A(MNLTEXstylefilev2.2)
Luminositysegregationinthreeclustersofgalaxies
(A119,2443,2218)
MichaelB.Pracy1,2,SimonP.Driver2,RobertoDePropris3,WarrickJ.Couch1andPaulE.J.Nulsen4
ofPhysics,UniversityofNewSouthWales,SydneyNSW2052,Australia
StromloObservatory,TheAustralianNationalUniversity,WestonCreek,ACT2611,Australia
3AstrophysicsGroup,HHWillsPhysicsLaboratory,UniversityofBristol,TyndallAvenue,BS81TL,UK
4Harvard-SmithsonianCenterforAstrophysics,60GardenSt.,Cambridge,MA02138,USA;onleavefromtheUniversityofWollongong,NSW2522,Australia
2Mount1School
arXiv:astro-ph/0510129v1 5 Oct 2005Received0000;Accepted0000
ABSTRACT
Weusedeepwide–fieldV-bandimagingobtainedwiththeWideFieldCameraattheprimefocusoftheIssacNewtonTelescopetostudythespatialandluminositydistributionofgalaxiesinthreelowredshift(0.04 .07+0.10+0.08 slopes:α=−1.22+0−0.06(A119),α=−1.11−0.09(A2443)andα=−1.14−0.07(A2218).Weperformageometricdeprojectionoftheclustergalaxypopulationandconfirmthatno‘statisticallysignificant’evidenceofachangeintheshapeoftheluminositydistributionwithcluster-centricradiusexists.Again,theexceptionbeingA2218whichexhibitsacoreregionwithaflatterfaint–endslope. Keywords:galaxies:clusters:general—galaxies:luminosityfunction:massfunction 1INTRODUCTION Galaxiesofdifferenttypesinclustersareknowntohavedifferentprojectedspatialdistributions.ThiswasrealizedbyOemler(1974),whoshowedthatlessluminousgalaxieshaveamoreextendedprofilethanthemoremassiveellip-ticals.Melnick&Sargent(1977)andDressler(1980)iden-tifiedwhatisnowknownasthe‘morphology-density’re-lation,wheretherelativefractionsofelliptical,lenticular(S0)andspiralgalaxiesdependonthesurfacedensity,whileWhitmoreetal.(1993)arguedthatthesetrendsarebettercorrelatedwithcluster-centricradius.Inarecentcompre-hensivestudyofanensembleclusterbuiltfrom59nearbyrichclustersBivianoetal.(2002),demonstratedclearsegre-gationbetweenellipticals,earlyandlate-typespirals.ThisisalsoseeninasingleHSTmosaicofAbell868byDriveretal.(2003)whichconcludesthatclustercoresaredevoidof,oratleastdepleted,inlate-typesystems. However,aswellasmorphologicalsegregation,ev-idenceisalsoemergingforluminositysegregation.Rood&Turnrose(1968)arguedthatdwarfswerelesscon-centratedthangiantsintheComacluster;Capelatoetal.(1981)detectedamass-densityrelationinAbell196;Yepesetal.(1991)studiedluminositysegregationinanum-berofclustersandfoundthatthedegreeofsegregationcorrelateswiththedynamicalstateofthecluster.ThestudyofFerguson&Sandage(1989)inVirgoandFor-naxdemonstratedthatdwarfellipticalswerehighlycon-centratedleadingtoadivisionofthedwarfpopulationintodistinctstronglyclusterednucleateddwarfellipticalsandadistributedpopulationconsistingofnon-nucleateddwarfellipticalsanddwarfirregulars.IntheComaclus-ter,Loboetal.(1997)andKashikawaetal.(1998)found 2Michael.B.Pracyetal. evidenceforstrongluminositysegregation,withthegiantsbeingclumpedintwosubstructureswhilethedwarfstracedamorediffuseandregulardistribution.Andreon(2002)ar-guedthatsomeformofmasssegregationisalsoatworkinthez=0.31clusterAC118(alsoknownasAbell2744).Thegiantellipticalsandlenticularsmayalsobekinemati-callysegregated(Stein1997),suggestingthattheseobjectsaretheoriginalkerneloftheclusterswhilespiralsanddwarfsarecomparativelylatearrivals.Conversely,Bivianoetal.(2002)findthattheonlyevidenceforluminositysegrega-tionisforellipticalsoutsideofsubstructuresintheirensem-blecluster. Smithetal.(1997)andDriveretal.(1998)foundthatthedwarf-to-giantratioshowsatrendwithdensityand,be-causeoftheapproximatelysphericalshapeofclusters,withradius.Thisleaddirectlytotheideaofadwarf-densityre-lation(Phillippsetal.1998).Togetherwithpreviouswork(Loboetal.1997;Kashikawaetal.1998)thismaysuggestthatdwarfsareespeciallyaffectedbytheclusterenviron-ment,asonewouldexpectforsuchfragileobjects.Pracyetal.(2004)haverecentlyinvestigatedluminos-itysegregationusingawide,deepmosaicofHSTimagesofAbell2218andfoundevidencethatdwarfgalaxiesavoidthecentralregionsofthisclusterandtraceamorespa-tiallyextendeddistribution.AsimilarresultwasfoundfortheNGC5044groupbyMathewsetal.(2004)andforasampleofloosegroupsbyGirardietal.(2003).Ifthesegre-gationfordwarfsisreal,itmayoriginatefrominitialcondi-tions,wherelowluminositygalaxiesareonlynowin-fallingintoclusters(e.g.,Crotonetal.2005),oritmaybeduetoprocessesinternaltoclusters,suchastidaldisruptionandgalaxyharassment.Forthesereasons,itisimportanttoin-vestigatetheexistenceofluminositysegregationfordwarfsinabroaderrangeofobjectsandtostudyitscorrelationwithclusterproperties.Thisisnowfeasiblebywide–fieldimagingofrelativelynearbyclusterswithpanoramicmosaiccamerason2mtelescopes,andwepresentheretheresultsofsuchastudyforthreeclustersobservedfromtheIsaacNewton2.5mTelescopewiththeWideFieldCamera.Inthispaperweuserelatively–deepwide–fieldimagingofthreegalaxyclustersintheredshiftrange0.04 TheObservations ThesampleconsistsofthreeAbellclusters:A119(Rich-ness=1,BM=II-III,z=0.044),A2443(Richness=2,BM=II,z=0.108)andA2218(Richness=4,BM=II,z=0.181).Theobservationswereobtainedonthenightsof2nd&3rdSeptember2000usingtheWideFieldCamera(WFC)mountedattheprimefocusoftheIsaacNewtonTelescope(INT).TheWFCconsistsofamosaicoffour2048×4096thinnedEEVCCDswithaplatescaleof0.333arcsec/pixel.Thetotalskycoverageis0.287deg2perpointing.Theimag-ingofeachclusterconsistsoffourpartiallyoverlappingpointingswiththeWFC,theexceptionbeingthehigherredshiftclusterA2218whichisamosaicofjust2pointings.EachclusterwasimagedthroughtheVfilterwithanexpo-suretimeof1200s.AsummaryoftheobservationsisgiveninTable1. 2.2Datareduction ThedatareductionwasperformedbytheCambridgeAstro-nomicalSurveyUnit(CASU)andfulldetailsofthepipelineprocedurecanbefoundinIrwin&Lewis(2001).Insum-mary,thedataarefirstbiassubtractedandtrimmed.Badpixelsandcolumnsareinterpolatedoverusingdatafromneighbouringregions.Allfourchipsarethencorrectedfornon-linearbehaviourinthetwoanalogue-to-digitalconvert-ers.ThedataarethenflatfieldedusingmasterskyflatsandagaincorrectionisappliedsothatalltheCCDshavethesamezero-point.Finally,anastrometricsolutionisderivedbymatchingbrightstarsinthefield-of-viewofeachchiptotheGuideStarCatalog. 2.3Photometriccalibration FourLandolt(1992)standardstarfields(SA92,SA95,SA110andSA113)wereobservedatvariousair-massesthroughouteachnight.Foreachobservationofastandardstarazero-pointwascalculated:ZPstar=m+2.5log f Luminositysegregationinthreeclustersofgalaxies Table1.Datacharacteristics. 3 Abell119Abell2443Abell2218 00h56m21s22h26m07s16h35m54s−01o1547 ′′′ +17o2017 ′′′ +66o1200 ′′′ 0.0440.1080.1811200120012001.141.180.944420.850.820.459.750.4120.513.7315.0716.40 magparameterwasusedtomeasuretotalgalaxymag-nitude(hereafterdenotedV);thiscorrespondstoaKron(1980)extractionaperture,exceptforcrowedregionswhereanextrapolatedisophotalmagnitudeisused.TheKronex-tractionapertureissetto2.5timesRKwhereRKisthefirstmomentoftheimagedistribution.Inregionswherepoint-ingsoverlap,theduplicateobjectswereremovedfromthecatalogs.2.5 Exclusionregions Aftertheinitialobjectdetectioneachfieldwasvisuallyin-spectedandanyCCDdefects,verybrightstars,diffractionspikesandsatellitetrailscausingspuriousdetectionswereidentified.Circularandrectangularregionsenclosingtheseareasweredefinedandexcludedfromthecatalogs.Inad-dition,theareaswithin20pixelsoftheCCDedgeandthevignettedcornerofCCD3werealsoexcluded.2.6 Objectclassification Weusedthepositionofobjectsinthecentralsurfacebrightness–magnitude(µo–V)planetoclassifyobjectsaseithergalaxies,starsorcosmicrays.Thedistributionofa subsetofdetectedobjectsinthisplane,foreachcluster,isillustratedinFig.2.Thecentralsurfacebrightnesswascal-culatedinacircularaperturewithanareaequaltothatofthedetectioncriterion(i.e.,8pixels).2.6.1 Cosmicrayrejection InFig.2agroupofobjectswithahighcentralsurfacebrightness(atagivenmagnitude)isclearlydiscernible(up-perright).Theseobjects,whichhavesurfacebrightnesseshigherthanthatofstars,arecosmicrays.Wethereforede-finearegionintheµo–Vplanesuchthat:µo≤aV+b (3) andclassifyallobjectsinthisregionascosmicrays.Equa-tion(3)isshownasthedot-dashedlineinFig.2.Theslope(a)andintercept(b),werechosenseparatelyforeachclus-ter,tobestmatchthedata.TheobjectsclassifiedascosmicraysareshownasbluepointsinFig.2.2.6.2 Star-galaxyseparation Theprocessofstar-galaxyseparationbeginsbyidentify-ingsaturatedstarsinthecatalogs.StarsbrighterthanV≈17.2magaresaturated,theseareclearlyidentifiableintheµo–Vplaneasahorizontallocusofpointswithµo<18.0magarcsec−2.Weclassifyobjectswith:µo<18.0andV≤17.2 (4) asfloodedstars(horizontaldashedlineinFig.2).ThestellarlocuscanbeseeninFig.2asadiagonallocusofpoints(red)withahighersurfacebrightnessthantheoverallgalaxypopulation(blackpoints),andextendingfromV≈17.2toV≈21mag.Wethereforedefinealineintheµo–Vplane:µo=aV+b′andV>17.2andV≤21.0 (5) topassbetweenthesepopulations,andweuseitasadividertoseparatestarsandgalaxies(seediagonaldashedlineinFig.2).AllobjectswithV≤21magwhichareclassifiedasstarsareshowninredinFig.2. ForobjectsfainterthanV≈21magstar-galaxysepa-rationbecomesproblematic.Atthesemagnitudesthestellarlocusmergeswiththatoftheoverallgalaxypopulationandthetwocannolongerbedistinguished.Inordertoper-formstar-galaxyclassificationfaintwardofV=21magweuseasimilarmethodtothatoutlinedinLiskeetal.(2003).Sincethe(logarithmic)slopeofthestarcountsshouldre-mainroughlyconstanttoV≈24mag(K¨ummel&Wagner2001),wecanusethestarcountsderivedfromthebrightobjectsinthecatalogandextrapolatethemtoderivetheexpectednumberofstarcountsatfaintermagnitudes.We 4Michael.B.Pracyetal. Figure2.Distributionofdetectedobjectsinthecentralsurfacebrightness–magnitudeplane.Bluepointsareobjectsclassifiedascosmicrays,redpointsareobjectsclassifiedasstarsdirectlyfromtheirpositionsinthisplane,greenpointsareobjectsclassifiedasstarsbyextrapolationfromthebrighterstarcountsandblackpointsaretheobjectsclassifiedasgalaxies.Toppanel:A2218.Middlepanel:A2443.Lowerpanel:A119.Onlyoneinsixobjects,randomlyselected,aredisplayed. thenclassifiedobjectsasstarsbasedontheirpositionintheµo–Vplane(objectswiththelowestvalueofµo−mV)untilwehadobtainedthepredictednumberofstars.Althoughthismethodwillresultinsomeindividualobjectshavingincorrectclassifications,theoverallstatisticalproprietiesofthecatalogswillbecorrect.Theobjectsthathavebeenclas-sifiedasstarsinthiswayareshowningreeninFig.2. 2.6.3 Completeness Atthispointeveryobjectinthecatalogshasbeenclassi-fiedaseitherastar,galaxyorcosmicray.Wearelimitedtogalaxieswithacentralsurfacebrightness(overanareaof8pixels)ofµo≤26magarcsec−2andfromFig.2weseethatobjectswithcentralsurfacebrightnessesclosetothislimitonlyoccurinsignificantnumbersatV>23.5mag,indicat-ingthebeginningofdetectionincompleteness(Garillietal.1999).Wetherefore,defineanapparentmagnitudelimitofV=23.5mag. 3RADIALPROFILES Thewidefield-of-viewprovidedbytheWFCmosaicsenableustosurveytheradialdistributionofgalaxiesbeyondthedomainofthecluster,welloutintothesurroundingfield.Toexplorethis,weplotforeachclusterthegalaxy-surfacedensityagainstcluster-centricradius.Thisisachievedbyderivingthegalaxycountsinconcentricannulicentredonthebrightestclustergalaxy.Thesurfacedensitywascalcu-latedtakingintoaccounttheareaofeachannuluswhichen-compassestheunmaskedfield-of-viewoftheavailableCCDarea(i.e.,correctedforanyexclusionregionswhichinter-secttheannulus).Wealsocorrectedforthe‘diminishingareaeffect’(Driveretal.1998)wherebytheareaoverwhichfaintobjectscanbedetectedisreducedbythepresenceofbrighterobjects.TocalculatethiseffectweusedtheSEx-tractorparameterISOAREA–whichreturnsthetotalareaassignedtoanobjectbySExtractor–tocalculatetheamountofareaoccupiedbybrighterobjects. TheSExtractorbestmagnitudeswerecorrectedforgalacticextinctionusingthemapsofSchlegeletal.(1998).TheobservedradialgalaxysurfacedensityprofilesforA2218,A2443andA119areshowninFig.3,Fig.4andFig.5,respectively,asopensquares.TheerrorbarsonthepointsarethoseexpectedfrompurelyPoissonstatistics.3.1 Clusterprofiles TheradialprofilesinFigs.3–5representthesuperpositionoftheclustersurfacedensityprofilesandaconstant‘field’galaxysurfacedensity.Weelecttodescribetheclustersur-facedensityinfunctionalformbyaKing(1962)profile,plusaconstantsurfacedensityof‘field’galaxies,thus: σ(r)=σ0 (6)rc whereσ(r)represents2+Nf theradially(r)dependentnumber-countsalongtheline-of-sight.Thefirstterminequation(6)representstheprojecteddistributionofclustergalaxiesandthesecondtermthesuperimposed‘field’population.InFigs.3–5wehavebinnedthegalaxynumbercountsinradialannuli.Wethereforeneedtointegrateourfittingfunction(equation6)overtheannulitoobtaintheaveragesurfacedensity,whichgives 1 r2N2+σ0r2 frmax−r2 clog(1+(r/rc)2)min rmax (7) rmin Luminositysegregationinthreeclustersofgalaxies5 Figure3.ThesurfacedensityofgalaxiesinA2218asafunctionofcluster-centricradiusforaseriesofmagnitudeintervals.Thesolidcurvesarethebestfitting‘King+constant’profilegivenbyequation(7).The(apparent)magnitudeintervalsandtheircorrespondingabsolutemagnitudeintervals(fortheclusterredshift)aswellasthebestfittingvaluesofthefitparametersaretabulatedineachpanel.ThedashedlinesshowthevalueoftheNfparameterfromequation(7). whererminandrmaxaretheinnerandouterradialbound-ariesofthebin,respectively.Thefittedprofilestothemea-suredgalaxysurfacedensityprofilesareshownasthesolidlinesinFig.3–5in1magintervalsofV.Overall,thesurfacedensityofgalaxiesarewelldescribedbyequation(6).InFig.6weshowtheKingprofilecoreradii[givenbytheparameterrcinequation(7)]asafunctionofabsoluteV-bandmagnitude,theerrorsonthepointsarecalculateddirectlyfromthecovariancematrixreturnedfromχ2min-imisation.InthecaseoftheclustersA2443(middlepanel)andA119(lowerpanel)wefindthatthecoreradiusises-sentiallyindependentofmagnitude,withbothclustershav-ingcoreradiiofrc≈0.2–0.5Mpcatallluminosities.Thebestfittingslopesaregivenby−0.001±0.033Mpcmag−1and0.058±0.040Mpcmag−1,respectively–bothconsis-tentwithzeroat∼1σ.InA2218,wefindthatthebright-estgalaxieshaveasmallercoreradiusthentheirfaintercounterparts,withmarginalevidencethatthistrend–in-creasingcoreradiuswithdecreasingluminosity–continuesfortheintermediatepopulation.Thebestfittingslopeisgivenby0.086±0.030Mpcmag−1.However,ifthebright-estpoints(MV<−21mag)areremoved,theslopebecomes0.051±0.054Mpcmag−1whichisconsistentwithzeroatlessthanthe1σlevel.ThistrendisgenerallyconsistentwithPracyetal.(2004)whofoundthatthespatialdistributionofgalaxiesinA2218ismoreextendedforthelowerlumi-nositypopulations.Unfortunatelythedatadonotextendtotheirdwarfandultra-dwarfregimes. Core radius (Mpc)10.80.60.40.20-230.80.60.40.20-231.210.80.60.40.20-23GiantsDwarfsUltra-dwarfs-22-21-20-19-18-17-16-15-14-13-22-21-20-19-18-17-16-15-14-13-22-21-20-19MV-18-17-16-15-14-13Figure6.Coreradii[rcfromequation(7)]versusabsoluteV-bandmagnitude.Toppanel:A2218.Middlepanel:A2443.Lowerpanel:A119.Thebestfittingslopesaredisplayedassolidlines.The‘Giant’,‘Dwarf’and‘Ultra-dwarf’regimes,asdefinedbyPracyetal.(2004),aredelineatedbythedashedlines.Thesedef-initionshavebeenadjustedduetodifferencesinthefiltersandtheassumedcosmology. 3.2Referencefieldcounts Inordertostudytheclustergalaxypopulationweneedtoremovethecontributiontothecountsalongtheline-of- 6Michael.B.Pracyetal. Figure4.SameasFig.3exceptforA2443 Figure5.SameasFig.3exceptforA119 Luminositysegregationinthreeclustersofgalaxies sightfromforegroundandbackground‘field’galaxies.Todothisweusethestandardtechniqueofstatisticalfieldsubtraction.Howeverratherthanusedataobtainedfromoff-clusterpointingswearenowabletousethecountsderivedfromtheradialfits(i.e.,Nfinequation7). ThefieldgalaxynumbercountsderivedinthiswayareshowninthetoppanelofFig.7,wherewehaveplottedthecountsfromtheA2218field(filledsquares),theA2443field(filledcircles)andtheA119field(stars),separately.ForcomparisonwealsoplotthegalaxynumbercountsfromtheMillenniumGalaxyCatalog(MGC)ofLiskeetal.(2003),whichwehaveconvertedfromtheB-bandtotheV-bandusingthemeanfieldgalaxycolour(B−V)=0.94(Norbergetal.2002).WenotethatthiscolourisonlystrictlyvalidforV<18mag;however,thenumbercountsagreequitewellovertheentirerangeofluminosities.The‘field’countsderivedforthelowredshiftclusterA119gen-erallyhavelargererrorbarsandmuchlargerscatterthanthosederivedfortheothertwoclusters.Thisisexpectedsincetheradialprofilesforthisclusterextendtoaradiusofonly∼2Mpc.ThescatterinthepointscanbeseenmoreclearlyinthelowerpanelofFig.7whereweshowthegalaxycountsrelativetoaN∝100.45Vrelation. Inordertogiveasmoothrepresentationofthe‘field’countswefittedaquadraticfunctiontothem.Since‘field’galaxycountscanvarysignificantlybetweenfields,aquadraticfitwasperformedseparatelyforeachsetofref-erence‘field’counts.ThesefitsareshowninthelowerpanelofFig.7asthesolid,dashedanddot-dashedlinesforA2218,A2443andA119,respectively.Forillustrativepurposesasi-multaneousfittoallthreedatasetsisshownasthesolidlineinthetoppanelofFig.7.WealsousedtheMGCcountsatV<18magtoprovideabrightend‘anchor’tothefit–weartificiallyintroducederrorsof10%onthesepointssoasnottoallowtheMGCpointstoinfluencethefitatthecriticalfaintend.Thequadraticfitsyield: dN 7 dV ln10 +2Vδab+2V2δac+2V3δbc where dN 2 222δa+V2δb+V4δc (9) 8Michael.B.Pracyetal. 1.1251.11.075Abell 2218Abell 2443Abell 0119snelf1.051.02510.975141516171819V2021222324Figure8.Thefunctionflensaveragedoverthecentral500kpcforA2218(solidline),A2443(dashedline)andA119(dottedline). ingeffectwefollowtheprocedureoutlinedinPracyetal.(2004)andreferencestherein.Weuseavaluefortheve-locitydispersionof1370kms−1forA2218(LeBorgneetal.1992)and778kms−1forA119(Struble&Rood1987);sincenovelocitydataisavailableforA2443weassumeavelocitydispersionforthisclusterof1000kms−1.WeusethelocalluminosityfunctionmeasuredfromtheMGC(Driveretal.2005)andconverttotheV-bandusingB−V=0.94(Norbergetal.2002). InFig.8thefunctionflensisshownforA2218asthesolidline,forA2443asthedashedlineandforA119asthedottedline.Clearly,theeffectislargestforA2218,pri-marilyasaresultofthecluster’shigherredshift.InA2218theeffectismostevidentforgalaxieswithV≈21withafractionalchangeinthe‘background’populationofap-proximately10%.Atthislevelthelensingeffectrepresentsaminorcomponentoftheerrorbudget.Howeveritisworthnotingthatthelensingcorrectiondependscriticallyontheassumptionsconcerningtheevolutionofthegalaxynumbercountsasafunctionofredshift,whichisnotwellknown.GiventhisuncertaintyandthesmallsizeofthecorrectionsinFig.8,wedonotcorrectforlensingatthistime. 4LUMINOSITYFUNCTIONS Wenowuseourdataalongwithourmeasured‘field’countstostudytheluminositydistributionofgalaxiesineachcluster.Thefaint–endlimitsforA2218,A2443andA119are,respectively,MV=−16.7,MV=−15.4andMV=−13.3mag.Theseincludecorrectionforgalacticdust(Schlegeletal.1998)andK-correction(Poggianti1997).4.1 Centralluminositydistribution Wefirstconstruct,foreachcluster,theluminositydistri-butionofgalaxieswithinacluster-centricradiusof1Mpc.Weuseequation(8)–scaledtotheappropriatearea–tocorrect‘statistically’forcontaminationbythesuperimposed‘field’galaxypopulation.TheseareshownintheleftpanelsofFig.9forA2218(top),A2443(middle)andA119(bot-tom)–andarealsotabulatedinTable2.Wefiteachof Figure9.Leftpanels:Theluminositydistributionsfortheclus-tersA2218(top),A2443(middle)andA119(bottom)withinacluster-centricradiusof1Mpc.ThedataareshownbythestarsandthesolidlineisaSchechter(1976)functionfittothedata.Therightpanelsshowthe1,2and3σerrorellipsesfortheSchechterfunctionparametersM∗andα.Alsoshown(opencir-cleintoppanel)isthebest–fittingSchechterfunctionparametersforthe‘bright-end’oftheluminositydistributionofA2218fromPracyetal.(2004). theluminositydistributionswithaSchechter(1976)func-tion;whichhasbeenconvolvedwiththemagnitudebinwidth.TheluminositydistributionsinallthreeclustersarewelldescribedbyaSchechterfunctionwithshapeparam-etersM.14+0V∗ =−21.54+0.08M21.32+0−0.11andα=−1.14+0.10−0.07forA2218, V∗ =−.39M−0.36andα=−1.11−0.09forA2443and .30+0.V∗ =−21.51+007−0.20andα=−1.22−0.06forA119.SincetheparametersM∗andαaredependentweplot,intherighthandpanelsofFig.9,the1,2and3σerrorcontoursfortheSchechterfunctionfit. TheluminositydistributionofgalaxiesinA2218hasbeenstudiedbyPracyetal.(2004)usingadeepHSTmo-saicofthecluster.Their‘bright-end’luminositydistribu-tioniscomparableinbandpass,arealcoverageandluminos-ityrangetotheonederivedabove–withaprojectedarea coveredof∼2.6h−0.227Mpc(comparedwith∼3.1h−0.22 7Mpcinthisstudy)andaluminosityrangecorrespondingtoMV<−17(comparedwithMV<−16.7here).HerewehaveconvertedtotheV-bandusingtherelationV=F606W+0.12(Norbergetal.2002;Driveretal.2003)andcorrectedfordifferencesinassumedcosmology,dustex-tinction,K-correction,andtheomissionofthecDgalaxy Luminositysegregationinthreeclustersofgalaxies 9 Table2.luminositydistributions A2218−23.68 MV ≤−13.31 254.88 78.41 whereζ(Mnc R,(10) i=1 i)isthecombinedgalaxynumber‘counts’inthemagnitudeintervalcentredonM,ncisthenumberofclustersinthecompositeluminositydistribution(nc=3)andNi(M)isthegalaxynumbercountsinthemagnitudebincentredonMfortheithcluster.Riisthe‘richnesscount’oftheithcluster,whichistakentobethetotalnumberofbackground–subtractedgalaxiesinthemagnituderange−21 7Mpc(Valottoetal.2001). Thecompositeluminositydistributionandbest–fittingSchechterfunction(solidline)isshowninFig.10.Theshapeofthebest–fittingSchechterfunctionisparameterisedby M21.82+0.2122+0V∗ =−.05errorcontours−of0.18andα=−1.theparametersM−0.04.The1,2and3σ V∗ andαforourcom-positeluminositydistributionareshownintherightpanel ofFig.10,alongwiththepositionsintheMV∗ –αplaneofasubsampleofthecompositeluminosityfunctionpa-rametersfromtheliterature(convertedtotheV-band).Theopencircleandstarrepresentthefieldgalaxylumi-nosityfunctionsderivedfromtheMGC(Driveretal.2005)andTwoDegreeFieldGalaxyRedshiftSurvey(2dFGRS;Collessetal.2001),bothofwhichexhibitfaint–endslopes(α)thataresimilartothatofourcompositeluminosityfunctionbuthaveabrighterandfaintercharacteristicmag-nitude(M∗),respectively.Theopensquarerepresentsthebest–fittingSchechterfunctionparametersforacompositeofclusters(DeProprisetal.2003)drawnfromthe2dFGRSwithameanredshiftofz=0.12.Ourcompositeluminosityfunctionhasamarginallybrightercharacteristicmagnitudetothatofthe2dFGRSclustercompositeandaslightlyflat-terα.TheopentriangleshowstheformalSchechterfunctionparametersfromGotoetal.(2002)foracompositeofclus-tersintheredshiftrange0.2 Thewidefield-of-viewoftheWFCmosaicsprovidescover-ageoftheentireclusterarea,inthesensethatthenumber 10Michael.B.Pracyetal. Table3.RecentmeasurementsoftheLFparametersfromwide–fieldV-bandCCDphotometry Coma†Coma Abell2151Abell119Abell2443Abell2218ABCG209ABCG209AC1180.0230.0230.0370.0440.1080.1810.2090.2090.310∼∼∼∼∼∼∼∼∼0.91.18.33.13.13.13.46.95.5−21.51 NANA .44 −21.56+0−0.41 .30 −21.51+0−0.20 .39 −21.32+0−0.36 .14 −21.54+0−0.11−22.18±0.3−22.03±0.3−20.93±0.4 .06 −1.43+0−0.03−1.59±0.02 .09 −1.29+0−0.08 .07 −1.22+0−0.06 .10 −1.11+0−0.09 .08 −1.14+0−0.07−1.27±0.10−1.25±0.08−1.02±0.18 Andreon&Cuillandre(2002)Loboetal.(1997)S´anchez-Janssenetal.(2005)ThisworkThisworkThiswork Mercurioetal.(2003)Mercurioetal.(2003)Busarelloetal.(2002) Table4.Schechterfunctionparametervaluesforthedeprojected(3-dimensional)luminosityfunctionsinthreeannuli:0.0Mpc A2443 A119 0–0.30.3–0.60.6–1.50–0.30.3–0.60.6–1.50–0.30.3–0.60.6–1.5 .57 −22.12+0−0.57 .60 −22.31+0−0.77 .37 −21.86+0−0.35 .58 −20.72+0−0.63 .72 −21.72+0−0.63 .02 −20.03+1−0.88 .54 −22.24+1−1.78 .71 −21.53+0−0.70 .51 −21.66+0−0.54.19 −0.94+0−0.16 .16 −1.30+0−0.15 .11 −1.36+0−0.10 .22 −1.00+0−0.19 .14 −1.19+0−0.12 .45 −1.01+0−0.18 .16 −1.25+0−0.11 .16 −1.16+0−0.12 .12 −1.23+0−0.10 3 πα 3 1− β2 α2 3/2 (12) (Beijersbergenetal.2002). Wesetradialbinpartitionsatcluster-centricradiiof0.3,0.6and1.5Mpc–splittingtheclusterfieldintofourregions(n=4)–andperformgeometricdeprojec-tionofthedatain1magnitudeintervals.Wefirstsub-tractfromthenumbercountsineachannulithecontribu-tionfromthesuperimposedfieldgalaxypopulationusingequation(8)–normalisedtotheareaof‘detectability’foreachannulus.Weusetheoutermostannuli(R>1.5Mpc)tobeginthedeprojection,thatis,seti=3inequa-tion(11)andtheniterativelycalculatethedeprojected(3-Dimensional)luminosityfunctionineachoftheinnerthreeannuli:0.0Mpc Luminositysegregationinthreeclustersofgalaxies11 Figure11.Leftpanels:thedeprojectedluminositydistributionsofgalaxiesincluster-centricannuliof0–0.3Mpc(opencircles),0.3–0.6Mpc(opensquares)and0.6–1.5Mpc(opentriangles)andtheirbestfittingSchechterfunctions(solid,dashedanddottedlines,respectively).Rightpanels:1,2and3σerrorcontoursfor theSchechterfunctionparametersM∗andα.A2218:toppanel,A2443:middlepanelandA119:bottomV panel. tion.Theluminosityfunctionremainsflatafterdeprojectionand(exceptforthecoreregionofA2218)wefindnostatisti-callysignificantevidenceforanychangewithcluster-centricradius–consistentwithourradialprofileanalysis. Thesegregationofgalaxiesofdifferentluminositiesisakeypredictionofhierarchicalmodelsofgalaxyfor-mationandevolution.ThenumericalCDMmodelsofKauffmannetal.(1997),forexample,predictthatlowlumi-nositygalaxiesshouldbelessclusteredthanthebright‘gi-ant’galaxies(seePhillippsetal.1998).Evolutionarymecha-nismsoperatinginclusterswhichshouldgiverisetoluminos-itysegregationhavealsobeensuggested.Mooreetal.(1998)havebeenabletoexplainthedwarfpopulation–densityre-lation(inwhichtheratioofdwarfgalaxiestogiantgalaxiesincreaseswithdecreasinglocalgalaxydensity)astheresultofgalaxy‘harassment’–whichoperatesmoreeffectivelyinregionsofhighgalaxydensity.Interactionwiththeclustertidalfieldwilldestroythelowestsurfacebrightness(leastbound)objectsinthecentralregionofacluster,resultinginadeficiencyoffaintgalaxiesintheclustercore.Iflumi-nositysegregationinclustersisnotpresentthentheimpactoftheseeffectsonthelow-luminosityclustergalaxieshasbeenexaggerated. Thekeyissueinsearchingforluminositysegregation inclustersisthatofthetechniqueofbackgroundsubtrac-tionemployed.Thefractionaldifferencebetweenthetotal(cluster+‘field’)galaxycountsandthe‘field’galaxycountsdecreaseswithdecreasingluminosity.Therefore,anysystem-aticerrorintheestimateofthefieldgalaxycountscanmimicbothafaint–endupturnintheluminosityfunctionandlu-minositysegregation–inthesensethatunderestimatingthefieldcountswillresultinalargerfractionoffaintgalaxiesatlowlocalgalaxydensities.Usingspectroscopytoconfirmclustermembershipisessentiallyuselessforallbutthenear-estclusters,sincethegalaxiesatthecriticalfaintendoftheluminosityfunctionaretoofaintforspectroscopicconfirma-tion.Hence,mostoftenastatisticalsubtractionofthefieldisperformedusinggalaxycountsmeasuredfromaregionoff-setfromtheclusterline-of-sight.Valottoetal.(2001)pointoutonepossiblesourceofbiasinstatisticalfieldsubtrac-tionduetothealignmentsbetweenfilamentsandclusterswhichcanresultinanunderestimateofthe‘field’galaxypopulation.Herewehaveusedananalyticrepresentation(equation6)oftheradialdistributionofgalaxiestowardtheclustersight-linetosimultaneouslyobtaintheclusterprofileandthesuperimposed‘field’galaxysurfacedensity.Note,fittingequation(6)totheradialprofilesinFig.3,Fig.4andFig.5doesnotrequirepriorsubtractionofthefieldgalaxypopulationandwe,therefore,suggestthatthisisasuperiortestforluminositysegregation.VeryrecentlyAndreonetal.(2005)havesuggestedanalternativemethodtoalleviateandquantifytheproblemsofbackgroundsub-tractioninderivingclusterluminosityfunctions–adetailedcomparisonofthesemethodsandthetraditionalmethodshouldbepursuedinafuturepaper. ACKNOWLEDGEMENTS BasedonobservationsmadewiththeIsaacNewtonTele-scopeoperatedontheislandofLaPalmabytheIsaacNew-tonGroupintheSpanishObservatoriodelRoquedelosMuchachosoftheInstitutodeAstrofisicadeCanarias.WethanktheCambridgeAstronomicalSurveyUnitforreduc-ingtheINTdata.WealsothanktheanonymousrefereeforaveryhelpfulreportwhichhasgreatlyimprovedthispaperandChrisBlakeforhishelpandadvicewiththiswork.M.B.P.wassupportedbyanAustralianPostgraduateAward.S.P.DandW.J.C.acknowledgethefinancialsupportoftheAustralianResearchCouncilthroughoutthecourseofthiswork.ThisresearchhasmadeuseoftheNASA/IPACExtragalacticDatabase(NED)whichisoperatedbytheJetPropulsionLaboratory,CaliforniaInstituteofTechnology,undercontractwiththeNationalAeronauticsandSpaceAdministration. 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