The WARPS X-ray survey of galaxies, groups and clusters I Method and first results

CLUSTERS–I.Methodandfirstresults

C.A.Scharf1,L.R.Jones

1

Lab.forHighEnergyAstrophysics,Code660,NASA/Goddard,GreenbeltMD20771,

USA,email:caleb@amadeus.gsfc.nasa.gov,lrj@clopper.gsfc.nasa.gov

H.Ebeling

InstituteofAstronomy,MadingleyRoad,CambridgeCB3OHA,UKandpresentaddress

InstituteforAstronomy,2680WoodlawnDr,HonoluluHI96822,USA,email:

ebeling@marvin.ifa.hawaii.edu

E.Perlman

2

Lab.forHighEnergyAstrophysics,Code660,NASA/Goddard,GreenbeltMD20771,

USA,email:perlman@baley.gsfc.nasa.gov

M.Malkan

Dept.ofAstronomy,UCLA,LosAngeles,CA90024,USA,email:

malkan@bonnie.astro.ucla.edu

andG.Wegner

Dept.ofPhysics&Astronomy,DartmouthCollege,6127WilderLab.,Hanover,NH03755,

USA,email:wegner@kayz.dartmouth.edu

Received

–2–ABSTRACT

WehaveembarkedonasurveyofROSATPSPCarchivaldatawiththeaimofdetectingallsignificantsurfacebrightnessenhancementsduetosourcesintheinnermostR≤15arcminofthePSPCfieldofviewintheenergyband0.5−2.0keV.ThisprojectispartoftheWideAngleROSATPointedSurvey(WARPS)andisdesignedprimarilytomeasurethelowluminosity,highredshift,X-rayluminosityfunctionofgalaxyclustersandgroups.Theapproachwehavechosenforsourcedetection[VoronoiTessellationandPercolation(VTP)]representsasignificantadvanceoverconventionalmethodsandisparticularlysuitedforthedetectionandaccuratequantificationofextendedand/orlowsurfacebrightnessemissionwhichcouldotherwisebemissedorwronglyinterpreted.Wealsouseenergydependentexposuremapstoestimatethefluxesofsourceswhichcanamounttocorrectionsofasmuchas15%.Inanextensiveopticalfollow-upprogrammeweareidentifyinggalaxies,groupsandclustersatredshiftsrangingfromz∼0.1toz∼0.7.

Inthispaperwepresentourmethodanditscalibrationusingsimulatedandrealdata.Wepresentfirstresultsforaninitial91fields(17.2deg2)atdetectedfluxes>3.5×10−14ergs−1cm−2(theWARPS-Isurvey).Wefindtheskydensityofextendedobjectstobeintherange2.8to4.0(±0.4)deg−2.AcomparisonwithapointsourcedetectionalgorithmdemonstratesthatourVTPapproachtypicallyfinds1-2moreobjectsdeg−2tothisdetectedfluxlimit,suggestingthattheconventionalmethodfailstodetectasignificantfractionofextendedobjects.ThesurfacebrightnesslimitoftheWARPSclustersurveyis∼1×10−15ergsec−1cm−2arcmin−2,approximately6timeslowerthantheExtendedMediumSensitivitySurvey(EMSS).TheWARPSLogN-LogS(whichcurrentlyrepresentsalowerlimit)showsasignificantexcessoverprevious

–3–

>8×10−14ergsec−1cm−2.WeattributethismainlytomeasurementsforS∼

alargermeasuredfluxfromextendedsourcesaswellasnewdetectionsoflowsurfacebrightnesssystemsintheWARPS.

Subjectheadings:galaxies:clustersof-Xrays:sources-cosmology:surveys

–4–

1.

Introduction

HierarchicalmodelsofstructureformationintheUniverse(suchasColdDarkMatter(CDM)cosmologies)predictthebasicevolutionarypropertiesofgravitationallyboundaggregates.ClustersofgalaxiesarethelargestsuchobjectstohavealreadydecoupledfromtheHubbleexpansionandthereforeofferauniqueopportunitytoevaluatethefundamentalpropertiesoftheUniverse.Thedominantbaryonicmasscomponentingalaxyclustersisobservedtobeintheformofhot(107−108K)intra-clustergas(∼90%oftheluminousmass)emittingradiationthroughthermalbremsstrahlungwithsomecontributionfromthermallineemission.WethereforeexpecttheX-rayluminositytobepositivelycorrelatedwiththesystemmass(assumingaconstantbaryonmassfraction,seee.g.Whiteetal1993).SincethemeasurementofclusterX-rayluminosityisrelativelyeasy,itfollowsthattoinvestigatethenatureofclustersandtheirformationweshouldchooseaprimaryselectionmethodbasedonX-rayobservations.

Inthepast,selectioneffectshavebesetopticalsurveysbecauseoftheprojectionofbackgroundandforegroundgalaxiesonthecluster,sometimesleadingtofalseidentifications(e.g.Frenketal1990),particularlyforpoorclustersathighredshift,wherethecontrastwiththebackgroundgalaxysurfacedensityislow.Evenwithaknowledgeoftheline-of-sightdynamicsofasystemitisonlypossibletoassignprobabilitiesforindividualobjectstobelong(gravitationally)toaclusterorgroupofgalaxies.X-raysurveyssufferlessfromsuchproblems.SincetheX-raysurfacebrightnessisproportionaltothesquareofthedensityofthehotgaswithinthecluster,thecontrastwithrespecttotheunresolvedX-raybackgroundishigh.X-rayobservationsalsoprovideinformationaboutthepotentialsizeandshapeleadingtomuchlessambiguousidentificationofrealphysicalsystems3.

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WellselectedcataloguesofgalaxyclusterscanthenbeusedtoinvestigatetheevolutionoftheclusterX-rayluminosityfunction,themorphologyandsubstructureofclusters,thetemperatureevolutionofthegascomponent,andtheevolutionoftheopticallyobservedgalaxypopulation.

WhatdoweexpecttheX-rayclusterevolutiontobeinahierarchicalmodel?Itwouldbefairtosaythatboththeobservationalandtheoreticalsituationarestilluncertain.Modelingofthegravitationalinstabilityandgashydrodynamicsofclustershasbeenpursuedwithsemi-analyticmethods(Kaiser1991)andnumericalsimulation(Evrard1990,Bryanetal1994a,Cen&Ostriker1994,Kangetal1994).Fromsuchstudiesitisevidentthattheevolutionarypropertiesofclustersaresensitivetoboththeassumed’internal’clusterphysics(e.g.thepresenceorabsenceofcoolingflowsorfeedbackmechanisms)aswellasthe’external’influenceoftheunderlyingcosmologicalmodel(e.g.Freidmannmodelparametersandthepowerspectrumofmassfluctuations).However,inthecaseofrelativelysimple’internal’clusterphysics(e.g.shockheatingduringgravitationalcollapseasadominantmechanism)andastandardCDMcosmologythereisapredictionofnegativeevolution(i.e.adecreasewithredshift)inthenumberdensityofthemostluminousclusters(withLx>5×1044ergs−1).

Currentsurveysbroadlyconfirmthisscenario.TheEMSSclustersampleofHenryetal(1992)showedevidence(atthe3σlevel)ofnegativeevolutionintheclusterX-rayluminosityfunction(XLF),withfewerhighluminosityclustersatredshifts0.3–6–

ofnegativeevolutionactuallymeasuredisstatisticallyhighlysignificant).Theearlierdetectionofevolutionatz<0.2byEdgeetal(1990)hasbeenshowntobeduetoanunfortunatesamplingofclustersatz=0.1to0.15,ratherthantoevolution(Ebelingetal1995).Athighredshifts(0.2TheslopeoftheclusterXLFsteepenedwithredshiftintheEMSSsurveyofHenryetal(1992)suchthatatlowerluminosities(around1044ergs−1)noevolutionwasrequired.IfthesteepslopeoftheEMSShighredshiftXLFisextrapolatedtostilllowerluminosities(LX<1044ergs−1),positiveevolutionoflowluminosityclustersispredicted,withlargenumbers(∼8deg−2)ofz>0.2clustersatlowX-rayfluxes(>3×10−14ergcm−2s−1).AccuratemeasurementsofthehighredshiftXLFwouldallowtheformoftheXLFevolutiontobedeterminedviathepositionoftheSchechterfunctionbreak.Thiswouldhelpdiscriminatebetweenluminosityanddensityevolution,anddiscriminatebetweendifferenthierarchicalmodels,e.gthoseincludingadifferentmixoffundamentalparticles(e.g.

Bryanetal1994b),aflatpowerspectrumoftheinitialfluctuations(Henryetal

1992)andreheatingoftheintraclustergasathighredshifts(Kaiser1991).TheWARPSclustersurveywasdesignedtomakethismeasurement(Jonesetal1996).

ToensurethecompletenessoftheWARPSsampleasourcedetectionmethod(VoronoiTessellationandPercolation,VTP)isusedwhichdoesnotdiscriminateagainstextendedsourcesoflowsurfacebrightnessand/orirregularmorphology.Thisisespeciallyimportantbecauseoftheevolutionthatmightbeexpectedinpropertiessuchascoreradius,temperatureandmorphology.Indeed,clustermorphologyhasbeenshowntobea

–7–

potentiallyimportantcosmologicaldiscriminator(Evrardetal1993,Crone,Evrard&Richstone1994).Whileluminousclustersathighredshift(z>0.4)arelikelytobedetectedbystandardpointsourcesearchalgorithms,thoseatlowerzandlowerluminositymaybemissedaltogetherbysuchmethods(Section5)orremovedfromafluxlimitedsurveyduetoanincorrectlylowfluxdetection.Ananalogoussituationexistsinopticallyselectedgalaxycatalogues-amagnitudeselectedsamplewithahighsurfacebrightnessdetectionthresholdwillbeincompleteindiameterandviceversa.Suchselectioneffectswillbiasconventionalcataloguesagainst(forexample)extendedlowsurfacebrightnessobjectsandcausefluxestobeincorrectlymeasured.

InthispaperwedescribethemethodsusedintheWARPSsurveyandpresentitsfirstresults.Thisworkisarrangedasfollows:inSection2wepresentabriefoverviewoftheWARPSsurveyandtheROSATPSPCdataarchive,inSection3,3.1,3.2and3.3wedescribetheVTPmethod,theconstructionofafluxlimitedcatalogueanddiscusstheaccuracyoffluxcorrectionsandextendedsourcedetection.Section4presentsthecalibrationofthesurveyskycoverage.Section5presentsacomparisonwiththeresultsofaconventionaldetectionalgorithm.InSection6wediscussthecurrentresultsandinSection6.1presentaLogN-LogSforWARPS-I.InSection7wesummarizethispaperandpresentconclusions.

2.TheWARPSsurveyandtheROSATdata

TheWARPSsurveyisbasedonarchivalROSATPositionSensitiveProportionalCounter(PSPC)X-raydata.TheaimoftheWARPSclustersurveyistoobtainawell-calibrated,completesampleofallsourceswhichemitX-raysfromhotgastrappedinagravitationalpotential,fromsinglegalaxiestorichclusters.TheX-rayimagesaresearchedforserendipitoussourcesusingasurfacebrightnesslimit,andthosesourceswithdetected

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flux>3.5×10−14ergs−1cm−2(0.5-2keV)areclassifiedasextendedorpoint-like.Inanongoingopticalfollow-upprogrammeoftheextendedsourcesandselectedpoint-likesources(specificallythosewithgalaxycounterparts)weareobtainingbothimaging(fromarchivedplatedataanddeeperCCDdata)andspectroscopydata.ThefollowupprocedurehasbeendesignedtominimizeincompletenessandmisidentificationsoftheX-raysourcecandidates(catalogueinpreparation).ThespectroscopicredshiftsofclustergalaxieswillthenallowustodeterminetheXLFandmeasureitsevolution.

TheROSATPSPCprovidesa2degreediameterfieldofviewwithanenergyrangeof0.1−2.4keVandamodestenergyresolution.Therelativepositionalaccuracyofthephotoncoordinatesintheinstrumentplaneis0.5arcsec.Theshapeandsizeoftheinstrumentalpointspreadpointspreadfunction(PSF)dependsonbothphotonenergyandoff-axisangle.Foraphotonenergyof1keVthePSFhasafullwidthhalfmaximum(FWHM)of25arcseconaxisandincreasesinsizewithoff-axisangletoaFWHMof58arcsecat15arcminoffaxis(Hasingeretal1993b).Welimitoursurveytosourceswithinthisoff-axisangle.Weusethe0.5-2keVbandtodetectsourcesratherthanthefull0.1-2.4keVPSPCbandinorderto(a)reducethecontributiontothebackgroundfromgasinourGalaxyat∼106K,(b)minimizethesizeofthePSF,and(c)tomaximizesensitivitytohardsourcessuchasclustersofgalaxies.

Therearecurrently4768PSPCfieldsintheROSATarchive.Some1400fieldshaveexposuretimesinexcessof8ksecandwechoosethisasonecriterionforselectingfieldsoursurvey.Ourfieldselectionisthenbasedonthefollowinggeneralcriteria.Wefirstconsiderfieldsinwhichtheprimarytargetsarestarsoractivegalacticnuclei(AGN)andwhichcontainnoverybrightopticalobjects(typicallybrightstarswhichthenmakeopticalfollow-updifficult).Weavoidpointingswhosetargetsarebrightclusterssincethelatterdominatetheinner15arcminofthePSPC’sfieldofviewandmakeserendipitousdetections

–9–

ofotherobjectsimpossible.Thisalsoensuresthatourclusterselectionisnotaffectedbytheknownangularcorrelationbetweenclusters.Inthisinitialsurveywehavealsochosenhighgalacticlatitude(|b|>20◦)fields.TheobserveddistributionofGalacticequivalentcolumndensitiesofneutralhydrogen(all<1021cm−2)impliesthatthereshouldbevirtuallynoabsorptioninthe0.5-2keVbandusedhere.ThecorrectionstothemeasuredX-rayfluxesare<2%onallfieldsandarethereforewellwithinthetotalfluxuncertainties.

Inthosefieldsselectedweexcludeobjectswithintheinner3arcminradiusofthefieldcentresincethesenormallyconstitutetheoriginaltargets.

InFigure1thepositionsofthe91ROSATfieldsselectedinthisinitialsurvey(WARPS-I)areplottedinGalacticcoordinates.Thesizeofthepointsisproportionaltotheexposuretimewhichrangesfrom∼8000secondsto∼48,000seconds,withmostfieldshavingexposures≥10,000seconds.

3.TheVTPmethod

TheVTPmethodofEbeling(Ebeling1993,Ebeling&Wiedenmann1993)isageneralmethodforthedetectionofnon-Poissonianstructureinadistributionofpoints.Inthecaseofadistributionofphotonsitwilldetectallregionsofenhancedsurfacebrightness(surfacedensity)relativetothePoissonianexpectation.WhiletheROSATPSPCphotonsareinfactregisteredonafinitegridmadefrom0.5arcsec‘pixels’,wecantreattheobservedphotondistributionasunbinnedsince,attheexposuretimestypicallyattainedinthepointings,thisgridiswellsampledonlyatthepositionsoftheverybrightestsources.TheVTPmethodcanbesummarizedasfollows.First,forarawphotondistribution(inthiscasetheinner15arcminradiusoftheROSATPSPCanda‘bufferzone’ofphotonsto18arcmin)theuniqueVoronoitessellationisdetermined(whenraremultiplephotoncounts

–10–

occuratagridposition,theseareflaggedandthisinformationisusedinthepercolationdescribedbelow).Eachphotondefinesthecentreofacellpolygonwhosesidesformtheperpendicularbisectorsofthenon-crossingvectorsjoiningthenearestneighbourphotonswhich,inturn,representtheverticesoftheequivalentDelauneytriangulation.ThesephotoncellsformtheVoronoitessellationofthefield.Sincemostcellscontainonlyonephoton,thesurfacebrightnessassociatedwiththisphotonequalstheinverseoftheproductofcellareaandlocalexposuretime.InFigure2theVoronoitessellationortilingisshownforatypicalROSATPSPCfield.Thesourcesinthisfieldareapparenttotheeyeastheclustersofsmallcells.

ThePSPCfieldexperiencesnon-uniformexposurewhichcanvarybyasmuchas15-20%fromthefieldcenterto15arcminradiusoffaxis,andbyasmuchas10-15%betweendifferentfields(accordingtothespacecraftparametersatagiventime).Extendedsourceswillthereforealsoexperiencenon-uniformexposureacrosstheirprojectedsurface(forexample∼5%acrossa3arcminsource).Tocorrectforthis,wegenerateexposuremapsforeachpointing(with15′′×15′′resolutionpixels)usinganalgorithmbasedonthedetailedworkofSnowdenetal(1992).Forgreateraccuracy,exposuremapsareconstructedintwoenergybands(0.5-0.9keVand0.9-2keV)andtheappropriatemapisusedtoyieldanexposurevalueforeachphoton.Althoughthemeandifferencebetweentheglobalbroadband(0.1-2keV)exposuremapandthoseusedhereisonly∼5%,thevariationbetweenindividualmapscanbeasmuchas15%.Thefinalimprovementonestimatedsourcefluxes(especiallyforextendedsources)obtainedbyusingthecorrectexposuremapscanthereforebeasmuchas10-15%whencomparedtofluxeswithonlyauniformexposurecorrection.

ThecumulativedistributionoftheinverseareasoftheVoronoicellscanthenbecomparedwiththatexpectedfromarandom(Poisson)distributionandacutoffcanbedeterminedwhichdefinestheglobalbackgroundcountforthatfield.Aspatialpercolation

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algorithmisthenrunonthecellswithareassmallerthanagiventhresholdabovethebackground,groupingthemaccordingtotheexcessabovethebackgrounddensityandformingsources.Thelattertwostepsareperformedinaniterativefashionsothatassourcesaredetectedthebackgroundestimateisrevisedandthesourcegroupingsredetermined.Typicallythisrequires∼6iterations.Finally,theminimumnumberofphotonsrequiredforatruesourceiscalculated(suchthatweexpect1fakesourceinthetotalsurveyarea)toeliminatebackgroundfluctuations.Thebackgroundlevelforagivenfieldisthensimplythemeansurfacebrightness(σback)calculatedfromallnon-sourcephotons.

ForeachsourceaseriesofparametersarethenobtainedbyVTP.Inouranalysisweusethefollowing:thesourceposition(determinedasaweightedsumoverphotons),thedetectedsourcecountrate(correctedforthebackgroundcountrate),thedetectedsourcearea,theminimalandmaximalmomentsofinertiaofthephotondistribution,anestimateofthebackgroundcount,andtheprobabilityofthesourcebeingastatisticalfluctuation(calculatedastheprobabilityofthePoissonbackgroundproducingafluctuationofthatnumberofphotonswithlocalsurfacebrightnessabovethedetectionthreshold).Inaddition,thefullsetofphotonsassociatedwitheachsourceisstored.

3.1.Sourcedeblending

WeperformVTPthreetimesforeachfieldusingdifferentsurfacebrightnessthresholds(denotedasfactorsofthebackgroundsurfacebrightness:1.0,1.3and1.7;seeSection4).Thisallowsustodistinguishrealsinglesourcesfromthosecomposedofblendsofseveralsources(point-likeorextended)andreducesanyuncertaintiesinsourceidentificationduetopositivebackgroundfluctuationswhichbecomegroupedwithsourcephotons.

Thefirsttaskinthesurvey(onceVTPhasbeenrun)isthereforetoperformthe

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deblendingandthresholdselections.Forthispurposewecombineanautomateddeblendingprocedurewithvisualinspectionofallfields.ThedeblendingalgorithmisrunoverallVTPresults.Itincludesallsourceswhichmatchthefollowingcriteria:

•Sourcesatthreshold1.0whichdonotdeblendathigherthresholds,liewithin15arcminofthefieldcentreandtypicallyoutsidetheinnermost3arcminradius(toavoidtargetsources)andwithanobservedcountrateof>3×10−3ct/s(correspondingtoanobservedfluxlimitof≃3.5×10−14ergs−1cm−2)

•Sourcesmatchingtheabovepositionandcountratecriteriaatthreshold1.3whichwerepartsofblendsat1.0butdonotdeblendatthreshold1.7

•Sourcesmatchingthepositionandcountratecriteriaatthreshold1.7whichwerepartsofblendsat1.3

Thisfirstrunofthedeblendingalgorithmprovidesalistofcandidateswhichisusedinavisualinspectionofeachfield.Thechoiceswhichmaythenbemadearetoalterthedetectionthresholdusedforeithertheentirefieldorforindividualobjects.Therationaleforthisisthatsometimesobjectsdetectedatthreshold1.0willinclude(becauseofthehighsensitivityofVTP)photonswhichareclearlypositivenoiseandacttobiastheareaestimateofthesource(i.e.spurious‘tails’ofverylowsurfacebrightnesswhichbecomeassociatedwithasource).Increasingthethresholdremovesthisnoiseandtypicallyonlyremoves<10%ofthesourcephotons(whichwillberecoveredinthefluxcorrectionstepdetailedbelow).ThethresholdusedforeachsourceisrecordedandusedinthecorrectionfromdetectedtototalfluxasdescribedinSection3.2.

Figures3and4demonstratethedifferencesbetweenthelowestandhighestthresholdresultsforthefieldinFigure2.ThosephotonsidentifiedasbelongingtosourcesbyVTPareplottedinheavytype.Sourcestypicallyaccountfor10-20%ofthephotonsinthe

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lowestthreshold,lessinthehighestthreshold.Thesourcesnumbered2and6inFigure3arestrongcandidatesforblendsofmorethanonesourcewhenobservedatthelowestthreshold.InFigure4itisapparentthatthesesourceshavebeendeblendedatthehigher(1.7)threshold.

Clearlytheremaybecasesofrealphysicalsystemswhichcontainstructurethatbecomesdeblended.However,avisualinspectionofall91fieldsrevealedonly2caseswheredeblendinghadsplitupwhatwasprobablyasingleextendedobject(whichhadafluxabovethesurveyfluxlimit)intoseparatecomponentswhichfellbelowthefluxlimit.These2objectswereplacedbackintothesurveysample.Inaddition,sinceweobtainopticalidentificationforallsources(bothextendedandpoint-like)likelytobeclusters,groupsornormalgalaxies,weexpecttobeabletocatchsuchcases,shouldtheyoccur.Asanadditionalaidindeblending,theWGACATpointsourcedetections(White,Giommi&Angelini1994)areplottedasverticalarrowsinFigures3and4.Notethat,sincetheWGACATsourcesweredetectedinthebroader0.24-2keVband,theycannotbecompareddirectlytotheVTPdetections;adetailedcomparisonbetweenVTPandconventionaldetectionalgorithmsismadeinSection5.

3.2.Fluxdeterminations

ThefinallistofdeblendedsourcesandtheirrespectiveVTPparametersarethenpassedtoanalgorithmwhichestimatesthetruefluxofthesources.Inordertodothis,thegeneralnatureofVTPmustbeabandonedandassumptionsmadeaboutthenatureofthesources.Weassumethatsourcesareeitherintrinsicallypoint-likeorextendedwithasurfacebrightnessdistributionfollowingaKingprofile:

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σ(r)=σ01+(r/rc)

󰀇󰀉

2−3β+1/2

,(1)

whereσ(r)istheprojectedsurfacebrightnessatdistancerfromthesourcecentre,σ0isthecentralsurfacebrightness,rcisthecoreradius,andβhasavalueof2/3(Jones&Forman1984).InmodelingthePSFwefollowHasingeretal.(1993b).

TheVTPalgorithmreturnsestimatesofthemeansurfacebrightnessofthebackground,abackgroundcorrectedestimateoftheobservedcountrateforeachdetectedsource,andtheareaofthesourceabovethesurfacebrightnessthreshold.Fromtheareaweobtainanareaequivalentsourceradius(rVTP=

󰀅

3(β−1/2)

.(2)

Forsimulateddata(usingidealizedsurfacebrightnessprofiles,suchastheKingprofile)theVTPcorrectedfluxesareaccurateforhighsignal-to-noisesources(describedinSection3.3andFigure6).Forlowsignal-to-noisesourcestheuncertaintyinthecorrectedfluxislarger(e.g.Figure5).FulldetailsofthisprocedurecanbefoundinEbelingetal(1996b).

Anobjectisthenclassifiedasextendediftheratioofthecorrectionfactorsf=strue/sdetectedforaKingprofileandapointsource,respectively,liesaboveacriticalvalue.Thetruecountrateisthenobtainedbymultiplyingthedetectedcountratewiththeappropriatecorrectionfactor.Sinceitisonlyintegralpropertiesthatareused,theresults

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aremuchmorestabletodeviationsofobjectsfromtheassumedidealthaninthefittingproceduresusedbyconventionaldetectionalgorithms.

3.3.Fluxcorrectionsandextents

TotestandcalibratethefluxcorrectionmethoddescribedabovewehaveusedMonteCarlosimulationsofPSPCfields.Sourcesaresimulatedwithpoint-likeorKingprofilesurfacebrightness,convolvedwiththeinstrumentalPSF(foranominalphotonenergyof1keV)andaddedtoarepresentativebackgroundofPoissoniannoise.Anensembleofsourcesaremadefor40setsoftypicalintrinsicparameters(extent,flux,off-axisangle)todeterminetheexpectedscatterintheVTPestimates.Tofurthermimictheselectionoftherealsurveydataweinspectthesimulatedsourcestochoosetheappropriatesurfacebrightnessthresholdtousewhicheliminatesfalsepositivenoisewings.

InFigures5(a,b)and6(a,b)resultsarepresentedacrossalargerangeofsourceparameters,fromextentsof∼0arcsecto1.5arcminandeffectivefluxes(0.5-2keV)of∼6×10−14to∼3.5×10−13ergs−1cm

−2

andforon-axis(circular)andoff-axis(triangular)

sources.Inallplotstheratiooftheraw,detectedcountratestothetruecountrateandtheratioofthecorrected(seeabove)countratestothetruecountrateareplottedonthey-axes.Multiplepointsatfixedintrinsicextents(orfluxes)havearangeofintrinsicfluxes(orextents).

TheeffectiveVTPdetectedsignal-to-noise(asdefinedinSection4below)ofasourceisagoodindicatorofthereliabilityofanyfluxestimate.Themediansignal-to-noiseoftherealX-raysourcedetectionsiss/n=8,andweusethistodividethesimulationresultsforpresentation.Theeffectofnoiseisapparentinthelargerscatterseeninfluxestimatesforthelowsignal-to-noise(s/n<8)sourcesplottedinFigure5(a,b)whencomparedtothose

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ofthehighsignal-to-noiseobjectsinFigure6(a,b).Forsourcesofmediumtosmallextent(i.e.<60arcsec)withsignal-to-noise>8wecanrecoverthetruefluxtowithin5-10%overthefluxrangeshownhere.Forsourcesoflargerextent(ofwhichwemightexpecttoseeveryfewinoursurvey)thefluxesaresystematicallyunderestimated,asexpectedsincemoreofthefluxnowliesbelowoursurfacebrightnesslimits.Forthelowsignal-to-noisesources(s/n<8)thesamegeneraltrendsarepresentbutdominatedbythescatterduetonoise.Forsmallextents(<30arcsec)wecanstillrecoverthetruefluxofthefaintestobjectstowithin10-20%.Tosummarize;allrecoveredcountratesarewithin1-σofthenominalcountrates,exceptforhighlyextended(>1arcmin)and/orfaintsources.

Indeterminingthefluxcorrectionfactorweareabletoclassifyobjectsasextendedorpoint-likeusingtheratiooftheKingprofilefluxcorrectionfactortothepoint-likefluxcorrectionfactorfKing/fPS(fKing=strue/sdetected),wheresdetectedisestimatedassumingaKingprofile,fPSisthesamefactorbutwithsdetectedestimatedassumingapointsource).Ifthisratioexceedssomevalue(notnecessarilyunity,becauseofnoise)thenwededucethatthesourceisbestfitbyanextendedsurfacebrightnessprofile(throughtheintegralquantities).Thisextentcriterionhasbeenempiricallydeterminedfromboththesesimulationresultsandthesurveydataitself.Iftheratioofthefluxcorrectionfactors(fKing/fPS)isgreaterthan1.2then>90%ofon-axisextendedsourceswithintrinsicextent

>7arcsecwillbecorrectlyclassifiedasextended,and<10%ofon-axispoint-likerc∼∼

sourceswillbemistakenlyclassifiedasextended(fromsimulationsofpoint-likesources).

>20arcsecwillbecorrectlyAllhighsignal-to-noiseoff-axissourceswithintrinsicextentrc∼

classedasextended.InFigure7(a,b)wesummarizetheresultsofapplyingthisclassificationtothesimulationdata.Thefractionofsourcesclassifiedasextendedisplottedagainstintrinsicsourceextent.Itisapparentthatoff-axisextendedsourcesaremorelikelytobemis-classified.GiventhatthePSFFWHM(at1keV)on-axisis25arcsecandincreasesto

58arcsec(Hasingeretal1993b)at15arcminoff-axiswemightexpectadegradationofthe

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method,especiallyatlowsignal-to-noise.

Theopticalfollow-upobservationsweperformforallcandidateswillallowustoreliablyidentifythefewexpectedmis-classifiedobjects.Toourfluxlimitof3.5×10−14ergs−1cm−2wedonotexpectanyextendedobjects(clusters,groupsorgalaxies)tohavecoreradiioflessthan≃20arcsec,basedonthecanonicalrangeofphysicalsizesandluminosities(seeFigure8).OursampleofX-rayextendedobjectswillthereforebecompletetothisfluxlimit,assumingnoevolutioninthesecanonicalsources.If,forexample,clustersofthesameluminositywerephysicallysmallerathigherredshifts,theymightnotbeclassifiedasextended.However,theywouldbeidentifiedcorrectlyasclustercandidatesfromouropticalimagingofpoint-likeX-raysources.

Avisualinspectionofasubsetoftherealdataconfirmstheseresults.Oftheobjectsclassifiedbyeyeasextended,92%(23of25)wereclassifiedasextendedbyVTP.Oftheobjectsclassifiedbyeyeaspoint-like,4%weremisclassifiedbyVTP.Manyofthemisclassificationsinvolvedtwoormoreclosepoint-likesources,separatedbyadistancesimilartothePSFfullwidthhalfmaximum,tooclosetobedeblended.

4.Skycoverage

Inordertocorrectlyevaluateanystatisticalmeasurementsofthesurveysample(suchasLogN-LogS,luminosityfunctions,extentdistributionetc.),theeffectiveskycoveragemustbeknown.SincetheWARPSusespointeddataeachfieldhasadifferentdetectionsensitivitytoobjectsofagivenextentandflux,accordingtoexposureandbackground.Toestimatethis,wehavecombinedananalyticmeasureofVTP’sdetectionsensitivitywiththeresultsofsimulatedPSPCdatatoensureitsvalidity.OnthebasisofsimulationswehavedeterminedthatwecanparameterizethecriterionforforVTPtosuccessfullydetect

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arealsourceusingadefinitionofthedetectedsignal-to-noise.Thecriterionforsourcedetectionisthenapproximatedas;

nVTP−nback

>3,

nVTP

󰀅

(3)

wherenVTPisthetotalnumberofphotons(sourceandbackground)thatliewithinaradiusrVTPwhichistheequivalentsourceradius

σ˜0

󰀈−2/3

−1

󰀍󰀍1/2

.(4)

Here,however,wehavedefinedthecentralsurfacebrightnesssoastoincludethe

2

background,σ˜0=(strue/2πrc)+σback,inunitsofcountsperunitarea.Thenumberof

photonsdetectedbyVTPshouldthenbe;

nVTP(rVTP)=

2

2πrcσ˜0



1−

󰀊

1+

󰀆

rVTP

2+PSF(θ)2whereθisoff-axisrcσ

angle).Thissimplificationappearsjustifiedwhenresultsarecomparedwithsimulations.Usingtheexposureandbackgroundinformation(asdeterminedbyVTP)foreachofthe91fieldsusedinthesurveywethenintegratetheskycoverageovertheradiusofeachPSPCfield,includingthePSFvariationwithoff-axisangle,usingthecriteriadescribedabovetodeterminethedetectionsensitivity(foragivenσ0andrc).ThefinalresultshowninFigure8isthecombinedskycoverageofallfieldsusedinthesurveytothelimitingthreshold(fmin=1.0).

InFigure8thefractionalskycoverageisshownasafunctionofprojected(intrinsic)extentandintrinsicflux,assumingaKingprofileasinEquation1.Thedashedcontour

–19–

denotes1%coverageandindicatesthatafewdeepfieldsinoursurveydoindeedallowdetectionstomuchlowerfluxes.Solidcontoursruninstepsof10%from10%to100%(withincreasingweight).FortheWARPS-Isample100%skycoveragecorrespondsto17.2deg2.

Thenear-horizontaldashed,dottedandsolidcurvesatthelowerrightinFigure8arethelociwithvaryingredshiftof(respectively)ellipticalgalaxies(withLx(0.5-2keV)=1×1042erg/sandeffectivecoreradiusrc=50kpc),groups(withLx(0.5-2keV)=1×1043erg/s,rc=100kpc)andclusters(withLx(0.5-2keV)=5×1044erg/s,rc=250kpc)(H0=50,q0=0).Redshiftisthereforeincreasingrighttoleftalongthesecurves.Theverticaldashedlineat3×10−14ergs−1cm−2(0.5-2keV)representstheapproximatelowerfluxlimitofthesurvey.TheredshiftsofthethreeobjecttypesatthisfluxlimitarelistedinFigure8.Asdiscussedelsewherewehavechosenafluxlimitinobservedanduncorrectedfluxof∼3.5×10−14ergs−1cm−2(correspondingtoa3×10−3ct/scountrate).Thetrueintrinsicfluxlimitisthereforeslightlyhigher.

Featurestonotefromthisplotarea)forthesecanonicalclassesofobjectwealwayshaveaskycoverageof∼60%orbetterandb)wehavegoodskycoverage(≥50%)formoderatelybrightbutveryextendedsources(rc>1arcmin)shouldsuchlowsurfacebrightnessobjectsexist.

InordertocheckthiscalculationwehavecompareditwiththeresultsofseveralhundredsimulatedobjectsprocessedbyVTP.Thesewereconstructedtohavearangeoffluxes,extentsandoff-axisangles.ThefullPSF(Hasingeretal1993b)wasusedtogeneratethefinal,simulatedPSPCfields.Theagreementwithsimulationsisextremelygoodandconfirmsthechoiceof3asasignal-to-noisedetectioncriterion.Notethatatthesurveyfluxlimitthelowestsignal/noiseofanyrealsourcedetectioninthe91fieldsis4.4,andmostsourceshaveasignal/noise>6.

InFigure9theWARPSfractionalskycoverageisshownasafunctionofredshiftfor

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threeclassesofobject.WehavenearlycompleteskycoverageforclusterswithLx(0.5-2keV)=5×1044ergs−1andcoreradiusrc=250kpcouttoaredshiftofz≃1,with50%coverageataredshiftofz∼1.4.Wehavegoodcoverageforgroups(orfaint,smallclusters)ofLx(0.5-2keV)=1×1043ergs−1outtoz∼0.2(80%coverage)andforgalaxiestoaboutz∼0.1(80%).Wewillusethisinformationinevaluating(forexample)theLogN-LogSmeasuredbytheWARPSclustersurvey.ItsupportsthediscussioninSection1onwhyX-rayselectedclustersampleshavemanyadvantagesoveropticallyselectedones.Ataredshiftof∼1thenumberdensityofgalaxiesontheskymeansthatthecontrastofanyclusterisgreatlyreducedintheoptical,whereastheX-raycontrastisstillhigh.

5.Acomparisonwithconventionaldetectionmethods

AnimportantresultofthisworkisthedemonstrationthatamethodsuchasVTPcandetectsources(especiallyextended,lowsurfacebrightnesssources)sometimesmissedbyconventionalsourcedetectionalgorithms(whichareknowntobelesssuitedtodetectionofextendedobjects).Previouswork(Ebelingetal1996b)hasshownthatVTPdetectsmoresourcesthantheStandardAnalysisSoftwareSystem(SASS,Vogesetal.1992)intheRosatAllSkySurvey(RASS).InordertobetterquantifythisdifferenceinsourcedetectionefficiencyforthePSPCfieldswehavecomparedourVTPmethodwithastandardslidingcellmethod.ThisslidingcellalgorithmispubliclyavailableaspartoftheXIMAGEdataanalysispackage4andisreferredtoastheDETECTalgorithm.Briefly,DETECTdividestheimagefieldintoboxestomakelocalestimatesofthebackground(rejectingthosewhichdeviatesignificantlyfromPoissonexpectations)andthenformsaglobalbackgroundestimate(rejectingthetailsoftheGaussiandistribution).Theslidingcellsizeischosento

–21–

optimizesignal-to-noise,andcorrectionsaremadefordeadtime,vignettingeffects,andthefractionofthesourcecountsthatfalloutsidetheboxwherethenetcountsareestimated.Countrateerrorsareincluded.

WehaverunDETECTonasubsetofoursurveyfields,intheenergyband0.5-2keV,andusingthedefaultparameters(suchasthreshold,sourceprobabilityetc.).InFigures10,11,12and13,14,15someexamplesoftheproblemsencounteredbyconventionaltechniquesareshown.

InFigure10,therawphotonmapforthisfieldisshown,withtheVoronoicellsplotted.Manypotentialsourcesareapparenttotheeyeinthiscrowdedfield.InFigure11theresultsofrunningVTPatthelowestthreshold(1.0)arepresented.Thosesourceswithbackgroundcorrectedcountsoflessthan20photonsarelabeledwith‘X’.TheverticalarrowsindicatesourcesfoundbyDETECT.ItisclearthatthereareseveralplaceswhereDETECTandVTPdiffer.VTPsources1,3andthephotonstotheNorthofsource15arenotseenasenhancementsbyDETECT.InFigure12thepictureiscleareratthehigherVTPthresholdof1.3.Source19whichwaspreviouslyblendedintosource15inFigure11isnowdistinct(alsoseeFigure10)andisagoodcandidate(giventhelowerthresholdobservation)foranextendedsource,butiscompletelymissedbyDETECT.

InFigures13,14,15theresultsforanotherfieldareshowninthesameformatasforFigures10,11,12.InFigure14,VTPsources1,21,26and27havenoDETECTcounterparts.InFigure15,atthehigherVTPthresholdof1.3wecanseethatthesesourcesarestillsignificant(nownumbered1,21,27and28respectivelyandaregoodcandidatesforextendedsources(seealsoFigure13).

Asafurthertest,DETECTwasrunwithagreatlyreducedthresholdforsourcedetectioninordertoseeifitcouldindeeddetectthesourcesseenbyVTPatlowersurfacebrightness.Evenwhenthethresholdwasloweredtoapointatwhichmorethantwice

–22–

theoriginalnumberofdetectionswereobtained,manyVTPsourcesremainedundetected.Furthermore,atthislowthresholdmanyoftheDETECTsourceswereclearlyspurious,indicatingthateveniftheDETECTparameterscouldbealteredtofindtheVTPsourcesitwouldbedifficulttodistinguishthesefromthefalsedetections.

WhilethosefieldsinFigures10–12and13–15werechosenspecificallytodemonstratetheabilityofVTPtodetectextendedsourcesmissedbyconventionalmethodstheyarenotatypical.Toquantifythedifferenceswehaveusedasubsetoftenfieldsfromthesurveyacrossarangeofexposuretimesandbackgrounds.UsingtheVTPandDETECTalgorithmswehavemadetwofluxlimitedsamplesusingthissubset(tothesamefluxlimitasWARPS-I).ToensuretherobustnessoftheVTPdetectionsweusedtheresultsofthe2ndsurfacebrightnessthresholdonly(fmin=1.3).Asdemonstratedinfields700114and600520abovetheDETECTalgorithmfindsfewerobjectstoagivenfluxlimit.Intermsof

>3.5×10−14ergs−1cm−2(0.5-2keV)VTPthenumbercountsofallobjectswithflux∼

findsanumberperunitareaof≃19.7±2.8deg−2comparedtoDETECTwhichfinds

≃18.1±2.7deg−2fromthesamedata.ThisdifferenceincountsisalmostexactlythatwhichwouldbeexpectedatthisfluxlimitiftheadditionalsourcesdetectedbyVTPareinfactextended(basedontheresultsofRosatietal1995whouseawaveletmethod).

Whilesuchslidingcelldetectionmethodscanbealteredtoimprovetheirefficiencyforextendedobjectsitisclearthatintheworstcasestheycanmissalmostallfainterextendedobjectsinafluxlimitedsurvey.Thishasprofoundimplicationsforanysurveyoffaintextendedobjectswhichdoesnotuseadetectionmethodsensitivetolowsurfacebrightnessobjects.Forexample,therecentresultsofCastanderetal(1995)(whoalsosurveyROSATPSPCfields)indicatethattothesamefluxlimitasusedheretheydetectapproximatelyoneobjectperdeg2lessthanthispresentworkortheworkofRosatietal(1995).ThissuggeststhattheremayindeedbeadifferenceinthesensitivityoftheX-ray

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detectionmethodsused.

6.ResultsandDiscussion

TheWARPSclustersurveyhasacurrentskycoverageof17.2deg2.UsingtheVTPmethodthissample(WARPS-I)contains298objects(uncorrectedforskycoverage)withdetectedflux>3.5×10−14ergs−1cm−2(0.5-2keV).Thereare58extendedsourcesaccordingtothecriterionusedinSection3.3.Thenumberofmisclassifiedpoint-likesourcesisestimatedtobe≈5%ofthetotalnumberofpoint-likesources(i.e.about12sources),givingapossiblerangeof2.8–4.0extendedobjectsdeg−2.Themaximumnumberofmisclassifiedpoint-likesources,assumingtheyallhavedetectionsoflowsignal-to-noise(which,inreality,theydonot)is10%,whichgivesalowerlimitof2.0extendedobjectsdeg−2.Thecombinationofadetectionmethodwhichisunbiasedbyshapeandsurfacebrightnesswitharigorousopticalfollow-upresultsinanextremelywellselectedandquantifiedcataloguewellsuitedtomeasuringpropertiessuchasclusterevolution.

Asimpletestoftheeffectivenessofourapproachinidentifyingextendedobjectscanbemadebystudyingtheresultsobtainedforknownhighredshiftclusters.InTable1below,4knownclustersspanningredshiftsfromz=0.13to0.66weredetectedbyVTPinthePSPCfieldsandflaggedasbeingextended.TheclusterJ1836.10RCwasdetectedtwiceinseparatepointingsofexposure21ksecand23ksec.TherawVTPfluxwas2.8x10−14ergcm−2s−1(0.5-2keV)(55photons),andthefluxvariationbetweenobservationswas20%or1.2σ,showingarepeatabilityoftheVTPmeasurementswithinthatexpectedfromPoissonianstatistics.

Wefindaskydensityof2.1–3.1(±0.4)extendedobjectsdeg−2toanintrinsic(asopposedtodetected)fluxlimitof4.5×10−14ergs−1cm−2.Thisisingoodagreementwith

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thesurveyofRosatietal.(1995),althoughtheirinitialsamplecontainedonly10extendedobjectsandournumbersarebasedonalowerlimitof40extendedobjects.ThesurveyofCastanderetal(1995)whichhadasimilarsurveyareaandafluxlimitof3×10−14ergs−1cm−2foundaskydensityof0.9±0.25extendedobjectdeg−2.Thereisclearlyadiscrepancybetweentheseobservations.Wehavedemonstrated(inagreementwithpreviousworks,Ebelingetal1996b)thattheVTPmethoddetectsmoreobjectsthanconventionalmethods,whichweredesignedwithpointsourcedetectionmoreinmind.Intheextremecase,basedonanexactcomparisontoourfluxlimit(∼3.5×10−14ergs−1cm−2)VTPdetectssome2objectsdeg−2morethanaslidingcellmethod.Thisindicatesthatalargefractionofextendedobjectsmaybemissedatthisfluxlimit.Untilwehaveredshiftsfortheselowsurfacebrightnessobjectswecannotestimatetheeffectoftheirexclusionfromprevioussurveys;howeverwesuggestthatcountsoflowluminosity,moderateredshiftclustersobtainedwithnon-optimaldetectionalgorithmsshouldnotbeconsideredreliable.

6.1.SurfacebrightnesslimitsandLogN-LogS

WhileoftenquotedinopticalsurveysthelimitingsurfacebrightnessisnotgenerallypresentedinX-raysurveys.InFigure16wepresentthedistributionofsurfacebrightnesslimitsfortheWARPSclustersurveyfieldsusedinthispresentwork.ThisissimplydeterminedfromtheobservedbackgroundcountsinthefieldsandtheVTPsurfacebrightnessthresholds.Theverticaldot-dashedanddashedlinesrepresentacomparisonoftheWARPSsurfacebrightnesslimitswiththatoftheEMSSrespectively.Forexample,alimitingsurfacebrightnessof1.3×10−15ergs−1cm−2arcmin−2(0.5-2keV)(dot-dashedlineinFigure16)inatypicalROSATPSPCfieldwithabackgroundlevelof3ct/arcmin2in15ksecexposurecorrespondstoatwosigmaexcessoverthebackgroundina2.4×2.4arcmincell(theEMSSdetectioncell).Tocomparethiswiththelimitingsurfacebrightness

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intheEMSS,parametersforatypicalEMSSfieldweretakenfromGioiaetal(1990).ForanEinsteinIPCexposureof3.5ksecandthesame2.4×2.4arcmincellsizecontaining9backgroundcounts,atwosigmaexcesswasgivenbyasurfacebrightnessof1.4×10−14ergs−1cm−2arcmin−2(0.3-3.5keV)or7.8×−15ergs−1cm−2arcmin−2(0.5-2keV)(dashedlineinFigure16),usinganEMSS(0.3-3.5keV)toROSAT(0.5-2keV)bandconversionfactorof0.55,appropriateforapowerlawspectrumofenergyindex1orathermalspectrumoftemperaturekT=6keV.ThetypicalWARPSsurfacebrightnesslimitistherefore≈6timeslowerthanthatoftheEMSS.Wethenexpecttodetectmorefluxfromlowsurfacebrightnessemissionthanin(forexample)theEMSS.

InFigure17wepresentthefirstnumbercountresultsfortheWARPS-Iclustersurvey.TheLogN-LogSrelationshipisshownforthe91PSPCfieldsand298objectsanalysedatthetimeofwriting(atotalskycoverageof17.2deg2).The0.5-2keVcountrateswereconvertedtofluxesusingaconstantfactorof1.15×10−11ergs−1cm−2(cts−1)−1.Thisconversionfactorisaccuratetowithin7%forathermalRaymond-Smith(1977)spectrumoftemperaturekT=1-20keV,abundances0.25-1timescosmicabundance,andcolumndensities1×1020cm−2-1×1021cm−2.Thesecountsincludeallsources(extendedorpointlike).Thecountshavebeencorrectedforskycoverageassumingallsourcestobepointlike,thiswillresultinanunderestimateofthenumbercounts.Therawfluxdatapointsthereforerepresentalowerlimit.Theinitialresultsforthecorrectedfluxpointsareshown(withpointlikeskycoveragecorrection)todemonstratethesizeofthefluxcorrection.WehavealsoplottedtheLogN-LogSrelationshipsfoundbyHasingeretal(1993a)andBranduardi-Raymontetal(1994)(hereafterBR94),fromROSATdataandGioiaetal(privatecommunicationinBR94)fromEinsteinEMSSdataconvertedtotheROSATband.ThecurvesrepresenttheLogN-LogSrelationshipsofallsources,asdetectedwithPSF-baseddetectionalgorithms.

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Weseeaclearexcessatthebrighterendcomparedwithothermeasurements.Therearetwopossibleexplanations;first,thattheVTPmethodsimplydetectsmoreobjectsbecauseitissensitiveacrossagreaterrangeofsurfacebrightnessthanotherdetectionmethods.Second,thattheobservedVTPfluxishigherforbrightextendedobjectsbecauseitincludesthesignalfromthelowersurfacebrightnesspartsofsources.Acombinationofthesetwoeffectsisalsolikely.Thisresultsuggeststhatasinglepowerlawisinsufficienttodescribethecountsoverthisrangeinflux(∼3−10×10−14ergs−1cm−2(0.5-2keV)).

Ifweassumethatthedeviationfromothermeasurementsisduetotheimproveddetectionofextendedsources(sincealldetectionmethodsshouldbeessentiallyequalinthedetectionefficiencyofpoint-likesources)thenwearedetectingapopulationoflowsurfacebrightnesssourceswithadensityof∼1deg−2atafluxgreaterthan∼1×10−13(withsomeconfidencesinceweactivelyavoidfieldswithknown,bright,clustersastargets).Alternatively,ifwearenotdetectinganadditionalpopulationbutratheragreaterfluxforpreviouslydetectedobjects(presumablyextendedones,usingtheabovereasoning)then

>20%increaseinmeasuredfluxforobjectswithfluxgreaterthan10−13.thisamountstoa∼

Wehavemadeapreliminaryinvestigationofthosesourcescontributingtothesehigher

fluxcountswhichsuggeststhattheexcessinourLogN-LogSisindeeddueinparttoanimproveddetectionofthelowsurfacebrightnesscomponentofbrighter,extendedsources.

7.SummaryandConclusions

Theabilitytotestcosmologicalmodelsthroughdetailedstudiesofgalaxyclusteringcallsforwellselectedsurveyswhichspantheentirerangeofclustertypes.Sincethedominantluminousmasscomponentinsuchsystemsishot,X-rayemittinggasthisoffersanidealwayofselectingobjects,itisalsofreeofmanyoftheuncertaintiesinopticallyderivedcatalogues.Inordertoextendthecurrentlyprobedsectionoftheclusterpopulation

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tolowerluminositiesandsurfacebrightnessesandhigherredshiftswemustusegeneral,unbiasedsourcedetectionmethodssuchasVTP.

ThelowerlimitLogN-LogSofallsourcesinWARPS-Ishowsasignificantexcessincountsforfluxesgreaterthan∼10−13ergs−1cm−2(0.5-2keV)comparedtopreviousworks.Thisexcessisconsistentwiththecombinedpoint-likeandextendedsourcecountsofRosatietal(1995)andappearstobeduetoanimproveddetectionofthefluxassociatedwithextendedsources.Wehavedeterminedoursurfacebrightnesslimittobe∼1×10−15ergs−1cm−2arcmin−2(0.5-2keV)whichisapproximately6timeslowerthanthatoftheEMSS,inagreementwithourexcesscounts.OnthebasisofapureX-rayclassificationwedetermineaskydensityof2.1–3.1(±0.4)extendedobjectsdeg−2inthepresentsamplewithintrinsicflux>4.5×10−14ergs−1cm−2(0.5-2keV).

Oursurveyhascompleteskycoverage(17.2deg2)forrichclusters(LX=5×1044ergs−1)toaredshiftof1.Atourfluxlimitof3.5×10−14ergs−1cm−2wecandetect(with∼50−60%skycoverage)richclusterstoz=1.16,groupsorpoorclusterstoz=0.23andindividualgalaxiestoz=0.08,assumingthecanonicalsizesandluminositiesofsuchobjects.Wehaveconfirmedourdetectionofextendedobjectsathighredshiftbycomparisonwithknownclusters(Table1).FurthermorewefindthatusingtheappropriateexposuremapsfortheROSATPSPCfieldscanimprovefluxestimatesbyasmuchas15%comparedtoauniformcorrectionandcanreducethevariationsbetweenfluxestimatesindifferentfields(ifonlyastandardcorrectionwereapplied)byasmuchas15%.

WehavedemonstratedthatVTPdetectsmorelowsurfacebrightnessemissionthanconventionalPSF/slidingcellbasedmethods.Intheworstcasessuchmethodscanmissalargefractionoffainterextendedobjectsinafluxlimitedsurvey.Thishasprofoundimplicationsforanysurveyoffaintextendedobjectswhichdoesnotuseadetectionmethodsensitivetolowsurfacebrightnessobjects.Forexample,therecentresultsofCastanderet

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al(1995)(whoalsosurveyROSATPSPCfields)whencomparedwiththeresultsinthispaperorofRosatietal(1995)suggestasignificantdifferenceinthedetectionsensitivityofthemethodsused.

WorkinprogresswilladdresstheissuesoftheclusterLogN-LogS,evolutionintheclusterXLF,clustermorphologiesandopticalclassificationsusingtheWARPS-Isurvey.

Acknowledgements

ThedatausedinthisworkhavebeenobtainedfromtheHighEnergyAstrophysicsScienceArchiveResearchCenter(HEASARC)atNASAGoddardSpaceFlightCenter(httpaddress).CASandLRJacknowledgeRegularandSeniorNRCResearchAssociateshipsrespectively.WeacknowledgediscussionswithNickWhiteandRichardMushotzkyandthankNickWhite,LorellaAngeliniandPaoloGiommiforproducingWGACAT,onwhichearlyworkwasbased.

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Table1:KnownclustersdetectedasextendedX-raysourcesbyVTP

Cluster

Reference

Redshift

Note

–30–REFERENCES

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Couch,W.J.,Ellis,R.S.,Malin,D.F.,Mclaren,I.,1991,MNRAS,249,606Crone,M.M.,Evrard,A.E.,Richstone,D.O.,1994,ApJ,434,402EbelingH.,1993,thesis,MPEreportno250,ISSN0178-0719EbelingH.,WiedenmannG.,1993,Phys.Rev.,47,704

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Figurecaptions:

Figure1:The91ROSATpointingsselectedforthisinitialsurvey(AitoffprojectioninGalacticcoordinates).Pointsareweightedbyexposuretime.Thedottedhorizontallinesdelimit|b|=20◦,thehatchedlineistheequatorialcoordinatesystemequator(δ=0◦).Figure2:TheVoronoitessellationofatypicalROSATPSPCphotondistribution(thetargetisastar,HD173524).Photonsareshownaspoints,thetessellationcellsoccupytheinner18arcminradiusofthefield.Sourcesareimmediatelyapparenttotheeyeasclustersofsmallcells.

Figure3:ThesourcephotonsandsourcesidentifiedbyVTPatthreshold1.0inthefieldshowninFigure2.HeavypointsindicateVTPsourcephotons,sourcesarelabellednumerically.TheverticalarrowsmarkthepositionsofsourcesfromWGACAT(whichusesaconventionaldetectionalgorithm,inabroaderenergyband).NotethatsomeVTPsources(suchas2and6)areclearlypotentialblends.

Figure4:ThesourcephotonsandsourcesidentifiedbyVTPatthreshold1.7inthefieldshowninFigure2.Notethatsources2and6atthreshold1.0havenowbeenresolvedoutintosources2,6,8,9,10and11,13,15respectively.

Figure5a,b:Themeanratiosofdetectedandcorrectedcountratestothetruecountrateoflowsignal-to-noise(s/n<8)simulatedsourcesplottedagainst(a)sourceextent(arcsec)and(b)sourcecountrate.EachpointisthemeanratiooftheMonteCarlorealisationswithinasimulationofagivensetofparameters.Opensymbolsrepresentraw,detectedcountrates,filledsymbolsrepresentcountratescorrectedasdescribedinSection4.Circularpointsdenotesourcessimulatedtobeon-axis,triangularpointsdenotesourcessimulatedtobe15arcminoff-axis.Errorbarsshowthe1σscatter.

Figure6:AsinFigure5(a,b)butforhighsignal-to-noisesources(s/n>8).

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Figure7a,b:Thefractionofsimulatedsourcesrecognizedasextended(withanextendedsourcecriterionthatfKing/fPS≥1.2)isplottedagainstintrinsicsourceextent.Ina)theresultsforlowsignal-to-noisesources(s/n<8)areplottedinb)theresultsforhighsignal-to-noisesources(s/n>8)areplotted.Circularsymbolsrepresenttheresultsforon-axissources,triangularsymbolsrepresentsourcesat15arcminoff-axis.Thesymbolsarescaledaccordingtothenumberofsourcephotons.

Figure8:Theskycoverageofferedbythe91fieldsusedinthisinitialsurvey.Skycoverageisplottedasafunctionofintrinsicfluxandintrinsic,projectedextent(assumingaKingprofile).Contoursaredrawnatpercentageoftotalsurveyarea.Thedashedcontourisatalevelof1%,subsequentsolidcontours(ofincreasingweight)are10%,20%...to100%.Thenearhorizontaldashed,dottedandsolidcurvesatthelowerrightarethelociwithredshiftof(respectively)ellipticalgalaxies(Lx(0.5-2keV)=1×1042erg/s,rc=50kpc),groups(Lx(0.5-2keV)=1×1043erg/s,rc=100kpc)andclusters(Lx(0.5-2keV)=5×1044erg/s,rc=250kpc)(H0=50,q0=0).Redshiftisthereforeincreasingrighttoleftandisdifferentforeachcurve.Theverticaldashedlineat3.5×10−14ergsec−1cm−2(0.5-2keV)representstheapproximatelowerfluxlimitofthesurvey.Theredshiftsofthethreeobjecttypesatthisfluxlimitarelisted.

Figure9:TheWARPSskycoverageasafunctionofredshiftforthreeclassesofobjects:Ellipticalgalaxies(withLx(0.5-2keV)=1×1042ergs−1andeffectivecoreradiusrc=50kpc),Groups(Lx(0.5-2keV)=1×1043ergs−1,rc=100kpc)andClusters(withLx(0.5-2keV)=5×1044ergs−1,rc=250kpc).Lightandheavycurvesrepresentcasesinwhichq0=0and0.5respectively.TheHubbleconstantH0(km/s/Mpc)is50inallcases.Figure10:TherawPSPCphotonsandVoronoicellsforfield700114.

Figure11:Thesamefield(700114)asinFigure10.VTPsourcedetectionsareplottedasheavypoints,detectionsaremadetothelowestsurfacebrightnessthresholdusedin

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thesurvey.ThoseVTPsourceswithbackgroundcorrectedphotoncountslessthan20arelabelledwith‘X’.Verticalarrowsindicatethesourcedetectionsoftheslidingwindowalgorithm.

Figure12:AsinFigure11,butthesurfacebrightnessthresholdusedbyVTPisnow1.3.Figure13:TherawPSPCphotonsandVoronoicellsforfield600520.

Figure14:Thesamefield(600520)asinFigure13.VTPsourcedetectionsareplottedasheavypoints,detectionsaremadetothelowestsurfacebrightnessthresholdusedinthesurvey.ThoseVTPsourceswithbackgroundcorrectedphotoncountslessthan20arelabelledwith‘X’.Verticalarrowsindicatethesourcedetectionsoftheslidingwindowalgorithm.

Figure15:AsinFigure14,butthesurfacebrightnessthresholdusedbyVTPisnow1.3.Figure16:ThedistributionofsurfacebrightnesslimitsintheWARPSclustersurveyfields.ThespreadinvaluesreflectsthespreadinbackgroundcountsinthePSPCfields.Theverticaldot-dashedlineatasurfacebrightnessof1.3×10−15correspondstoatwosigmasurfacebrightnessdetectioninasquarecell(seetext)foratypicalROSATfield.TheverticaldashedlinetotherightrepresentstheequivalentsignificancetypicalsurfacebrightnessdetectionlimitoftheEMSS,adjustedtothe0.5-2keVband.Itis∼6timeshigherthanthemeanWARPSlimit.

Figure17:TheLogN-LogSofallsourcesintheinitialWARPSsurvey(0.5-2keV).Thenumbercountsforraw(correctedonlyforbackgrounds)fluxes(plottedasfilledsymbols)havebeencorrectedforskycoverageassumingzeroobjectextents,thesedatapointsshouldthereforebeconsideredaslowerlimitsforthesurvey.Thenumbercountsforcorrectedfluxes(opensymbols)havealsobeencorrectedforskycoverageassumingzeroextentobjects.Thecurvesaretheresultsofearlierworks,Hasingeretal(ROSATPSPCdata)

–35–

1993a(solidcurve),BR(ROSATdata)1994(dashedcurve)andtheEinsteinMediumSensitivitySurvey(EMSS)(Gioiaetal,privatecomm.BR94)(dot-dashedcurve).Errorbarsaredisplayedononlytwodatapointsforillustration,sincetheseareintegralquantitiestheerrorsarenotindependent.Thefaintestpointforthecorrectedfluxesisnotplottedsincethesurveylimitindetectedfluxexcludedsourceswhichwouldotherwisehavebeenmovedintothisbinfromfainterfluxesbythefluxcorrection.

1.4s/n < 81.21.00.80.60.40.20.0110100intrinsic extent (arcsec)1.4s/n < 81.21.00.80.60.40.20.00.0020.010.04intrinsic count rate (s-1)VTP count rate / true count rateVTP count rate / true count rate1.4s/n > 81.21.00.80.60.40.20.0110100intrinsic extent (arcsec)1.4s/n > 81.21.00.80.60.40.20.00.0020.010.04intrinsic count rate (s-1)VTP count rate / true count rateVTP count rate / true count rate1.00.80.60.40.2s/n < 80.0110100intrinsic extent (arcsec)1.00.80.60.40.2s/n > 80.0110100intrinsic extent (arcsec)fraction recognized as extendedfraction recognized as extendedHasinger 93BR 94EMSSRaw fluxesCorrected fluxes