Astronomy&Astrophysicsmanuscriptno.elyiv c ESO2012 (cid:13) January19,2012 Angular correlation functions of X-ray point-like sources in the full ⋆ exposure XMM-LSS field A.Elyiv1,2,N.Clerc3,M.Plionis4,5,J.Surdej1,M.Pierre3,S.Basilakos6,7,L.Chiappetti8,P.Gandhi9,E.Gosset1, O.Melnyk1,10,andF.Pacaud11 1 Institutd’AstrophysiqueetdeGe´ophysique,Universite´deLie`ge,4000Lie`ge,Belgium 2 MainAstronomicalObservatory,AcademyofSciencesofUkraine,27AkademikaZabolotnohoSt.,03680Kyiv,Ukraine 3 DSM/Irfu/SAp,CEA/Saclay,F-91191Gif-sur-YvetteCedex,France 2 4 InstituteofAstronomy&Astrophysics,NationalObservatoryofAthens,Thessio11810,Athens,Greece 1 5 InstitutoNacionaldeAstrof´ısica,O´pticayElectro´nica,72000Puebla,Mexico 0 6 AcademyofAthens,ResearchCenterforAstronomyandAppliedMathematics,SoranouEfesiou4,11527,Athens,Greece 2 7 HighEnergyPhysicsGroup,Dept.ECM,UniversitatdeBarcelona,Av.Diagonal647,E-08028Barcelona,Spain 8 INAF-IASFMilano,viaBassini15,I-20133Milano,Italy n 9 Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, a Sagamihara,Kanagawa252-5210,Japan J 10 AstronomicalObservatory,KyivNationalUniversity,3ObservatornaSt.,04053Kyiv,Ukraine 8 11 ArgelanderInstitutfu¨rAstronomie,Universita¨tBonn,Germany 1 Received31August2011/Accepted13November2011 ] O ABSTRACT C Aims.Ouraimistostudythelarge-scalestructureofdifferenttypesofAGNusingthemedium-deepXMM-LSSsurvey. . h Methods.Wemeasurethetwo-pointangularcorrelationfunctionof 5700and2500X-raypoint-likesourcesoverthe 11sq.deg. p XMM-LSSfieldinthesoft (0.5-2keV) andhard (2-10keV) bands∼. Fortheconversion fromtheangular tothespatia∼l correlation - functionweusedtheLimberintegralequationandtheluminosity-dependentdensityevolutionmodeloftheAGNX-rayluminosity o function. r st Ranedsuγlt=s.2W.0e0hav0e.0fo4u,nθds=ig7n.i3ficant1a.0ngufloarrtchoerrhealardtiobnasndwsi.thThtheeapmowpleitru-ldaewopfatrhaemceotrerreslaγti=on1.f8u1nc±ti0o.n02w,(θθ0)=is1h.i3g′h′e±r0i.n2′t′hfeohrathrdesthoaftn, a inthesoftban±dfor f <010 14e′′rg±s 1c′′m 2andlowerabovethisfluxlimit.Weconfirmthattheclusteringstrengthθ growswiththe [ x − − − 0 fluxlimitofthesampl∼e,atrendwhichisalsopresentintheamplitudeofthespatialcorrelationfunction,butonlyforthesoftband.In v3 tdhieffehraerndtbhaanrddn,eitssrermataioinsssahlomwosstthcaotntshteanstowurictehsrw0 ≃ith1a0hha−r1d-Msppecc,tirrurmespaerectmivoeroefctlhuestfleurexdlitmhaint.sOouftr-sapneaclytrsuimsoofnAeGs.NThsiusbrseasmulptlmesawyibthe 2 ahintthatthetwomaintypesofAGNpopulatedifferentenvironments.Finally,wefindthatourclusteringresultscorrespondtoan 8 X-rayselectedAGNbiasfactorof 2.5forthesoftbandsources(atamedianz¯ 1.1)and 3.3forthehardbandsources(ata 9 medianz¯ 1),whichtranslatesinto∼ahostdarkmatterhalomassof 1013 h−1M ≃and 1013∼.7 h−1M forthesoftandhardbands, 5 respective≃ly. ∼ ⊙ ∼ ⊙ . 1 Keywords.X-rays:galaxies–galaxies:active–surveys 1 1 1 1. Introduction AGNcanbedetectedoverawiderangeofredshiftsincontrastto : v normalgalaxies(Hartwick&Schade,1989),andthereforethese i The study of the large-scale structure for the universe and of objects are excellent tracers of the cosmic web and a conve- X structure formation processes makes it necessary to carry out nienttoolforstudyingevolutionaryphenomenaintheUniverse. r wide-field surveys of extragalactic objects. These surveys are It is known that the optical and X-ray classification of type 2 a performed in almost all accessible wavelength bands. X-ray (obscured)AGN agreequitewell, seeforexampleGarcetetal. surveys constitute an important part of these surveys because (2007)andreferencestherein.X-rayselectedAGNalsoprovide of the weak absorption at such high energies. The most re- a relatively unbiased census of the AGN phenomenonbecause cent and prominent observational X-ray results have been ob- obscuredAGN,whicharelargelymissedinopticalsurveys,are tainedwiththeXMM-NewtonandChandraspaceobservatories includedinX-raysurveys. (Brandt&Hasinger, 2005). More than 95% of all detected ob- jects in X-ray surveys away from the galactic plane are point- The clustering pattern of the AGN population can provide likeandpredominantlyactivegalacticnuclei(AGN),therestare importantinformationregardingthecosmographyofmatterden- mostlyextendedsources(groupsandclustersofgalaxiesandrel- sityfluctuationsatdifferentscalesandthecosmologicalparam- ativelynearbygalaxies).OwingtotheirhighX-rayluminosity, eters(e.g.,Hickoxetal.,2007;Engelsetal.,1999;Plionisetal., 2010;Ebreroetal.,2009;Basilakos&Plionis,2009,2010),the Sendoffprintrequeststo:A.Elyiv evolution of the AGN phenomenon (e.g., Comastri&Brusa, ⋆ Thispaper isdedicatedtothememoryof OlivierGarcetwhohas 2008; Koulouridisetal., 2009; Allevatoetal., 2011), the rela- initiatedthepresentworkjustbeforehissuddendeath. tionbetweenAGNactivityandtheirdarkmatterhalohosts,su- 1 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield permassiveblackholeformation(e.g.,Mandelbaumetal.,2009; AGNclusteringresultsbasedonthe previousreleaseof4.2sq. Miyajietal., 2011; Allevatoetal., 2011), and so on. The most deg.ofthissurvey.Aweakpositivecorrelationsignalwasfound common approach to quantify AGN clustering, without red- in the soft band (angular scale θ = 6.3 3 with a slope 0 ′′ ′′ ± shiftinformationistomeasuretheAGNtwo-pointangularcor- γ = 2.2 0.2). At present the full XMM-LSS field is one of ± relation function (ACF; Akylasetal., 2000; Yangetal., 2003; the widest ( 11 sq. deg)medium-deepsurveys.It is part of an ∼ Mannersetal.,2003;Basilakosetal.,2005;Gandhietal.,2006; evenlargerproject,theXXL,observationsofwhicharecurrently Puccettietal., 2006; Miyajietal., 2007; Carreraetal., 2007; beingimplemented(Pierreetal.,2011). Garcetetal., 2007; Ebreroetal., 2009), which provides an es- In the following sections we present the description of the timate of how significant the excess of AGN pairs is, within XMM-LSS survey (Section 2). Results of the numerical simu- some projected angular separation over that of a random dis- lationsof the X-raypoint-likesourcesare presentedin Section tribution. Once the angular correlationfunction is measured, it 3. Basic properties of the XMM-LSS field, like its source dis- ispossibletoreconstructthespatialclustering,undersomespe- tributionontheskyandthepoint-sourcelogN logS relation, − cific assumptions, using the Limber integral equation (Limber, are shown in Section 4. Section 5 includes the method used to 1953;Peebles,1980).However,spectroscopicfollow-upaswell producethe randomcatalogsand the ACF analysis for the dif- asmultiwavelengthphotometricobservationsinanumberofdif- ferentsamples. Invertingfromangularto spatialclusteringand ferentbandsallowustomeasureorestimateredshiftsforalarge the derivedbias of AGN are presentedin Sections 6 and 7, re- numberofAGNandtoapplythedirectspatialcorrelationanal- spectively,whilethemainconclusionsarelistedinSection8. ysis(e.g.,Gillietal., 2005;Yangetal.,2006;Gillietal.,2009; Coiletal.,2009;Cappellutietal.,2010;Miyajietal.,2011). ClusteringanalysesofthevarioussurveysofX-rayselected 2. ThesampleofX-raypoint-likesources AGNinthesoftandhardbandshaveprovidedawiderangeof Inthepresentcorrelationfunctionanalysis,wehaveusedpoint- angular and spatial clustering lengths. Strong indications for a like X-ray sources from the XMM-LSS field, which consists flux-limitclusteringdependenceappeartoreconcilemostofthe of 87 pointings with maximum available exposures from 10 diverseresults,however(Plionisetal.,2008;Ebreroetal.,2009; to 28 ks. Also we used 7 pointings of the independent deeper Krumpeetal.,2010). Subaru/XMM-NewtonDeepSurvey(SXDS)(Uedaetal.,2008) Another importantquestion is whether the clustering of X- whose data we reanalyzed with our pipeline because it is fully ray selected AGN evolves with time. Gillietal. (2009) did not enclosedintheXMM-LSSarea,althoughwithadifferentspac- find any significant difference between the X-ray AGN clus- ingpattern.ForS01pointingofSXDSwekeptonly40kschunk tering below and above z = 1. Even so, the X-ray AGN bias topreventpossiblesourceconfusion. factor should evolve with time, and indeed Yangetal. (2006) Altogether,the XMM-LSSfield is contiguousand contains found a rapid increase of the bias factor with redshift with 5700 sources in the soft (0.5 - 2 keV) band and 2500 in b(z = 0.45) = 0.95 0.15 and b(z = 2.07) = 3.03 0.83. ∼ ∼ the hard (2 - 10 keV) band, out of which 180 are extended ± ± Similarly, Allevatoetal. (2011) estimated the average bias in ∼ (mainlygalaxyclusters).Althoughallextendedsourceswerere- theCOSMOSAGNsurveyandfoundaredshiftevolutionofthe movedfromouranalysis,itisinterestingtonotethattheywere bias factor with b(z = 0.92) = 2.30 0.11 and b(z = 1.94) = categorized according to their extension likelihood1 (EXTlike) ± 4.37 0.27. andcoreradius(EXT)intotwoclasses:”C1”whicharethetrue ± The AGN clusteringpatterncan also be usedfor the verifi- extended sources with EXTlike > 33 and EXT > 5 , con- ′′ cationofthe unificationmodel,becausebothobscuredandun- taining54objects,and”C2”whichisaclasswithalmost50per obscuredAGNshouldhaveidenticalcorrelationfunction,ifthe centcontaminationat15 < EXTlike < 33andEXT > 5 , ′′ orientationofthetorusistheonlydeterminingfactoroftheAGN containing129objects(seePacaudetal.2006fordetails). phenomenology. Gillietal. (2009) used the 2 sq. deg. XMM- Separately,wehavemadeuseofamoreuniformXMM-LSS COSMOSfieldanddidnotfindanysignificantdifferenceinthe surveyforouranalysiswhichconsistsof10kschunks.Thiscat- spatialdistributionofthebroadandnarrowlineAGN.Similarly, alogwillbepublishedsoon(Chiappettietal.,inprep.) Ebreroetal.(2009),studying1063XMM-Newtonobservations, We considered all point-like sources as AGN, although we foundconsistentcorrelationpropertiesforsourceswithhighand do expect a 3% stellar contamination (Salvatoetal., 2009). low hardness ratios, which mostly correspondto obscured and ∼ More details about the source classification will be given in unobscuredAGN, respectively.These results postulatethat ob- Melnyketal.inprep.Thesensitivitylimitsofthejoinedsample scured and unobscured objects populate similar environments, arenear10 15 and3 10 15 ergs 1 cm 2 forthesoftandhard − − − − whichagreeswiththeunifiedmodelofAGN. × bands,respectively. However, the analysis of the 9 sq. deg. Bootes multiwave- Theaveragedistancesbetweenthecentersofadjacentpoint- length survey showed slightly different clustering properties ings were substantially shorter than the FoV diameter of the for the two types of AGN (Hickoxetal., 2011). Similarly, EPIC cameras to gain a more homogeneous coverage. This Puccettietal.(2006)investigatedthecentral0.6sq.deg.region caused overlaps between adjacent pointings. Because each oftheELAIS-S1fieldandfoundthatthecorrelationamplitudein pointing was processed individually, the final merged catalog thehardband(θ =12.8 7.8 )is2.5timeshigherthanthatin 0 ′′ ′′ wasproducedaposteriori(Pierreetal.2007;Chiappettietal.,in ± thesoftband(5.2 3.8 ),butwithaweaksignificance( 1σ). ′′ ′′ prep).Asafirstpossibility,weonlyconsideredsourceswithan ± ∼ Gandhietal. (2006) used the hardness ratio (HR) and divided off-axisdistance< 10.Inthisway,wedidnothavetoconsider ′ thepoint-likesourcesinmainlyobscured(HR > 0.2)andun- boundarysourcesthatare oftendetectedwith largeerrors.The − obscured(HR< 0.2)subsamples,findingapositiveclustering total effective area of the fields was 8.3 sq. deg. The distribu- − signalonlyfortheobscuredsourcesinthehardband. tionofthecorresponding4066X-raysourceslocatedwithinthe In this work we will revisit these questions by present- bordersisshowninFig.1.Asanalternativemergingpossibility ing the final results of the point-like source distribution of the XMM-Newton Large Scale Structure (XMM-LSS) survey of 1 Bytheterm”likelihood”asusedhereinafter,wemeanformallythe Pierreetal. (2004). In Gandhietal. (2006) we presented the log-likelihood. 2 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield -2.5 -2.5 -3.0 -3.0 -3.5 -3.5 -4.0 -4.0 g g e e d d c, -4.5 c, -4.5 e e D D -5.0 -5.0 -5.5 -5.5 -6.0 -6.0 -6.5 -6.5 37 36 35 34 33 37 36 35 34 33 RA, deg RA, deg Fig.1. Distribution of the X-ray point-like sourcesobserved in Fig.2. Distribution of the X-ray point-like sources observedin thesoftbandwithinthewholeXMM-LSSfieldwithanoff-axis thesoftbandwithinthewholeXMM-LSSfieldwiththeVoronoi distancelessthan10′.Theredcirclesrepresentthebordersbe- tessellationmethod.NotethatusingtheVoronoitessellationwe tweenthedifferentpointings.Notethatevenwhenusingthe10′ didnotexceedthe13′off-axisdistanceforanypointing. limitation,wemayhavesomeoverlappingregions.Wediscarded theseminoroverlapsusingtheVoronoitessellationmethod. ing their likelihoodsand measured count-rates2; iv) correlating thedetectedsourcelistwiththeinputcatalogusinga6 radius ′′ andderivingtheratesoftrueandfalsedetectionsaswellasthe weappliedaVoronoiboundarydelimitation(Matsuda&Shima, detectionprobabilities. 1984) without imposing an off-axis cutoff and using sources The simulations were performed in the soft and the acrossthefullexposureXMM-LSSfield.Inotherwords,inany hard bands. The original source distribution was taken from overlapregion among two pointingswe only kept those detec- Morettietal. (2003) using either their soft or hard band fitting tionsin ourfinalcatalogthathadthe shortestoff-axisdistance. formulae,downtoafluxwhichapproximatelycorrespondsto2 Inthisway,wewereabletousethewidestpossiblearea10.9sq. photonson-axis(i.e.belowXMM-Newtondetectionlimit).This deg.oftheinvestigatedfield.Thedistributionofthe5093point- value dependson the exposure time chosen for each particular likeX-raysourcesisshowninFig.2.ThebasicACFresultswere simulation. Non-resolved AGN photon background was added checkedconsideringbothapproachesanditwasfoundthatapart followingRead&Ponman (2003), then we subtractedthe con- from larger uncertainties in the case of the < 10′ delimitation tribution of the AGN resolvedby our detection algorithm.The method,theresultswerestatisticallyidentical. constantconversionfactorcf betweenthetotalcount-ratesand thephysicalfluxesS wascalculatedonthebasisoftheMOSand PNcamerafactorsprovidedbyPierreetal.(2007). Particle background was also added according to values 3. SimulationsofXMM-LSSAGN quoted in Read&Ponman (2003) and was subsequently mod- Fora propercorrelationfunctionanalysiswe needto knowthe ifiedbymultiplyingthesevaluesbyanarbitraryfactorbetween values of the detection probability for each registered source. 0.1 and 8 to allow for pointing-to-pointing background varia- Thereforewe performedextensivesimulationsof eachindivid- tions. In any case, this componentwas not vignetted.We sum- ual XMM pointing. We briefly describe our procedure and the marizeourtypicalbackgroundvaluesinTable1.ThePSFmodel set of simulations that were used for the representation of the was taken from the XMM-Newton medium model calibration XMM-LSSfield. files. The vignettingwasmodeledthroughitsoff-axisvariation ontoeachdetector. Thedetectionalgorithmprovidesforeachsourceanestimate 3.1.DescriptionoftheXMM-Newtonpoint-sourcesimulation ofitscount-rateoneachdetectoraswellasthelocalbackground value at the source position. A key parameter is the source de- The principleof the simulationsis similar to the onepresented tectionlikelihood.FollowingPacaudetal.(2006),thisquantity inPacaudetal.(2006)andGandhietal.(2006).Themainsteps wascomputedusingtheC-statistic.Itsvalueisthedifferencebe- of the procedure consist in i) generating an input source list tween the likelihood of the best-fitting point-sourcemodel and drawn from a fiducial flux distribution that is randomly dis- the likelihood of a pure background fluctuation. As such, the tributedacrossthe pointingfieldofview;ii) simulatingimages ofthefieldasitwouldbeseenbyXMM-Newtonbyreproducing 2 Throughout thispaper, count-rates areexpressed intermsof total themaininstrumentaleffects(vignetting,PSFdistortion,detec- MOS1+MOS2+PN count-rates, corrected for vignetting. That is why tormasks,backgroundandPoissonnoise);iii)detectingsources two sources with the same count-rate but different off-axis positions with the XMM-LSS pipeline (Pacaudetal., 2006) and obtain- willhavedifferentprobabilitiesofdetection. 3 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield Photonbackground Particlebackground softband hardband softband hardband MOS1 1.21 1.77 0.764 1.16 MOS2 1.32 1.88 0.730 1.09 PN 2.49 3.55 2.80 6.03 Table1.Typicalbackgroundvaluesforthepointingsimulations. Weallowedtheparticlebackgroundtovaryfromonepointingto theotherthroughamultiplicativefactorchosenamong0.1,0.25, 0.5,1,2,4and8.UnitsforeachXMM-Newtondetectorare10 6 − ctss 1pixel 1. − − T Limitingflux Particlebackground Number exp (ks) (10 16ergs 1cm 2) factors offields − − − Softband0.5 2keV − 7 1.43 0.10.250.51248 7 540 × 10 1 0.10.250.51248 7 540 × 20 0.5 0.10.250.51248 7 540 Fig.5.Efficiencyofoursourcedetectionalgorithmintheinner- × 40 0.25 0.10.250.51248 7 540 mostannulus(0 5arcmin)ofthesimulatedsoftbandXMMob- × 80 0.125 0.10.250.51248 7 540 − × servations,asafunctionoftheinputsourcecount-rate(orequiv- Hardband2 10keV − alently,fluxforatypicalAGNspectrumandagalactichydrogen 7 14.3 0.113 3 540 10 10 0.113 3×540 column density fixed to 2.6 × 1020 cm−2). The exposure time × differsfromonecurvetotheother,butnotthebackgroundrate. 20 5 0.113 3 540 × 40 2.5 0.113 3 540 × Table2. Summaryofthesoftandhardbandsimulationsets.The balancebetweencompletenessofthesampleandcontamination second column refers to the lowest flux of the input simulated byspurioussources. sourcesin the bandofinterest. Differentbackgroundlevelsare We numerically computed the rate of false detections as a accounted for by applying a multiplicative factor to the values function of the off-axis angle, background level and exposure from Table 1. This set of simulation encompasses most of the timeandinanyconfiguration.Theaveragerateofspuriousde- XMM-LSSpointingcharacteristics. tectionsisbetween2and5perpointing(upto13arcminoff-axis angle).Atypicalpointing(T = 10ks,backgroundratio= 1) exp gives from 40 to 50 detections in the [0 10] arcmin off-axis, − whichleadstoacontaminationrateofabout5%. sourcelikelihoodLHrepresentsthesignificanceofthedetection. A value of 15 providesa good balance between contamination 3.2.2. Detectionefficiencyasafunctionofpointing andcompleteness(seePacaudetal.2006andparagraph3.2for characteristics adiscussionofthestabilityofthiscriterion). WeshowinFigs.5,6and7theprobabilitycurvesderivedfrom our simulations. These curves were computed by dividing the 3.2.Setofsimulations number of detected (ML> 15) sources by the number of input To fully account for the variations of the detection efficiency sources in a given input count-rate bin and for a given expo- across the XMM-LSS fields, we simulated 18900 and 6480 sure time, backgroundratio and off-axis bin. The detection ef- pointings in the soft and the hard bands, respectively. Table 2 ficiency is close to the flux-limited efficiency, whose limit de- details the simulation set. Fig. 3 illustrates the influence of ex- pendsonthelocalpointingcharacteristics.Astrongdependence posuretimeandbackgroundratiovalueforthreepointingsfrom on the off-axis position is noticeable in Fig. 7 because the ef- our simulation set at 10 and 40 ks and for backgroundratios 1 fectofvignettingandPSFdistortionsaregrowingwithoff-axis and4. distance. The exposuretime dependence(Fig. 5) is compatible Thankstothehighnumberofsimulatedfields,wewereable witha T improvementfactoroverthesignal-to-noisera- exp ∝ to bin ourresults bysource off-axisangle.We havechosensix tio, whilepthe background level has a milder influence on the annuli of equal area to obtain approximately the same level of detection efficiency. In a typical pointing (T = 10 ks, back- exp significance in each bin. Values defining the bin bounds are 0, groundratio=1)thefluxlimitis2.5 10 15(4 10 15)ergs 1 − − − 5.3,7.5,9.2,10.6,11.9and13.0arcmin. cm 2at50%(90%)completeness. × × − 3.2.1. Completeness/contaminationbalance 3.2.3. Relatingrealdatatosimulations Thesourceselectionwasbasedonthedetectionlikelihoodvalue Sensitivity maps across the entire XMM-LSS field can be de- (ML); all detected sources with ML> 15 were included in the rived through interpolation between simulated pointings. The final sample of point-like sources. A fraction of these sources exposuretime ofa givenpointingis astraightforwardquantity, comesfromfalsedetections.Fig.4showsthedistributionofthe asistheoff-axisangleatthepositionofasource.Torelatethe recoveredsourcesforthreeconfigurationsintheinnermostoff- backgroundratioquantitytorealdata,weusedestimatesofthe axisbin(0 5.3arcmin).Weseelittledependenceofthecontam- local background fitted by our detection algorithm at each de- − inationrateonthebackgroundlevelandexposuretime,andthe tectedsourceposition(seePacaudetal.2006foradescriptionof ML= 15thresholdappearsasthebestchoiceforhomogeneous thefittingprocedure).Estimatednumbersofbackgroundcounts 4 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield Fig.3. Examples of simulated XMM-Newton pointings in the soft band. The large blue circle indicates the region in which the source detection is performed(13 arcmin maximaloff-axisangle).Green boxesindicate the positionsof sourcesdetected with a likelihoodML > 15.Left: T = 10ks,backgroundratio=1;Middle: T =10ks,backgroundratio= 4;Right: T =40ks, exp exp exp backgroundratio=1. Fig.4.Examplesoflikelihoodversuscount-rateplotsforthreecombinationsofpointingexposuresandbackgroundratiosfromour soft band simulation set. Green symbols show detections with a real input counterpartwhile red points indicate spurious (false) detections.Allsourceswithin5arcminfromthepointingcenterareshownhere.Left: 540pointingswithT =10ks,background exp ratio= 1;Middle: 540pointingswithT = 10ks,backgroundratio= 4;Right: 540pointingswithT = 40ks,background exp exp ratio= 1.ThehorizontallinecorrespondstoML=15,thethresholdabovewhichdetectedsourcesareincludedinthecatalog.The separationbetweenfalseandrealdetectionsisrelativelyindependentofthepointingquality. per pixel are put out as two quantities PNT BG MAP MOS The effectivearea A(S)is calculatedwhile integratingoverthe and PNT BG MAP PN. Fig. 8 shows the relationship between wholefieldareaΩ: theinputbackgroundratioandthesequantitiesasderivedfrom simulations.Asexpected,localbackgroundestimatescomputed A(S)= p(S,R,T,B)dΩ. (1) Z by the detection algorithm are well correlated with the back- groundratiovaluesintroducedin thesimulations.We fittedthe Fig. 9showsthe effectiveareacurvesforthe investigatedsam- localbackgroundvaluesbyPNT BG MAP MOS(PN)usingthe plesin thesoftandhardbands,with a minimumflux10 15 for − least-squaresmethodseparatelyforeachpointing.Withthiswe the softand 3 10 15 ergs 1 cm 2 forthe hardbands.Forthe − − − determinedthe backgroundratio level B,whichcorrespondsto constructionof×the illustrated area curveswe used the Voronoi thebestparameterofthefitting. tessellationdelimitationmethod. Fig. 10 shows a comparisonbetween the normalizedeffec- tive area curves of various recent X-ray surveys. The effective 4. Skycoveragesandlog N logS distributions − area curve as a function of flux depends mainly on the depth An important characteristic of an X-ray survey is the sky cov- ofthesourcedetection(indicatedbythesignal-to-noiseratioor erageor,inotherwords,theeffectiveareacurve.Thisindicates likelihoodthresholds).Italsodependsonthedistributionsofthe the maximum effective area over which we can detect sources pointingexposures,particlebackgroundlevelandtheprocedure brighterthansomegivenfluxlimit.Wehaveconstructedthearea ofhandlingthepointingoverlaps.Evidently,theCOSMOSfield curvesusingthenumericallycalculatedprobabilitiesptodetect hasthe lowestflux limitandthe steepestareacurveamongthe sourceswithacertainfluxS,anoff-axisdistanceRinapointing considerablesurveyswiththelikelihoodlimitforthesourcede- withsomeeffectiveexposureT andparticlebackgroundlevelB. tection being equal to 6 (Cappellutietal., 2007). Our full ex- 5 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield Fig.8.Pipeline-estimatedbackgroundvaluesonMOS(left)andPN (right)detectors,inthesoftband,asseenin thesimulations. CurvesfrombottomtotopstandforbackgroundratiosBequalto0.1,0.25,0.5,1,2,4and8.Thisplotshowshowthelocalback- groundestimate outputofthedetectionalgorithmcanberelatedtothebackgroundratioparameterintroducedinthesimulations. Theerrorbarsrepresent1-σstandardvariationcomputedfromthesourcesample.Theverticallinescorrespondtoboundsofour equal-areaoff-axisbins.Onlytheresultsfor10ksaredisplayedandsimilarrelationsareextractedfor7,20,40and80kspointings. Fig.6. Same as Fig. 5 for various backgroundrates in the soft Fig.7. Same as Fig. 5 for the six off-axisbins in the soft band band(definedbyamultiplicativefactortimesthevaluesquoted (see text). Exposure time is held at 10 ks in all cases, and the inthe2nd columnofTable1).Exposuretimeisheldat10ksin particlebackgroundratioissetto1. allcases. Totakethiseffectintoaccount,weusedthenumericallysim- posure XMM-LSS survey, having a significant fraction of the ulateddependenciesbetweentheinputCR andtheoutputCR in out contributingpointingswithexposuresbetween10and15ksand countratesindividuallyforeachpointing(seeFig.11forexam- a source detection threshold of ML= 15, has the next lowest ple).Clearly,whenwedetectsomefluxCR ,itcorrespondstoa out flux-limitaftertheCOSMOSsurvey,andaquitesteeplyincreas- realinputCR distributedoverawiderange.ForeachCR bin in out ingarea-curve.Thecorresponding10ksXMM-LSSfieldhasits weconstructedthedensityprobabilitydistributionasafunction area curve shifted to the right and its flux limit increased by a ofCR .Fig.12representsthenormalizeddistributionsofCR in in factorof 1.2. forthreedetectedCR .Atlowflux,wemayseeanasymmet- out ∼ Using those area curvesandthe differentialdistributionsof ric shape in the distribution that is shifted toward smallerCR in the sources as a function of their flux, we constructed the log because of an artificial flux boosting. Therefore, we randomly N logS relation.Notethatitis importantto takeintoaccount chose some CR for each detected source with CR accord- in out − thefluxboosting.Thisphenomenonespeciallyaffectsfaintob- ing to the density probability function. In this way, we carried jects with a low detectionprobability.Owing to Poisson noise, outMonte-Carlosimulationswiththedeconvolutionoftheout- we may detect objects fainter than the flux limit in successful putintotheinputratesandconstructedlog N logS curvesfor − cases and sometimes not detect sources brighter than the flux variousconsideredsamples(Figs.13-14). limit in unsuccessful cases. This may cause the creation of an The currently estimated logN logS are lower for both − artificialbumpinthelogN logS distribution. bands than those of the 2XMM (Ebreroetal., 2009) and − 6 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield 12 11 10-1 10 -2 g 9 de 8 ve area, 67 put, cts/s10-2 ecti 5 R in Eff 4 C -3 10 3 2 soft band hard band 1 10-15 10-14 10-13 10-12 10-3 10-2 10-1 -1 -2 Flux, S erg s cm CR output, cts/s Fig.9.EffectiveareacurvesforthewholeXMM-LSSfieldinthe Fig.11. Example of the dependence between input and output soft(0.5-2keV)andhard(2-10keV)bands. count-rates for the hard band, T = 20 ks, b = 1. The red line correspondstoCR =CR . in out 0.10 -3 -2 deg 0.9 0.08 CR output=10 a, e ar ve 0.06 -3 cti 0.6 CR output=3x10 effe n/n d e full XMM-LSS 0.04 z ali XMM-LSS, 10 ks chunks CR output=10-2 m or 0.3 XMM-LSS, 4.2 sq. deg. N XMDS 0.02 2XMM COSMOS 0.010-15 10-14 10-13 0.000.0 2.0x10-3 4.0x10-3 6.0x10-3 8.0x10-3 1.0x10-2 1.2x10-2 1.4x10-2 Flux, erg s-1 cm-2 CR input, cts/s Fig.10. Comparison of the normalized effective area curves in Fig.12.DistributionsofCRinforthreedetectedCRoutcreatedon the soft band for the full exposure XMM-LSS field, the 10 thebasisofthesimulateddistributioninFig.11. ks version (see subsection 5.1), the XMM-LSS 4.2 sq. deg. (Gandhietal.,2006),theXMMMediumDeepSurvey(XMDS Chiappettietal.,2005),the2XMM(Ebreroetal.,2009)andthe 5. Theangularcorrelationfunctionanalysis COSMOS(Miyajietal.,2007;Cappellutietal.,2007). To determine the ACF, we generated random catalogs in the following way. Firstly, we distributed the fiducial point-like sources with random coordinates over the whole investigated field.Secondly,wechoseforeachrandomsourceafluxaccord- ingtothelogN logS distributionandcalculatedtheprobability − p of detecting the corresponding point-like source in the rele- COSMOS(Cappellutietal.,2007)surveys,with deviationsnot vantpointing,takingintoaccounttheexposuretime,theparticle exceeding the 2 3σ Poisson level. However, they excel- backgroundlevel(B)ofthepointingandtheoff-axisdistanceof − lently agree with those derived by Gandhietal. (2006) and the correspondingsource. Then, we chose a random number ρ Chiappettietal. (2005), based on previous releases of XMM- for each random point-like source that is uniformlydistributed LSS fields. Moreover, the XMDS (Chiappettietal., 2005) was between 0 and 1. If the ρ value was less than p, we kept the based on a totally different pipeline used for extracting the X- source, if it was higher, we discarded the source. If a random raypoint-likesources.Thissuggeststhattheobserveddeficiency source was closer than 10 arcsec to another one, we removed couldbeanintrinsiccharacteristicoftheXMM-LSSfield. it because the extension of the EPIC PSF ( 6′′ minimum, on ∼ 7 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield andtheLandy&Szalayestimator(Landy&Szalay,1993): DD(θ) 2DR(θ)+RR(θ) 1+w(θ)= f − , (3) 1000 LS RR(θ) where DD, RR and DR represent the numbers of data-data, 100 random-random and data-random pairs with a separation θ, while f and f are the corresponding normalization factors H LS -2 eg 10 ofthetwoestimators.Ingeneralthetwoestimatorsprovidecon- >S), d F Vuollr oXnMoMi b-LoSrdSe:rs osinstbeontthreessutilmtsabtourtsiinnatnhyeccoarsreelwateiownifllunpcretisoenntpltohtes.results based N( 1 < 10’ limitation Tospeed-upourcalculations,wedividedtherandomcatalog XMDS ofthosesampleswithmorethan2000X-raysourcesintoamax- 0.1 2XMM imumof10randomsubcatalogs,andweaveragedw(θ)foreach XMM-LSS 4.2 sq. deg. θ binoverthewholerandomcatalogs.Notethatweverifiedby COSMOS investigatingonesuchsamplethattheaboveprocedureprovides 0.01 -15 -14 -13 -12 stable correlationresults. The w(θ) uncertaintyin each θ-bin is 10 10 10 10 -1 -2 givenby Flux, erg s cm σ =(1+w)/√DD. (4) Fig.13. Log N log S distributions in the soft band for the w − whole XMM-LSS sample and for the two different procedures TheACFcalculationswereperformedforangularscalesin of handling the pointing overlaps. The results of the XMM therange:20 < θ < θ ,whereθ = 12000 .Weused20 ′′ max max ′′ ′′ MediumDeepSurvey(XMDS)(Chiappettietal.,2005),2XMM as ourlowestangular-separationlimit becauseof thelargesize (Ebreroetal., 2009), XMM-LSS 4.2 sq. deg. (Gandhietal., oftheXMM-NewtonPSFneartheFoVborders.Weverifiedthat 2006) and COSMOS (Miyajietal., 2007; Cappellutietal., pairs,constitutedbysourcesbelongingtoadjacentpointings,are 2007) are shown for comparison. The vertical bars denote 1σ realonlyforpairseparations>20 .Wethenfittedtheresulting ′′ uncertainties. ACFwiththepower-lawinth∼eangularrangewhereitwaspos- sible,i.e.,usingonlythepositivewvalues: w(θ)=(θ /θ)γ 1 . (5) 0 − We analyze here the ACF of the full exposure XMM-LSS 1000 field. However,because there are strong indications for a flux- limit dependence of the correlation function amplitude (e.g., 100 Plionisetal., 2008), we also analyzed a homogeneous sample of an effective 10 ks exposure over the whole XMM-LSS re- -2 deg 10 gion.Tothisendwecuttheeventlistofthepointingsinto10ks N(>S), F V<ul ol1 rX0oM’n lioMmi -ibLtaoStriSdoe:nrs cghinunniknsga.nWdereaplseoasteedpathraetesolyuercsetimdeatteecdtitohnepAroCcFedoufrseamfropmlesthbeasbeed- 1 onthehardnessratio(HR). XMDS 2XMM 0.1 XMM-LSS, 4.2 sq. deg. 5.1.ThewholeXMM-LSSfield COSMOS We first presentin Figs. 15 and 16 the ACF results of the full -14 -13 -12 10 10 10 exposureXMM-LSSregionforboththesoftandhardbandsand -1 -2 Flux, erg s cm fortheVoronoidelimitationandoff-axisangle<10 overlapap- ′ proaches.Intheinsetpanelswepresentthe1,2and3σcontours Fig.14. Log N log S distributions in the hard band for the ofthefittedparametersinthe(θ ,γ)plane,whileinTable3we − 0 whole sample and for the two differentproceduresof handling presentthecorrespondingbestfitθ andγparametersandtheir 0 the pointing overlaps. For comparison we present the logN standard deviation, as well as the value of θ for a fixed slope − 0 logS distributionsforthesamesamplesasinFig.13. γ = 1.8 and the integral ACF signal within separations of 3.3 arcmin, w(< 3.3′). Evidently, that there are no significant dif- ferences between the results based on the correlation function axis) prevents one from detecting such close pairs and blends estimators(as seen in Figs. 15 - 16) or onthe two delimitation themintoasinglesource.Wegeneratedrandomcatalogsinthis methods. Therefore we used for the remaining study only the way thatcontain100timesthe numberofpoint-likesourcesin samplesbasedonthespace-fillingVoronoidelimitationmethod the real source catalog, that was used in the present analysis. andtheLandy&SzalayACFestimator(seealsoKerscheretal. Thelargerthepointpopulationoftherandomcatalog,themore (2000)foradetailedcomparisonofdifferentestimators). accurate the ACF measurement because it suppresses random Furthermore, we find that the hard band correlation func- fluctuationscausedbysmallnumbers. tion is slightly but clearly stronger than the corresponding TocalculatetheACF,weusedtwoestimators,theHamilton soft band, as can be also verified by comparing the corre- estimator(Hamilton,1993),asinGandhietal.(2006): sponding inset contour plots, which agree with the results of DD(θ)RR(θ) Basilakosetal. (2005), Puccettietal. (2006) but disagree with 1+w(θ)= f , (2) H DR2(θ) thoseofEbreroetal.(2009). 8 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield Fig.15. Soft band ACF for the whole sample: Voronoidelimi- Fig.16.HardbandACFforthewholesample:Voronoidelimi- tation(toppanel);off-axisangle< 10′ (lowerpanel).Thefilled tation(upperpanel);off-axisangle<10′ (lowerpanel). (black) points correspond to the Hamilton estimator while the open (red) squares to the Landy & Szalay estimator. The error Table4.Correlationfunctionforthe10kschunksamples. barsrepresent1σstandarddeviation.Thedashedlinerepresents thebestpower-lawfit,whilethecontinuouslinecorrespondsto Band N θ′′ γ θ′′ w(<3.3′) theconstantγ = 1.8fit.Theinsetplotpresentsthe1,2and3σ 0 0,γ=1.8 Soft 4360 3.2 0.5 1.93 0.03 1.3 0.2 0.005 0.007 contoursinthefitted(θ0,γ)parameterspace. Hard 1712 9.9±1.4 1.98±0.04 3.8±0.7 0.092±0.019 ± ± ± ± Table 3. The soft and hard band correlation functions for the wholeXMM-LSSfield, aswell asforthe two possibleoverlap approaches.N indicatesthenumberofX-raysourcesinthecor- respondingsample, while the last columnshows the integrated Wealsoinvestigatedtheflux-limitdependenceofclustering ACFsignal,anditsuncertainty,within20 <θ<200 . with ourhomogeneous10kssample.Tothisendwe estimated ′′ ′′ the angular clustering length, θ for various flux-limited sub- 0 Band Overlap N θ′′ γ θ′′ w(<3.3′) samples by keeping the slope of the ACF fixed to its nominal 0 0,γ=1.8 Soft Vor. 5093 1.3 0.2 1.94 0.02 1.3 0.2 0.006 0.007 valueofγ=1.8.Fig.18showsthecorrespondingresultsforthe <10 4066 1.4±0.3 1.81±0.02 1.3±0.2 0.009±0.003 softandhardbands.Evidentlytheknowndependenceisclearly ′ Hard Vor. 2369 7.5±0.9 2.00±0.03 2.5±0.4 0.075±0.013 reproduced with our data, and it will be interesting to investi- ± ± ± ± <10 1988 6.5 0.8 1.91 0.03 3.7 0.5 0.080 0.014 gatewhetherthisdependenceispresentinthespatialcorrelation ′ ± ± ± ± length, via Limber’s inversion(see further below). Another in- teresting result is that the amplitude of the hard band ACF is largerthanthatofthesoftbandonlyinthelowestflux-limits.At fluxlimits 10 14ergs 1cm 2thetrendisreversedandthesoft − − − ≥ As discussed above, to provide a “clean” ACF, that is un- bandisstrongerthanthehardbandclustering. affected by the convolutionof (a) the variable flux-limit in the HowdoourresultscomparewiththoseofotherXMMsur- differentpartsofthesurveyand(b)theflux-limitclusteringde- veys ? With respect to our previous release of the 4.2 sq. deg. pendence, we considered a sample with a homogeneous10 ks XMM-LSSsurvey(Gandhietal.,2006),ournewcatalogintro- exposure time across the whole XMM-LSS area. Table 4 and ducesmanyimprovements.Amongthemisthewider(by 2.6 ∼ Fig. 17 show the parameters of the ACFs for both bands. The times)sampledarea,andtheinclusionofadeeperSXDSfield. main variation with respect to the previous analysis is that the Furthermore,we updatedthepoint-likesourcedetectionproce- ACF difference between the soft and hard bands is now even dureandintroduceda noveldefinitionoftheselectionfunction moreprominent. andrandom-cataloggenerationprocedure. 9 A.Elyivetal.:AngularcorrelationfunctionsofX-raypoint-likesourcesinthefullexposureXMM-LSSfield -12 10 -13 10 -2 m c -1 s g er x, 10-14 u Fl -15 10 10 100 1000 10000 Maximum Likelihood Fig.19. Dependencebetween flux and ML in the soft band for the point like sources of 44 pointings from the present XMM- LSS survey (black open circles) and from Gandhietal. (2006) (redfilledcircles). ML 40. It is also evident,inspecting Fig. 19, that a value of ∼ ML 40isassociatedwithasignificantlyhigherflux-limitwith ∼ respectto that of ML = 15, causing the observeddifferenceof thecorrespondingareacurves(seeFig.10). Fig.17.ACFforthe10kssampleinthesoftband(upperpanel) The above mentioned changes and improvements, particu- andforthehardband(lowerpanel). larlythelowerMLdetectionlimit,haveresultedinavariationof someofourresultswithrespecttothoseofGandhietal.(2006). Specifically,wefoundaslightlydifferentclusteringsignalinthe softband;θ =1.3 0.2 forγ=1.81vs6.3 3 forγ=2.2 0 ′′ ′′ ′′ ′′ ± ± inGandhietal.(2006).However,atthefixedcanonicalvalueof theexponent(γ = 1.8),theGandhietal.(2006)softbandanal- ysisprovidesaclusteringamplitudeofθ = 1.7 0.9 versus 0 ′′ ′′ ± 1.2 0.2 forthecurrentXMM-LSSsurvey.Thelowercorrela- ′′ ′′ ± tionsignalofourcurrentXMM-LSSsurveyshouldbeattributed to the lower ML limit, which introduces a significantly higher fractionof faintsourceswith respectto the higherML limit of the Gandhietal. (2006) catalog. Also, we found a significant clusteringsignalin thehardband,in contrastto theabsenceof anysignificanceinGandhietal.(2006). With respect to the COSMOS (Miyajietal., 2007) and 2XMM (Ebreroetal., 2009) surveys, we find (at fixed canoni- Fig.18.Best-fitcorrelationlengthθ forγ=1.8asafunctionof cal γ = 1.8) a lower soft band correlation function amplitude, 0 thefluxlimitofthehomogeneous10kssampleinthesoft(filled θ0 = 1.2′′ 0.2′′, comparedto 1.9′′ 0.3′′ and to 7.7′′ 0.1′′ ± ± ± circles)andthehardbands(opencircles). fortheCOSMOSandthe2XMMsurveys,respectively.Ourhard band(2-10keV)XMM-LSScorrelationamplitudeof3.6 0.7 ′′ ′′ ± isalsolowerthanthecorresponding2XMMvalueof5.9 0.3 , ′′ ′′ ± Our currentXMM-LSSarea curveis substantiallydifferent while the COSMOS hard band correlation results are not very from that of Gandhietal. (2006) (see Fig. 10). To investigate significant, probably because they are divided into two sub- thereasonsofthisdifferenceindetail,weusedthe44pointings bands(2-4.5and4.5-10keV). commontobothstudiestocomparethecorrespondingpoint-like Note,however,thatthe widecontiguousareaoftheXMM- sourcecatalogsinthesoftband.ThecurrentXMM-LSScatalog LSS survey implies that we should have a better estimation of contains 2106 objects with off-axis distances less than 10 and w(θ) on large angular scales (ie., 1000 <θ<10000 ), while ′ ′′ ′′ the Gandhietal. (2006) catalogue contains 1093 such sources, COSMOS and 2XMM are limited to 6∼00∼0 and 1000 , ′′ ′′ ∼ ∼ while the commonsourcesare 1048.Fig. 19 shows the depen- respectively. dence between flux and ML for both catalogs. Obviously, the InFig.20wecomparethesoftbandw(θ)ofourXMM-LSS chosenMLlimitoftheGandhietal.(2006)catalogissubstan- and the 2XMM surveys. The large 2XMM w(θ) amplitude at tiallyhigherthanthecurrentlimitofML=15anditisequalto smallangularscalesisevident,althoughat 1000 thetwocor- ′′ ∼ 10