinthelowerpanel.84Figure3.8ComparisonbetweenmeasuredcolorsforMACS0416intheASTRODEEPcatalogandthiswork.Pointsarecoloredaccordingtothedeviationofthephotometricredshiftmeasuredinthisworkandtheclusterredshift,asindicatedbythecolorbarontheright.85WhiletheHFFobservationsaredeeperthanthoseofCLASH,theyonlyhave7HSTsoourcolorcomparisonislimited.ThecomparisonisshowninFigure3.8.WeseeaslighttrendforgalaxiesinoursampletobebluerinF435WthanintheASTRODEEPcatalog,butthatcolordiscrepancyisdiminishedforalloftheredderNumerically,themedianbetweencolorsis0:0430:233(F435W-F606W),0:0490:182(F606W-F814W),0:0440:178(F814W-F105W),and0:0130:150(F105W-F140W),wherethereporteduncertaintiesarethestandarddeviationofForgalaxieswithjzpzcj<0.1andredmagnitude<25,thesevaluesare0:1110:235,0:0130:107,0:0040:160,and0:0020:139,respectively.Forthesameredshiftandmagnitudelimitedsubsample,wealsocomparethemedianbetweencolorsmeasuredinthisworkandbyASTRODEEPtothemediancoloruncertaintyforourphotometryalone;inthesamecolororderasbefore,wecolortocoloruncertaintyratiosof-0.111to0.127(uncertainty),-0.013to0.028,-0.004to0.017,and0.002to0.011,whereallvaluesareinmagnitudes.Theslightforbluecolorsisthereforewithintheuncertaintiesofourphotometry.AsMACS0416isatredshiftz=0:397,F435Wiswellbelowthe4,000Abreakforclustergalaxies,whileF606Wstraddlesthebreak;wethereforedonotexpectthecolortermtocausetvariationsinSEDtingbetweenthetworesults.Onewaytocheckthatistocompareourmeasuredphotometricredshifts.Here,AS-TRODEEPusedmultiplemethodsforredshiftestimationandcombinedthemallforaanswer,whileweonlyconsiderourredshiftestimatesfromBPZ.WeshowinFigure3.9acom-parisonbetweenourreportedphotometricredshiftsandthephotometricandspectroscopicredshiftsreportedbytheASTRODEEPcollaboration.Whenconsideringtheuncertaintiesonthesemeasurements,wegoodagreementbetweenourreportedredshiftsandthecom-86Figure3.9ComparisonbetweenredshiftsmeasuredbytheASTRODEEPCollaborationandthisworkforMACS0416.Pointsarebinnedintohexagons,withthetotaldensityofpointsscaledlogarithmicallyfrom1to30countsperhex,asindicatedbythecolorbar.Detailsoftheareprovidedinthetext.Azoom-intojustmatchesbelowredshift1.0isprovidedontherightpanel.Theclusterredshiftisindicatedbytheverticalandhorizontallines;thediagonallineistheidentityline.parisonsample.Forgalaxieswithphotometricredshiftszp<0:8ineitherofoursamples,themedianredshiftbetweenourcatalogsis-0.007,whilethemedianabsoluteredshiftis0.099.ThiscomparisonservestovalidatebothourresultsandthoseoftheASTRODEEPcol-laboration.Bothtechniques{iterativebackgroundmodelingandstatisticalbackgrounddecomposition{producesimilarresultsforthesameclusterofgalaxies,and,dependingonthetimeconstraintsandpurposesoffuturestudies,canbothbeusedtomeasureclustergalaxypopulations.Nevertheless,asourtechniqueonlymakesbasicassumptionsaboutbackgroundlightdistributions,wewouldrecommenditsusefordeterminingthepropertiesofclusterswithonlyminimalpriors.87Table3.2.CLASHScalingPropertiesClusterNamersM2500r2500N2500Source(h170Mpc)(h1701014M)(h170Mpc)Abell2090:6600:1003:1400:7100:5900:210588aAbell3830:4700:0603:7100:7100:6100:150507aAbell6110:5900:0903:0000:5700:5300:1809310aAbell14230:2800:0501:8200:1700:4700:010517cAbell22610:7300:1604:8601:7100:6600:3109010aCLJ12260:5000:0706:1401:0000:5500:16018117aMACS03290:4700:1102:8600:8600:5200:20014813aMACS04160:6500:1802:2100:5300:4100:0309210bMACS04290:5900:1102:7101:5700:5300:240809aMACS06470:4800:2103:7200:9800:4200:04011212bMACS07171:3100:3103:4200:8700:4200:04019916bMACS07440:4000:0602:8600:4300:4800:12016015aMACS11150:8900:1602:1400:7100:4400:190749aMACS11491:1200:3503:7301:1100:4300:04016715bMACS12060:4400:0903:5701:1400:5300:23015514aMACS13110:3400:0402:0000:2900:4500:1008910aMACS14230:3400:0902:5701:1400:4800:28010211aMACS17200:4400:0903:1400:8600:5300:23010411aMACS19310:5900:1002:2900:4300:4700:130578aMACS21290:6500:3504:7001:7000:5600:06016214dMS21370:6900:0703:2900:5700:5500:140598aRXJ13470:5400:1104:4301:8600:6000:28015213aRXJ15320:5600:1401:5700:7100:4500:230608aRXJ21290:4300:0702:5700:4300:5100:180527aRXJ22480:6900:1003:8601:0000:5500:21014313aars,R2500,andM2500fromMertenetal.(2015).brs,R2500,andM2500fromUmetsuetal.(2016).crs,R2500,andM2500fromDonahueetal.(2014).dR2500,andM2500fromDonahueetal.(2014).3.5OpticalScalingRelationsAswellasstudyingtheindividualclustergalaxies(seeChapter4),ourcatalogandoutputphotometricresultsenableustobetterunderstandthescalingrelationsoftheseCLASHclusters,particularlytheamountofintrinsicscatterpresent.Tofacilitatetheseanalysis,weutilizepreviousobservationsofrs,R2500,andM2500frompreviousCLASHstudies,wherersisthescaleradiusoftheclusterdensityFor19oftheseclusters,weusethevalues88Figure3.10ComparisonbetweenmeasuredvaluesofE(z)N2500andE(z)M2500fromthiswork(purple)and(Hoekstraetal.,2011,orange).Wealsoshowourblineinblack,andabesttoourdataaloneinpink.DetailsoftheselectionofN2500areprovidedinthetext.presentedinMertenetal.(2015).Forfourofthestrongclusters,weusethepropertiesfromUmetsuetal.(2016),assumingc=1,asinthatwork.Twoclusters,Abell1423andMACS2129,didnothavemeasurementsreportedineitherofthoseworks;weinsteadusevaluesfromDonahueetal.(2014).AsMACS2129didnothaveanyvalueofrsinanyliterature,wesetittors=0:650:35Mpc,whichisconsistentwithclustersofsimilarmassandR2500values.ThepropertiesforeachclusteraregiveninTable3.2.Tominimizebiasintheserelations,weonlyconsiderclustermembers;theprocessweusetoselectmembersisdescribedinSection4.3.893.5.1Mass-RichnessRelationWeconsidertherelationbetweenmassandclustermembercounts.WeconsiderthesameclustersamplediscussedinChapter2,25moderate-luminosityclusterswithweaklensingmeasurementsfromHoekstraetal.(2011).ThatworkalsoreportedmeasurementsofN2500,theoverdensityofgalaxieswithrestframeB-bandabsolutemagnitude22<MB<18:5withinr2500.Weasimilarvaluebycountingthenumberofclustermemberswithk-correctedi-bandabsolutemagnitude22<Mg<18:5withinr2500;detailsonthek-correction5which,ifinaccurate,canbiasslopemeasurementsandmemberselectionaregiveninChapter4.OurvaluesofN2500arereportedinTable3.2.ThesampleofclustersfromHoekstraetal.(2011)providesanexcellentcomparisonsampletoourown,asbothhaver2500massesderivedfromHSTobservations(weak-lensingmassmeasurementswerepresentedinHoekstraetal.,2011),bothareX-rayselected(theselectionofCLASHclustersispresentedinPostmanetal.,2012b),andbothsamplescoversimilarredshiftranges.ThisclustersampleisalsothebasissampleforourstudyofX-rayscalingrelationsinChapter2(Connoretal.,2014).Here,weusetheWLSroutine(Akritas&Bershady,1996)toapower-lawscalingrelationtothecombinedsample;weabestofE(z)M1014M=100:700:04(E(z)N2500)0:651:(3.4)DuetothelargemeasurementerrorsoftheHoekstraetal.(2011)sample,theintrinsic5Ak-correctionisacorrectionfromobservedmagnitudestorestframemagnitudes,accountingforthedualectsofsamplingbluerregionsoftherestframespectrumathigherredshiftandoftherelativespectralwidthoftherestframespectrumbeingsampledinsmallerincrementswithincreasingredshift.K-correctionsareinformedbyassumedspectralpropertiesofagalaxy;thisiswhyitisimportantwesamplethespectraofourgalaxiescontinuouslyacrossawiderangeofwavelengthsinthiswork.90Table3.3.CLASHLuminosityFunctionFitClusterNameMi˚Det.LimitRS(mag)(mag)Abell3830:86+0:050:0421:54+0:360:4032:9+5:65:0M+6:790:65+0:070:06Abell2090:79+0:040:0421:36+0:300:3349:1+7:67:0M+6:610:72+0:060:06Abell14230:83+0:050:0520:93+0:320:3543:5+7:26:5M+6:180:63+0:080:07Abell22610:83+0:040:0321:20+0:250:2773:2+9:18:3M+5:950:68+0:050:05RXJ21290:82+0:050:0421:15+0:290:3251:1+7:87:0M+4:900:67+0:070:05Abell6110:68+0:060:0621:22+0:240:2679:8+11:910:8M+4:970:53+0:090:06MS21370:84+0:060:0621:31+0:320:3543:0+7:36:6M+5:560:61+0:090:08RXJ15320:72+0:050:0521:33+0:240:2681:7+11:410:5M+5:080:50+0:100:06RXJ22480:76+0:040:0421:38+0:200:22112:5+12:812:1M+5:130:59+0:060:05MACS19310:98+0:040:0421:13+0:260:2859:9+7:46:7M+4:880:77+0:060:06MACS11150:82+0:050:0521:66+0:250:2870:1+9:68:7M+4:410:62+0:070:07MACS17200:87+0:040:0421:80+0:250:2770:6+8:88:2M+5:050:66+0:060:06MACS04160:72+0:050:0421:72+0:220:2398:2+12:511:5M+4:970:56+0:070:06MACS04290:79+0:060:0521:20+0:250:2773:0+10:39:5M+4:950:54+0:090:09MACS12060:80+0:040:0422:02+0:210:22109:9+11:811:1M+5:270:62+0:060:05MACS03290:81+0:040:0422:07+0:220:2496:9+11:010:3M+5:320:61+0:050:05RXJ13470:76+0:040:0421:69+0:200:22113:0+13:011:9M+4:940:60+0:060:06MACS13111:09+0:040:0322:58+0:330:3631:7+4:23:9M+5:330:65+0:080:07MACS11490:76+0:040:0421:96+0:170:19155:6+15:414:3M+4:710:53+0:090:04MACS14230:89+0:040:0422:16+0:250:2870:1+8:88:1M+4:910:51+0:080:08MACS07170:75+0:040:0321:92+0:160:17189:9+17:016:2M+4:670:50+0:080:04MACS21290:87+0:040:0421:88+0:220:2397:0+10:810:2M+4:630:53+0:090:08MACS06470:83+0:040:0421:94+0:220:2397:2+11:110:1M+4:690:63+0:070:06MACS07440:90+0:040:0422:20+0:210:2497:8+10:710:0M+4:450:50+0:100:06CLJ12260:96+0:050:0422:21+0:230:2482:9+9:89:1M+3:960:50+0:200:10scatterisconsistentwith0.Byjustourdata,weaslightlytslope,E(z)M/E(z)N0:510.Thesedata,aswellasbothareshowninFigure3.10.3.5.2LuminosityFunctionOnewaytocharacterizethequalityofourphotometricpipelineistomeasuretheluminosityfunctionofclustergalaxies;thisalsoservesasawaytocharacterizetheclusterpopulation91Figure3.11Thek-correctedi-magnitudeluminosityfunctionsforall25CLASHclusters.Galaxiesareshownbinnedinhalf-magnitudeintervals.ThebSchechterluminosityfunctionisshowninorange(purple)forX-rayselected(highmclusters.Galaxiesareplottedinorderofincreasingredshift.valuesof,M*,and˚areprovidedinthatorderoneachplot.Detailsoftheareprovidedinthetext.92withrespecttopreviousclusterstudies.Todothis,weconsideraSchechterluminosityfunction(Schechter,1976),oftheform˚(M)dM=0:4˚ln(10)100:4(MM)(1+)exp(100:4(MM))dM;(3.5)where˚isthedensityofgalaxies,M*isthecharacteristicmagnitudeofthefunction,Mistheabsolutemagnitudeofagalaxy,andisthefaint-endslope.Wecautionthereaderthat,inthisform,aslope"occursat=1.Foreachcluster,wedeterminedtheparametersoftheSchechterfunctionusingunbinnedluminositydata,byfollowingthemaximumlikelihoodtechniquedescribedinMarshalletal.(1983)andDonahue&Voit(1999).Usingi-bandk-correctedmagnitudes,wefoundtheminimumofalikelihoodfunctionsuchthatS=2ln(L)=2NXiln(˚(Mi))+2ZMfaint˚(M)dM(3.6)inagridofvaluesfor,M*,and˚.thisway,theincrementsinSaresimilartotheincrementsin˜2forthedeterminationofuncertainties.Thisstatisticalmethoddoesnotbyitselfgiveagoodnessofhowever.Mfaintissetforeachclustertobethefaintestobjectasamember.Weuseda50x50x25gridcovering=[-1.3,-0.5],M*=[-23,-18],and˚=[101;104],where˚isinunitsofgalaxiespermagnitudeperclustereld(withintheobservedofview).Afterthebestvalue,weexaminedasub-gridcoveringthe9x9x9boxcenteredonthebestparameters.Werepeatedthesub-samplingstepasecondtime,foratotalofthreeresolutionlevelsforthethreeluminosityfunctionparametersofinterest.Todeterminethe1˙uncertaintiesweheldtwoparametersanditeratedthe93thirduntilS)3:53(The˜2value=3.53for1˙constraintsforthreefreeparameters,e.g.Lamptonetal.,1976).WepresentourbvaluesforeachoftheCLASHclustersinTable3.3.Uncertain-tieslistedare1˙values.Wealsoplotourluminosityfunctions,aswellashistogramsofclustermembers,inFigure3.11.˚hasbeendividedby2inthistomatchthehalf-magnitude-widebins.Foroursample,webvaluesintherange1:0..0:7andM*valuesintherange22.M.21.WecomparethesevaluestothosederivedbyRudnicketal.(2009).TheySDSSclustersdrawnfromthesamplepresentedinvonderLindenetal.(2007)toamaximumredshiftofz60:06.Fori-bandobservations,theirbestwasMi=21:46+0:030:04,=0:75+0:020:01.Thatworkalsoexaminedtheluminosityfunctionof16clustersintheESODistantClusterSurvey(EDisCS)spanningredshifts0:4<z<0:8.Whenonlyincludingredsequencemembers,theEDisCSclusterstogetherwerebestbyanibandluminosityfunctionofMi=21:80+0:220:17and=0:34+0:160:10.DeProprisetal.(2013)studied11mergingclustersat0:2.z.0:6,bestSchechterslopesofˇ1.Stottetal.(2007)derivedvaluesof=0:910:02,MV=21:390:05for10MACS(Ebelingetal.,2001)clustersatz˘0:5,includingsev-eralconsideredinthiswork.Martinetetal.(2015)presentedmeasurementsofluminosityfunctionsfor0:4z<0:9atrest-frameIandR;theirred-sequenceselectedresultsareR=0:800:14,MR=22:40:2andI=0:370:18,MI=22:00:2.94Figure3.12Themeasuredslopesoftheluminosityfunctionsforall25CLASHclusters.Weshowtheresultsforallclustermembersinpurpleandforonlythosealongtheredsequenceinorange.Asaslope"inmagnitude-spaceisgivenby=1,valuesgreaterthanthatshowaluminosityfunctionwithfewerfaintgalaxiesthangalaxiesatM*.Weseeacleartrendforasteepeninginthefaintendslopewhenonlyincludingredsequencemembers.Figure3.13ThemeasuredvaluesofM*fori-bandluminosityfunctionsofCLASHclusters.Showninpinkandorangearefori-bandM*valuesforall(orange)andonlyred(pink)galaxies,withevolutionparametersfromLovedayetal.(2012),althoughassumingthevaluesofM*foradouble-power-lawasdiscussedinthetext.95Theresultspresentedinthisworkareconsistentwiththosedescribedabove.ThevaluesofM*wereportareinagreementwithotherstudies,whichsupportsourdeterminationofphotometryforrelativelybrightclustergalaxies.Severalworksreportamuchsteeperslope(lowervalueof),namelyMartinetetal.(2015)andRudnicketal.(2009);theseonlyconsideredredsequencegalaxies.Whileseveralotherstudieshavefoundsteeperfaint-endslopesforredsequence-onlysamples(e.g.,DeLuciaetal.,2004b),worksthatdonotselectonlyredsequencemembersvaluesmoreconsistentwithwhatwepresenthere(Straz-zulloetal.,2010;Manconeetal.,2012).Asacomparison,weusedgalaxieswithgrcolorswithinjgr)j<0:1ofourredsequenceslopes(discussedinSection4.4)tocomputearedsequence-onlyluminosityfunctionforeachcluster.Faintendslopes,denotedasRS,foreachclusterareshowninTable3.3.Weseeaconsistentsteepeningofthefaint-endslopebyonlyconsideringredsequenceobjects,whichweshowinFigure3.12.WealsoconsiderourmeasuredevolutioninM*.InFigure3.13weplotourmeasuredvaluesofM*ini-bandforallclustermembers.WeseeatrendforincreasingM*brightnesswithincreasingredshift,whichisnotunexpected(e.g.Xiaetal.,2006).WealsoplotthebevolutionaryparametersfromtheGalaxyandMassAssembly(GAMA)k-correctedi-bandluminosityfuctionspresentedbyLovedayetal.(2012).WhilethelinearslopetheytotheredshiftevolutionofM*isbasedonthebvaluesfromasingle-componenttheyfoundthatdouble-power-lawprovidedtlybetterfori-band.Becauseofthat,theplottedresultfromLovedayetal.(2012)isnormalizedtothebM*atz=0.1fromthedouble-power-lawbutevolveswiththeslopederivedfromsingle-componentGAMAobservationscoverrelativelylargeareasofsky,asopposedtocenteringongalaxyclusters,sotheyprovideagalaxycomparison.WeseeasimilarevolutioninM*withthe96GAMAsampleintheredshiftrangetheysampled,albeitwithpreferentiallyfaintervaluesofM*.Havingthevalidityofourluminosityfunctionmeasurements,weuseourmea-suredgalaxycountstoinferadetectionlimitforeachclusterintermsofMM.Todothis,weconsidereachhalf-magnitudebinshowninTable3.11;wethefaintestbinforwhichthetotalgalaxycountiswithin90%ofthatpredictedbyourbSchechterfunction.WereportthosevaluesinTable3.3.Wethat,evenouttoz˘0:5,wedetectgalaxiesdowntoMM˘5.Asthismeasurementofourdetectionlimitmaybebiasedbyalackofdetectedgalaxiespullingtheslopedown,wealsoalimitingmagnitudebythefaintestbinthatiswithin80%ofthatexpectedbyaSchechterfunctionwiththesamevaluesofM*and˚but=1;theselimitsareexactlythesame.ObtainingrobustdetectionsofgalaxiesthisdeepintotheclusterluminosityfunctionvalidatesourassertionthatwecanusemodetectionandphotometrytoextractfaintclustermembersfromtheCLASH3.5.3StellarMassWeexaminethetotalstellarmassofthe25CLASHclustersbyintegratingtheirluminosityfunctionsandutilizingamass-to-lightratiotoconvertfromluminositytostellarmass.Toprovideauniformmeasureacrosstheentiresample,welimitourselvestotheluminositywithinr2500.Weluminosityfunctionsforthegalaxiescontainedinsidethisradiusforall25clusters;theresultsofthisaregiveninTable3.4.97Table3.4.CLASHr2500valuesClusterNameMi˚LiBoostaM(mag)(1012L)(1012M)Abell3830:86+0:050:0421:54+0:360:4032:9+5:65:01:40+0:700:481.644:24+1:682:75Abell2090:79+0:040:0421:36+0:300:3349:1+7:67:01:56+0:620:461.484:72+1:682:58Abell14230:82+0:050:0520:93+0:320:3543:4+7:26:60:66+0:290:201.041:99+0:741:16Abell22610:83+0:040:0321:20+0:250:2773:2+9:18:32:18+0:680:531.586:58+2:173:10RXJ21290:82+0:050:0421:18+0:300:3349:2+7:66:80:95+0:390:281.052:87+1:011:57Abell6110:67+0:060:0621:16+0:240:2680:0+12:011:01:40+0:450:351.004:23+1:392:04MS21370:85+0:060:0521:40+0:340:3738:8+6:86:20:88+0:400:291.002:67+1:011:58RXJ15320:73+0:070:0621:30+0:300:3351:4+9:18:11:03+0:430:311.003:12+1:151:73RXJ22480:77+0:050:0421:43+0:220:2398:0+11:911:12:24+0:630:491.006:77+2:142:98MACS19310:99+0:050:0421:17+0:300:3243:7+6:25:70:86+0:330:241.002:59+0:901:39MACS11150:84+0:060:0621:84+0:320:3642:0+7:26:51:43+0:650:461.004:32+1:632:63MACS17200:89+0:050:0421:89+0:290:3251:1+7:36:71:86+0:710:521.005:61+1:992:96MACS04160:69+0:060:0621:72+0:280:3059:7+10:19:01:76+0:650:501.005:30+1:862:79MACS04290:81+0:060:0621:17+0:300:3351:2+8:57:70:93+0:380:271.002:81+1:011:55MACS12060:84+0:040:0422:15+0:260:2869:7+9:08:43:16+1:040:791.009:54+3:184:62MACS03290:83+0:040:0422:13+0:250:2870:1+9:38:53:11+1:020:801.009:39+3:144:56RXJ13470:75+0:050:0521:63+0:220:2496:7+12:111:22:65+0:760:601.007:99+2:523:57MACS13111:04+0:050:0422:70+0:410:4923:0+3:93:51:91+1:190:741.005:76+2:494:28MACS11490:61+0:070:0621:81+0:220:2497:2+14:113:03:08+0:920:731.009:29+2:984:21MACS14230:95+0:050:0522:33+0:340:3937:0+6:15:52:07+1:020:681.006:26+2:433:83MACS07170:73+0:060:0522:06+0:220:2497:8+12:811:83:96+1:140:921.0011:96+3:835:55MACS21290:76+0:050:0621:79+0:240:2681:4+11:410:42:59+0:840:631.007:82+2:593:74MACS06470:80+0:070:0621:86+0:290:3253:0+8:87:91:82+0:730:541.005:49+2:003:01MACS07440:71+0:070:0721:83+0:240:2682:1+12:511:22:68+0:830:691.008:09+2:713:96CLJ12260:94+0:070:0622:32+0:290:3351:2+8:27:42:83+1:160:861.008:54+3:094:64aFactorbywhichluminositywasscaledtoaccountforincompleteaperture98ASchechterluminosityfunctionhasthepropertythattheintegratedluminositycanbefoundanalytically,L=Z10L˚(L)dL=˚L+2);(3.7)where˚(L)istheluminosityfunctionintermsofluminosityandistheGammafunction.and˚arethesameforaluminosityfunctioncharacterizedbymagnitudesorluminosity,whileListheluminositythatMcorrespondsto.Toaccountforthefactthatseveralclustersdonothavefullphotometriccoverageouttor2500,wecalculateacorrectionfactorbasedontheradiusatwhichthetotalclustercoverageintheF814Wdropsbelow60%.AssuminganNFW(Navarroetal.,1997),thetotalmassinsidearadiusrcanbefoundasM(r)/r3slog(rs+r)log(rs)rrs+r:(3.8)Thescaleradiusrsforeachcluster,aswellasr2500,isgiveninTable3.2.Forthosegalaxieswithoutfullcoverageouttor2500,wecalculatetheNFWmassatr2500andattheradiusatwhichcoveragedropsbelow60%;theratiobetweenthosetwovaluesisthecotweusetoscaleupourluminositymeasurements.ThisvalueisgivenforeachclusterinTable3.4.InSection4.6wethatthei-bandstellarmass-to-lightratioislog(MM)=(LL)=0:480:12forluminousredsequenceclustermembers.Asthesegalaxiesmakeupthemajorityofthelightinoursample,weusethisvalueofthestellarmass-to-lightratio,asopposedtothevaluecomputedforallclustermembers,whichhaslargeruncertaintyduetothepopulationofbluecloudgalaxies.Weconvertintegratedluminositiesintostellarmasses;theresultsofthisaregiveninTable3.4.Todeterminetheerrorsontheluminositiesandstellarmasses,werandomlydraw10,000samplesfromtheuncertaintydistributionsof,99Figure3.14Comparisonbetweenstellarmassesandtotalmasseswithinr2500.Clustersarecolor-codedbyredshift.TotalmassesaremostlydrawnfromlensingmeasurementsbyMertenetal.(2015)andUmetsuetal.(2016),butalsoincludeX-raymassesfromDonahueetal.(2014).Stellarmassesarederivedfromtotalclusterluminositymeasurements,asdescribedinthetext,adjustedasneededtoaccountforapertureShownarelinescorrespondingtoM=0:01MTot(solid),M=0:02MTot(dot-dashed),andM=0:04MTot(dotted).M*,˚,andthestellarmass-to-lightratio;upperandlowerlimitscorrespondtothe68.27percentiles(1˙)aboveandbelowthenominalvalue.WeplotourresultsforMagainstthelensingmassesderivedbyMertenetal.(2015)andUmetsuetal.(2016),aswellastwoHSEmassestimatesfromDonahueetal.(2014),inFigure3.14.Theseresultsshowamedianstellarmassfractionof1.8%,withascatterof0.7%.Measurementuncertaintiesaretoolargeforustocalculateanintrinsicscatterofthissample,however.Whilethesamplelacksthedynamicrangetoconsiderscalingrelations,theseclustersshowconsistencywitheachother.Asourmeasurementofstellarmassisbaseddirectlyonmeasurementsofluminosity,theinternalconsistencyisfurtherevidencethatwe100arewell-samplingtheluminosityoftheclusterpopulation.Linetal.(2012)measuredthestellarmassfractionfor96massiveclustersbetweenred-shifts0:0<z<0:6.Theyfoundthat,forahaloofmassM500=1014h171M,thestellarmassfractionisM=M500=0:0180:001,withascatterof31%(ourmeasuredscatteris41%).Linetal.(2012)alsotookmassscalingintoaccount.Gonzalezetal.(2013)mea-suredastellarmassratioofM=M500=0:0390:002,butwithasteepslopesuchthatatM500=41014M(ahalomasscharacteristicofwhatwestudyhere,althoughwithinr500)thatratioisM=M500ˇ0:021:3.6SummaryInthischapter,wepresentedanewphotometriccatalogofCLASHclustersources,withpho-tometricredshifts.Objectsinthiscatalogweredetectedusingmultiplescalesofmode-basedbackgroundsubtractiontobestidentifysmallobjectsembeddedinthecomplexlightofthesemassiveclusters.Weusedlocalbackgroundmodelingandannulardegradationtophotometergalaxieswhileleavingbehindthelarge-scalelightstructure.Highlightsofthisworkinclude:1.Wedetectandphotometer22,557objectsintheof25massivegalaxyclusters,withamedianof683objectsperclusterbrighterthanABMaginF814W=25.Amedianof459oftheseperclusterarewelldetectedinatleast8318in12,and154in14,spanningtheultraviolettothenearinfrared.Suchcompletephotometrywillallowustomodelthephysicalpropertiesoftheseobjects,asisdiscussedinChapter4.1012.Thankstotheoptimizedbackgroundmeasurement,sourcedetection,andphotometrytechniquesdescribedinthispaper,weobtainaccuratemeasurementsofphotometricred-shiftsforˇ82%ofobjectswithspectroscopicredshiftwith˙z)=0:0438.Additionally,ourcatalogisabletoobtaincomparablenumbersofdetectedobjectswithphotometricredshiftsconsistentwithclustersaswasreportedintheoriginalattemptfortheCLASHclusters,yethasasigtlyreducedamountofexcessdetections.3.WevalidateourphotometryandthatoftheASTRODEEPcollaborationbycross-comparingresultsforMACSJ0416,agalaxyclusteralsoobservedaspartoftheHubbleFrontierFields.Weminimalinmeasuredphotometricredshiftsandphotom-etrybetweenourtwotechniques.4.WecharacterizeourdetectionlimitsfortheseclusterswithaSchechterluminosityfunction.Fork-correctedi-bandvalues,17clustersaredetectedouttoMi&M+5andall25aredetectedtoMi˘M+4.Theseluminosityfunctionsalsoprovidemeasuresoftheclusterpopulationsacrossarangeofredshifts.Weevidenceforadecreaseinthefaint-endslopecausedbyselectingonlyredsequencemembers.5.Inconjunctionwithobservationsofmoderate-luminosityclustersbyHoekstraetal.(2011),wearelationshipbetweentheopticalluminosityofaclusteranditsmass,wherebothpropertiesareforwithinr2500.WeE(z)M/(E(z)N2500)0:651.6.UsingSchechterluminosityfunctionstoderivetotalintegratedluminositiesforthe25102CLASHclusterswithinr2500,incombinationwithamass-to-lightconversiondescribedinChapter4,wecomparethestellarmasstototal(mostlylensing-measured)masses.Wethattheseclustershavestellarmassfractionsofaround1:80:7%relativetothetotalmass.Theinternalconsistencyofoursample,incombinationwiththemeasuredconsistencyfromtherichness-massscalingrelation,isfurtherevidencethatweareaccuratelyestimatingthetotalclusterlight.ThomasConnoracknowledgessupportfromafellowshipfromtheMichiganStateUnver-sityCollegeofNaturalScience.ThisresearchhasmadeuseoftheNASA/IPACExtragalacticDatabase(NED)whichisoperatedbytheJetPropulsionLaboratory,CaliforniaInstituteofTechnology,undercontractwiththeNationalAeronauticsandSpaceAdministration.WeusedthecosmologicalcalculatorpresentedinWright(2006)inthiswork.Facilities:HubbleSpaceTelescope/ACS,HubbleSpaceTelescope/WFC3,103Chapter4GalaxyProperties,Membership,andRedSequenceEvolutioninCLASHClusters4.1IntroductionClustersofgalaxies,includingtheirassociateddarkmatterhalosandhotbaryonicgas,arethelargestgravitationallyboundsystemsintheUniverse,andthereforeareanimportanttoolforstudyingcosmology,structureformation,andtheevolutionoftheUniverse(Voit,2005;Giodinietal.,2013;Reiprichetal.,2013).Bulkpropertiesofclusters,measuredthroughX-rayobservationsofthehot,ionizedintraclustergas,showself-similar1scalingfromlowtohigh-masssystems,withminimalevolutionwithredshift(Maughan,2007;Sunetal.,2009;Mahdavietal.,2013;Connoretal.,2014).Clustergalaxiesaresensitivetotheirenvironment(Delayeetal.,2014;Darvishetal.,2016),andtheythereforeprovideanopportunitytostudythebetweenclustersacrossmass(Weinmannetal.,2006)andredshiftspace(Erfanianfaretal.,2014;Andreonetal.,2016;Nantaisetal.,2016).Inparticular,clustergalaxieshavebeenobservedtofollowalinearrelationshipincolor-1Self-similarscalingmeansthatsmallclustersareelyjustscaled-downversionsoflargerclusters.104magnitudespace(Baum,1959;Visvanathan&Sandage,1977),whereinclustergalaxiesappearasatightbunchingincolorthatisdistinctfromthegeneralpopulationofgalaxies.Thisrelationship,calledtheredsequenceorcolor-magnituderelation,isfoundinclustersouttoatleastzˇ1:5-2:0(Blakesleeetal.,2003;DeLuciaetal.,2007;Lemauxetal.,2012;Rudnicketal.,2012;Andreonetal.,2014).Theredsequenceisalsousedasancientmeansforblindlydetectinggalaxyclusters(Annisetal.,1999;Gladders&Yee,2000;Gladdersetal.,2007;Haoetal.,2010;Murphyetal.,2012)andforestimatingtheirphotometricredshifts(Koesteretal.,2007a;Galetal.,2009;Thanjavuretal.,2009;Ryketal.,2014).Oneimportantparameteroftheredsequenceisitsslopeonacolor-magnitudediagramforgalaxies,whichmanifestsaslowerluminositygalaxiesbeingbluerthanbrightergalax-ies.Itisbelievedtheslopeisdeterminedbyamass-metallicityrelation,suchthatlessmassiveobjectsarelessmetal-richthanmoremassiveobjects(Kodama&Arimoto,1997;Stanfordetal.,1998;Ferrerasetal.,1999;Gallazzietal.,2006).Duetometallinesblan-ketingthebluestpartsofstellarspectraandmetalopacityincreasingthephysicalsizesofstars,moremetalrichstars(and,byextension,galaxies)areredderthanmetal-poorgalaxies(e.g.,Bruzual&Charlot,2003;Maraston,2005).Moremetal-richgalaxiesappearredder(Faber,1973;Worthey,1994),sotheredsequenceslopestowardthemoremassivegalaxiesbeingredder.Aqualitativeoriginforthemass-metallicityrelationisthat,inlessmassivegalaxies,supernova-drivenwindismoreeatejectinggasduetothesmallerpotentialwellofthegalaxy(Larson,1974;Arimoto&Yoshii,1987;Matteucci&Tornambe,1987;Lillyetal.,2013;Voitetal.,2015);bydrivingoutmetal-richgas,less-massivegalaxiesarethereforemoremetal-poorthantheirlargerneighbors(Tremontietal.,2004).Whilethis105isacompellingmodel,detailednumericalsimulationshavehaddyreproducingthemass-metallicityrelationwithout(e.g.,DeLuciaetal.,2004a;deRossietal.,2007;Mouhcineetal.,2008).Alternatively,agemayhaveanctonthepropertiesoftheredsequence.Galaxycol-orsaresubjecttoanage-metallicitydegeneracy;changesineithercanmakegalaxiesredder(Worthey,1994,1999).Onewaytobreakthisentanglementistoobservetheevolutionoftheredsequence;sinceitexistsbeyondevenmoderateredshifts(zˇ0:3),theredsequencemustbeaconsequenceofthemass-metallicityrelation(Kodama&Arimoto,1997;mann&Charlot,1998;Kodamaetal.,1998).Wereitdrivenbyage,thepassiveevolutioninthatredshiftrangewouldcausetevolutionintheslopeasbluergalaxieswouldhavetlyyoungerpopulationsatearlierredshifts.However,othershavearguedthatagestillcttheobservedredsequenceslope(Ferrerasetal.,1999;Terlevichetal.,1999;Trageretal.,2000;Poggiantietal.,2001;Rakos&Schombert,2004).Anotherwayforagetoimpacttheobservedcolor-magnituderelationisbyadjustingthescatterabouttherelation.Apopulationwithanearlyidenticalformationtimehasalargerscatteratearlytimes,whenthesmallencesinformationtimehaverelativebutthisscatterreducesasthepopulationages.Earlyobservationsoftherelationshowedatightscatter,implyingthatclustergalaxiesformedatthesametimeandearlyon(Boweretal.,1992;Ellisetal.,1997;Stanfordetal.,1998;Boweretal.,1998;Andreon,2003;McIn-toshetal.,2005).Recentworkshaveshownthatthemeasuredscatteroftheredsequenceevolveswithtime(Hiltonetal.,2009;Papovichetal.,2010;Foltzetal.,2015)andincreasesatthefainterendoftheredsequence(Conseliceetal.,2002;Gallazzietal.,2006).This106observedtightscatterimpliesalong-lived,quiescentpopulation,whilethescatterincreasingwithageisevidencethatthescatteristheresultofage.Itisalsoimportanttoconsidertheevolutionoftheslopeoftheredsequenceitself.Clustersarenotstaticobjects;theyareconstantlygrowingandaccretingnewgalaxies(e.g.,Ichinoheetal.,2015).Porteretal.(2008)foundasuddenenhancementinstarformationforgalaxiesjustoutsidethecluster'svirialradiusthatarefallingintoaclusterviaasuperclustert.Previousworkshavefoundevidenceforinfallinggalaxieshavingtheirstarforma-tionshinthehostileclusterenvironmentandmergingontotheredsequence(DeLuciaetal.,2007;Stottetal.,2007;Smithetal.,2008;Stottetal.,2009).Inthiscontext,theevolutionoftheredsequence{particularlyatthefaintend{isasensitivemarkerofclusterevolution.Incontrast,others(Andreon,2008;Crawfordetal.,2009)noevolutionintheslope.Stottetal.(2009)havearguedthatthisdiscrepancyiscausedbyk-correction,2which,ifinaccurate,canbiasslopemeasurements.RecentworkonredsequenceresearchhasfocusedontheextensivecoverageprovidedbytheSloanDigitalSkySurvey(SDSS)andotherlargesurveyprograms(Hoggetal.,2004;Bernardietal.,2005;Cooletal.,2006;Haoetal.,2009;Ryketal.,2014;Oguri,2014).Thesestudieshaveprovidedanexcellentopportunitytostudythepropertiesoftheredse-quenceforalargenumberofclusters,buttheyareinherentlylimitedtoonlystudyclustersatashallowdepth.Breakingtheage/metallicitydegeneracyfortheinterpretationofindi-2Ak-correctionisacorrectionfromobservedmagnitudestorestframemagnitudes,accountingforthedualectsofsamplingbluerregionsoftherestframespectrumathigherredshiftandoftherelativespectralwidthoftherestframespectrumbeingsampledinsmallerincrementswithincreasingredshift.K-correctionsareinformedbyassumedspectralpropertiesofagalaxy;thisiswhyitisimportantwesamplethespectraofourgalaxiescontinuouslyacrossawiderangeofwavelengthsinthiswork.107vidualgalaxycolorsrequiresphotometriccoveragebeyondopticalimagesalone.Modelsoftheredsequencepredictchangesatthefaintend,whichthesesurveyscannotwellsamplebeyondthelocalUniverse.Inordertoproperlyunderstandwhatshapestheredsequence,itisapparentweneedasampleofclustergalaxiesthat1)spansarangeofredshift,2)includesfaint(M*+4)members,3)hasageandmetallicityinformation,and4)canbeplacedonthesamephotometricsystem.Inthiswork,weexploitr,multi-wavelengthcoveragewiththeHubbleSpaceTele-scope(HST)of25massivegalaxyclustersatredshiftsz=0.187toz=0.890toexaminetheredsequenceingreatdetail.Inparticular,weoptimizeourphotometricanalysistorecoverthefaintpopulationofgalaxiesembeddedinthelightpofmassivegalaxies.Weusespectralenergydistributiontoconstrainthepropertiesofredsequencemem-bers,whichweusetostudytheofage,metallicity,andstar-formationhistoriesonthegrowth,evolution,andscatterintheobservedclusterredsequenceacrosscosmictime.Weexploitthe16bandpassesandSEDttingtoobtainthehighlyrobustestimatesofk-corrections,basedoninterpolationsofthephotometryofoverlapping4.2DataThedatausedinthisworkaredescribedinChapter3,butwedescribethemhere.Weusedmoimagestodetectgalaxiesthroughoutthe25clustersoftheClusterLensingandSupernovasurveywithHubble(CLASH,Postmanetal.,2012b).Objectsweredetectedinatleast4intotal,wehad16ofdataforeachclustercoveringthe108Table4.1.CLASHRedshiftedFilterAnalogsClusterNameRedshiftugrYJmMAbell3830.189F435WF625WF775WF125WF160W39.82Abell2090.206F435WF625WF775WF125WF160W40.03Abell14230.213F435WF625WF775WF125WF160W40.11Abell22610.224F435WF625WF775WF125WF160W40.23RXJ21290.234F435WF625WF775WF125WF160W40.34Abell6110.288F435WF606WF775WF140WF160W40.85MS21370.313F475WF625WF814WF140WF160W41.06RXJ15320.345F475WF625WF814WF140WF160W41.31RXJ22480.348F475WF625WF814WF140WF160W41.33MACS11150.352F475WF625WF814WF140WF160W41.36MACS19310.352F475WF625WF814WF140WF160W41.36MACS17200.391F475WF625WF814WF140WF160W41.63MACS04160.396F475WF625WF814WF140WF160W41.66MACS04290.399F475WF625WF814WF140WF160W41.68MACS12060.440F475WF625WF814WF140WF160W41.93MACS03290.450F475WF625WF814WF140WF160W41.99RXJ13470.451F475WF625WF814WF140WF160W41.99MACS13110.494F475WF775WF105WF140WF160W42.23MACS11490.544F555WF775WF105WF140WF160W42.48MACS14230.545F555WF775WF105WF140WF160W42.49MACS07170.548F555WF775WF105WF140WF160W42.50MACS21290.570F555WF775WF105WF140WF160W42.60MACS06470.584F555WF775WF105WF140WF160W42.67MACS07440.686F555WF814WF105WF140WF160W43.09CLJ12260.890F625WF814WF125WF140WF160W43.79ultraviolettoinfraredbands.Foreachgalaxy,backgroundsubtractionwasperformedusingamode-basedestimateofthelocallight.PhotometryforeachgalaxywasperformedinthesameapertureforallAsthepointspreadfunction(PSF)fullwidthathalfmaximum(FWHM)is˘0:07000:1500(Fordetal.,2003;Siriannietal.,2003),whichissmallerthanourapertures,wedonotincludeaPSFcorrection.All25clustersusedinthisworkarelistedinTable4.1inorderofascendingredshift.Tocomparetheseclusterstootherworksandeachother,weasetofeersforeachclusterthatactasanalogstotheu,g,r,Y,andJHSTnamedinTable4.1werechosentobestsampletherest-framebandpassesoftheseewhilealsoavoidinganHSTbeingastheanalogfortwoadjacentground-basedforthesamecluster(apotentialproblemforclustersatthehighredshiftendofoursample).109Figure4.1ModeledSEDtoagalaxyintheofMACS1423(z=0:545).Inthisparticularrun,theredshiftwasallowedtovary.Upperlimitsaremarkedwithdownwardpointingarrows.TheemptyboxcorrespondstotheF555Wnodataweretakenusingthatforthiscluster.Theparametersoftheshownbspectrumarelistedontheleft.4.2.1SEDFittingWeSEDstoeverygalaxyinourcatalogwithABMagm<25:5intheF814Wor,forthosegalaxiesoutsideoftheF814Wofview,theapparentmagnitudeintheclosestavailableToaccomplishtheseweusediSEDfit(Moustakasetal.,2013),anIDL-basedBayesianinferenceroutineforextractingphysicalparametersfrombroadbandphotometry.iSEDfitisawidely-usedcodeforestimatinggalaxypropertiesatallredshifts(e.g.,Zitrinetal.,2012a;Airdetal.,2013;Brodwinetal.,2013;Zeimannetal.,2013;Fogartyetal.,2015).Whilethemethodsused,aswellassystematicissuescausedbypriorselection,110aredetailedinMoustakasetal.(2013),weexplainthetechniquehere.iSEDfitcomputesanintegratedSEDofagalaxyusingtheconvolutionintegralC(t;Z)=Zt0 (tt0)S(t0;Z)100:4A(0)dt0:(4.1)Here,isthewavelength,S(t0;Z)isthespectralevolutionofasimplestellarpopulationofmetallicityZ,andA(t0)isthewavelength-dependentdustattenuation. (tt0),thestarformationhistory(SFH),heretakestheformadelayed˝-model, (t)=M˝2tet=˝:(4.2)characterizedby˝,thecharacteristictimeforstarformation,andnormalizedtoM.Bothtand˝areinunitsofyears,sothat (t)isinunitsofSolarmassesperyear.ThisformoftheSFHallowsforalinearriseandanexponentialEachgalaxyisinputintoiSEDfitashavingbroadbandFi,uncertainties˙i,andredshiftz.iSEDfitcomputesaposteriorprobabilitydistributionfunctionp(QjFi;z)=p(Q)p(Fi;zjQ);(4.3)whereQarethemodelparametersandp(Q)istheparameters'spriorprobabilities.Thelikelihoodofthemodelgiventhedataisp(Fi;zjQ)=L/exp(˜2(Fi;zjQ)=2);(4.4)111where˜2iscomputedas˜2(Fi;zjQ)=NXi[FiACi(Q;z)]2˙2i:(4.5)HereAisanormalizationfactorandCi(Q;z)arethebroadbandfromeachmodelwithparametersQatredshiftz.Valuesofaparameterarederivedbyrandomlydrawingvalueswithprobabilitygivenbytheprobabilitydistribution(Equation4.3).Errorsarefoundbytaking1/4oftherangecoveredbythe2.3-97.7percentiles,whichreducesto1˙foraGaus-siandistribution.WeperformedananalysiswithiSEDfitwiththeredshiftattheredshiftoftheclustereachgalaxywasnear.Forasimplestellarpopulationmodel,weusedFlexibleStellarPopulationSynthesismodels(v.2.4;Conroyetal.,2009;Conroy&Gunn,2010)basedontheMILESstellarlibrary(ancazquezetal.,2006).WeassumedaSalpeter(Salpeter,1955)initialmassfunctionandatime-dependentattenuationcurveofCharlot&Fall(2000).OurpriorsincludedstellarmetallicityZ2[0:005;0:03]suchthatZ0:019),starformationtimescale˝2[0:0;5:0]Gyr,andgalaxyaget2[1:0;11:5]Gyr.AnexampleofawgalaxyisshowninFigure4.1.Forgalaxiesnotdetectedinsomeweusedthemeasured3˙upper-limitinthatapertureasanupperlimitfortheSEDs.However,forthosegalaxiesnotobservedinagivenwedidnotincludethatinouralthoughwerequiredgoodphotometryinatleastthreebandsinordertothegalaxy.DuetotheuncertaintiesintheHSTzeropoints(Bohlinetal.,2014;Bohlin,2016),weadda0.02magnitudeerrorinquadraturewith112ourmeasuredphotometryerrorsbeforeThissystematicuncertaintyisparticularlyimportantforbrightgalaxiesintheinfrared,whichhavetinystatisticalphotometricerrors.Oneoftheimportantparameterswederivefromtheseisthestar-formationrate(SFR)-weightedage.Forastarformationhistory, (t0),theSFR-weightedageisashtiSFRRt0 (t0)(tt0)dt0Rt0 (t0)dt0;(4.6)wheretistheageofthegalaxyatwhichhtiSFRisbeingevaluated.ely,thistermprovidesameasureofacharacteristicageofthestellarpopulationofthegalaxy.Forastarformationhistoryconsistingofasingleburstattimet0( (t0)=(t0t0)),thenumera-torofEquation4.6isanintegraloveradeltafunction,andtheSFR-weightedageistheelapsedtimesincethatburstoccurred,tt0.Forconstantstarformation( (t0)=ct0),Equation4.6integratestohtiSFR=t=3{thatis,theSFR-weightedageisone-thirdofthetotalageofthegalaxy.Finally,foranexponentially-decayingstar-formationhistory( (t0)=˝1expt=˝),aftertheexponentialtermhasdecayedtoward0,htiSFR.t˝.WeshowinFigure4.2thedistributionofbvaluesformetallicity,tform(describedbelow),totalmass(including,butnotlimitedto,stellarmass),andb˜2,aswellastheuncertaintiesonmetallicityandtform,forgalaxiesweclassifyasmembers(inSection4.3).ThesevaluesarefromtherunofiSEDfitassumingtheclusterredshift.Ascanbeseen,theerrorsarenon-negligible,particularlyformetallicity.Wethereforecautionagainstdrawingconclusionsfromindividualvalues;inthiswork,weonlyconsidertheaggregatepropertiesoflargesamples,particularlyinthecaseofmetallicity.113Figure4.2Bestparameters(orange)anduncertainties(purple)fromourSEDtformistheageoftheUniverseatthecluster'sredshiftminustheSFR-weightedage.Onlygalaxiesasclustermembersareshownhere.Derivationoftheseparametersisexplainedinthetext.114AspartoftheSEDttingroutine,wealsoobtainedk-correctedu,g,r,i,andzmag-nitudesforeveryobject.Toderivethesevalues,iSEDfitbeginsbydeterminingtheclosestmatchedtoeachtargetattheredshiftofthegalaxy.Itthencomputesamag-nitudebasedonthebSEDandreturnstheoriginalphotometrycorrectedbythatThisprocedureretainsthephotometricerrorsontheoriginalr.Forgalaxieslackingphotometryinthebest-matchedthecodewillsynthesizeamagnitudefromtheSEDbutwillnotreturnaphotometricerror,asthosearelimitedtoobservederrors.Syntheticmagnitudesareneededwhengalaxiesareoutsideoftheofviewofcertainandthereforearenotobservedintheclosest-matched4.3ClusterMembershipHavingassembledacatalogofphotometryandSEDforalargesampleofgalaxiesaround25galaxyclusters,wenextdeterminedclustermembership.AlongwiththeSEDwealsousedspectralredshiftcatalogsandpreviously-determinedphotometricredshiftprobabilities(bothofwhicharedescribedinSection3.3.2).Wecomparetheresultsofourselectiontotheresultsofanalternativetechnique:redsequencememberselection.HereweconsideronlythosegalaxieswithSEDthatis,weagainexcludegalaxieswithF814WmagnitudemF814W>25:5.Wecombinethephotometry,photometricredshiftpa-rameters,SEDvalues,k-correctedmagnitudes,andspectroscopicredshiftmeasurementsforallofthesegalaxiesintoonecatalog.Foreachgalaxy,weusethediscreteprobabil-115itydistributionsproducedbyBPZtodetermineatotalprobabilityofthatgalaxybeingwithinsomeredshiftrangeofthenominalclusterredshift.Here,weconsiderjzj<0:03,jzj<0:05,jzj=(1+zc)<0:03,andjzj=(1+zc)<0:05;welabelthesummedprobabili-tieswithinthoserangesP03,P05,P103,andP105,respectively.Foreachgalaxyinthiscatalog,weconsiderspectroscopicredshifts.Anygalaxywithjzj=(1+zc)<0:03isconsideredaclustermember;thosewithjzj=(1+zc)>0:10areconsiderednon-members.Therestofthegalaxies{eitherthosewithindeterminatespectro-scopicredshiftsornospectroscopicredshifts{arethencharacterizedbytheirphotometricredshiftprobabilities.Asapass,thosegalaxieswithtotalprobabilityP03>0:8areassignedasmembers,whilethosewithP105<0:1areasnon-members.Wenextconsideredtwopossiblewaystoidentifyclustermembers:awSEDorabphotometricredshiftsolution.Galaxieswith˜2<1:5and˜2>0:7(toavoidselectinggalaxieswithpoorly-constrainedsthroughthiscut)intheSEDattheclusterredshiftwereasclustermembers,aswerethosewithamostlikelyorbestredshiftdeterminationfromBPZwithinjzj=(1+zc)<0:05.Fortheremainingobjects,weexam-inedthedistributionsofP03,P05,P103,andP105;weonlyclassifythoseremaininggalaxieswithP103>0:2andP105>0:6asmembers,whiletherestareasnon-members.Ourcatalogcontainsalloftheinformationusedtomakethisdecision,soalternativecutscanbetested.116Figure4.3TheanaloggrCMDforall25clusters.Shownontheleftarethosegalaxieswecallmembers,whilethosecasnon-membersareplottedontheright.Hexbinsarescaledlogarithmicallywiththenumberofgalaxiescontainedinside.4.3.1AlternativeSelectionsSelectingclustermembersfromtheredsequenceisacommontaskinclusterscience(e.g.,Koesteretal.,2007b;Haoetal.,2009;Ryketal.,2014,2016,amongmanyothers).Asthisprojectleveragesover500hoursofHSTobservationsandacoordinatedspectroscopicfollowupcampaigntodetermineclustergalaxyproperties,ourclustermembercatalogscangreatlysurpassthoseusingonlyground-based,few-colorobservations.Tobetterenablethesciencefromthoseobservations,wequantifytheofredsequenceselectiononourmorerigorouslycompiledmembershipdeterminations.ShowninFigure4.3isaplotofgranalogcolorsvs.rmagnitudeusingtheanalogslistedinTable4.1.Ontheleftpanelisshownthosegalaxiesasmembers;ontherightarethoseasnon-members.Readilyapparentinthisimageisasecond117Figure4.4Thek-correctedgrCMDforall25clusters.Shownontheleftarethosegalaxieswecallmembers,whilethoseasnon-membersareplottedontheright.Apotentialredsequenceselectionregionisshownasashadedbox.Hexbinsarescaledlogarithmicallywiththenumberofgalaxiescontainedinside.redsequence.Thisisanoftheanalognotexactlymatchingtherest-framebandpassesfromclustertocluster.Thus,severaljumpsarevisiblebetweenclusters,andwecautionagainstusingevenbest-matchedanalogsinlieuofk-correctedmagnitudes.Nevertheless,wefurtherexaminetheofredsequencefor\best-matchedinSection4.4.Similarly,inFigure4.4weshowaplotofgrcolors,thistimeusingk-correctedmag-nitudes.Bymitigatingtheof(thatis,interpolatingtoauniformsetofrest-framemagnitudes),weseetheredsequencesareallatsimilarlocations.Here,weaselectionregion,countingthosegalaxieswith0:5<gr<0:875.Forgalaxiesbrighterthanr<16,67.0%ofclustermembersareinsidethiscolorregion,butsoisanadditionalpopulationofnon-memberswithsizeequalto68.3%ofthetotalmemberpopulationabove118thatbrightnessthreshold.Increasingthemagnitudecuttor<16,89.9%ofmembersfallwithinthatcolorregion,whilethecontaminantpopulationisonlyequalto18.1%ofthetotalclusterpopulationinthatluminosityrange.Basedontheseresults,selectinggalaxiesusingtheredsequenceiswellsuitedforselectinggalaxiesatthetipoftherelation.However,thisselectionnotonlyfailstoaccountfortheentireclusterpopulationatfaintermagnitudes,italsobecomestlybycontamination.4.4RedSequenceFittingNumerousstudieshaveexaminedtheredsequenceacrossredshift,makinguseofanumberofground-andspace-basedobservatories.Here,wehaveaccessto16withwhichtoselectacolorandmagnitudecomponent.TobestmatchourresultswiththoseoftheSloanDigitalSkySurvey(SDSS),weselectgrcolors,usingbothk-correctedmagnitudesandtheHSTeranalogsthatbestmatchtherestframecharacteristicsofthosetwougrizThechosentoaccomplishthisarespinTable4.1.Asthedataweareaslopetohaveerrorsonbothvariables,wealinearslopetoourphotometryusingapythonBCES(Akritas&Bershady,1996)routineusedinNemmenetal.(2012).Here,weusedtheorthogonalestimator,althoughweobtainedsimilarresultswiththeyjxestimator.Ourwastotherelationgr=A(r+20)+B:(4.7)119Figure4.5Thegrvs.rcolormagnitudediagramsforgalaxiesascolormembersusinganalogmagnitudesideninTable4.1.Clustersareplottedinincreasingredshiftorder,startingintheupperleftandinthelowerright;thesecond-lowest-redshiftclusteristhesecondframeinthetoprow.ClusternamesforallclustersexceptCLJ1226.9+3332aredisplayedfollowingtheconventioninTable1.1.120Figure4.6Thegrvs.rcolormagnitudediagramsforgalaxiesascolormembersusingk-correctedmagnitudes.ThedetailsofthisplotareotherwisethesameasforFigure4.5.121Table4.2.RedSequenceFitsAnalogFilteraK-correctedaClusterNameA100BA100B˙intAbell3830:6100:1310:4250:0032:0530:2090:7230:0050.008Abell2091:1800:0940:4260:0021:8080:2400:7220:0050.016Abell14230:9890:1500:4360:0030:7590:3150:7480:006bAbell22610:6870:1290:4460:0031:2180:1860:7290:004bRXJ21290:8010:2460:4500:0051:7680:3170:7240:0070.010Abell6111:1320:1810:7800:0021:1020:2970:7220:0050.018MS21370:9720:3010:6160:0041:3520:3240:7140:006bRXJ15320:5380:3180:6400:0040:9190:3230:7210:005bRXJ22481:1380:2020:6140:0041:4600:1760:6900:003bMACS11150:9690:2500:6420:0051:1720:2400:7160:005bMACS19311:8770:2550:6300:0031:3370:2310:7150:003bMACS17201:7940:2270:6410:0041:8760:2520:6750:0040.011MACS04160:8840:1960:6750:0031:0380:2820:6990:003bMACS04291:4160:2390:6780:0031:6950:4190:7100:004bMACS12061:0530:2210:7590:0032:6740:2020:6790:003bMACS03290:9650:2090:7650:0031:5220:2560:6990:0040.021RXJ13471:3570:2840:6490:0051:1910:2090:7080:003bMACS13112:2240:4820:5770:0062:0910:3200:6580:005bMACS11492:6420:3100:5750:0042:1320:2390:6700:003bMACS14231:5090:4020:6030:0051:2170:3010:6770:004bMACS07172:7560:3410:5680:0052:5500:2710:6600:0030.028MACS21292:8640:3250:6110:0063:6510:2970:6700:004bMACS06473:0500:4740:6120:0062:9590:3940:6420:0050.034MACS07442:0340:3620:6520:0062:0180:3270:7020:0040.024CLJ12261:3140:3601:2400:0071:8770:5330:6310:007bNote.|Foreaseofunderstanding,Aisscaledupbyafactorof100inthistable.avaluesofgr=A(r20)+Bb˜2valueofbestbelow1.122Figure4.7Measuredredsequenceslopesforthe25CLASHclustersasafunctionofredshift.K-correctedvaluesareshowninorange;observedvaluesareinpurple.Theeclusterschosenfortheirpropertiesaremarkedwithboxes,whilethe20X-rayselectedclustersaredenotedwithcircles.AbofjusttheX-rayselectedclustersforbothsetsofmagnitudesisshownwithsolidlines;thosesamewhenincludingthestronglenssourcesareshownbydashedlines.Toavoidweappliedacutincolor-magnitudespacetoexcludegalaxieswelloftheredsequenceforeachcluster.Wereporttheresultsofourbestforall25clus-tersinTable4.2andshowtheminFigure4.5.Additionally,weconsiderthek-correctedvaluesofthisrelationshipforeachcluster.Afteragainapplyingaselectioncut,wetheredsequenceforgandratz=0;thesearealsoshowninTable4.2andshowninFigure4.6.OurbslopesareshowninFigure4.7.WeagainusedBCESwiththeyjxestimatortoperformalineartoArs/mz,wheremisthechangeintheslopeoftheredsequence,asafunctionofredshift.Forthek-correctedvalues,m=(18:648:17)103,whileforthenotk-correctedvalues,m=(26:1511:08)103.However,theseslopesaresigtlybytheslopesoftheredsequencesintheeCLASHclusterschosenduetotheirstrongpotential.Selectingonlythe20X-rayselectedclusters,theseslopes123Figure4.8Measuredredsequenceinterceptsforthe25CLASHclustersasafunctionofredshift.Theeclusterschosenfortheirpropertiesaremarkedwithorangeboxes,whilethe20X-rayselectedclustersaredenotedwithpurplecircles.AbestofjusttheX-rayselectedclustersisshownwithasolidline;thesamewhenincludingthestronglensingsourcesisshownbyadashedline.TheexpectedbehaviorofapopulationwithmetallicityZˇ0:5Zformedatz=2isshownbythedottedblackline.becomem=(8:334:37)103withthek-correctionandm=(14:146:38)103without.Inallfourmethods,weseeanevolutionintheredsequenceslopeontheorderof2˙,buttheimportanceofaccuratek-correctionisclearlyshownbythedecreaseinthemagnitudeoftheevolution.Althoughweignoretheinterceptoftheredsequenceforobservedcolors(asitisin-herentlybiasedbychoices),weshowtheevolutionoftheinterceptwithk-correctedmagnitudesinFigure4.8.Again,weuseBCEStoalinetothesevalueswithredshift.Here,thebestslopeis0:130:02whenincludingonly20clustersand0:150:02withall25.Theseresultsareclearevidencethattheredsequencegetsredderwithage.Whilethisresultisnotsurprising(reddeningwouldbeanaturalconsequenceofpassiveevolution;cf.galaxies,Brownetal.,2007),wedofurtherpopulatethelimitedsampleofrest-frame124measurementsofredsequenceintercepts(e.g.,Foltzetal.,2015,whoreportednointerceptvaluesbelowz=0:8).Weshowanexpectedtrackforastellarpopulationformedatz=2.0withmetallicityZˇ0:5Zandanexponentialburststarformationhistorywithdecaytime˝=0:5Gyr.ThesemodelsweregeneratedwithEzGal(Mancone&Gonzalez,2012)usingthemodelsofConroyetal.(2009)andConroy&Gunn(2010),assumingaKroupa(2001)initialmassfunction.Wealsoconsidertheintrinsicscatterabouttheredsequencefortheseclusters.Weattempttoaterm,˙inttotheredsequencegalaxiessuchthat,foracluster,˜2=1n2Xi((giri)(A(ri+20)+B))2˙2gr+˙2int=1:(4.8)However,for16clusterswhenusingk-correctedmagnitudes,˜2wasalreadybelow1with-outanyintrinsicscatter,implyingthatthemeasurementerrorsweretoolargetomeasureanyintrinsicscatter.Fortheremaining9,ourmeasuredintrinsicscatterisgiveninTable4.2.4.5IndividualGalaxiesWhilephotometricanalysisoftheCLASHclustersisobviouslyimportant,wealsohavetheabilitytoconsiderthephysicalpropertiesofindividualgalaxiesalongtheredsequence.Twopropertiesofparticularinterestarethemetallicityandageofgalaxies,aswepredicttheywilltheslopeandscatteroftheredsequence,respectively.Tothatend,weusethefullresultsofourSEDtoconsidertheaggregatebehaviorofclustergalaxies.125Figure4.9Themetallicityfunctionofclustermembers,givenbyfromandpositionalongtheredsequence.Hexbinsarecoloredaccordingtotheirmedianmetallicity,asindicatedbythecolorbar.Forlegibility,onlythosebinswithatleasttwocountsareshown.gandrmagnitudesarek-corrected.Themedianmetallicityinonemagnitude-widebinsisshownatthebottomoftheplot,whilethemedianmetallicityin0.05magnitude-widecolorbinsisshownontheleft.First,weexaminedtherelationshipbetweenmetallicityandabsolutemagnitudeforthegalaxiesinoursample.Usingk-correctedmagnitudes,weconsideredonlythosegalaxieswithgrcolorwithin0.1magsofthemeasuredredsequence.WeshowtheresultsofthissamplecutinFigure4.9.Tomaximizethestatisticalpowerofoursample,weonlyshowhexbinswithatleasttwogalaxies,andthemetallicityforeachbinisthemedianmetallicity.Strikingly,anincreaseinmedianmetallicityasredsequencebrightnessincreasesisvisibleinFigure4.9.Toverifythis,weconsiderthemedianmetallicityvalueforgalaxiesinone-magnitude-widebins,startingwith23<Mr<22anddecreasingto19<Mr<18,ignoringthosegalaxieswithgrcolorsfromtheredsequencebymorethan0.1126Figure4.10TheSFR-weightedformationagefunctionofclustermembers.Hexbinsarecoloredaccordingtotheirmediantform,whichisdescribedinthetext,asindicatedbythecolorbar.Forlegibility,onlythosebinswithatleasttwocountsareshown.gandrmagnitudesarek-corrected.Themedianagein9colorbandsareshownontheleftoftheandin6magnitudebinsatthetop.magnitudes.Themedianmetallicityinthesebins(withsamplesizeinparenthesis)are0:4870:032Z(164),0:4040:018Z(556),0:3570:015Z(851),0:3400:016Z(698),and0:3320:018Z(535),respectively.ThistrendisshowninFigure4.9asthebaronthebottom.Inadditiontometallicity'sontheslopeoftheredsequence,ourSEDalsoprovideinformationonhowgalaxyagesdeterminethepropertiesoftheredsequence.Toinvestigatethistrend,weconsidertheSFR-weightedagesderivedfromtheSEDbestBysubtractingfromtheseagestheageoftheUniverseateachclusterredshift(calculatedusingWright,2006),wecomputeaparameter,tform,thatdescribestheageoftheUniverseatwhicheachgalaxy'sstellarcomponentwasformed.127Asweexpectthatage'sprimaryontheredsequenceistoplacegalaxiesaboveorbelowthemeasuredline,wealsocalculatedancolor,gr),ofhowfarfromtheredsequenceofitshostclustereachgalaxywas.Thismetricwassothatpositivevaluesareredderthanthemeasuredredsequenceslope.Wethenplottedourre-sultsasbefore,withhexesshowingthemediantformvalueforallgalaxiescontainedinsideofit,andonlyhexeswithatleasttwogalaxiesbeingshown.ThisresultisshowninFigure4.10.Weseeagradientalongthecoloraxis,wherebyobjectsredderthantheredsequenceformedearlierthanthosebluerthantheredsequence.Thisresultisseenatallmagnituderanges.Asacheck,wecomputethemediantformvaluesingr)binsof0.05magni-tudes,beginningatgr)=0:1andworkingdownto(gr)=0:35forthosegalaxiesbrighterthanr<17;thetformvaluesineachbinare4:10:1,4:10:1,4:60:1,5:60:1,6:40:1,6:00:1,7:40:2,7:60:1,and7:70:2Gyr,respectively.Wenotethatthismini-mumvalueoftformreachedisconsistentwithclusterformationbeginningataroundz˘1:5.Wealsoconsiderthetwoorthogonalgradients{changesinmetallicitywithcolorandchangesintformwithabsolutemagnitude.Tomeasuremetallicity,weusedfour0.05magnitude-widebinsfrom(gr)=0:1togr)=0:1extendingtor<19,andfoundmedianmetallicitiesof0:3410:025Z(268),0:3700:015Z(827),0:3620:015Z(818),and0:3840:022Z(367).Thisisshownontheleft-handsideofFigure4.9.Wealsolookatagevariationbythemedianagesin1magnitude-widebinscontainingallgalaxieswithingr)=0:1togr)=0:1.Here,wetformvaluesof3:80:2,3:90:1,4:40:1,4:60:1,4:90:1,and5:40:1Gyr,respectively.TheseresultsareshownonthetopofFigure4.10.1284.6Mass-to-LightRatiosWeusedourk-correctedphotometryandSEDmassestimatestoderivemass-to-lightval-uesforthegalaxiesinoursample.Usingk-correctedi-bandmagnitudes,wecalculatedluminositiesusingL=L=100:4(M;iMi);(4.9)whereM;iistheabsolutemagnitudeoftheSunini-band.WeusedavalueofM;i=4:57;thisistakenfromtheSDSSonlinedocumentation3,butitalsoagreeswithreportedvaluesfromBlantonetal.(2003),althoughthatworkusedasolarmodelredshiftedtoz=0.1.InFigure4.11weshowthedistributionofstellarmasstoi-bandluminosityratiosforalloftheclustermembersinoursample.Weseetwopopulationsinthisagroupingofhighermass-to-lightratiogalaxiesthatextendsfrombrighttofaintgalaxiesandalowmass-to-lightclumplimitedtofaintergalaxies.Whenweselectonlythosegalaxiesneartheredsequence,weseethatthesepopulationstraceredsequenceandbluecloudpopulations,respectively.Forthosegalaxieswithgrcolorswithin0.05magnitudesoftheredsequence,themeanmass-to-lightvalueislog(MM)=(LL)=0:410:18.WhenonlyconsideringthosegalaxieswithL=L>10,thisbecomeslog(MM)=(LL)=0:480:12.3http://www.sdss.org/dr13/algorithms/ugrizVegaSun/129Figure4.11Stellarmasstoi-bandlightratiosforallclustermembers.Inthebottompanel,weshowthedistributionofmass-to-lightratioswithrespecttooverallluminosity,inSolarunits.Onlyhexbinswithatleastonecountareshown.Intheupperpanel,weshowthedistributionofmass-to-lightratios;purpleisallgalaxies,fuchsiaisthosegalaxiesgrcolorswithin0.1magnitudesoftheredsequence,andorangeisthosegalaxieswithgrcolorswithin0.05magnitudesoftheredsequence.Thedistributionoflowmass-to-lightratiogalaxiesisdominatedbylow-luminositygalaxiesoftheredsequence.1304.7DiscussionInthiswork,wehavecharacterizedtheredsequencepropertiesfor25massivegalaxyclusterscoveringaredshiftrangeofzˇ0:2tozˇ0:9.Welittle(<2˙)evidenceforanevo-lutionintheslopewithredshiftouttoredshiftz=0:89;themagnitudeofthisevolutionisreducedwhenexcludingthe5higclustersintheCLASHsample.Weobservethereddeningoftheredsequencegetsredderwithage,herepresentedinrest-framecolors.And,whilelimitedbythescaleofphotometricerrors,weseeanincreaseintheintrinsicscatterabouttheredsequenceforincreasingredshift.Incombinationwiththese,weuseSEDtostudythepropertiesofredsequencegalaxies.Weatrendofincreasingmetallicitywithincreasingbrightnessaswellasatendencyforgalaxiesbluerthantheredsequencevaluetohaveformedlater;however,wealsoafaintagegradientalongtheredsequenceitself.Here,weconsiderhowtheseresultsfactorintoourunderstandingofclusterevolution.Ceruloetal.(2016)littleevolutionintheredsequenceslopefromz=1:5toz˘0,apicturesupportedbynumerousotherworks(e.g.,Lidmanetal.,2004;Ascasoetal.,2008;Lidmanetal.,2008;Meietal.,2009;Snyderetal.,2012).Incontrast,Stottetal.(2009)aslopeevolutionfromz=0:5toz˘0:1.Others,suchasHaoetal.(2009)evidenceofasmallamountofslopeevolution,comparabletothiswork.Constrainingthisevolutioniscriticalforuncoveringtheoriginoftheredsequence(Kodama&Arimoto,1997).Determiningtheexactformationepochoftheredsequenceisanongoingchallenge.Whileproto-clustershavebeendiscoveredbeyondz>3(Deyetal.,2016),detectionofthe131redsequenceitselfistougher.Katoetal.(2016)identifyanenhancementofstar-formationdensityaround2.z.3protoclusters.Francketal.(2015)idenaredsequencepre-cursorinagalaxyclusteratz=1:83,althoughtheredsequencewasnotwelldeveloped.Andreonetal.(2014)observedaComaprogenitoratz=1.803withamassfunctionsimilartolow-redshiftclusters.However,Eisenhardtetal.(2008)ainthepopulationofcolor-magnitudeidenclustersataroundzˇ1:5,despitethesebeingwithinthelimitoftheirsurvey.Theoriginofmetalsingalaxiesacrosscosmologicaltimescaleshasbeenpreviouslystud-ied.Dave&Oppenheimer(2007)usedcosmologicalsimulationstoshowthatgalaxieshavemetalsearlyon{atz˘6,starsalreadyhavemeanmetallicitiesof0:1Z.Similarly,Hop-kins&Beacom(2006)foundthatthemetalmassbuild-upratepeaksbetween1<z<3.Yuanetal.(2013)foundonlya0.35dexmetallicityfromz=2.07toalocalsample.Forclustersinparticular,DeLuciaetal.(2004a)foundthat35-60%ofthecurrentICMmetalvaluewasinplacebyz=2.Aformationepochoftheredsequenceintheregimeofzˇ1:52wouldimplythatmetalaccumulationhasalreadyoccurred,andclustergalaxiescouldshowmetallicitydeviationsaccordingtotheirmass.Andreonetal.(2014)anagegradientamongclustergalaxiesinaclusteratz˘1:8,wherebylessmassivegalaxiesareyoungerattherateof650Myrperorderofmagnitudedecreaseinmass.WealsoconsidertheresultsofTanakaetal.(2005),whopresenteda\down-sizing"hypothesisthatlargergalaxiestheirstarformationbeforesmallergalaxies,andthisresultpropagatesdownward.Similarly,DeLuciaetal.(2004b)evidenceforongoingevolutionoflowluminosityclustergalaxies.Likewise,DeLuciaetal.(2007)arguethathigh132redshiftclustersstillhavegalaxiestransitioningontotheredsequence.EvidenceforthisisseenbyLemauxetal.(2012),whofoundnotonlyaoflow-luminosityred-sequencegalaxiesintheCl1604(z˘0:9)superclusterbutalsoevidencethattheaverageclustergalaxyinthishasthespectrumofastar-forminggalaxy.Oneofthemainargumentsforabuildupoftheredsequencecomesfromtheofthefaint-endslopeintheclusterluminosityfunctionforredsequencemembers(e.g.,Rudnicketal.,2009).Strazzulloetal.(2010)andManconeetal.(2012)didnotlimittheirsampletoredsequenceselectedmembersonly,andtheyreportluminosityfunctionsatz˘1:4.Theseresults,intandem,implythatclustergalaxieswereinplaceattheformationoftheredsequence,butfaintgalaxiesdidnotimmediatelyoccupytherelation.Inthiscontext,weconsiderourresults.Toorder,ourofagradientinmetal-licitydowntheredsequence,minimalageevolutionfrombrighttofaintredgalaxies,andonlyaweakevidenceofevolutionintheslopeoftheredsequencesupportsthewell-defendedparadigmthattheredsequenceisitselfaconsequenceofametallicitygradientbetweenlargeandsmallgalaxies.However,oursecondaryindicators{asmallagegradientfrombrighttofaintmembers,theaforementionedsmallyetpresentevolutionoftheslope,thegrowthofintrinsicscatterwithincreasingage,andtheincreaseingalaxyageforbluergalaxiesthemainrelation{tantalizingevidenceoftheongoinggrowthandevolutionofsmallerclustermembersontothemainrelation.WeshowtwotoymodelsofredsequenceslopeevolutioninFigure4.12.Inpink,weshowaslopecausedbytwogalaxiesspacedthreemagnitudesapart,inwhichthebrighterobject133Figure4.12Measuredslopesofthegrredsequenceforthe25CLASHclustersasafunctionofredshift.Measuredslopesareshowninpurple.Weshowtwotoymodels:ametal-drivenslopemodel(orange)andanage-drivenslopemodel(pink),bothofwhicharedescribedinthetext.Neitherisabletocompletelymodelthebehavioroftheredsequence.formedatz=2.25andthefaintergalaxyformedatz=1.0.Inorange,weshowtheslopecausedbythesetwogalaxiesbothformingatz=1.8,butwiththebrightergalaxyhavingametallicityZ˘0:5ZandthefaintergalaxyhavingametallicityZ˘0:3Z.ThesemodelsweregeneratedwithEzGal(Mancone&Gonzalez,2012)usingthemodelsofConroyetal.(2009)andConroy&Gunn(2010),assumingaKroupa(2001)initialmassfunction,assum-inganexponentiallydecayingstar-formationwithcharacteristictimescale˝=0:1Gyr.Neithermodeldescribestheredsequenceslopeevolution,meaningthattheredse-quenceformationmechanismismorecomplexthanjustmetallicityInSection4.6wefoundaconnectionbetweenmass-to-lightratiosandtheredsequence,withtheredsequenceonthecolor-magnitudediagramhavingthesamemembershipasa134mass-to-lightsequencewhencomparedtostellarmasses.Previousstudieshavenotedacon-nectionbetweenredgalaxieshavinghighermass-to-lightratios(Bell&deJong,2001;Belletal.,2003;Zibettietal.,2009;Tayloretal.,2011).Here,wequantifythevalueoftherelationspforredsequenceclustergalaxies,whichevolveindenserenvironmentsthangalaxiesandmaythereforebesubjecttotevolution.WealsoconsidertheconcernofcircularityinourFindingagradientofmetallicityalongtheredsequence,aswellasanagegradientoftheredsequence,couldbothbecon-sequencesofiSEDfitmakingredgalaxiesmoremetal-enrichedandolder.However,whilewehaveonlydiscussedtheredsequenceasitappliesinonecolor,ourSEDleveragetlymorecolors,withspectralcoveragefromtheultraviolettotheinfrared.Figure4.13showstracksofconstantageandmetallicityforgalaxypopulations,asseeninthreecolorsets.ThesedataweretakenfromtheMILESstellarlibrary(ancazquezetal.,2006;Vazdekisetal.,2010)usingPadovaisochrones(Girardietal.,2000)andarevisedKroupa(2001)initialmassfunction.Thesetrackscoveragesfrom˘0:01to˘15Gyrandmetallicitiesof[M=H]˘2:2to[M=H]˘0:2.Althoughsingle-colormeasurementsdonothavetheabilitytotiatebetweenageandmetallicitytracks,color-colormeasurementsdo.And,whilesomeregionsshowpile-up(suchasVRˇ0:2whencomparedwithU-B),athirdcolorcanbreakthatdegeneracy.Forthatreason,whiletheredsequencemaybeinthisworkasagrcolor,ourSEDtscanutilizealloftheotheravailabledatatomakeadeterminationofmetallicityandage.Ourofthepropertiesinonecolorarenotcircularlybasedonthatonecolor.135Figure4.13Color-colorplotsshowinghowgalaxiesoftmetallicitiesandagesoccupysimilarspacesincolor-colorplotsthatcanbebrokenapartbyfurtherphotometricinfor-mation.Inthetoppanel,tracksshowlinesofconstantmetallicity,whilethebottompanelshowsisochrones.ColorsarefromJohnson/Cousinrs.Inthetop(bottom)panel,linesarecoloredbyincreasingmetallicity(age),withthebluestlinesbeingthemostmetal-poor(youngest).Squaresdenotetheyoungest(mostmetal-poor)partofeachtrack,whilecirclesdenotetheoldest(mostmetal-rich).ThesetracksaretakenfromtheMILESstellarlibrary.1364.8SummaryWeexpanduponthephotometriccatalogproducedinChapter3byintegratinggalacticparametersfromSEDanddeterminingclustermembership.WeusetheseexpandedcatalogstotheredsequencesoftheCLASHsample.Additionally,weexploitourSEDparameterstocomparethepropertiesofclustergalaxiesatentpartsoftheredse-quence.Ourresultsaresummarizedbelow.1.Weuseallavailableredshiftinformationtoderivemembershipprobabilitiesforthe22,557galaxiesinourphotometriccatalog.We6,185(27%)ofthegalaxiesinourcat-alogareclustermembers.Usingthesedeterminationsandgalaxyphotometry,wemeasuretheimpactofredsequenceselectionaloneinclassifyingclustergalaxies.Wetcontamination(ontheorderoftheextractedclusterpopulation)forselectionswellbelowM*,butwhenonlyselectingthetipoftheredsequence,clusterpurityisattheorderof80%.Additionally,k-correctedmagnitudes,ifavailable,performbetteratclustergalaxyselectionthanobservedmagnitudesfordeterminationsacrossmultipleclusters.2.Wemeasuretheslopeandinterceptsoftheredsequenceforall25CLASHclustersinbothobservedandk-correctedbands.Whileweseeweakevidenceforanincreaseintheredsequenceslopewithredshiftforobservedmagnitudes,thisisreducedbothbyusingk-correctedvaluesandexcludingthe5CLASHclustersnotintheX-rayselectedsample.However,wedomeasureadecreaseintheredsequenceinterceptwithincreasingmagnitude;137thisentailsthattheredsequenceitselfgetsredderwithage.3.Usingmetallicitymeasurementsforourclustergalaxiesinaggregate,wemeasurethetotalmetallicityasafunctionofpositionalongtheredsequence.Wethatbrightergalaxiesaremoremetal-richthantheirfaintercounterparts.4.Inasimilarfashion,wedeterminetheSFR-weightedagesforgalaxiesinall25clusters,andusetheageoftheUniverseattheclusterredshifttoestimateaformationtime.Bycomparingthesevaluestothecolorfromourmeasuredredsequenceslopes,wenotonlythatclustermembersbluerthantheredsequencepreferentiallyformedafterthosegalaxiesontheredsequenceitself,butthatagradientexistsintheclusteritself,suchthatfainterredsequencemembersareslightlyyoungerthantheirbrightcounterparts.5.Weinvestigatethestellarmass-to-lightratiosofgalaxiesidenasclustermem-bers.Wethatgalaxiesfallintotwopopulations,whichalignwiththeirassociationwiththeredsequence.Redsequencemembersshowagreaterratioofstellarmasstolight,bylog(MM)=(LL)=0:480:12atthebrightend.Incontrast,clustermembersnotassociatedwiththeredsequencearemoreluminousfortheirstellarmass.ThomasConnoracknowledgessupportfromafellowshipfromtheMichiganStateUn-versityCollegeofNaturalScience.WeusedthecosmologicalcalculatorpresentedinWright(2006)inthiswork.Facilities:HubbleSpaceTelescope/ACS,HubbleSpaceTelescope/WFC3,138Chapter5SummaryThebodyofthisdissertationhasstudiedtheevolutionofgalaxyclusterpropertiesacrossmassandredshiftusinghigh-qualityspace-basedobservations.InChapter2,weusednewandarchivalXMMimagingtore-examineasampleofmoderate-luminosity,intermediate-redshiftgalaxyclusterswithwellweaklensingmasses.Ourmeasurementsofthescalingrelationsbetweenmass,luminosity,andtemperaturepushedtothelimitofthegroup/clusterboundary,wherewesawnoevidenceforabreakinscalingrelationproperties.InChapter3,wedetailedanovelnewtechniquefordetectingandphotometeringgalaxieswellbeyondM*inclustersofgalaxies.Ourconsistencymeasurementswithsimilardatasetsverifytheaccu-racyofourtechnique,theutilityofwhichwedemonstratedwithameasurementofclusterluminosityfunctions.InChapter4,weusedSEDinconjunctionwithphotometricredshiftstoclassifythemembersfromournewclustergalaxysample.WeusedtheseSED-derivedparameterstoinvestigatethepropertiesoftheredsequence,whichshowedevidenceofadelayedonsetforfaintluminositygalaxiestojointhecolor-magnituderelation.Weconcludethisworkwithabriefdiscussiononthefuturestepsofthisresearch.139Figure5.1Luminosityfunctionsforthe25CLASHclustergalaxies,takingonlythosewithinjgr)j<0:2ofthemeasuredredsequence.ThisisotherwisethesameasFigure3.11.1405.1RevisitingtheLuminosityFunctionInChapter3,wediscussedtheresultsofaSchechterluminosityfunctiontotheCLASHclustergalaxies.However,thesedataanunprecedentedlaboratorytodelveevendeeper.Asastartingpoint,weconsidertheluminosityfunctiononlyforredsequencemembers.Whileourmeasuredvaluesofareconsistentwith˘0:8,implyingonlyaminimumamountofinclusterpopulation,onlythosegalaxieswithredse-quencecolorswithinjgr)j<0:2,weasharpdeclinein.ThisisshowninFigure5.1.Inthecontextofaclustercolor-magnituderelation,faintergalaxiesarebelievedtoar-rivelaterintime.Thisisevidencedbydinfaint,red-sequenceobjectsatgreaterredshiftsrelativetolowerredshifts.Asweareabletosampleapproximately5magnitudesbelowM*,wewillbeabletomeasurethemagnitudeofthisfromz˘0:2toz˘0:9withourclustersample.Additionally,wehavewell-constrainedk-correctedcolorsacrossalargemagnituderangeandalargeexpanseofredshift.WewillbeabletostudytheevolutionofM*atmultiplewavelengths.Althoughinterestinginitsownright,wewillbeabletoprovideauniformstandardwithwhichtocompareclustergalaxiesacrossahostofphotometricsystemsandredshifts,facilitatingfurtherinvestigationofclusterluminosityfunctionsbyourselvesandothers.141Figure5.2Thegivs.icolormagnitudediagramsforgalaxiesascolormembersusingk-correctedmagnitudes.ThedetailsofthisplotareotherwisethesameasforFigure4.6.Thevalueofthegrslopeisstillshowntoillustratethechangebetweensets.1425.2WhichRedSequenceInthiswork,weonlyconsideredtheredsequenceusinggrcolors.However,wehavemultipleothertochosefrom.Constrainingtheevolutionoftheredsequenceinonesetprovidesapivotarmwithwhichtoinvestigateclusterevolution.Constrainingtheevolutioninmanysetssetsapaththroughwhichclustergalaxyevolutionmusttravel,asopposedtosimplyaregionitmustavoid.WeshowanexampleofhowtheredsequencemeasurementschangewithregardtolterchoicesinFigure5.2.Aswellasbeingbytvaluesoftheslopeandinterceptoftheredsequence,theadditionalcolortermallowsustoevenmoreselectclustermemberstoas\redsequencemembers."Iterativepassesofinmultiplesetscanbeusedtomoreaccuratelycharacterizetheintrinsicscatterforeachcluster,whilealsominimizingcontaminationfromgalaxieswithphotometrythatonlypartiallyfollowsthecolorridgeline.Onefurtherproductofmorecompleteredsequencemeasurementswillbemodelsofgalaxyevolution.Previousworkshaveevolutionarytracksusingtheirmeasuredredse-quencestosetmandatoryphotometricvaluesatcertainredshifts.However,wecantakethisonestepfurther,byutilizingourageandmetallicityconstraintsfromSEDtorequiregalaxieswithcertainphysicalparameterstohavecertainphotometryatagivenredshift.AsshowninFigure4.13,agetracksareapparentwhenutilizingmultiplecolors.1435.3BringtheBackgroundtotheForegroundThroughoutthiswork,wehavemadefulluseofourphotometryforgalaxiesintheclusterHowever,oneadvantageofourphotometrictechniquenotcurrentlyutilizedistheabilitytoaccountforalllightinaclusternotjustthatofgalaxies.OurresiduallightmapscontaininformationonICL,clustersubstructure,non-detectedlensedbackgroundsources,andtheunder-detectedwingsofextendedsources.AnobviousstepistoconsidertheICLintheseclusters.WhilepreviousstudieshavebeenreleasedoftheCLASHICL,wecanleveragedualtoICLpropertiesandthefaintgalaxypopulation.Additionally,CLASHisnotthelastHSTobservationofgalaxyclusters,andtheFrontierFieldsarestillripeforexploration.Weintendtofurtherutilizeourtechniquestopushdeepintotheclusterlight5.4PublicReleaseAsanote,weconsiderourplansforpublicreleaseofthedatawehavepresentedhere.Weintendtoreleaseourdetectioncatalogsthroughtwosources:VizieR1andtheMikulskiArchiveforSpaceTelescopes(MAST)2.Bothwillallowustohostourcatalogforconvenientaccesstotheastronomicalcommunity.Weintendtoreleasethecompletephotometriccata-log.Thisentailsthespatialandgeometricparametersofeachellipseaperture,themeasuredCLASHphotometry,photometricandspectroscopicredshiftdeterminations,SEDbest1http://vizier.u-strasbg.fr/2https://archive.stsci.edu/hst/144parameters,andthek-correctedandanalogmagnitudesusedinChapter4.Afulldescrip-tionofourcatalogisprovidedinAppendixB.145APPENDICES146AppendixAAppendicesforChapter21ConversionofROSATestof300kpcInthisappendix,wediscusshowweconvertedthereportedbyVikhlininetal.(1998)intoapertureAstheoriginalwerefoundbyintegratinga-modeltoy,wederivedameansofobtainingthenormalizationfromagivenWethenintegratedthe-modeltoadesiredangularapertureusingthisnormalization.Theofa-modelisfoundbyintegratingtheintensityf=ZI0 1+c2!3+0:52ˇ:(A.1)Substitutingx=3+0:5,thisisananalyticintegralwithsolutionf=2ˇI0(2c+2)(22c+1)x2(x+1)+c(A.2)Whenevaluatingthisas!1foranyx<1,theupperpartofthefractionwillgoto0.Whenevaluatingat=0,thisbecomesf(=0)=2ˇI02c2(x+1):(A.3)1Theseappendicesaretakenmostlyword-for-wordfromConnoretal.(2014),aspublishedintheAstro-physicalJournal147AsVikhlininetal.(1998)reportedtheiruxesastheaverageofthefoundwith=0:6and=0:7,wecandeterminetheirnormalization,I0,byinsertingtheappropriatevaluesofxandrearrangingEquation(A.3).Weusex0:6andx0:7todenotethevaluesofxfoundwith=0:6and=0:7,respectively,andincludeafactorof1/2toaccountforaveraging,sothatwehaveI0=2fROSATˇ2c1x0:6+1+1x0:7+11:(A.4)Wenotetheleadingnegativesignisaconsequenceofourofx,whichwillbenegativeforall>1=6.Fromthis,thetotalthatwouldbemeasuredinsideaapertureofradiuscanbecomputedforagivenvalueofusingfx()=2fROSAT2c(x+1)1x0:6+1+1x0:7+11"(2c+2)22c+1x2c#:(A.5)TocomparetheROSATtoourown,wesolvethisfortheangleequivalentto300kpcfor=0:6and=0:7,averagingthetworesults.ReplicationofPreviousXMMAnalysesRXJ0110.3+1938Bruchetal.(2010)analyzedthisclusterwiththesameobservationusedinthispaper.Whiletheiranalysisfollowedasimilarpathtoourown,theirreportedresultsarenotthesameasours.Ourreportedbolometricluminosityissimilartotheirs(2:19+0:120:14and2:08+0:220:221043ergs1,respectively),buttheirreportedtemperatureisnoticeablylowerthanourown(1:46+0:260:19keVcomparedto2:95+0:720:62keV).Theintheresultmayarisefrom148theirlessstringentcutforselectinggoodtimeintervals,theirgroupingoftheirdataintoenergybins,theiruseofasmalleraperture,andtheirlackofpnobservations,whichsupplyaround50%ofthecountsbutwereoftenproblematictocalibrate5yearsago.Ifwealsomakethesechoices,wemeasureanewtemperatureof1:27+0:060:11keV,whichagreeswiththeearlierresult.However,whenwereduceouraperturesizeandbinthespectraldata,weanevenlowerluminosity;ournewbolometricluminosityis0:79+0:040:051043ergs1.AfterprivatecommunicationwithS.Bruch,wediscoveredthatthesamespectralttingresultswereobtainedbutnotpublishedforanapertureof0.5Mpc.Usingthe4.647kpcarcsec1scaleprovidedintherefereedpaper,weextractspectrafroma107.6000aperture.Whenlettingtheabundancevary,weTX=1:50+0:450:32keVandLbolo=1:83+0:100:191043ergs1.Inaddition,we252and219netcountsforMOS1andMOS2,respectively.Theseresultsareinagreementwiththeearlierresult,whichfound231and205countsforthetwocameras.WethereforeconcludethattheirreportedX-rayapertureradiusof3200isincorrectlyreported,andtheactualapertureusedwas0.5Mpc.Usingthisaperture,weobtainsimilarresults.RXJ0847.1+3449Lumbetal.(2004)originallylookedatRXJ0847.1+3449usingXMM-Newtonobservation0107860501.Theyreportedhighervaluesforandbolometricluminosity,butacoolertemperature.Onesourceofthiscemaybethelargerspectralextractionareatheyused{itwas12000,whileourswasˇ7000.Thereforeweattemptedtoreproducetheirresultsbyusingthesameapertureandmasks,asthatworkincludedimagesofwherepointsourceswereexcluded.BolometricluminositiesreportedbyLumbetal.(2004)arenotforthe12000apertures.149Rather,theyareforaperturesscaledtotheentirevirialradius,asfoundbyusingthetemperaturesandtheT{rvrelationofEvrardetal.(1996).Inaddition,theyincreasedtheestimatedphotoncountratetoaccountforlackofspatialcoverageduetochipgapsormaskedpointsources.WeacomparableluminositybyaMEKALmodeltotheparametersspinTable5ofLumbetal.(2004).Unlikethereportedluminosity,theseparametersareforthebestofthespectrumwithin12000andarethebestmeasureofwhatasimilarapertureluminositywouldbefromthatwork.InordertoallowforchangesinMEKALoverthepasttenyears,welettheabundancevarybutmatchthereportedintheoriginalwork.Whentodatafromthelargeraperture,ourtemperatureestimatechangesfrom4:16+0:580:39keVto3:72+0:510:41keV,whichagreeswiththereportedvalueof3:62+0:580:51keV.Similarly,ourestimatechangesfrom5:20+0:120:141014ergs1cm2to6:77+0:140:121014ergs1cm2,inagreementwiththepredicted7:040:31014ergs1cm2.Forbolometricluminosity,ourvaluewithinr2500is1:31+0:040:031044h270ergs1,whileinsidea12000apertureitis1:70+0:060:051044h270ergs1.Theexpectedluminosityinsidethatapertureis1:751044h270ergs1.RXJ1354.20221RXJ1354.20221wasalsooriginallyinvestigatedbyLumbetal.(2004),and,asbefore,theyahigherhigherluminosity,andalowertemperaturethanwedo.AswithRXJ0847.1+3449,theirtechniquedeviatedinaperturesize,binning,andoflumi-nosity.Additionally,wethisdataforintervalsofrentlythantheydid,whichweadjustforinourreanalysis.Weagainadropintemperature,whichchangesfrom7:60+1:921:22keVto3:88+0:930:59150keVwhenexpandingtheaperture,incomparisontotheoriginallyreportedvalueof3:66+0:60:5keV.Likewise,theincreasesfrom6:90+0:150:191014ergs1cm2to10:17+0:180:221014ergs1cm2,whichmatchestheearlierresultof9:80:51014ergs1cm2.Finally,ourluminosityrisesfrom2:11+0:100:121044h270ergs1to2:47+0:090:061044h270ergs1,whichagreeswiththepredictedexpectationof2:411044h270ergs1.Asbefore,weareabletoreproducetheearlierresults.RXJ1117.4+0743Carrascoetal.(2007)usedthesameobservationsanalyzedheretolookatRXJ1117.4+0743.Theirreportedtemperature(3:3+0:70:6keV)isslightlylowerthanourown(4:30+0:700:38keV),buttheylargerluminositiesfrom0.5-2.0keV(4.190.35toour1:84+0:030:03,inunitsof1043ergs1)andinabolometricband(11.80.9toour5:27+0:080:16inunitsof1043ergs1).Thereareafewinouranalysisthatcanbringthoseresultsintocloseralignment.Alongwithusingalargeraperture{6600toourchoiceof4700{thepreviousworkbinneditsdatatoaminimumof12countsperenergybin.Makingthoseadjustmentsisnotenoughtomatchthepreviouswork,however,withoutalsousingatbackground.Intheinitialpaper,thebackgroundwasdescribedonlyas\alargerextractionregionnearthedetectorborderwithoutanyvisiblesources."Tothatend,weusedabackgroundcenteredaround2000=11h17m40s,2000=+0755m10sthatwas7200insize.Withthisbackground,werecoversimilarresultstotheoriginalreporting:TX=3:13+0:300:29keV,F[0:52:0keV]=5:29+0:120:131014ergs1cm2,L[0:52:0keV]=3:90+0:180:141043ergs1,andLbolo=8:90+0:470:371043ergs1.Evenwithoutknowingtheirexactbackgroundregion,wereproducetheresultsofCarrascoetal.(2007).151AppendixBAppendicesforChapters3and4DescriptionofparametersinPhotometryTableThefollowingparametersaretobeincludedinourcataloguponpublicrelease:1.GALID{Auniqueidenforeachgalaxy2.2000{TherightascensioninJ2000coordinates3.2000{ThedeclinationinJ2000coordinates4.X{XpixellocationonCLASHmosaicedimages5.Y{YpixellocationonCLASHmosaicedimages6.a{Semi-majoraxisofphotometricellipse,inpixels(0.06500/pix)7.b{Semi-minoraxisofphotometricellipse,inpixels(0.06500/pix)8.PA{Positionangle,measuredeastofnorth,indegreesForthefollowingmagnitudes,valuesof-99indicatethattheobjectwasnotobservedinthatwhilevaluesof99indicateitwasnotdetectedaboveerrorvalues9.mF225W{ABapparentmagnitudeinF225Wafterextinctioncorrection10.mF275W{ABapparentmagnitudeinF275Wafterextinctioncorrection15211.mF336W{ABapparentmagnitudeinF336Wafterextinctioncorrection12.mF390W{ABapparentmagnitudeinF390Wafterextinctioncorrection13.mF435W{ABapparentmagnitudeinF435Wafterextinctioncorrection14.mF475W{ABapparentmagnitudeinF475Wafterextinctioncorrection15.mF555W{ABapparentmagnitudeinF555Wafterextinctioncorrection16.mF606W{ABapparentmagnitudeinF606Wafterextinctioncorrection17.mF625W{ABapparentmagnitudeinF625Wafterextinctioncorrection18.mF775W{ABapparentmagnitudeinF775Wafterextinctioncorrection19.mF814W{ABapparentmagnitudeinF814Wafterextinctioncorrection20.mF850LP{ABapparentmagnitudeinF850LPafterextinctioncorrection21.mF105W{ABapparentmagnitudeinF105Wafterextinctioncorrection22.mF110W{ABapparentmagnitudeinF110Wafterextinctioncorrection23.mF125W{ABapparentmagnitudeinF125Wafterextinctioncorrection24.mF140W{ABapparentmagnitudeinF140Wafterextinctioncorrection25.mF160W{ABapparentmagnitudeinF160Wafterextinctioncorrection26.zb{BPZmostlikelyredshift27.zbmin{BPZ95%lowerlimitonbestredshift28.zbmax{BPZ95%upperlimitonbestredshift15329.tb{BPZbestspectraltype30.˜2BPZ{BPZgoo31.M0{PrimarymagnitudeusedbyBPZ32.zs{Spectroscopicmagnitude;=-1ifnomatch33.uanalog{ABapparentmagnitudeinu-analog34.uanalog{ABapparentmagnitudeing-analog35.uanalog{ABapparentmagnitudeinr-analog36.Yanalog{ABapparentmagnitudeinY-analogr37.Kanalog{ABapparentmagnitudeinK-analogr38.uk{K-correctedabsolutemagnitudeinu39.gk{K-correctedabsolutemagnitudeing40.rk{K-correctedabsolutemagnitudeinr41.ik{K-correctedabsolutemagnitudeini42.zk{K-correctedabsolutemagnitudeinz43.P03{Integratedphotometricredshiftprobabilitywith0:03<zzc<0:0344.P05{Integratedphotometricredshiftprobabilitywith0:05<zzc<0:0545.P103{Integratedphotometricredshiftprobabilitywith0:03<(zzc)=(1+zc)<0:0346.P105{Integratedphotometricredshiftprobabilitywith0:05<(zzc)=(1+zc)<0:0515447.Age{SEDbage,inGyr48.SFRAge{SEDbstar-formation-weightedage,inGyr49.Zmetal{SEDbabsolutemetallicity50.Mtot{SEDbtotalmass,inM51.M{SEDbstellarmass,inM52.˜2SED{SEDgoo53.Cluster{Galaxyclustergalaxyisassociatedwith54.mM{Distancemodulusmagnitudecorrection,inmagnitudes55.Member{Binaryvalue;1ifasaclustermember,0ifnot.ExtendedTables155156TableB.1:ACSDataProperties{Exposuretime(s),Zeropoint(ABMag),andA(Mag)ClusterF435WF475WF555WF606WF625WF775WF814WF850LPAbell209413641284096406641268080823625.66626.05626.49325.90025.66225.94724.8570.0700.0630.0480.0430.0320.0300.024Abell383425041284210412840848486842825.65826.05926.49125.90725.66525.94324.8420.1120.1010.0770.0690.0510.0470.039Abell61141184160432041288092821625.66626.05926.51125.66525.94724.8420.2050.1860.1400.0930.0870.071Abell1423389039283850392842388480806225.66626.05626.49325.90025.66225.94724.8570.0720.0650.0500.0440.0330.0310.025Abell22614154412841144128414481981186825.65826.05926.49125.90725.66525.94324.8420.1560.1420.1070.0960.0710.0660.054CLJ122643724396320004428441844720848825.66626.05626.51025.90025.66225.95624.8570.0690.0620.0470.0420.0310.0290.024MACS0329414441284104412841348168826625.65826.05926.49125.90725.66525.94324.8420.2180.1970.1490.1340.0980.0920.075MACS0416410441284036403440628074817225.66626.05626.49325.90025.66225.94724.8570.1480.1340.1010.0910.0670.0620.051MACS0429395237283938372839428016809025.66626.05626.49325.90025.66225.94724.8570.2180.1970.1490.1340.0980.0920.075MACS06474248449615480412842624324255208650157TableB.1(cont'd)ClusterF435WF475WF5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9560.5300.4160.3380.2960.0740.0670.0550.0470.039MS213772507419475648272815251525152312729424.09724.17424.64525.37126.27126.82526.24726.46425.9560.3550.2790.2260.1980.0490.0450.0370.0310.026161TableB.2(cont'd)ClusterF225WF275WF336WF390WF105WF110WF125WF140WF160WRXJ134772437354478148202515502624152312774124.09724.17424.64525.37126.27126.82526.24726.46425.9560.4320.3390.2750.2410.0600.0540.0450.0380.032RXJ153272627428476448402815251525152312502924.09724.17424.64525.37126.26926.82526.24726.45225.9560.2060.1620.1320.1150.0290.0260.0210.0180.015RXJ212969787238457445542615241534212312623824.09724.17424.64525.37126.26926.82226.23026.45225.9460.2820.2210.1800.1570.0390.0360.0290.0250.021RXJ224871487274471847402815251525152312502924.09724.17424.64525.37126.26926.82226.23026.45225.9460.0850.0670.0540.0480.0120.0110.0090.0070.006TableB.3:MaskedStarsinCLASH(R>200)20002000radiusCluster(00)1:31:53.938-13:35:58.122.467Abell2091:31:47.744-13:37:24.032.048Abell2092:48:05.482-3:30:58.992.223Abell3832:48:00.143-3:31:34.712.004Abell3832:47:58.373-3:31:46.082.173Abell3832:47:59.301-3:30:57.462.245Abell3838:00:55.966+36:03:55.392.218Abell6118:01:01.746+36:03:31.902.019Abell6118:00:53.077+36:05:21.712.712Abell6118:00:59.310+36:04:49.792.128Abell6118:01:05.045+36:04:25.202.394Abell6118:01:02.811+36:04:08.192.742Abell6118:01:04.748+36:04:00.513.112Abell6118:01:03.745+36:03:44.432.461Abell6118:01:00.700+36:02:12.822.239Abell61111:57:25.503+33:36:52.942.816Abell142311:57:14.500+33:35:13.272.824Abell142317:22:26.566+32:08:51.682.351Abell226117:22:30.646+32:08:50.852.496Abell226117:22:23.255+32:08:37.202.302Abell226117:22:28.732+32:08:34.292.418Abell226117:22:26.414+32:07:44.612.292Abell226117:22:31.752+32:07:42.202.756Abell226117:22:22.004+32:07:39.362.388Abell226117:22:22.702+32:07:18.102.366Abell226117:22:26.461+32:07:15.102.270Abell226117:22:28.701+32:07:02.652.432Abell226117:22:29.668+32:06:54.042.657Abell226117:22:26.000+32:06:50.592.240Abell226117:22:26.715+32:06:49.762.058Abell226117:22:24.348+32:09:43.622.137Abell226117:22:34.834+32:08:53.882.602Abell226117:22:34.272+32:07:11.322.513Abell226117:22:23.040+32:06:17.222.256Abell226117:22:22.437+32:06:06.142.859Abell226112:26:59.747+33:33:31.342.010CLJ122612:26:58.996+33:33:12.473.096CLJ122612:26:56.518+33:33:12.102.023CLJ122612:26:58.195+33:31:49.792.779CLJ12263:29:40.192-2:11:58.002.502MACS0329162TableB.3(cont'd)20002000radiusCluster(00)3:29:44.866-2:10:19.272.918MACS03293:29:45.807-2:10:27.062.076MACS03293:29:48.030-2:12:37.463.408MACS03293:29:47.153-2:13:14.592.841MACS03293:29:38.482-2:13:25.043.002MACS03294:16:10.089-24:05:10.084.046MACS04164:16:03.772-24:02:58.022.576MACS04164:16:15.565-24:03:43.223.554MACS04164:16:06.967-24:05:42.512.025MACS04164:29:36.659-2:51:50.592.542MACS04294:29:39.676-2:52:53.132.479MACS04294:29:38.960-2:53:03.392.372MACS04294:29:40.023-2:53:26.192.806MACS04294:29:32.624-2:53:43.722.799MACS04294:29:33.989-2:53:52.352.586MACS04294:29:37.282-2:54:06.142.353MACS04294:29:35.863-2:51:26.502.683MACS04294:29:33.347-2:51:52.812.059MACS04294:29:42.013-2:53:06.822.570MACS04294:29:37.370-2:54:21.082.347MACS04296:47:38.640+70:14:48.922.172MACS06476:47:39.959+70:14:48.602.180MACS06476:47:46.323+70:14:25.942.720MACS06476:47:39.875+70:14:29.952.189MACS06476:47:51.066+70:13:45.622.014MACS06476:47:44.684+70:12:49.742.650MACS06476:47:57.864+70:16:30.592.174MACS06476:47:42.894+70:16:27.082.651MACS06476:48:01.146+70:16:21.202.714MACS06476:48:01.227+70:13:59.012.145MACS06477:17:25.932+37:45:18.772.421MACS07177:17:37.044+37:45:01.742.030MACS07177:17:34.425+37:44:14.912.328MACS07177:17:33.642+37:43:46.662.125MACS07177:17:34.634+37:46:40.442.714MACS07177:17:40.790+37:46:16.302.736MACS07177:17:42.875+37:44:15.922.944MACS07177:17:26.522+37:44:11.743.032MACS07177:17:28.085+37:43:13.562.921MACS07177:44:50.660+39:28:41.722.449MACS0744163TableB.3(cont'd)20002000radiusCluster(00)7:44:55.141+39:28:29.712.255MACS07447:44:55.204+39:28:14.082.029MACS07447:44:59.384+39:27:57.192.882MACS07447:44:49.728+39:27:52.022.397MACS07447:44:55.316+39:27:45.622.748MACS07447:44:57.299+39:27:26.172.546MACS07447:44:53.177+39:26:12.322.323MACS07447:44:58.033+39:28:23.152.789MACS07447:44:51.012+39:28:52.433.014MACS07447:44:56.250+39:28:36.724.060MACS07447:44:48.332+39:25:49.142.727MACS07447:44:52.036+39:25:43.712.469MACS074411:15:52.740+1:30:11.052.921MACS111511:15:52.895+1:29:18.372.276MACS111511:15:47.699+1:29:06.372.896MACS111511:15:57.631+1:28:16.352.422MACS111511:49:38.832+22:24:23.382.934MACS114911:49:32.707+22:24:08.692.534MACS114911:49:35.330+22:23:37.462.953MACS114911:49:40.629+22:23:35.882.414MACS114911:49:32.156+22:23:26.962.681MACS114911:49:39.579+22:23:21.852.624MACS114911:49:42.479+22:25:38.872.659MACS114911:49:45.077+22:24:15.892.687MACS114911:49:30.635+22:22:41.762.200MACS114911:49:35.910+22:22:12.662.654MACS114912:06:06.232-8:46:24.872.336MACS120612:06:05.031-8:48:01.422.066MACS120612:06:05.136-8:49:40.172.582MACS120613:11:03.609-3:09:48.512.803MACS131113:11:01.906-3:09:56.022.346MACS131113:10:58.724-3:10:27.502.362MACS131113:11:02.523-3:10:30.652.206MACS131113:11:00.729-3:08:49.573.003MACS131113:11:04.761-3:09:21.512.562MACS131113:11:06.025-3:09:32.102.306MACS131113:11:03.823-3:12:09.352.555MACS131114:23:46.627+24:05:18.892.448MACS142314:23:50.123+24:04:21.722.455MACS142314:23:45.444+24:03:43.632.593MACS1423164TableB.3(cont'd)20002000radiusCluster(00)14:23:55.542+24:03:43.472.298MACS142317:20:19.823+35:37:32.342.531MACS172017:20:12.998+35:37:29.072.909MACS172017:20:16.042+35:37:02.742.046MACS172017:20:13.036+35:36:32.462.094MACS172017:20:12.922+35:35:48.283.094MACS172017:20:18.557+35:35:48.672.337MACS172017:20:19.769+35:35:25.682.598MACS172017:20:17.492+35:35:18.172.510MACS172017:20:15.871+35:35:15.182.495MACS172017:20:15.102+35:38:37.482.736MACS172017:20:13.104+35:38:14.212.438MACS172017:20:24.181+35:36:48.832.853MACS172017:20:26.990+35:36:27.752.030MACS172017:20:27.567+35:36:06.683.295MACS172017:20:08.116+35:35:56.132.547MACS172017:20:25.281+35:35:42.042.252MACS172019:31:53.021-26:33:37.022.500MACS193119:31:54.476-26:33:48.412.118MACS193119:31:44.427-26:34:25.832.820MACS193119:31:52.496-26:34:33.912.302MACS193119:31:44.440-26:34:40.642.510MACS193119:31:49.075-26:34:44.272.092MACS193119:31:49.161-26:34:47.612.140MACS193119:31:46.201-26:34:43.462.274MACS193119:31:46.391-26:34:56.832.357MACS193119:31:47.359-26:34:58.842.649MACS193119:31:53.706-26:35:05.892.878MACS193119:31:46.249-26:35:05.482.151MACS193119:31:52.953-26:35:18.132.657MACS193119:31:52.630-26:35:27.882.092MACS193119:31:48.850-26:35:48.512.078MACS193119:31:51.263-26:32:50.274.281MACS193119:31:54.879-26:33:23.672.653MACS193119:31:56.886-26:33:29.272.110MACS193119:31:54.527-26:33:39.222.521MACS193119:31:57.454-26:33:41.182.261MACS193119:31:57.717-26:33:45.082.110MACS193119:31:55.965-26:33:49.732.094MACS193119:31:43.941-26:33:57.252.514MACS1931165TableB.3(cont'd)20002000radiusCluster(00)19:31:43.982-26:34:10.332.538MACS193119:31:43.255-26:34:37.152.030MACS193119:31:56.659-26:34:51.652.166MACS193119:31:55.991-26:34:52.112.780MACS193119:31:55.074-26:35:09.382.906MACS193119:31:43.908-26:35:15.422.334MACS193119:31:58.446-26:35:20.602.508MACS193119:31:55.150-26:35:22.422.779MACS193119:31:53.941-26:35:28.202.326MACS193119:31:45.744-26:35:36.272.084MACS193119:31:57.344-26:35:49.852.353MACS193119:31:55.475-26:35:52.672.322MACS193119:31:42.393-26:35:56.222.532MACS193119:31:49.650-26:36:03.562.831MACS193119:31:54.493-26:36:02.532.450MACS193119:31:45.645-26:36:18.692.483MACS193121:29:27.213-7:40:31.322.859MACS212921:29:22.338-7:40:55.862.638MACS212921:29:29.118-7:41:13.542.212MACS212921:29:27.712-7:41:18.712.464MACS212921:29:23.572-7:41:43.732.705MACS212921:29:28.434-7:42:28.142.276MACS212921:29:27.703-7:39:08.912.098MACS212921:29:27.070-7:39:44.662.621MACS212921:29:20.697-7:40:47.172.442MACS212921:29:21.333-7:40:55.362.555MACS212921:29:31.184-7:42:20.052.502MACS212921:29:30.485-7:42:36.602.507MACS212921:29:33.191-7:42:38.062.565MACS212921:29:23.636-7:42:49.542.285MACS212921:29:30.730-7:42:54.602.913MACS212921:29:23.007-7:43:11.322.310MACS212921:40:17.670-23:38:59.262.996MS213721:40:14.094-23:39:59.622.367MS213721:40:17.522-23:40:33.322.622MS213721:40:07.770-23:39:07.192.918MS213721:40:20.674-23:39:48.822.028MS213721:40:15.278-23:41:29.033.024MS213721:40:17.614-23:41:31.902.709MS213713:47:34.344-11:44:30.072.916RXJ1347166TableB.3(cont'd)20002000radiusCluster(00)13:47:27.362-11:45:08.452.133RXJ134713:47:28.584-11:45:36.972.831RXJ134713:47:32.518-11:46:01.792.245RXJ134713:47:27.808-11:43:52.032.944RXJ134713:47:34.858-11:44:01.042.186RXJ134713:47:33.412-11:46:53.162.607RXJ134715:32:59.519+30:20:50.702.515RXJ153215:32:48.512+30:20:44.252.523RXJ153215:32:56.525+30:22:59.462.327RXJ153215:32:58.078+30:19:52.872.293RXJ153221:29:36.235+0:06:18.152.230RXJ212921:29:44.089+0:05:59.022.215RXJ212921:29:44.792+0:05:55.152.385RXJ212921:29:42.193+0:05:15.154.314RXJ212921:29:43.597+0:05:04.822.440RXJ212921:29:40.542+0:04:42.772.012RXJ212921:29:39.536+0:04:32.552.976RXJ212921:29:44.260+0:06:47.852.895RXJ212921:29:46.893+0:06:07.202.403RXJ212921:29:33.738+0:05:28.132.842RXJ212921:29:34.948+0:04:42.232.440RXJ212921:29:34.857+0:04:32.272.342RXJ212922:48:44.045-44:30:47.962.978RXJ2248167REFERENCES168REFERENCESAbell,G.O.1958,ApJS,3,211Abell,G.O.,Corwin,Jr.,H.G.,&Olowin,R.P.1989,ApJS,70,1Agulli,I.,Aguerri,J.A.L.,anchez-Janssen,R.,etal.2016,MNRAS,458,1590Aird,J.,Coil,A.L.,Moustakas,J.,etal.2013,ApJ,775,41Akritas,M.G.,&Bershady,M.A.1996,ApJ,470,706Allen,S.W.,Evrard,A.E.,&Mantz,A.B.2011,ARA&A,49,409Allen,S.W.,Rapetti,D.A.,Schmidt,R.W.,etal.2008,MNRAS,383,879Anders,E.,&Grevesse,N.1989,Geochim.Cosmochim.Acta,53,197Anderson,J.,&Bedin,L.R.2010,PASP,122,1035Andreon,S.2003,A&A,409,37Andreon,S.2008,MNRAS,386,1045Andreon,S.,Dong,H.,&Raichoor,A.2016,ArXive-prints,arXiv:1606.03996Andreon,S.,Newman,A.B.,Trinchieri,G.,etal.2014,A&A,565,A120Annis,J.,Kent,S.,Castander,F.,etal.1999,inBulletinoftheAmericanAstronomicalSociety,Vol.31,AmericanAstronomicalSocietyMeetingAbstracts,1391Annunz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