Galaxy clusters in the CFHTLS

13 Pages·2006·1.8 MB·English

A&A461,81–93(2007) Astronomy
DOI:10.1051/0004-6361:20066088 &
(cid:1)c ESO2006 Astrophysics
Galaxy clusters in the CFHTLS
(cid:1)
First matched filter candidate catalogue of the Deep fields
L.F.Olsen1,2,C.Benoist2,A.Cappi2,3,S.Maurogordato2,A.Mazure4,E.Slezak2,C.Adami4,
C.Ferrari5,andF.Martel2
1 DarkCosmologyCentre,NielsBohrInstitute,UniversityofCopenhagen,JulianeMariesVej30,2100Copenhagen,Denmark
e-mail:[email protected]
2 ObservatoiredelaCôted’Azur,LaboratoireCassiopée,BP4229,06304NiceCedex4,France
3 INAF-OsservatorioAstronomicodiBologna,ViaRanzani1,40127Bologna,Italy
4 Laboratoired’AstrophysiquedeMarseille,UMR6110CNRS-UniversitédeProvence,BP8,13376MarseilleCedex12,France
5 InstitutfürAstro-undTeilchenPhysik,UniversitätInnsbruck,Technikerstraße25,6020Innsbruck,Austria
Received21July2006/Accepted19September2006
ABSTRACT
Weapplyamatched-filterclusterdetectionalgorithmtotheCanada-France-HawaiiTelescopeLegacySurvey(CFHTLS)i-banddata
fortheDeep-1,Deep-2,Deep-3andDeep-4fieldscoveringatotalof4squaredegrees.Totesttheimplementedprocedurewecarry
outsimulationsforassessingthefrequencyofnoisepeaksaswellasestimatetherecoveryefficiency.Weestimatethatuptoz∼0.7
thecatalogue isessentiallycomplete forclustersof richness classR >∼ 1.Therecovered redshiftsareingeneral overestimatedby
∆z = 0.1 with a scatter of σ∆z ∼ 0.1, except at redshifts z >∼ 1 where the estimated redshifts are systematically underestimated.
Theconstructedclustercandidatecataloguecontains162detectionsoveraneffectiveareaof3.112squaredegreescorrespondingto
adensityof∼52.1persquaredegree.Themedianestimatedredshiftofthecandidatesisz = 0.6.Theestimatednoisefrequencyis
16.9±5.4detectionspersquaredegree.Fromvisualinspectionweidentifysystemsthatshowaclearconcentrationofgalaxieswith
similarcolour.Thesesystemshaveadensityof∼20persquaredegree.
Keywords.methods:dataanalysis–surveys–galaxies:clusters:general–cosmology:large-scalestructureofUniverse
1. Introduction tothoseofpresentdayclusters(e.g., Stanfordetal.1997,1998;
vanDokkumetal.2000;Lidmanetal.2004),whentakinginto
Clusters of galaxies, the most massive gravitationally bound
accountthepassiveevolutionofthestellarpopulations.Mostof
systems in the Universe are located at the nodes of the cos-
the studied systems have been X-ray selected, which is likely
mic web and are thus goodtracers of the large-scalestructures
totracethemostmassivesystemsatanyredshift.Therefore,the
(e.g., Bahcall 1988; Huchra et al. 1990; Collins et al. 2000).
currentstudiesmaybebiasedtowardsold,well-evolvedsystems
Their intimate connection with the power spectrum of the ini-
missingthetrueprogenitorsofpresentdayclustersandgalaxies
tial density fluctuations as well as to the cosmological param-
(vanDokkum&Franx2001).Inordertobetterunderstandsuch
eters make them important targets in observational cosmology biasesandselectioneffectsitisimportanttousedifferentdetec-
(e.g. Bahcall et al. 1997; Oukbir & Blanchard 1997; Holder
tionmethodsandwavelengthregimes.
etal.2001;Schueckeretal.2003).Additionally,theyarestillac-
cretingmatteralongfilamentsandevenatz = 0alargefraction
Anumberofdifferentdetectionalgorithmsandwavelengths
of them do present signs of substructures in their morphology
have been used for identifying systems at increasingly higher
and in the galaxy velocity distribution. Therefore, a prerequi-
redshifts.Thelargestclustersampleshavebeenconstructedus-
siteforaddressinganycosmologicalissuefromaclustersample
ingeitheroptical(e.g.,Postmanetal.1996;Olsenetal.1999b;
is not only to have a large homogeneous sample with a well-
Gladders & Yee 2001; De Propris et al. 2002; Postman et al.
understoodselectionfunction,butalsoagoodunderstandingof
2002;Gotoetal.2002;Kimetal.2002;Galetal.2003;Bahcall
clusterevolutionincludingconstraintsontheirdynamicalstate.
et al.2003;Milleretal. 2005;Tagoetal. 2006)orX-ray(e.g.,
Theevolutionofgalaxyclustershasinrecentyearsobtained
Böhringeretal.2000,2004, andreferencestherein)data.More
a lotof attention.This is partlydue to the adventof largetele-
recently,theSunyaev-Zeldovicheffecthasalsobeenusedforde-
scopes and sensitive instruments which allow to carry out de-
tectingclustersofgalaxies(Carlstrometal.2002).Eachmethod
tailed studies ofhighredshiftsystems. Manystudieshavecon-
is based on one or at most a few characteristics derived from
centratedonthecolouroftheredsequencegalaxies.Thesehave
known clusters and may thus introduce biases against certain
shownthatmostoftheknownsystemsexhibitpropertiessimilar
typesofsystems.Therefore,itisofutmostimportanceforeach
(cid:2) Full Table 3 is only available in electronic form at the CDS via method to have a well-defined selection function including
anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via a clear understanding of the built-in biases. Furthermore, di-
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/461/81 rectlycomparingcataloguescoveringthesameareaextractedby
Article published by EDP Sciences and available at http://www.aanda.orgor http://dx.doi.org/10.1051/0004-6361:20066088
82 L.F.Olsenetal.:GalaxyclustersintheCFHTLS
differentmethodswill yield importantinsightinto the different
biasesintroducedbythedifferentmethods.
TheSloanDigitalSkySurvey(SDSS)datawithitslargearea
and multi-colour coverage, as well as complementing spectro-
scopicinformation,hasrecentlyprovidedanimportanttest-bed
for a number of optical cluster detection methods at low red-
shifts (e.g., Kepner et al. 1999; Kim et al. 2002; Goto et al.
2002). Thorough comparisons between the different methods
have been carriedoutby Kim et al. (2002);Goto et al. (2002);
Bahcall et al. (2003). These comparisons show that, not sur-
prisingly,there are alwaysdifferencesbetween the variouscat-
alogues,partofwhichare causedby thedifferentwaysthe pa-
rameterssuchasforexamplerichnessareestimated.TheSDSS
data aresufficientfordetectingclustersto atmostintermediate
redshifts (z ∼ 0.5). At higher redshifts only smaller data sam-
Fig.1. Average galaxy number counts (filleddotswitherror bars) for
ples have been available, such as the KPNO/Deeprangesurvey thefourDeepfieldsinthei−band.Thenumbercountsfortheindividual
by Postman et al. (2002) and the ESO Imaging Survey (Olsen fields are shown as follows: D1 – solid line; D2 – dotted line; D3 –
et al. 1999a,b; Scodeggio et al. 1999). Recently, the Red se- short-dashedline;andD4–long-dashedline.Theverticaldottedlines
quenceClusterSurveybyGladders&Yee(RCS,2005)covering denoteouradoptedmagnitudelimitforthepresentanalysis.
100squaredegreeshasbeenachievedthusstartingtoprobelarge
volumestohighredshift.However,adetailedcomparisonofthe
efficiencyofdifferentmethodsathigh-zhasyettobecarriedout. To investigate the advantages of using additional colour infor-
mationwewillapplyacoloursearchtechniquetothesamedata
For detailed comparison between different methods, wide, andcross-comparethedetectionsbetweenthedifferentmethods.
deep and preferentially multi-passband homogeneous surveys Inparallelweareworkingondetectionmethodsbasedonpho-
arerequiredinordertoprovidethenecessarydataforanumber tometricredshiftslicingtofullyexploitthemulti-passbanddata
ofdifferentdetectionmethods.ThedesignoftheWidesurveyof foridentifyingstructures,aswellasonsearchesbasedonweak
theCanada-France-HawaiiTelescopeLegacySurvey(CFHTLS) lensing studies (see Gavazzi & Soucail 2006).In future papers
providesadatasetthatisparticularlywell-suitedforcarryingout we will also characterizethe detectedsystemsin terms oftotal
such studies. This surveyis currentlyunderwayand is planned luminosity,concentration,shape parametersand colourproper-
tocover∼170squaredegreesin5passbandsspreadin4patches tiessuchastheexistenceandsignificanceoftheredsequence.
with limiting magnitudes up to 25m. It will provide the neces- Thepresentpaperisstructuredasfollows:inSect.2wede-
sary ground for building a large, well-controlled cluster candi- scribethegalaxycataloguesusedinthepresentwork.Thesecat-
date sampleatredshiftsz (cid:1) 1.3,derivedfroma setofdifferent alogues are a modified version of the Terapix CFHTLS galaxy
searchtechniquesusingthespatialaswellasphotometricprop- catalogues. Section 3 describes the matched-filter cluster iden-
erties in one or more passbands.Such catalogueswill allow us tification method which is an improved version of that imple-
totestaccuratelythez > 0.5componentoftheclusterdistribu- mentedforthe ESO ImagingSurvey(Olsenet al. 1999a).This
tion. Using automatic search techniques will allow us to build section alsodescribesa seriesofsimple simulationsto account
selectionfunctionsforeachofourindependentlyextractedcata- fortherateoffalse-positivesaswellastheselectionfunction.In
logues.Acarefulcomparisonbetweenthevariousindependently Sect.4weapplythedetectiontothei−bandgalaxycatalogueof
extracted cluster samples will allow us to understand the ad- thefourDeepfieldsofthesurveycoveringatotalof∼4square
ditional difficulties in detecting clusters at successively higher degreesandcomparethe constructedclustercatalogueto those
redshifts as well as improve our knowledge about clusters at ofpreviousworks.InSect.5wesummarizeourfindings.
theseredshifts.Combiningthecataloguesfromseveralsearches Throughout the paper we use a cosmological model with
we will create a robust cluster sample well suited for both Ωm =0.3,ΩΛ =0.7andH0 =75kms−1Mpc−1.1
cosmologicalandgalaxyevolutionstudies.
Thispaperisthefirstinaseriesdescribingdetectionandin-
2. Galaxycatalogues
vestigationsofprimarilythephotometricpropertiesoftheiden-
tified systems. In this first paper we describe our implementa- Thegalaxysamplesusedinthisworkareobtainedfromthecat-
tion of the matched filter detection method which we apply to alogues released by the Terapix team as part of the CFHTLS
thei−banddataoftheDeepSurveyoftheCFHTLS.Thedepth releaseT0002inAugust20052.Thereleasedcataloguesareex-
presentlyreachedbytheDeepCFHTLScorrespondsroughlyto tracted with SExtractor using a gri-chi-squared image (Szalay
the finaldepthoftheWidepartofthesurvey.Furthermore,the et al. 1999)asreferenceandmeasuringmagnitudesin each in-
smallsize oftheDeepprovidesa goodtest-bedforvariousde- dividual band. Here we concentrate on the i−band catalogues
tectionalgorithmsforinvestigatingthepotentialoftheWidesur- of the four Deep fields with a total sky coverage of 4 square
vey.Themotivationforexploringthei−bandin this firstpaper degrees. The 80% completeness limits of the catalogues are
istwo-folded:first, thesurveyareaisplannedtobecoveredby reached at magnitudes of i = 24.8–25.4.Starting from the re-
i−band as high priority, later followed by the other passbands; leasecataloguesweapplyourownstar-galaxyseparationbased
second,mostpreviousopticalclustersearcheshavebeencarried onthelocusoftheobjectsinahalf-lightradiusversusmagnitude
outini−band,thusfocusingonthisfilterfacilitatescomparisons diagram,wherethestarsareclearlyseparatedfromthegalaxies
with previoussurveys minimising the effect of the variation in atmagnitudesi(cid:1)21–22.Furthermore,weapplyacorrectionfor
wavelength.In future paperswe will apply the same algorithm
to data in other passbandsin orderto investigatehow sensitive 1 Weuseh75 = 75kmsH−10Mpc−1
thistechniqueistothechoiceofpassbandatdifferentredshifts. 2 http://terapix.iap.fr/rubrique.php?id_rubrique=198
L.F.Olsenetal.:GalaxyclustersintheCFHTLS 83
GalacticextinctionbasedonthemapsbySchlegeletal.(1998). Table 1. Detection and filtering parameters for building the cluster
Aspartoftherelease,theTerapixteamprovidesmaskfilesfor catalogues.
filtering out false detections, usually caused by saturated stars
Parameter Value
orghostimages.Thosemasksareproducedbasedonthei-band
Filter
images.Wehavevisuallyinspectedtheimagestogetherwiththe Coreradius,r 0.133h−1Mpc
masks and,in areaswhere spuriousdetectionscausedby ghost Cutoffradius,cr 1.33h−175Mpc
imagesorspikesfrombrightobjectswere still present,defined FaintendslopeocofLF,α –1.1575
afewadditionalmasks. Schechtermagnitude,M∗ –22.24
i
In Fig. 1 we show the galaxy number counts obtained for Likelihoodmaps
thesepost-processedcataloguesforthefourDeepfields.Theav- Pixelscale 0.5r =21.6–8.5arcsec
c
eragecountsareshownaspointswitherrorbarscomputedasthe z-interval 0.2–1.3,∆z=0.1
standarddeviationbetweenthefields.ItcanbeseenthattheD2 Peakdetection
field is slightly shallower than the others as was also indicated Threshold 3.5σ
by the 80% completeness limiting magnitudes as given by the Minimumarea ∼π(rc(z)/2)2 ∼4pixels
Aposteriorifiltering
Terapixteam(24.8–25.4).Itcanbeseenthatthe80%complete-
Minimumnumberofshells 2
nesslimitsroughlycorrespondstothepeakofthecounts.Asa
compromisewechooseinallfieldstousegalaxieswithi ≤ 25.
Thislimitisalsoindicatedinthefigure.
apparentSchechtermagnitudeswe have used k-correctionsde-
3. Clusterdetection rived from model spectra for an elliptical galaxy from the
Colemanlibrary(Colemanetal.1980),thusignoringluminosity
Theclusterdetectionalgorithmusedinthepresentpaperisbased evolution of the galaxies. The main impact of this is that red-
on the matched-filter technique (e.g., Postman et al. 1996) as shiftsoftheclustersmaybebiasedlowforthehigh-zpartofthe
it was implemented for the ESO Imaging Survey (Olsen et al. sample.
1999a). To this version a number of improvements have been As discussed in Sect. 2, each galaxy catalogue has an as-
added for the present work. Here, we summarize the main as- sociated mask file usually maskingfalse detectionsaroundsat-
pects of the implementation, in particular focusing on the new urated stars or ghost images. Since such false detections often
implementationsdoneforthiswork. comeinfairlydensegroups,theyareveryefficientlydetectedby
the clusterfindingalgorithm.Toavoidsuchfalse clusterdetec-
3.1.Matched-filterclusterdetection tions, objects within masked regions are discarded in the anal-
ysis. While it is of course important to avoid spurious cluster
Thematched-filterdetectionprocedureisbasedonamaximum
detectionscausedbyfalseobjectswithinthesemasks,themask-
likelihoodanalysiswiththefollowingsteps:
ingofregionscreatesholesinthegalaxydistribution,whichin
turnhamperstheassumptionforthematchedfilteralgorithmof
1. creationofafilterbasedonanassumedclustergalaxylumi-
a homogeneousbackground.This has to be taken into account
nosityfunctionandradialprofile;
bothwhenestimatingthebackgroundasfunctionofmagnitude
2. creationoflikelihoodmapsforaseriesofredshifts;
(inthiscaseinparticularthedensityofbackgroundobjects)and
3. detectionofsignificantpeaks;
4. cross-matchingofpeaksfordifferentredshifts; whenevaluatingthefilterinthevicinityofthemaskedareas.The
lack of objects will decrease the signal compared to the ideal
5. creationoflikelihoodcurvesandidentificationoftheredshift
case of complete coverage,thus the clusters situated in the af-
ofmaximumlikelihoodusedfordefiningtheclusterproper-
fected regions will have a lower probability of being detected.
tiessuchasredshiftandrichness.
Asaresultofthespatialextentoftheappliedfilter,theregions
The current implementation uses the Postman et al. (1996) affected by the holes are not only the masked regions but also
matched-filter algorithm, which filters the galaxy catalogue theirimmediatevicinity.Duetothelargerangularextentofthe
based on positions and apparent magnitudes. The filter is con- filteratlow-z,theholesaffectlargerregionsinthelow-redshift
structed to enhance galaxy overdensities that resemble that of shells than in the higher redshift domain. This may in the end
a cluster with the assumed radial profile and luminosity func- cause large regions of the catalogue to be significantly incom-
tion(LF)embeddedinabackgroundoffieldgalaxies.Wehave plete. To diminish the effect of the holes in their vicinity we
adoptedtheHubbleradialprofilecharacterizedbya coreanda addrandomlydistributedgalaxiestofilltheholesinthefiltered
cut-offradius.TheLFisaSchechterfunction(Schechter1976) galaxycataloguesbeforeapplyingthematched-filteralgorithm.
characterized by the faint-end slope and Schechter magnitude, The density of the added galaxies corresponds to the average
M∗. The chosen values for these parameters are taken from densityofthefield.
Popesso et al. (2005) and listed in Table 1 after conversion to Analogously,thesignalattheedgeswillbedecreaseddueto
our cosmology. For details of the matched filter algorithm and thelackofgalaxiesoutsidetheobservedregions.Tocounteract
itsvariantswereferthereadertoPostmanetal.(1996);Kepner thiseffectwealsoaddaborderofrandomlydistributedgalaxies
etal.(1999);Olsenetal.(1999a)andKimetal.(2002). again with a density corresponding to the average in the field.
Thematchedfilterisappliedtoobservedquantities(thusan- The width of the added frame correspondsto the extent of the
gulardistancesandapparentmagnitudes).Thefilteriscomputed largest filter radius correspondingto the one used for z = 0.2.
in a gridcoveringthe galaxycatalogue,where we havechosen The magnitude distribution of the added mock galaxies is the
thepixelscaletocorrespondtohalfthecoreradius.Toconstruct one of the catalogue itself. Of course, this approach can never
the likelihood curves the filter is tuned to a series of redshifts fullyrecoverthesignalofapartiallymaskedclusteroracluster
fromz = 0.2toz = 1.3instepsof∆z = 0.1andappliedtothe situated at the limit of the survey, but it assures that the back-
galaxycatalogueforeachofthem.Theusefulredshiftrangede- groundsignal is kept constantacross the field allowing a more
pendson the passband and the depth of the data. To derivethe homogeneousdetectionovertheentirearea.
84 L.F.Olsenetal.:GalaxyclustersintheCFHTLS
Foreachredshift,alikelihoodmapwiththepixelscalecor-
responding to half the core radius at this redshift is created.
The maps are stored as FITS files to facilitate the use of stan-
dard image analysis tools (here we use SExtractor, Bertin &
Arnouts 1996) for detection and characterization of the peaks.
Eventhoughthe maskedareasare filled,the signalin these re-
gions is useless, and therefore we use weight maps to discard
theseregionsinthepeakdetection.Theweightmapsarecreated
with the same pixel grid as the likelihood maps starting from
the updated mask files for each field. To avoid splitting clus-
ters with substructureswe do not use the deblendingoption of
SExtractor,eventhoughthisprobablyreducesthesensitivityto
clustersclosetothesamelineofsight.
After peak detection, the significant peaks in the different
Fig.2.Variationofstandarddeviationofthelikelihoodmappixelvalue
maps,correspondingtodifferentredshifts,arecrossmatchedus- distributions as function of redshift. Each of the Deep fields are rep-
ing the association program of the LDAC-tools3. This tool as- resented by individual symbols (diamonds for D1, triangles for D2,
sociates detections by their position, such that, if the detection squaresforD3andcrossesforD4).Thelinesdenotetheaverageover
areasintwoshellsoverlap,thedetectionsareassociatedtoeach 20mockcatalogswiththeerrorbarsgivingthestandarddeviation.The
othertocreatetherawlikelihoodfunctions. solidlinemarkstherelationforthe“correlated”backgroundcatalogues
Duetotheslowvariationoftheappearanceofclusterswith andthedottedlinethatofthe“uniform”backgroundcatalogues.
redshiftandtheluminositywidthofthefilter,aclustercausesa
significantpeakinanumberofconsecutiveshells.Itisnotlikely
that a cluster absentin one shell is recoveredat a more distant Forinstance,sinceclustersareexpectedtopersistthroughmore
redshift. Therefore, the raw likelihood functions are analysed thanoneredshiftshellwedemandthecandidatestoshowupin
andsplitintwoifitoccursthatforagivenredshiftnodetectionis atleasttwoconsecutiveshells.Eventhoughweusethenumber
found.Inthiswayitisassuredthatalllikelihoodcurvesarecon- ofredshiftbinscontributingtothelikelihoodcurve,otherparam-
tiguous as is expected for real clusters. Additionally, since the eterssuchassignal-to-noiseorrichnesscouldalsobeimportant
filtersizeismuchlargeratlowredshiftsthanathigherredshifts discriminators.
it may happen that two detections are blended at low redshift In principle, the optimum way for addressing this point is
butdeblendedathigherredshifts.Therawlikelihoodcurvesare by using mock galaxycatalogueslike the ones producedin N-
thereforesearchedforshellswheretwodetectionsareassociated bodysimulationsincludingthe fullhierarchyof structures.For
tothesamecluster.Insuchcasesonlythedetectionclosesttothe suchacatalogueonewouldknowthepreciselocationofclusters
foregroundoneiskeptinthepresentdetectionandtheotherone aswellastheirphysicalproperties.Therefore,applicationofthe
usedinanewseriesofdetections.Bothoftheseproceduresare clusterdetectiontosuchcatalogueswouldallowatthesametime
improvingthesensitivitytoclustersalongthesamelineofsight. toidentifyhowmanyclustersweredetectedandhowmanyad-
Theaboveprocesscreatesthefinallikelihoodcurveforeach ditionaldetections,causedbysuperpositioneffects,werefound.
cluster candidate. Again due to the persistency of real clusters Hence onecould immediatelybalancethe false and realdetec-
werequireadetectiontoappearinatleasttwoconsecutivered- tionsbasedonthesamesimulatedcatalogues.However,inreal-
shiftbinsinordertobeconsideredfurther.Thepropertiesofthe itythesimulationofthegalaxydistributionaswellasidentifying
cluster candidatearedeterminedfromthe redshiftatwhichthe galaxysystemsisacomplextask,whichwillbeinvestigatedin
likelihoodsignalis maximized.Thecluster positionis takento afuturepaper.
bethepositionofthemaximumsignal. Here,weadoptasimplerapproachsimulatingseparatelythe
Comparedwith the implementationforthe EISproject,the distributionofthebackgroundandclustergalaxies,wherebywe
main improvements are the handling of masked regions in the havefullcontroloftheinputparametersoftheclustersandthus
galaxydistributionaswellasthediminishingoftheedgeeffects notonlytherecoveryrate,butalsotheprecisionoftheestimated
using randomly distributed galaxies. Also, the analysis of the parameterscanbedirectlyassessed.
likelihood curves has been improved.The EIS implementation To build backgroundsas realistic as possible means repro-
wasusingwhatweherecalltherawlikelihoodcurves. ducing both the magnitude distribution of galaxies and their
spatial distribution properties. In this process we encounter
a coherence issue since a fair reproduction of the clustering
3.2.Balancingrealandfalsedetections
of galaxies (in particular at small scales) would mean that
When constructing a cluster candidate catalogue, the aim is clusters are naturally built in. However, densities and clus-
to identify as many real systems as possible while discarding tering amplitudes can be reproduced in spatially independent
chancealignments.Asitisclearfromtheabovedescriptionthere bins of 1 mag. Such a procedure allows then to limit the lu-
are a numberof steps whereparametershave to be selected by minosity coherence of a possible clump to 1 mag, whereas
theuserinordertooptimizethisbalance.Whenthepixelscale a real cluster is expected to span over a much larger mag-
hasbeenchosen,amongtheremainingparametersarethedetec- nitude range. A set of correlated backgrounds have been
tion thresholdand minimumacceptedarea used by SExtractor. constructed based on the algorithm by Soneira & Peebles
Theseparametersarerelatedtothe“raw”peakdetectioninthe (1978), allowing to reproduce fairly well the slope of the
likelihood maps. After constructing the raw catalogues several two-point correlation function as well as its amplitude as a
parametersmayalsobeusefultosuppressthenoisecontribution. function of magnitude. Our reference for the number counts
and correlation functions are those measured directly from
3 LeidenDataAnalysisCenter, the D1 field. Besides the correlated backgrounds we also cre-
ftp://ftp.strw.leidenuniv.nl/pub/ldac/software atedforcomparisonspatiallyuniformbackgroundsreproducing
L.F.Olsenetal.:GalaxyclustersintheCFHTLS 85
thecorrelatedbackgroundsfortheseestimates.Thecomparison
of the number of detections in the real data and in the corre-
lated backgrounds is shown in Fig. 3. It shows the number of
detections in the real data versus the number of detections in
thebackgroundcataloguesfordifferentsettingsofthedetection
threshold and minimum area. Even though the clustered back-
groundcataloguesseem to representthe backgroundwell, it is
possible that the noise fraction in this way is slightly overesti-
mated. This (slight) overestimate is caused by the fact that the
catalogueisbuiltinslicesofonemagnitudeandthereforecon-
centratedclumpsofgalaxieswithverysimilarmagnitudesmay
beincludeddespitethewrongluminosityfunctionofthesystem.
However,weexpectthistobeaminoreffect,sincethecorrela-
tion of position and magnitude is limited to a relatively small
magnituderangeofonemagnitude.
Fig.3. The number of real and false detections per square degree for
differentdetectionthresholdsandminimumarea.Thenumberoffalse Themostefficientsuppressionofthefalsedetectionsisinthe
detectionsisestimatedfromthecorrelatedbackgroundcatalogues.The steepestpartofthecurves.Whenitturnsflatterthedetectionsin
upper curves with open symbols give the numbers for the minimum thecataloguesbecomemorenoisecontaminated.Therefore,the
areacorrespondingtoπ(0.5rc)2andthelowercurveswithfilledsymbols mostefficientthresholdjudgedfromthisrelationaloneiswhere
thoseforπ(1rc)2.Thenumbersateachpointmarkthe“n”inthe“nσ” thecurvesbendoff.Fromthefigureitcanbeseenthatthechoice
scalingofσdet.Thethinsolidlinemarksthelocusofequalnumberof ofminimumareaisnotanefficientnoisediscriminatorandthus
falseandrealdetections.Thedashed,dottedanddot-dashedlinesmark
toensurethedetectionofthemostconcentratedsystems(often
afractionof5%,10%and33%falsedetections,respectively.
beingthoseatthehighestredshifts)wechoosetousethesmall
minimumareacorrespondingtoπ(0.5r )2.Fromthebendingof
c
theuppercurveitcanthenbeseenthatathresholdof4.0σ,cor-
onlythegalaxynumbercounts.Foreachtypeofbackgrounds20 respondingto∼20%falsedetectionsforatotalofabout∼30de-
simulationswerebuilt. tections persquare degreewouldbe the mostefficientin terms
Forbalancingthenumberoffalseandrealdetections,weap- ofrateoffalse-positives.However,otherconsiderationssuchas
pliedthematched-filteralgorithmtothefourDeepfieldsaswell completeness as function of redshift have to be taken into ac-
astoeachofthetwosetsofsimulatedcatalogues.Toinvestigate count as well. For investigating this we compare the resulting
the impact of the clustering propertieson the likelihood maps, cataloguesusingboththe4.0σand3.5σdetectionthresholds.In
andthusonthepeakidentification,wefirstcomparethestandard thelattercasethetotalnumberofdetectionsis∼50with∼30%
deviationsofthepixelvaluedistributions.InFig.2weshowthis falsedetections.
comparisonforeachredshiftbin.Forthesimulatedbackgrounds
Wehavecarriedouttwocomparisons:oneinternalbetween
weusethemeanstandarddeviationineachbinwhileforthereal
the two catalogues and one to an externalcluster sample. First
dataeachcatalogueisshownbyanindividualsymbol.Itcanbe
wevisuallyinspectedallthecandidatesinthe3.5σ(162candi-
seen thatin generalthe standarddeviationsof the realdata are
dates) and 4.0σ (98 candidates) cataloguesand found that 122
largerthan thoseof bothof the two typesof mockbackground
from the 3.5σ catalogue were graded A or B (see Sect. 4 for
catalogues. This is expectedsince in the real data the presence
a definition) corresponding to the most reliable candidates. Of
ofclustersincreasesthedensityvariations,andthusthevariation
those candidates∼43%are notincludedin the 4.0σcatalogue.
inthepixelvalues.Whiletheuniformbackgrounds,asexpected,
A large fraction of these missing candidates were identified at
showmuchsmallervariations,theclusteredbackgroundvalues
highredshift,amaintargetofthepresentsurvey.Therefore,we
representwellthelowerlimitofthestandarddeviationfoundin
considerthe 3.5σthresholda goodcompromisedespite the in-
therealdata.
creased frequency of false-positives. This choice is supported
Whendeterminingthedetectionthresholdtobeusedforthe
bytheresultsofcomparingtotheXMMLarge-ScaleStructure
peakidentificationonewouldliketousethestandarddeviation
Survey sample (XMM-LSS, Pierre et al. 2006) as discussed in
ofthebackgroundpixeldistributionofeachlikelihoodmapand Sect. 4.2.We findthatalltheirz ≥ 0.5detectionsaremissedif
setthethresholdinastandard“nσ”fashion.However,duetothe
we use the 4.0σ detection threshold, but included using 3.5σ,
variationsinclusteringthebackgroundstandarddeviationvaries
whichisourchoicefortherestofthispaper.
aswasseenabove.Inordertohaveacommonreferenceforthe
backgroundstandarddeviation,weusedthosederivedfromthe
averageofthe20correlatedmockcataloguessincetheseappear 3.3.Towardsaselectionfunction
to representa clusteredbackgroundwell.Hence,inthefollow-
ing the detectionthresholdscaling,σdet = nσ, willreferto the Having determined the optimum detection parameters it is im-
values of the average of the standard deviations, σ, of the 20 portanttoinvestigatetherecoveryrateasfunctionofredshiftand
correlatedbackgroundmockcatalogues. richness(selectionfunction).Forbuildingtheselectionfunction
Havingdefinedthisreferenceitisnowpossibletocompare itisnecessarytohavecontrolonthelocationofclustersaswell
the number of detections in different cases to define the opti- as their basic properties. Therefore we have created simulated
mumdetectionthresholdandminimumarea.Thetwokeyissues galaxycataloguesbasedonthebackgroundcataloguesdescribed
are to keep the fraction of false-positives low, while keeping a above and clusters with the same characteristics (radial profile
high detection efficiency. The first issue relates to the number and LF) as the one used for the detection filter. A similar ap-
of detections in the background only simulations and the sec- proach has been used by many authorsfor estimating recovery
ondtothenumberofdetectionsinthedatacatalogues.Tohave efficiency(e.g.,Kepneretal.1999;Loboetal.2000;Gotoetal.
a fair representation of the number of false detections we use 2002;Kimetal.2002;Postmanetal.2002).
86 L.F.Olsenetal.:GalaxyclustersintheCFHTLS
Table2.TherelationbetweentheinputΛ -richnessandtheAbellrich-
cl
ness classes. For the transformation between the counts and richness
classweusetherelationfoundbyPostmanetal.(1996).
Λ (cid:6)N (cid:7) R
cl R
10 15 <0
20 24 0
30 31 0
40 38 1
50 45 1
60 50 1
70 56 1
80 62 2
90 67 2
100 72 2
150 95 3
200 118 3
250 137 3
300 156 4
Foreachbackgroundsetupwecreate20mockcataloguesto
which we add clusters with redshifts in the range 0.2–1.3 and
Λ -richnessfrom10–300,asdetailedinTable2.Thesimulated
cl
clustersarebuilttoresemblethemodelclusterusedtoconstruct
the detection filter. In each field we add 12 clusters with dif-
ferentredshifts from z = 0.2 to z = 1.3, but constantrichness.
Foreachrichnessweconstruct20suchcatalogues.Altogethera
set of 280galaxycataloguesincludingclusters were produced,
containing a total of 3360 galaxy clusters. Figure 4 shows one
exampleofasetof12clusterswithrichnessΛ = 100(R ∼ 2)
cl
embeddedinafieldbackground.Fromthefigureitcanbeseen
that at the highestredshifts the numberof galaxiesincludedin
thecatalogueisverysmall,thereforethecontrastofthecluster
againstthebackgrounddecreasessignificantlywithredshifteven
forthesefairlyrichsystems.Itisalsoclearthatitismoredifficult
toidentifytheclustersontheclusteredbackgroundthanonthe
uniformone,duetothelargernumberofbackgroundsuperposi-
tions.TheconversionbetweentheinputΛ -richness,theAbell
cl
richnesscounts, N (numberofgalaxieswithmagnitudesinan
R
intervalofsize2maglimitedatthebrightendbythethirdbright-
estmagnitude)andAbellrichnessclass,R,isgiveninTable2.
In order to determine the recovery rate, we apply the de-
tectionprocedureto thesemockgalaxycataloguesandidentify
clustersaroundthenominalclusterpositions.Weuseasearchra-
diusof1.(cid:8)5.Werejectdetectionsthathaveamatchingdetection
(in terms of position and redshift) in the corresponding back-
groundgalaxypopulation.In Fig. 5 we show the computedre-
coveryefficiencyasfunctionofredshiftandrichness.Fromthis
figureandTable2itcanbeseenthat,overall,thesesettingsal- Fig.4.Anexampleofasimulatedgalaxycataloguefortheclustersonly
low clusters with Abell richness class R (cid:2) 1 to be detected up (upperpanel),embeddedintheuniform(middlepanel)andcorrelated
toredshiftsz ∼ 0.7withatleast80%efficiency,whileatz (cid:2) 1, (lower panel) backgrounds. In all cases the catalogues are cut at the
systemswithR(cid:2)2aredetectedat80%completeness. limitingmagnitudeofi = 25.TheclustersallhavearichnessofΛcl =
100(R∼2)andtheredshiftsindicatedintheupperpanel.
3.4.Recoveryofproperties
Intheprevioussectionwediscussedtheefficiencyofdetectinga ourselves in redshift and richness to cases where at least 50%
clusteratthepositionofthesimulatedclusters.Anotherimpor- (10cases)ofthe20inputclustersarerecovered.Thisisdonein
tant question for using the constructed cluster catalogue is the ordertomakesurethatwedonotestimatetheoffsetsononespe-
accuracyoftheestimatedclusterproperties. cialcasebutobtainareasonablestatisticalsignificance.Itcanbe
Thefirstpropertyweinvestigateistheaccuracyoftherecov- seenthattheaverageoffsetsfromthenominalpositionisofthe
eredpositions.InFig.6weshowthemeanoffsetsasfunctionof order or sligthly larger than the core radius for all richnesses.
redshiftandrichness(uppertolowercurve)andcompareitwith Here the detections are recovered within 1.(cid:8)5 from the input
the core radius (smooth dotted line). We have chosen to limit center.
L.F.Olsenetal.:GalaxyclustersintheCFHTLS 87
Fig.5. The detection efficiency for the correlated background σ =
det
3.5σ,area∼π(0.5r )2.ThelinescorrespondtoΛ =10–300fromleft
c cl
toright.
Fig.6.Theaveragematched-filterpositionoffsetasfunctionofredshift
andrichnessusingasearchradiusof1.5arcmin.Thedifferentlinescor-
respondtodifferentrichnessasinFig.5.Thesmoothdottedlinegives
the corresponding angular extent of the core radius. We only include
caseswithatleast50%recovery.
Fig.7. Redshift offsetsasfunction ofinput redshiftsfor richnesses of
Λ = 30(upper panel), 150 (middlepanel) and combined for all the
The main properties estimated by the matched filter algo- cl
investigatedrichnesses(lowerpanel).Eachpointisslightlyoffsetbya
rithm are the redshiftand richness. To investigatethe accuracy
randomnumbertoallowallpointstobeseendespitethediscretenature
of these estimates, we use the same matching as above adopt-
oftheredshiftmeasurements.
ingasearchradiusof1.(cid:8)5.InFig.7weshowtheredshiftoffsets
betweentheinputandrecoveredredshiftsforeachoftherecov-
ered clusters mixingall richnessesin the lower panel. The two
top panels give the offsets for richnesses of Λ = 30 and 150. intermediateredshiftstheaverageisingoodagreementwiththe
cl
Itcanbeseenthatingeneraltherecoveredredshiftsareingood inputrichness.Atallredshiftsthescatteroftherecoveredrich-
agreementwiththeinputones,eventhoughthescatterincreases ness is large. The richness estimate depends on the estimated
forthepoorersystems.Furthermore,inthelowestredshiftbins redshift, thereforewhen the redshifts are overestimatedwe ex-
there is a tendency of overestimating the redshift while in the pectthe same forthe richness(an M∗ galaxyathigherredshift
highestredshiftendtheoppositeeffectisseen.Since themock has an apparent flux that is smaller than at lower redshift and
clustersareconstructedusingno-evolutionk-corrections,thisef- therefore the equivalent number of M∗ galaxies is larger). To
fectisnotthesameasmentionedinSect.3.1,butisanadditional investigate this effect, we corrected the measured richness to
offsetintroducedbythe method.Asdiscussed bySchuecker& thevaluecorrespondingtotheinputredshift.Thiscorrectionis
Böhringer(1998)thismaybeaneffectoftheadoptedalgorithm madebymultiplyingtherecoveredrichnessbythefluxratiobe-
andotherchoicescouldpossiblyperformbetterin thisrespect. tweenan L∗ galaxyattherecoveredredshifttooneattheinput
However,itis worthnotingthatspectroscopicconfirmationsof redshift.Theresultofthiscorrectionisshowninthelowerpanel
clustersatlowredshiftdetectedintheEISprogramconfirmthe ofFig.8.Itcanbeseenthatmostofthesystematicoffsetisre-
consistencybetweenrealandestimatedredshiftsshowingnoor moved, thus we attribute the systematic offsets in the richness
a slightly lower systematic offset increasing at the highestred- estimatetotheoffsetinredshift.
shifts(e.g., Benoistetal.2002;Olsenetal.2005a;Olsenetal. Eventhoughbasedonsimplesimulations,thepresentresults
2005b). The scatter is found to be consistent with the spectro- willserveasareferenceforfutureworkinvestigatingtheeffects
scopicresults. (cid:1) ofclustersthatdonotexactlyresemblethemodelcluster.Itisan
Lastly, w(cid:2)e show the relative richness offsets [Λcl,out− important step for understandingthe strengths and weaknesses
Λ ]/Λ in the upper panel of Fig. 8. It can be seen that ofthedetectionunderwell-controlledconditionsbeforeadding
cl,in cl,in
at low redshiftthere is an overestimateon averageup to 100% the entire complexityof differentcluster morphologiesand su-
and a slight underestimate at the highest redshifts, while at perpositionsthroughtheuseofN-bodysimulations.
88 L.F.Olsenetal.:GalaxyclustersintheCFHTLS
gradeAsystemsis∼20persquaredegree.Itisworthnotingthat
the fraction of grade C and D systems is slightly smaller than
the estimated noise fraction possibly indicating that the corre-
lated backgroundsindeed slightly overestimates the true noise
frequency.However,some of the grade B systemsmay also be
due to superposition effects and thus contribute to the noise of
thecatalogue.
InFigs.9and10weshowthespatialdistributionofcluster
candidatesforeachfieldforredshiftsz ≤ 0.6andz ≥ 0.7,
MF MF
respectively. We show the masks (polygons) and the detected
clusters (filled circles). The size of the circles reflects the es-
timated richness of the systems with larger circles indicating
richer systems. It can be seen that the number of detections in
eachfieldvariesinbothredshiftintervals.
InFig.11weshowtheredshiftandrichnessdistributionsand
comparethemtotheestimatedcontributionfromfalse-positives.
For the redshift distribution the error bars indicate the field-
to-field variation. To investigate the expected variance of the
counts we used cluster samples extracted from N-body simu-
lations (Evrard et al. 2002). From this paper we used the re-
sults of the ΛCDM simualtionsandthe deep wedge(DW)sur-
vey with a total (simulated) sky coverage of 10 × 10 square
degreesandamaximumredshiftof4.4.Theadoptedmasslim-
its are only rough estimates obtained from the conversion be-
Fig.8. The relative richness offsets as function of input redshift. The tweenΛcl-richnessandAbellrichnessclassgiveninTable2.To
horizontaldashedlinegivesthezerooffsetline.Theupperpanelshows convertAbellrichnessclassestoamasslimitweusedthesam-
themeasuredrelativeoffsetsfromtheinputvalueswhilethelowerpan- ple by Girardi et al. (1998). For each Abell richness class we
elsshowtherichnessoffsetsaftercorrectingfortheredshiftoffsetsas computedtheaveragemassandusedthisasourroughestimate.
detailedinthetext. When extracting cluster samples from the N-body simulations
we rescaled the mass threshold as a function of redshift to ob-
tain samples with sizes similar to the density in the candidate
4. ApplicationtotheCFHTLSdeepfields
catalogue.Extractingrandomlyfromthesesimualtionssetsof4
Thematchedfilteralgorithmasdescribedabovewasappliedto realisationsof1squaredegreeyieldsavarianceconsistentwith
thei−bandcataloguesofthefourDeepCFHTLSfields.There- thefieldtofieldvariationmeasuredfromthe4Deepfields.
sultingclustercandidatecatalogueispresentedinTable3giving Finally,Fig.12showstheredshiftandrichnessdistributions
thefirstfiveentries.TheentirelistisavailableattheCDS.The indicatingthecontributionofgradeAandBsystems.Itcanbe
table lists in Col. 1 the cluster name, in Col. 2 and 3 the right seenthatthedistributionsareatanyredshiftandrichnessdom-
ascensionanddeclinationinJ2000,inCol.4theestimatedred- inated by gradeA and B systems which are bothcharacterized
shift, in Col. 5 the Λ richness, in Col. 6 the S/N of the peak byaclearoverdensityofgalaxies.
cl
value of the detection, in Col. 7 the number of redshift bins
where the candidatewas detected,in Col. 8 the fractionof lost
4.1.Statisticalcomparisontoprevioussurveys
areawithinadistanceof1h−1Mpcfromtheclusterpositionand
75
in Col. 9 the grade as defined below. The total number of de- Eventhoughthenumberofhigh-redshiftclustersearchesisstill
tections is 162 corresponding to 52.1 per square degree for an limited,anumberofsamplesareavailableforcomparison.First,
effective area of ∼3.112 square degrees. From the density of wecomparethepresentcataloguewiththatfromtheEISproject
detections in each field we compute the average density to be (Olsen et al. 1999a,b;Scodeggioet al. 1999)since the adopted
∼52.1±7.8persquaredegree,wheretheerrorindicatesthescat- methodhereis essentiallythe same butappliedto anotherdata
terbetweenthefourfields.Fromthesimulatedbackgroundswe set. Afterwards we compare with two other opticalcatalogues:
estimatetohave∼16.9±5.4falsedetectionspersquaredegree. the KPNO/Deeprange distant cluster survey using a different
This correspondsto a noise fraction of ∼32%. Below we com- data set covering16 square degreesalso in the I−bandandus-
parethepropertiestoresultsofotherauthors. ingamatched-filteralgorithm(Postmanetal.2002)andtheRed
All the detected systems were visually inspected using the SequenceClusterSurvey(RCS; Gladders&Yee2005)thatused
related gri and grz colour images. The candidates were split bothadifferentdatasetandadifferentdetectionmethod,namely
into four categories denoted by the following grades: grade searchingforsimultaneousoverdensitiesincolourandspace.
A systems show a clear concentration of galaxies with similar InFig.13we comparethedistributionsofthepropertiesof
colours; grade B systems are characterized by an overdensity clustercandidatesintheCFHTLScataloguepresentedhereand
of galaxies, less concentratedthan grade A systems or without thoseintheEISclustercandidatecatalogue.Thedifferencebe-
any obvious colour concentration; grade C systems do not re- tweenthesurveysisboththepassband(EISusedawideI−band
veal any clear galaxyoverdensity;and finally grade D systems filterwithalimitingmagnitudeofI ∼23.4,whileinCFHTLS
AB
are systems that were detected because of lack of masking of the more narrow Sloan i−band filter is used) and the depth of
the galaxy catalogue or because of an artefact due to the pres- the data. Already this is expected to have some impact on the
enceofanedge.Therelativefractionsofeachgradeare38.3% obtainedclustercandidatesamples,butinparticularatlowred-
for grade A, 37.0% for grade B, 22.8% for grade C and 1.9% shift,thisisnotexpectedtobealargeeffect.Thetwocatalogues
for grade D. From these numbers we find that the density of arebuiltwithessentiallythesamealgorithm,however,itcanbe
L.F.Olsenetal.:GalaxyclustersintheCFHTLS 89
Table3.Thefirstfiveentriesoftheclustercandidatecatalogue.TheentiretableisavailableatCDS.
Name α(J2000) δ(J2000) z Λ S/N #Bins Frac.oflostarea grade
MF cl
CFHTLS-CL-J022410-041940 02:24:10.3 –04:19:40.7 0.9 79.5 4.32 3 0.10 A
CFHTLS-CL-J022411-042511 02:24:11.6 –04:25:11.1 1.1 123.0 4.10 2 0.08 C
CFHTLS-CL-J022413-040412 02:24:13.4 –04:04:12.7 1.1 120.1 4.01 2 0.01 B
CFHTLS-CL-J022423-044044 02:24:23.1 –04:40:44.3 0.4 27.2 4.27 3 0.03 B
CFHTLS-CL-J022423-044303 02:24:23.3 –04:43:03.6 0.5 29.1 3.90 4 0.02 A
Fig.9.Theprojecteddistributionofclusterswithz ≤0.6(filledcircles)detectedinthefourfields.ThedarkcirclesdenotethegradeAsystems,
MF
whilethegreyonesindicateanyothergrade.Thediameterofthecirclesincreasewiththerichnessofthecluster.ThefirstrowshowsD1(left)and
D2(right)andbelowarethefieldsD3(left)andD4(right).Theadditionalpolygonsmarkthepositionofmaskedregions.
seenthattheCFHTLSincludesmoresystemsthantheEISsam- each field. For the richnesses (Fig. 14) we compare the detec-
ple at all redshift. The large difference is likely to result from tions in three differentredshiftbins, since the average richness
theadopteddetectionthresholds,whichisamajordifferencebe- increaseswithredshift(duetotheselectionfunction).Eachline
tween the two detection procedures. In contrast to the present typecorrespondstoadifferentredshiftrangeasindicatedinthe
project,inEISthedetectionthresholdsweredefinedintrinsicto caption. In general the CFHTLS identifies a larger number of
90 L.F.Olsenetal.:GalaxyclustersintheCFHTLS
Fig.10.SameasFig.9butforclusterswithz ≥0.7.
MF
poorersystemsthanwasdoneinEISwhichisprobablyacom- Table4.Foreachofthethreesurveysthedensityofclusters(persquare
binationofthedifferentdetectionthresholdsanddeeperdata. degree) infourdifferentrichnessintervals.Therichnessintervalscor-
In Fig. 15 we compare the redshift distribution with that respond roughly to Abell richness classes R (cid:1) 0, R ∼ 1, R ∼ 2 and
of the KPNO/Deeprange distant cluster survey (Postman et al. R(cid:2)3.
2002)as wellasthatof theRCS (Gladders& Yee 2005).Both
Richness CFHTLS EIS Deeprange
of these surveys are estimated to cover roughly the same red-
Λ <35(R(cid:1)0) 22.5 3.6 4.2
shiftintervalasin thepresentsurvey.We findthatatmostred- cl
35≤Λ <75(R∼1) 18.3 10.5 15.9
shiftstheCFHTLSdistributionincludesmoresystemsthanthe 75≤Λcl<125(R∼2) 9.3 2.6 7.0
KPNO/Deeprangecatalogue,andiscomparabletothedistribu- 125≤Λcl (R(cid:2)3) 1.9 4.3 0.6
tion of the RCS. Since the RCS is using a different detection cl
method also the definition of the richness of the detected sys-
temsdiffersandthusadirectcomparisonisnotpossibleinthis
case.
For the three surveys where Λ -richnesses are available
cl
(CFHTLS, EIS and KPNO/Deeprange) we present the break- richnessclassesR (cid:1) 0,R ∼ 1,R ∼ 2andR (cid:2) 3.Fromthetable
downbyrichnessinTable4.Therichnessintervalsareselected itcanbeseenthattheadditionaldetectionsintheCFHTLScata-
based on the values in Table 2 to correspond roughly to Abell logueislikelyduetoalargernumberofrelativelypoorsystems.