11A&Amanuscriptno.
(willbeinsertedbyhandlater)
ASTRONOMY
AND
ASTROPHYSICS
1.Introduction
In1993/1994westartedalong-rangephotometryprogramonclustersofgalaxiesinordertoestimateindetailtheclusterLuminosityFunction(LF)andthemorphologyofthebrightestclustergalaxies.Ouraimwastogainmoreaccurateknowledgeonthistopicbothtobetterunder-standformationandevolution,andtoimprovethecom-parisonwithnumericalsimulations.Straightforwardsci-entificdriversareatthebasisofthisinvestigation:theLuminosityFunctionofclustergalaxiesatpresenttimeistheresultofclusterinitialformationandsubsequentevolution-takingintoaccountinternalphenomenaandexternalinteractions.
Morettietal.:ClustergalaxyLF.Datareduction.3
(avoidingorcomparingduplications)anditwillhelpthereadertofollowourworktoitsthecompletion.
Secondly,wedetailourobservationalstrategyandmethodsofdatareduction,particularlyinthosepointswheretheydifferfromthestandardanalysisusedintheliterature.Theywillthenformabasicreferenceforotherpapersinpreparation.Theobservingstrategiesarestronglyrelatedandtunedtothedataanalysismethods.TheseprocedureshavefirstbeenappliedtotheclusterAbell496(seealsoMolinarietal.1998,paperI,fordis-cussiononLF),forwhichwepublishherethephotometry.2.TheProject2.1.Thesample
ThesamplehasbeenselectedfromthecataloguegiveninDeGrandietal.(1999)bychoosingonlyclustersatdeclination<0o,withX-rayfluxesmeasuredinthe0.5-2.0keVenergybandlargerthan10−11ergcm−2s−1,andwithextendedX-rayemission(i.e.,sourceswithproba-bilitytobepoint-like,ascomputedbyDeGrandietal.1997,smallerthan1%).Theresultingsampleof20clustersisreportedinTable1.ColumnslistthemainX-rayandopticalpropertiesforeachsourceasfollows:Column(1)—Clustername.Column(2)—X-rayposition:J2000.0rightascension(hhmmss.s).Column(3)—X-raypo-sition:J2000.0declination(ddmmss.s).Column(4)—Clusterred-shift.Column(5)—UnabsorbedX-rayfluxcomputedinthe0.5-2.0keVbandinunitsof10−11ergcm−2s−1.Column(6)—Bautz-Morgantype.Column(7)—Opticalrichness.Column(8)—Statusofobservations(Obs.=observed)
Fig.1.Theefficiencyoftheg,r,ifiltersasfunctionofthewavelength.Incomparison,atypicalearlytypegalaxyspectrumissuperimposedattwodifferentred-shifts:z=0andz=0.12,theextremesofthecatalogueredshiftrange.
2.2.Imaging
CCDobservationsofthesampleclusterswerecarriedoutsinceDecember1994atLaSillawiththe1.5mDanishTelescopeequippedwithDFOSCcamera.Foreachclus-terweobservedamosaiccomposedof3or4slightlyover-lappingfields(Fig.2showsthemosaicofAbell496).IneachmosaicthecentreofthefirstfieldcorrespondstothecentreoftheX-rayisophotes(seetheFig.1inMolinarietal.1998.).Theotherfieldsarecentredalongaradialdirection.Foreachmosaic,thetypicaltotalobservedareais250arcmin2withatypicalmaximumangulardistanceof30arcmin(equaltoalineardistanceof2.5Mpcatz=0.05).Foreachclustertheobservationofthemostex-ternalfieldisusedmainlytoevaluatethebackground.Eachfieldisobservedwiththeg,r,ifiltersoftheGunnphotometricsystem(Thuan&Gunn1976,Wadeetal.1979).ThespectralresponseisillustratedinFig.1alongwiththeobservedspectrumofanellipticalgalaxy.Obser-vationsofeachfieldconsistof3600sexposureasaresultoftheintegrationof4×900sdifferentexposures.Uptodate,wehavecollectedphotometricobservationsof15outof20clustersofthesample(Table1).Spectroscopicobser-vationsarealsobeingplannedandwilllikelystartshortlybeforecompletionofthephotometricsample.Thispaperwilldeal,inparticular,withthedataanalysiscarriedoutfortheclusterAbell496.Howeveritreflectsthemethodwewillalsousefortheotherclusters.
Fig.2.TheobservedfieldoftheclusterAbell496withthecDgalaxyintheNEcorneroftheimage.Themo-saiciscomposedof4adjoining,andslightlyoverlappingfields:theiridentificationnumber(Table2)increasesmov-ingfromNE(field0)toSOcorner(field3).TheangulardistancebetweenNEandSOcornersis30arcmin.
4Morettietal.:ClustergalaxyLF.Datareduction.
Table1.Thesample.DatarelativetoX-rayfluxandred-shiftarefromDeGrandietal.(1999).DatarelativetoopticalrichnessandmorphologyarefromAbelletal.(19).Datalabelledwith∗areourestimate.
NameA0085
00h56m11.69s
A0133
03h42m53.06s
A3186
04h25m51.02s
A3266
04h33m37.07s
A3376
06h26m20.10s
A3395
20h12m35.08s
A3695
21hm10.21s
A3827
22h10m20.09s
A3921
23h44m15.98s
A4038
23h57m00.02s
-34d45m24.5s
0.04600
-04d22m24.5s
0.07860
-12d10m49.0s
0.08380
-57d52m05.5s
0.07590
-56d50m30.5s
0.05560
-53d41m44.5s
0.05310
-13d15m20.0s
0.03284
-08d33m38.5s
0.03971
-53d37m43.0s
0.05910
-01d14m52.5s
0.04420
.8
2.406+0−0.708.2062.250+0−0.184.1881.870+0−0.179.4234.652+0−0.3.1831.313+0−0.152.9273.2+0−0.668.2021.099+0−0.170.2401.172+0−0.199.3021.214+0−0.232.11.974+0−0.178
II-IIII-III∗IIIIII-IIIII∗I
22–10222–1
Obs.–Obs.Obs.–Obs.Obs.Obs.–Obs.
3.Abell496imageprocessing
Abell496isaclass1richcluster,BautzMorgantype
I(Abelletal.19),dominatedbyasinglecentralcDgalaxy,MGC-02-12-039(α2000=4h33′37.7′′,δ2000=−13o15′43.2′′,z=0.032).ThepeakoftheX-rayemissionliesinsidethecoreofthecDgalaxy(Table1).CCDob-servationsoftheclusterwerecarriedoutduringthefirstobservingrunfrom24to27December1994.Theeffec-tivefieldoftheDFOSCcameraandThomsonTHX31156CCDis8.68×8.68arcminwithasinglepixelcorrespond-ingto0.508arsec.Thetotalareaoftheobservedfieldis224arcmin2foreachfilter(Fig.2).WelistthejournaloftheobservationsinTable2.
3.1.Flat-fieldingandmagnitudecalibration
Basicdatareduction,includingbiassubtraction,flat-fieldcorrection,magnitudecalibrationandcosmicrayssub-traction,isdoneusingtheESO-MIDASsoftwareenviron-ment.
Foreachfilterwebuildtwodifferentflat-fieldframes.Forthefirstweusetheditheringmethodtoobtaintheflatfieldframedirectlyfromscientificexposures(seeforexampleMolinarietal.1996).Thesecondflatfieldframeisbuiltusingthemedianofthedistributionofthesunsetandtwilightskyimages.Weobtaintheminimumvalueoftherationoise/sky,atbothsmallandbigscalesintheframes,usingthefirstflat-fieldingprocedureforfilteri.Forthegandrfiltersweadopttheaveragebetweenthetwodifferentflat-fieldframes,sincethisgivesthemin-
Fig.3.Thecalibrationstraightlineforfilterr.Foreachofthethreestandardstar,thetypicaluncertaintyontheoffsetmeasureis0.02magnitude.Moreover,the3differ-entaverageoffsetvaluesshowalineardependenceonthecolourofthestar.Bythelinearfit,weextrapolatetheoffsetvaluecorrespondingtog−r=0.
imumrms.Afterthereduction,thetypicalrmsoftheskyis1.5%,1%,0.75%ofthebackgroundfortheg,r,iframes,respectively.Cosmicraysareidentifiedbytheirappearanceinonlyoneoftheditheredimages.Thestarsobservedasstandardareselectedinthephotometricsys-temofThuan&Gunn(1976)andarelistedinTable3.Theoffsetofthecalibrationismeasuredasthedifferencebetweeninstrumentalmagnitude(asmeasuredwiththeg,r,ifiltersatESOtelescope)andthemagnitudeofthestandardstars.Inspiteofthefactthatweevaluatea
Morettietal.:ClustergalaxyLF.Datareduction.5
Table2.Thejournalofobservations.TheDate,Univer-salTime,airmass,exposuretime,andseeingforeachframeareshown.IneachframeseeingiscalculatedastheFWHMofthestars.
Objectfield0
2:48
1.040”1.2:331.133”1.50r
1:371.092”1.253:241.048”1.502:311.044”1.2:16
1.102
”
1.50
field1
2:14
1.050”1.504:061.093”1.15r
1:121.128”1.503:241.050”1.152:501.039”1.504:40
1.157
”
1.15
field2
5:04
1.233”1.3528-12-941:491.0”1.25r
27-12-94
1:051.134”1.305:391.372”1.351:56
1.061”1.301:161.106”1.25g
28-12-94
2:141.046900s.1.255:351.371”1.504:28
1.147”1.506:041.538600s.1.50i
2:481.040900s.1.255:02
1.240
”
1.50
α1950
δ1950
HD849378.3258.3838.43Ross683
11.4011.08-BD−1506290
10.7
9.4
8.334
Table4.kcorrection(Buzzoni1995)andgalacticextinc-tion(Burstein&Heiles1982)valuesusedfortheE/S0galaxiesinAbell496.
filterkcorr.
0.07
0.04
0.03
3.2.Objectsearchandanalysis
AutomaticobjectdetectionandmagnitudeevaluationhavebeendonebyusingtheINVENTORYpackage(West&Kruszewski1981)implementedintheMIDASenviron-ment.Galaxiesofthesamplespanaverylargerangeinmagnitudefromthemagnitudelimit(mag∼24,seenextsection)totheisophotalmagnitude(mag∼13)ofthecDcentralgalaxy.Thisrangecorrespondstoacomparablerangeinthesizeofthegalaxies.ItvariesfromthePSFlimit(∼3pixels)totheisophotalradiusofthecDgalaxy(∼100pixels).Becauseofthisinherentheterogeneity,thesampleisnotperfectlysuitableforautomaticsearchandanalysisofthesources.Inparticular,wemustseparatethesignalofveryextendedobjectsfromtherestoftheimagetoavoidtheproblemofmultipledetection.Theprocedureweuseiscomposedofthefollowingthreepoints.First,wemodelandsubtractthelightofthemostextendedobjects.Second,weapplytheINVENTORYstandardre-searchandanalysisproceduretoframesinwhichthere-mainingobjectsarecomparableinsize.Finally,weapplytheINVENTORYanalysisroutinetothesingle-objectim-agesofthemodelledandrebuiltextendedobjects.Herewedescribeonlythefirstpointoftheprocedurewhichistheoriginalpart.Wemodelandrebuildtheextendedsources,typicallygiantellipticalgalaxies,withaproce-duresimilartotheonedescribedbyMolinarietal.(1996).Weimprovedtheiralgorithmbymakingitmoreflexible.First,foreachdistancefromthecentreofthegalaxy,thealgorithmanalysestheazimuthalintensityprofilealongthecircularpaths(seetheleftpanelinFig.4).Thepro-jectionofanellipticalisophoteonthecircularpathsyieldsaperiodicvariationofsurfacebrightness,asshowninthepanelAoftheFig.5.ItcorrespondstotheintensityprofilealongthecircularpathmarkedontheleftpanelofFig.4.Themaximacorrespondtotheintersectionsofthecircu-larpathwiththemajorsemi-axisoftheisophote.ThenthealgorithmfitstheprofileusingaFourierseriesandalow-passfilter.Thisprocedureeliminatesthephysicalandgeometricalhighfrequencynoiseduetothediscrete
6Morettietal.:ClustergalaxyLF.Datareduction.
Fig.4.IsophotesofthecDgalaxyofAbell496fromtherawimage(leftpanel),andfromtherebuiltmodel(rightpanel).Thecoordinaterefertothepixelsoftheimage:1pixel=0.508arsec.Intheleftpanelthecircularpathat24pixelradiusismarked;theintensityprofilealongthispathisreportedinthepanelAofFig.5.Themodelisbuiltusingrawdatawherepossibleandfitvaluewhenanexternalobjectissuperimposedonthelineofsight.natureoftheCCDpixelgrid.Finally,wecalculatethedis-tributionofthedifferencesbetweenthedataandthefit:weexcludefromtheprofilethepointswhoseintensityisgreaterthan3timesthestandarddeviationofthedistri-bution(Fig.5,panelB).Thosepointsarereplacedbytheexactfitvalues.Byiteratingafewtimestheprocedure,wecanseparatethesignalsofthesuperimposedsources(Fig.5panelsC),withoutanyassumptionontheshapeoftheisophotes.Wealsomadethealgorithmmoreflexiblebyintroducingothergeometricalparameters.Inparticu-lar,weallowfortheexclusionofselectedangularprofilesintervalsfromthecalculationoftheFouriercoefficientofthetrigonometricseries.Intervalstobeexcludedarese-lectedbyvisualinspection.Theexclusionoptionisusefulwhentwoobjectsofcomparablesizeoverlapandhaveverycloseintensitymaxima.Inthisway,wecanrebuildthehid-denisophothesassumingacentralsymmetry.InFig.4wecomparetheisophotesoftherawimageofthecDgalaxy(leftpanel)withtherebuiltmodel(rightpanel).There-builtmodelisthensubtractedfromtheoriginalframetokeepthephotometricanalysisofveryextendedsourcesseparated.
Althoughtime-consuming(duetoitsinteractiveness),thisprocedureyieldsaccuratephotometricmeasurementsofboththeextendedandsmallsources.Thedescribedprocedure,infact,allowsthecompletephotometricanal-ysisofthesurfacebrightnessoftheextractedobjects(seeSect5.1fortheAbell496cD).Contrarytootherpopularautomatedprograms(e.g.SExtractor,Bertin&Arnout1996),wedonotassignapixelanditsvaluetoaunique
object,butpartitionthefluxineachpixelamongthedif-ferentobjectsdetected.Thustheisophotesarerecoveredintheirshapeandintensityforallsources.4.ThecatalogueofAbell49.1.Isophotalmagnitudedefinition
Todefineproperlyanisophotalmagnitudewefirstneedtoconsidersomedefinitionsandcorrelations(seealsoTren-tham1997).
4.1.1.Isophotalversustotalmagnitude
Thedifferencebetweentotalandisophotalmagnitudeisthedifferencebetweenthetotalflux,extrapolationofthecurveofgrowth,andthefluxintegratedwithinafixedSBvalue.Tosimulatesuchdifference,weextractfromtheframessomebrightsources(∼magnitude16)ofdiffer-entmorphologicaltypesandintegratethetotalfluxonanextrapolatedmodel.Wethenincreasethemagnitudeuptoourframelimitsbydividingtheoriginalfluxbyanumericalcoefficient.Inthisway,weobtainalistofexpectedtotalmagnitudesintherangeofinterest.Wecomparethesevalueswiththeisophotalmagnitudesasmeasuredbytheanalysisroutinewiththethresholdlistedbelow.Theamplitudeofthedifferencesisdependentonthesourceprofile.Inourdataatr∼24thedifferencesrangefrom0.1magforpointlikesourcestofewtenthofmagforE0/E6galaxiesand,littlemorethanamagni-tudefordiskdominatedobjects(Fig.6showsthecaseof
Morettietal.:ClustergalaxyLF.Datareduction.7
Fig.5.Stepsofthemodellingprocedure.A.Therawellip-ticalisophoteisprojectedonacircularpath.Theprofileshownherecorrespondstothe24pixelradiusofthecDgalaxyofAbell496asshownwithamarkedlineintheleftpanelofFig.4.Theazimuthalcoordinatehasthezeropointtowardtherightoftheimage,anditincreasescoun-terclockwise.Theperiodicshapeofperiodπoftheprofileisevident:thetwomaximaareat90and270degrees,correspondingtotheintersectionsbetweenthepathandthemajoraxisoftheellipticalisophotes(seeFig.4).Theprofileofasuperimposedsourceisevidentat30degreesasadeparturefromtheperiodicshape.WecanfindthesuperimposedobjectalongthepathmarkedinFig.4at30degreesfromthe0pointoftheazimuthalcoordinate.ThehighfrequencynoiseintheprofileshapeisduebothtoPoissonianandgeometricalnoises.B.Fitprocedureisperformedrepeatedlyexcludingstepbysteptheexter-nalobjectidentifiedat3σ.C.Whenanexternalobjectisidentified,theextendedobjectisrebuiltusingthefitvalue.Otherwise,theprofileisleftuntouched.
anelliptical-r1/4-galaxy).Thedifferenceisseeingdepen-dent.Toshowtheindependenceweconvolvetheoriginalframes(seeing≃1.3arsec)withaGaussianpointspreadfunctiontosimulateworseseeing(1.6arsec).TheeffectisillustratedinFig.6.
4.1.2.Dependenceontheseeing
Toreachinternalconsistencyonframesobtainedwithdif-ferentseeingwemustcorrecttheisophotalmagnitudesfortheseeingofeachframe.Ourapproachisasfollows.Wechoosenottoapplydirectlyanycorrectiontotheisopho-talmagnitude,but,varyingthevalueoftheSBofthelast
Fig.6.Thedifferencesbetweentheisophotalmagnitudeandthetotalmagnitudeofanellipticalgalaxy(seeing=1.3arsec)areplotted(filledsquares)versusthetotalmagni-tude.Dashedlineandcrossesshowthefeatureofthesameellipticalgalaxywithanartificiallydegradedseeing(1.6arsec).Opensquaresshowtheseeing-degradedgalaxyaf-terthecorrectionperformedaccordingtotherelationshipseeing-threshold.
isophoteasafunctionoftheseeingoftheframe,weensurethattheisophotalmagnitudevalueofafixedmorpholog-icaltypealwayscorrespondstothesamefractionofthetotalfluxofthesource.Theprocedureiseasilyjustified.Consider,forsimplicity,asourcewithaGaussianspatialbrightnessprofile:inthiscasedifferentseeinglevelscor-respondtodifferentvaluesofthestandarddeviationσ(Fig.7)andtheproblemhasasimpleanalyticalsolution.LetusconsiderabidimensionalsymmetricGaussianpro-fileI1withσ=σ1;giventhethresholdΣ1wehavetoconsiderthefluxFsubtendedbyI1from0tor1,suchthatI1(r1)=Σ1:
F=
1
2σ2
2πrdr.
Aftertheintegration,wecanwriteitasfunctionofΣ1
F=1−2πσ2
1Σ1.
Thereforegivenadifferentσ=σ2(andthesamenormal-ization),thesameisophotalfluxFisobtainedusingthe
thresholdΣ2suchthat
Σ2=(
σ1
8Morettietal.:ClustergalaxyLF.Datareduction.
Fig.7.ThetwoGaussianprofilessimulatethesameob-jectobservedwithdifferentPSF.Theprofilesarethepro-jectionsoftwobidimensionalprofileswiththesamenor-malizationanddifferentFWHM.Themarkedareasrepre-sentthesamequantityofflux.Theyrepresenttheisopho-talfluxeswithdifferentthresholdsattwodifferentseeinglevels.Accordingtoequation(1),thesecondthresholdΣ2ischoseninasuchawaythattheisophotalfluxoftheleftprofileiskeptconstant.
Therelation(1)hasbeendeducedinthecaseofGaus-sianprofilesource.Wefindthatthecorrectionsdrawnfrom(1)givegoodresultsalsofordifferentmorphologi-caltypesasshowninFigs.6and8.InFig.6weshow,inthecaseofanelliptical-r1/4galaxy,thedifferencebetweenisophotalandtruemagnitudeattwodifferentseeinglev-els(oneartificiallydegraded),andthedifferenceafterthecorrection.Atlowluminositythecorrectionsubstantiallyremovestheseeingdependence.
Thequalityofthecorrectiondiscussedabovecanbetestedintheintersectionregionsoftwooverlappingframes,whichhavebeenobtainedindifferentseeingcon-ditions.Inthisregionwehave2differentmeasuresper-formedwithdifferentseeingofalistofsourcesofrandommagnitudeandmorphologicaltype.Forthedifferencesbe-tweenthe2independentmeasures,weexpectasymmet-ricdistributionwithadispersionexponentiallyincreasingwiththemagnitudeduetothePoissonianuncertainty.Ifweremovethisdependencebynormalizingbyanexpo-nentialfactor,weexpectaGaussiandistribution.InFig.8wecanobservethatthedistributionofthemeasuresperformedwiththesamethresholdisslightlyasymmet-ric;afteradoptingthethresholdcorrectedaccordingtherelation(1)wefindthatthedistributionofdifferencesisperfectlysymmetricasatestofriliabilityofthemethoddescribed.
4.2.Samplecompleteness
Backgroundstatisticalvariationsandsourcecrowdingmayaffecttheaccuracyoftheautomaticdetectionrou-tineandthecompletenessofthephotometriccatalogue.
Fig.8.Thedistributionofthedifferencesbetween2mea-sureswithdifferentseeing(1.3arcsecvs1.4arcsec)of75sourcesafterthecorrection.Thedistributionofthediffer-encesofthemeasuresbeforethecorrectionisshownwiththesolidlineanditisslightlyasymmetric.Thedashedlineshowsthesymmetricdistributionafterthecorrection.Weuseabootstrappingtechniquetotestthesensitivityofourresultstobothfactors.First,weextracttheimageofagiantellipticalgalaxyfromoneoftheframes.Then,divid-ingbyanumericalcoefficient,wegenerateasetofmorethan30differentimagesforeachfilterintherelevantrangeofisophotalmagnitudes:16.07≤r≤24.56,15.86≤g≤24.85,15.87≤i≤24.01.Thetestimagesareaddedtotheobservedframespositionedat25subsequentdistancesfromthecentreofthecluster(assumedtobeinthecen-treofcDgalaxy).Foreachvalueofthedistancefromthecentreandmagnitude,werepeatthisprocedure100timesineachfilter,randomlychangingtheangularcoordinateoftheaddedtestimage.These100repetitionsaredividedinsmallgroupsindifferentrunstoavoidbiasduetoarti-ficialadditionalcrowding.Thisallowsustoestimatetheprobabilityofdetectingagalaxyofmagnitudematdis-tancerfromthecentreoftheclusterP(r,m).ForeachP(r,m)weestimatetheuncertaintybythebinomialdis-tributionPB[x,100,P(r,m)],whichgivestheprobabilityofobservingxsuccesseson100attemptsgivenaprobabil-ityP(r,m)forasinglesuccess.Atafixeddistancerfromthecentrewefinda100%detectionrateforbrightgalax-ies,andadropintherateatcharacteristicmagnitude∼m0(Fig.9).Theanalyticalformulaofthisfunction,givenbyafitperformedwithaFermifunctionis:
P(r,m)=
1c
+1
.
Wealsofindthatm0dependsonthedistancer.Smallerradiiareassociatedwithbrighterm0.Therelationshipcanbeparameterizedbyanhyperbole
m0=m0(r)=A−
B
Morettietal.:ClustergalaxyLF.Datareduction.9
Fig.9.BootstrapresultsattwodifferentdistancesfromthecentreofthecDgalaxyareshown.ThetwodifferentcurvesarefittedbyFermi-Diracfunctionwithdifferentvalueofthecharacteristicmagnitudem0.Goingoffcentrem0increases:atfixedmagnitude,findingafaintgalaxyiseasier.Theuncertaintyofthetestresultsisestimatebybinomialstatisticand1σlevelisshowninthefigure.whereAandBareslightlydifferentforthe3filters.Asweexpect,thisrelationisaffectedbybackgroundstatisticalvariationandsourcescrowding.Thefirststeepincreaseofm0isduetocrowdingeffectofthecentralpartoftheclus-terandtothecDhalo.Theflatshapenearanasymptoticvalueisduetothestatisticalvariationsinthebackgroundnoise.Theasymptoticvalueofm0correspondsto50%de-tectionprobabilityindependentlyofanycrowdingeffectandforeachfilterweassumeitasthelimitingmagni-tudevalueofthecatalogue(24.14,24.46,23.75,forfilterg,r,irespectively).Thetestisperformedontherawimage,withouttheexclusionofthebright,extendedob-jects.Indeed,westressthatsubtractingthesignalfromextendedsources(seeprevioussection)doesnotsubstan-tiallyimprovetheautomaticroutinedetectioncapabilityoffaintgalaxies.
Table5.ByusingfunctionP(r,m),wecanestimateoursamplecompleteness.Herewegivethecompletenessvalueofthelastthree-1magnitudebinforeachfilter.
filterg
[22.14,23.14]
[-13.39,-12.39]
95+1.7
−2.4
filterr
[22.46,23.46]
[-13.07,-12.07]96+1.5−2.2
filteri
[21.75,22.75]
[-13.79,-12.79]97+1.2−2.0
21.25
22.2523.2524.25
stars290/1867
stars
47/530
10Morettietal.:ClustergalaxyLF.Datareduction.
4.4.Errorestimate
ThePoissonianuncertaintyisthelargestsourceoferrorinourphotometricmeasurementsandcanbeestimatedbycomparingindependentmagnitudemeasurementsofthesameobjects.Inoursample,wehaveindependentpho-tometricmeasurementsoftheobjectsbelongingtotheintersectionsoftwoadjoiningfields.AsshowninTable7,theyrepresentastatisticallysignificantsubsample.Table7.Numberofobjectsbelongingtotheintersectionofdifferentfields.
Filter
Field1∩Field0
95
126
107
StartingfromthePoissonianstatistics,duetotheer-rorspropagationlaw,forthemagnitudeuncertainty,weexpect
σ(m)=const100.2m,wheretheconstantisgivenbythecharacteristicsoftheelectronics.Atmagnitude22weestimatethattheuncer-taintyofthephotometricmeasuresσ22is0.20,0.19,0.22magnitudeforfilterg,r,irespectively.Then,foreachmagnitudemwecandrawσmas
σ(m)=σ22100.2(m−22),
whichistheuncertaintyofourphotometricmeasuresasfunctionofthemagnitude.
Fig.12.WesplituptheplaneinthreedifferentregionsonthebasisoftheColour-MagnitudeRelation.UsingMet-calfeetal.(1994)terminologythethreeregionsaredefinedasthe“blue”,“thesequence”andthe“red”.Weidentify637galaxieswithinthesequencezone(littlesquares),371intheredzoneand47intheblueone.Thefilledcircleatr∼13referstocDgalaxyisophotalmagnitudeandcoreindexcolour(seenextsubsection).4.5.Descriptionofthecatalogue
Thederivedcatalogueconsistsof2355objects:2076areclassifiedasgalaxies,956galaxieshavemagnitudemea-suresinallthreefilters,1081,2055,1500galaxieshavemagnitudevaluesbelowthefilterg,r,ilimit,respectively.Weestimateg-rcoloursof1058galaxiesandg-iof955galaxies.Thewholecatalogueisavailableinelectronicform(http://www.merate.mi.astro.it/∼molinari/A496-cat.dat),whileinTable8thelistofthe40brightestgalaxiesisreported,andinTable9wesummarisethestatisticsofthecatalogueofgalaxies.Inthedifferentcolumnswelist:
–(1)IDnumberoftheobject;
–(2)EASTandSOUTHcoordinates,inarseconds,withrespecttothecentreofthecDgalaxy;
–(3)g,r,iisophotalmagnitudes,eachcomputeddowntothethresholdquotedintheprevioussection;–(4)g,r,iisophotalradius;
–(5)g-randg-icoloursindexcomputedthrougha1.5,3or5pixelaperturephotometry,dependingonthecomputedrisophotalradius;
–(6)classificationoftheobjectasstarorgalaxy.
Fig.11.Differencesbetweenrmagnitudemeasurementsofthesameobjectsperformedfromtwoframes.Plottedagainstmagnitude,theyshowtheexpectedexponentialslope.1and2σmlevelcurvesareshown.
Morettietal.:ClustergalaxyLF.Datareduction.11
Table8.Asubsampleofthephotometriccatalogue(http://www.merate.mi.astro.it/∼molinari/A496-cat.dat)report-ingthe40brightestobjectsinthecompletelistispresented.Theluminositysortinghasbeenmadeintherfilter.TheIDnumberreferstothepositioninthewholecatalogue.
ID1429
-553.3
2251
-292.9
1061
-272.2
249
-286.8
968
-587.8
935
-437.4
573
-418.3
113
-1077.9355
-25.6
632
-186.1
480
-922.3
1200
-482.8
1522
-77.7
2032
-236.8
2308
-420.9
982
-629.4
925
-516.1
826
-360.6
1604
-68.4
2082
-580.7
-60.5-1.4
17.13
16.93
16.96
8.2
9.2
7.9
159.0
17.86
16.87
16.52
6.9
9.0
9.7
0.17
0.22
121.2
17.30
16.80
16.62
8.7
9.3
8.2
0.95
1.34
200.5
17.31
16.76
16.61
8.7
9.5
8.5
0.50
0.68
4.4
17.88
16.74
16.06
19.0
20.0
18.0
0.55
0.70
69.3
17.83
16.70
15.97
20.0
22.0
19.0
1.15
1.81
star
175.2
17.44
16.63
16.44
8.8
9.3
8.4
1.10
1.87
star
304.7
16.96
16.61
16.58
9.0
9.3
8.8
0.79
1.01
681.2
17.12
16.58
16.52
7.8
9.3
9.6
0.41
0.50
-217.7
16.92
16.44
16.18
8.1
10.4
9.5
0.53
0.62
-93.0
16.91
16.38
16.19
7.4
9.7
11.8
0.46
0.72
942.2
16.50
16.18
16.18
14.0
17.0
15.0
0.56
0.74
373.6
16.61
16.08
15.
9.9
10.4
9.0
0.35
0.32
star
514.5
16.19
15.83
15.81
20.0
21.0
18.0
0.55
0.74
-198.7
16.27
15.76
15.59
11.0
11.6
9.9
0.43
0.43
star
440.7
15.98
15.48
15.42
27.0
30.0
27.0
0.
0.71
55.5
15.
15.34
15.29
31.0
37.0
30.0
0.50
0.58
star
501.1
15.66
15.15
15.25
26.0
29.0
25.0
0.56
0.60
star
23.8
14.81
14.87
14.87
11.6
13.6
12.3
0.47
0.33
star
g15.22
r14.70
i14.
36.0
40.0
34.0
-0.17
-0.10
g-r0.50
g-i0.68
star
5.Abell496photometricproperties
Inthissectionweanalysethegeneralpropertiesofthecluster.Weexaminecloselythefollowingpoints.First,bymeansoftheColour-MagnitudeRelation,weselectthemain,earlytype,componentoftheclusterpopulation.Second,weestimatetheprojectedspatialdistributionofthedifferenttypesofgalaxiesandwemeasurethecoreradiusoftheclusterastrackedbybrightgalaxies.Third,weanalyzethephotometricpropertiesofthecDcentralgalaxy.Fourth,westudythedistributionofgalaxycolourasfunctionoftheirpositionwithintheclustercore.
5.1.Thecoloursofthegalaxies
Onther/(g−r)plane(Fig.12)weemphasizethenar-rowsequenceofthelinearColour-MagnitudeRelation(CMR):thesequencedefinesthelocusofearlytypegalaxiesoftheclusterwithintheplane(Visvanathan&Sandage,1977,Arimoto&Yoshii,1987).Thecontinuouslineisdeterminedbyfittingthelocusofpointsasdefinedbyellipticalgalaxiesbrighterthanmagnitude18,exclud-ingthecDgalaxy.Theequationderivedbythebestfit
CMR(r)=−0.025r+0.914
12Morettietal.:ClustergalaxyLF.Datareduction.
Fig.13.Colour-colourplanes.Ourdataaresuperimposedontheexpectedcoloursofellipticalgalaxiesatdifferentred-shifts:eachcrossonthecontinuelinerepresentsa0.05red-shiftvariation.ThefilledsquarerepresentsthecDgalaxy,perfectlyplacedonthetheoreticalpathatred-shift0.03.Reddergalaxiesshowexpectedcoloursofellipticalgalaxiesathigherred-shift.SequencegalaxiesareslightlybluerthancDgalaxywithdispersionincreasingwiththemagnitude(seefig.12)Finally,bluegalaxieshavecoloursunmatchablewiththeearlytypegalaxycolours.Table9.Statisticsofthecatalogueofgalaxies;279clas-sifiedbrightstarsareincludedinthecatalogue,butnotinthepresentsummarytable.Atfaintmagnitudes(>20.75)weexpect15%oftheentriesareforegroundstars.Inparenthesesabsolutemagnitudelimitsarereportedas-sumingH0=50km/sec/Mpc.
Skill
−1332244h32′48′′12.(-22.93)12.04(-22.62)11.88(-22.55)
-0.50-0.61
o
′
′′
Gal.enters
−13112h33′49′′24.14(-12.28)24.47(-11.96)23.75(-12.67)
1.983.28
o
′
′′
σg(g)2+σr(r)2+0.06),
wherewetakeintoaccountphotometricuncertaintyat1σlevel(seesection4.4)andtheinherentdispersionoftherelation(estimateduponthemostluminousgalaxies).Theplaneredwardofthesequence(redzone)isexpectedtobemainlypopulatedbyhigherred-shiftgalaxies,whilethe
Morettietal.:ClustergalaxyLF.Datareduction.13
Fig.14.Projectedspatialdistributionofall(upperpanel),bright(r≤20.0)galaxies(centralpanel),andbrightsequencegalaxies(lowerpanel).WefitbrightgalaxiesdistributionswithKingfunctionsandweshowthetwodifferentcoreradiusbestvalues.Comparisonbetweentheupperandcentralpanelsuggestsaluminositysegregationeffect;comparisonbetweencentralandlowerpanelsuggestacoloursegregationeffect.Thedensityprofileisobtainedastheaverageof36profiles,andtheerrorscorrespondto1standarddeviationofthe36valuesdistribution.Intheleftpanelthedottedlinesshow1e2coreradius.
bluewardzoneislikelythelocusofclusterandforegroundlate-typegalaxies.
Tofurtherclarifythisconceptoflikelymembershipweplotourdatainthecolour-colourplane,g−rversusg−i(Fig.13).ThecontinuouslineintheplanerepresentsthelocusofpointsdefinedbyellipticalgalaxiesatdifferentredshiftsaccordingtothemodelsofBuzzonietal.(1993).Theseplotsareconsistentwiththepreviousdiscussion:a)thecDgalaxy,filledsquare,isneartheexpectedlocationofanEgalaxyattheclusterredshift,b)galaxieslocatedintheredzoneofFig.13aredisplayedalongthesequenceofhigherredshiftellipticals,andc)bluegalaxiesdonotmatchtheredshiftsequenceforellipticalgalaxies.
5.2.Spatialdistribution
Thestrategyweadoptfortheobservationshastheadvan-tageofallowingmeasuringfieldsataratherlargedistance,about2700pixels(∼1275kpc)fromtheclustercentreinareasonableamountoftelescopetime.Ontheotherhandweareforcedtoselectanadhocradialdirection.Thatiswearemoresensitivetoclusterandbackgroundfieldden-sityfluctuations.Weproceedasfollows.First,webuildthedensityframerelativetothewholemosaic.Thenwedividethedensityframein36circularsectorscentredontheclustercentreandaveragethecontributionofeachseg-mentatfixedradiusgoingfromthecentretotheexternallimitofthemosaic.Thewholesamplemeanradialsurface
14Morettietal.:ClustergalaxyLF.Datareduction.
Fig.15.Spatialdistributionofredgalaxies(upperpanel)andbluegalaxies(lowerpanel)aslabelledonthemagnitude-colourplane.Redgalaxiesdonotshowanyparticularbehaviourlinkedtoclusterstructure.Bluegalaxiesremarkablycrowdat1coreradiusdistancefromthecentreofthecluster.Table10.BestfitvaluesofKingfunctionforthedistri-butionofbrightgalaxies(r<20).
SampleALL
1.807±0.2
497+22−25
0.12±0.01
structure(Fig.15upperpanel).Galaxiesbelongingtothe
bluezoneofthecolour-magnitudeplaneareidentifiedasclusterorforegroundlatetypegalaxies.Theirprojecteddistributionseemstobeinfluencedbyclusterpotential:theirdensityabruptlypeaksat1coreradiusdistancefromtheclustercentre.Thiseffecthasbeennoticedalsoinsomeoftheotherclustersthatweareanalysing.5.3.ThecentralcDgalaxy
ThecDcentralgalaxyisthebrightestmemberoftheclus-ter:itis2magnitudesbrighterthanthesecondmember.InMolinarietal.(1998)itsluminosityisregardedastoobrighttobeconsistentwithotherellipticalsanditisnotincludedinthecomputationofLF.However,asseenintheprevioussubsection,thecDmagnitudeandcolourareconsistentwiththeCMRextrapolatedfromthepopula-tionofthebrightellipticalsgalaxies.
cDgalaxiesaregenerallycharacterisedbyasurfacebrightness(SB)profilethatfallsoffmoreslowlywithra-diusthanmostellipticalgalaxies.InFig.16theprofileoftheAbell496cDgalaxyalongthemajoraxisisshownuptoadistanceof100arcsec(∼92kpc)fromthecen-tre.Inthisprofilethepresenceofthehaloisparticularly
densityprofile(Fig.14,upperpanel)doesnotclearlymakeevidenttheexcessofgalaxiesdefiningthecluster.
Duetothesegregationeffectofthemostluminousgalaxies,r<20.0,aKingprofilewellfitsthedensityprofileatthesemagnitudes(Fig.14centralpanel,andTa-ble10).ThesequencegalaxiesasdefinedbytheCMR,withr<20.0,presentahighercentralconcentrationasindicatedbythesmallercoreradius(Table10).ThisisalsotobeexpectedinarelaxedclustersincetheCMRsequencehasbeendefinedbyusingthebrightellipticalclustergalaxies.
Galaxiesbelongingtotheredregionofcolour-magnitudeplaneareidentifiedasgalaxiesathigherred-shift(seeFig.12and13).Theirdistributionishomoge-neousovertheobservedfieldwithoutanylinktocluster
Morettietal.:ClustergalaxyLF.Datareduction.
15
noticeable,itdepartsstronglyfromadeVaucouleurlaw(thestraightlineinthefigure).ThecomparisonoftheSBprofilealongthenorthernmajorsemi-axis(N)withtheonealongthesouthernsemi-axis(S)(Fig.16)showsanevidentasymmetry.TheNregionofthehaloexhibitsanexcessofintensitywithrespecttotheSineachofthe3filtersintheinterval25-50arcsecofdistancefromthecentre.ThiseffectisclearlydepictedbytheisophotesinFig.17.Inspiteofthelargeextensionofthehalo,thisis
Fig.16.TheintensityprofilesofthecDgalaxyofAbell496alongtheNandSmajorsemi-axisaresuperimposed(therandiprofilesareshiftedof2and4magnitudetomakethefigureclearer).Theexcessofintensityofthenorthernsemi-axisisnoticeableintheinterval(25,50)ar-secfromthecentre.ThestraightlinesrepresentsthedeVaucouleurprofile.
somewhatfainterthanthecore.AfterfittingthecorebyadeVaucouleurlaw,wecouldsubtractitfromthecDim-ageandestimatethemagnitudeofthehalo.ThederivedtotalmagnitudesinthethreefiltersarelistedinTable11.Asalreadystated,theluminosityofthecoreisdominant.Theaveragecolourindexofthetotalprofilepresentsagradienttowardthebluemovingfromthecoretotheout-ermostpartofthegalaxy.Thisisduetothecolourofthehalothatisbluerthanthatofthecore.Withinthehaloitselfadifferenceexistsbetweenthecolourofthenorthernhemisphereofhighersurfacebrightness,andthecolourofthesouthernhemisphere.Thenorthernzoneisbluer(markedascolourexcessinFig.18).InothercDgalaxies(seeforinstanceMolinarietal.1994)thehalohasbeenfoundredderthanthecore.Therefore,thechar-acteristicsofthehalopopulationareundoubtedlyrelatedtothespecifichistoryofthecDunderconsideration.5.4.Colourgradientofthegalaxypopulation
Finally,thedistributionoftheg−rcoloursofthesequencegalaxiesisanalysedasafunctionoftheirprojecteddis-
Fig.17.ThefilterrhaloisophotesaresuperimposedtotheimageofthecDgalaxy(theNorthistowardthebot-tomoftheimage),thelastisophotecorrespondingtotheSBthreshold.Theasymmetryofthehaloemissionisclearlyevident.
Fig.18.Theaveragecolourindexofthethreecompo-nentsofthegalaxyisshown.TheyarecomparedwiththeexpectedcoloursofthestarsconvolutedfromthespectralcatalogueofVilnius,Strajzhis&Sviderskene(1972)(starsarelabelledwiththenameofspectralclass)andalsowiththecoloursofthestarsofourcatalogue(smallpoints).tancefromthecentreofthecluster.Wefindasignificantcorrelationrelativetothepopulationoffaintgalaxies.
Aspartlyexpected,brightergalaxiestendtodominateinthecentralregionofthecluster.Suchgalaxies(seealsothediscussionontheCMRrelation)tendtobesome-whatredder.Thereforeweexpectamildcorrelationbe-tweentheclusterintegratedcolour-definedasthemeancolourderivedfromthegalaxypopulationlocatedata
16Morettietal.:ClustergalaxyLF.Datareduction.
Table11.PhotometricparametersofthecDgalaxy.
Fg
51.7±5.1i
25.12±0.10
12.04±0.02
12.22±0.03
13.99±0.06
Morettietal.:ClustergalaxyLF.Datareduction.
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17
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