Optical and infrared counterparts of the X-ray sources detected in the Chandra Cygnus OB2 Legacy Survey 5 1 0 M. G. Guarcello1,2, J. J. Drake2, N. J. Wright3,2, T. Naylor4, E. Flaccomio1, V. L. 2 Kashyap2, D. Garc´ıa-Alvarez5,6,7 n a J 5 1 ] ABSTRACT R S TheyoungmassiveOBassociationCygnusOB2,intheCygnusXcomplex,isthe . h closest (∼ 1400pc) star forming region to the Sun hosting thousands of young low p mass stars and up to 1000 OB stars, among which are someof the most massivestars - o knownin ourGalaxy. This regionholdsgreat importancefor severalfields of modern r t astrophysics, such as the study of the physical properties of massive and young low- s a mass stars and the feedback provided by massive stars on star and planet formation [ process. 1 Cygnus OB2 has been recently observed with Chandra/ACIS-I as part of the v 1 1.08Msec Chandra Cygnus OB2 Legacy Project. This survey detected 7924 X-ray 6 sources in a square degree area centered on Cyg OB2. Since a proper classification 7 3 and studyoftheobserved X-ray sources also requires theanalysis oftheiropticaland 0 infrared counterparts, we combined a large and deep set of optical and infrared cata- . 1 logsavailableforthisregionwithournewX-raycatalog. Inthispaperwedescribethe 0 5 matching procedure and present the combined catalog containing 5703 sources. We 1 also briefly discuss the nature of the X-ray sources with optical and infrared counter- : v partsusingtheirpositioninthecolor-magnitudeand color-colordiagrams. i X Subjectheadings: r a 1. Introduction 1INAF-OsservatorioAstronomicodiPalermo,Pi- azzadelParlamento1,I-90134,Palermo,Italy The study of young stellar clusters, to- 2Smithsonian Astrophysical Observatory, MS-67, gether with the correct classification of their 60GardenStreet,Cambridge,MA02138,USA stellarcontent,generallyreliesonacombina- 3CAR/STRI, University of Hertfordshire, College tionofavailablemulti-wavelengthdata,from Lane,Hatfield,AL109AB,UK 4School of Physics, University of Exeter, Stocker Spain Road,ExeterEX44QL,UK 5Dpto. deAstrof´ısica, UniversidaddeLaLaguna, 7Instituto de Astrof´ısica de Canarias, E-38205La Laguna,Tenerife,Spain 38206-LaLaguna,Tenerife,Spain 6Grantecan CALP, 38712 Bren˜a Baja, La Palma, 1 X-rays to optical and infrared. A key aspect identified in Cygnus OB2 some of the most ofsuchstudiesofcrowdedstellarfieldsisthe massive stars known in our Galaxy, such as procedure adopted for merging the different O3 stars and B supergiants (Walborn, 1973; datasets. Itisimportanttominimizethenum- Massey&Thompson, 1991; Comero´net al., ber of spurious coincidences and false nega- 2002;Hanson,2003;Negueruelaetal.,2008). tives (i.e. sources in one waveband that fail Despite the extinction toward Cyg OB2 to be matched with their real counterparts being high due to the intervening nebulos- in another). A lack of accuracy and com- ity associated with the Cygnus Rift (roughly pleteness in the data merging process might ranging from A ∼ 2.5m to A ∼ 8m for V V adversely affect source classification and the theopticallyidentifiedmembers;Drewet al., subsequentinterpretationoftheresults. 2008;Saleet al.,2009;Guarcelloet al.,2012; When sparse catalogs are matched, the Saleet al., 2014), its relative proximity (∼ chances of spurious coincidences are reason- 1400pc, Ryglet al., 2012) has made it the ably low. In these cases, simple matches subject of several studies aimed at under- based on source positions can be safely standingitsrichstellarcontent. Indeed,being adopted. When the source density of one the massiveassociation with the largest mas- or more of the catalogs is high, such that sive star content in the proximity (i.e. within the probability of finding more than one ob- 2 kpc) of our Sun, with a massive popula- ject within the bounds of a source position tion that has no equal in the other nearby uncertainty is deemed significant, the use of young clusters such as the Orion Nebula more complicated methods that take into ac- Cluster, and begin also rich in pre-main se- counttheexpectedmultiwavebandproperties quence stars (AlbaceteColomboet al., 2007; of the source populations must be used. To Wright& Drake,2009;Guarcelloet al.,2013), thisaim,severalMaximumLikelihoodmeth- Cyg OB2 is also arguably the best available odshavebeenproposedintheliterature(e.g.: target to study star formation, disk evolution, Sutherland &Saunders, 1992). and planet formation in presence of massive Cygnus OB2 is the central massive OB stars (e.g. Wright etal., 2014b). The aver- association of the giant Cygnus X complex, age age of the stars in the central part of the with a rich population of young stars spread association has been estimated to range be- over an area of more than one square de- tween 3 and 5Myrs(Wright et al., 2010), but gree. Because of its very rich population several new star forming sites hostinga large of massive stars, Cygnus OB2 has been de- fractionofveryyoungstarsstillembeddedin scribed as a very young globular cluster in a contracting envelope or thick circumstellar the Milky Way (Kno¨dlseder, 2000). The disk have been discovered (Vinket al., 2008; census of the massive population of this Wrightet al., 2012; Guarcello et al., 2013). association ranges from the first count by TherearealsoindicationsthatsomeOBstars Reddishet al. (1967) of 300 OB members, in the association are younger than 2Myrs to the estimate based on 2MASS data of (Hanson,2003),whileapopulationofAstars more than 2600 OB stars by Kno¨dlseder foundin thesouthernarea appears tohavean (2000). More recent studies found some- agebetween 5−7Myrs(Drew et al.,2008). what lower population of massive stars and The promise of Cyg OB2 to be able to 2 shed new light on the workings and products ground and background observed popula- of massive star forming regions motivated a tions, simple nearest neighbor approaches large Chandra X-ray Observatory 1.08Msec can fail because several potential counter- Legacy Project (Drake, 2014,in preparation; parts can fall within the positional uncer- Wrightet al., 2014a). At ages of a few mil- tainty of a given source. More sophisticated lion years, stars of all masses are about three approaches have employed likelihood ratio and four orders of magnitude stronger X-ray methodsthatseektoutilizeotherinformation emitters compared with older populations. than simply source position, such as com- HardX-rayphotonscanpenetratemanymag- parative brightness (see, e.g., Richter, 1975; nitudes of visual extinction and provide an Sutherland &Saunders, 1992; Smithet al., effectivediagnosticof youththat is free from 2011). biases resulting from accretion from a pro- Here, we describe the matching of multi- toplanetary disk and the presence of circum- wavelength sources to those detected in the stellarmaterial. Chandra Cyg OB2 survey. A brief overview The direct aim of the survey was to use of the X-ray, optical and infrared catalogs is the selective power of X-rays together with presented in Sections 2 and 3; the methods the arcsecond spatial resolution of Chandra employed to cross-match objects in different to perform a deep census of the stellar popu- catalogs are described in Section 4 and the lation and its X-ray properties, but with the final catalogisdescribedinSect. 5. Wesum- main scientific goals of understanding the marizethemainpointsofthestudyinSection evolutionofprotoplanetarydisksandstarfor- 6. mation in an association approaching stellar superclusterdimensions. TheresultingChan- 2. The X-ray catalog dracatalogcontains7924X-raysourcesover The Chandra Cyg OB2 Legacy survey an area of about one square degree centered design employed 36 pointings of 30ks ex- on Cyg OB2 (Wrightet al., 2014a). Supple- posure each in a 6x6 raster array heavily mentaryopticalandinfrareddata,requiredto (∼ 50%) overlapped in order to overcome classifytheX-raysourcesandfollowthrough the Chandra lower off-axis sensitivity and with the scientific objectives of our survey, produce a relatively uniform exposure over have been retrieved from available public surveys(SDSS/DR8, IPHAS/DR2, UKIDSS, the inner 0.5 deg2 corresponding to a depth of 116 ks. The full survey exposure was 2MASS) and obtained from dedicated obser- 1.08 Msec, it covered about 1 square degree vationswithOSIRIS@GTC(Guarcelloet al., centered at 20h 33m 12s +41 19′ 00′′, and 2012)andSpitzer(Beerer et al.,2010;Guarcello et al., was performed over a 6-weeks period from 2013). January–March 2010, employing the Ad- A crucial step in being able to use the vanced CCD ImagingSpectrometer (ACIS-I; available multi-wavelength catalogs consists Garmireet al.2003). of determining which objects in one catalog The point source catalog was constructed correspond to sources in another. Given the using a combination of standard CIAO pro- largestellardensityinCygOB2,thedepthof cessing tools, source detection algorithms, the OIR catalogs used, and the large fore- 3 and theACIS Extract(AE; Brooset al. 2010) X-ray luminosity of 7 × 1029 erg cm2 s−1 in software package. In order to have an ho- thecentral0.5squaredegrees. Afulldescrip- mogeneous astrometry among the various tion of the catalog construction is presented Chandra pointings,Chandra astrometry was byWrightet al.(2014a),whileanassessment re-mapped to that of the Two Micron All ofthecatalogcontentsandsensitivityaredis- Sky Survey (2MASS; Cutri et al. 2003) us- cussed byWright(2014,in preparation). ing bright X-ray sources with unambiguous cross-matchesto2MASSobjects. Sourcede- 3. The optical-infrared catalog tection was applied to the reduced and pro- Theoptical-infrared (OIR)catalogusedin cessed Chandra data in three energy bands: thiswork containsphotometricdataretrieved soft (0.5–2.0 keV), hard (2.0–7.0 keV), and broad (0.5–7.0 keV) using different algo- from severalpubliclyavailablecatalogs: rithms: An enhanced version of the CIAO toolwavdetectthatperformssourcedetection • the optical catalog in r, i, z bands on multiple non-aligned X-ray observations, (65349 sources) obtained from obser- detecting sources that may not be detected vations with the Optical System for in the individual observations, and pwde- ImagingandlowResolutionIntegrated tect (Damianiet al., 1997). This process Spectroscopy (OSIRIS), mounted on was augmented by several hundred sources the10.4mGranTelescopioCANARIAS from lists of known Cyg OB2 members, in- (GTC) of the Spanish Observatorio cluding O and B-type stars (Wrightet al., del Roque de los Muchachos in La 2014,submitted) and young A-type stars Palma (Cepaet al., 2000) compiled by (Drew et al.,2008), creating atotalof13,041 Guarcello etal. (2012); sourcecandidates. • thesecondreleaseoftheopticalcatalog Candidate source photometric extraction inr′, i′, Hαbands(24072sources)ob- andvalidationwasperformedusingAEinan tainedfromobservationswiththeWide iterative fashion, whereby validated sources Field Camera (WFC) on the 2.5m were excluded from regions used for back- Isaac Newton Telescope (INT) for the ground estimation, followed by a repeat of INT Photometric Hα Survey (IPHAS, the AE extraction and validation. Owing to Drew etal.2005;Barentsen et al.2014); the overlapping source and background re- gions in the most crowded areas of the sur- • the SDSS catalog (eighth data release, vey, several iterations of this process were DR8, 27531 sources, Aiharaet al., required. The resulting X-ray catalog con- 2011)in u, g, r, i, z bands; tains 7924 verified sources, the vast major- • the UKIDSS/GPS catalog in the JHK ity of which were observed at least 4 times bands(Hewett etal.,2006;Lucas et al., in overlapping tiles, and detected within 4 2008),containing273473sources,from arcmin of the telescope optical axis at least observationstaken withtheWideField once. The source positional uncertainty is typically< 0.5′′ andweestimatea90%com- Camera (WFCAM, Casali et al., 2007) on the United Kingdom InfraRed Tele- pleteness for stellar X-ray sources down to scope (UKIRT), compiled adopting a 4 newphotometricprocedure(Kinget al., 4. The adopted matching procedures 2013) based on the UKIDSS images TheX-raysourcesinoursurveyneedtobe (Dyeet al.,2006); classified also according to their OIR prop- • the2MASS/PSCcataloginJHK (Cutri et al., erties (Kashyap, 2014,in preparation). Erro- 2003, 43485sources); neous matches between the OIR and X-ray catalogs will result in wrong classifications, • thecatalogintheSpitzer/IRAC3.6, 4.5, affectingthescientificoutcomeofoursurvey. 5.8, 8.0µm and MIPS 24µm bands For this reason, particular attention must be (149381 sources) from the Spitzer given to how the OIR and X-ray catalogs are LegacySurvey ofthe Cygnus X region merged. Spitzer(Beerer etal., 2010). Asimplematchingprocedurebasedonthe positions of the sources and using a fixed As described in Guarcello et al. (2013), matching radius (i.e. considering as real these catalogs have been combined into a counterparts the OIR and X-ray pairs with a largeOIRcatalogcontaining329514sources. separation smaller than a given threshold) is The matching procedure was divided into unsuitable to our case for two reasons. First, three steps. First, a combined optical cata- thePointSpreadFunction(PSF)oftheChan- log was produced by matching the OSIRIS, dra mirrors increases in size with increasing IPHAS, and SDSS catalogs. Second, an off-axis angle. For this reason, the positional infrared catalog was created by matching accuracy of the X-ray sources is not constant UKIDSS, 2MASS and Spitzer data. In the across the field. Second, while the optical last step, the two catalogs were merged data are dominated by the foreground stel- into an unique OIR catalog. All the data lar population, and the infrared data by the used here, except those from OSIRIS, are background sources, in both cases with an available over the entire area surveyed with approximately uniform spatial distribution, Chandra/ACIS-I. The OSIRIS data are only most of the X-ray sources with OIR coun- availableina central 40′ ×40′ field. terparts are expected to be associated with The OIR catalog includes stars associ- Cygnus OB2 and clustered at the locations ated with Cygnus OB2 down to very low of the various subclusters of the association. masses. Assumingadistanceof1.4±0.08kpc Thedensityofthesourcesnotassociatedwith (Rygl et al., 2012), an average extinction the X-ray population (the uncorrelated pop- A = 4.3m (Guarcello et al., 2012), and V ulation) is high, and any attempt at match- adoptingtheisochronesofSiess etal.(2000), ing the OIR and X-ray catalogs using only we can estimate that we have good quality positional information will inevitably result optical and infrared data for members down in large numbers of spurious matches. It is to 0.2M , allowing us an unprecedentedly ⊙ necessary, then, to use a more sophisticated deep andcompletestudyofthepopulationof approach. CygnusOB2. Onemethodusedsuccessfullyinsimilarly challenging matching procedures is based on MaximumLikelihood(ML,Sutherland& Saunders, 5 1992)approachesthattakesintoaccountboth lated OIR sources and the observed magni- the spatial separation between the different tude probability distribution of all the OIR catalog sources (OIR and X-ray in our case) sources in the m band, respectively, are de- and how the magnitude of the OIR sources scribed inthenextsections. comparewiththoseexpectedfortherealOIR counterparts of the X-ray sources (the corre- 4.1.1. The observed magnitude distribu- lated population). Several ML methods have tions been used in the literature (i.e. Tayloret al., In Eq. 1 q(m) and n(m) are the probabili- 2005; Gilmouretal., 2007; Rumbaughet al., ties to observe, respectively, a correlated and 2012). In thiswork, rather than rely on a sin- ageneric OIRsourcewithmagnitudem. The gle matching procedure, we adopt three dif- main differencebetween themethodweused ferent methods. The final OIR-X-ray catalog and that defined in Smithet al. (2011) is that will contain all the pairs matched with each the latter method is applied using one optical of the three methods, with the subsample of catalog. Our multi-wavelength catalog con- themostreliablematchesproperly tagged. tains data from various optical and infrared catalogs, and most of the sources lack a de- 4.1. Modified Smith etal. (2011) proce- tection in one or more of them. For instance, dure highly embedded or extinguished objects in Oneofthemethodsthat weadoptedis de- the background, or even associated with the fined inSmithet al.(2011),slightlymodified mostobscuredregionsofCygnusOB2, often in order to optimize it for our specific multi- lack opticalcounterparts. wavelength case. In this approach, the prob- Forthisreason,weseek tousealltheOIR ability that a given OIR source is the correct information availablein order to improvethe counterpart of a nearby X-ray source is cal- completeness of the final OIR+X-ray cata- culatedstartingfromthefollowinglikelihood log. We calculated, then, q(m) and n(m) for ratio: each band available in our OIR catalog. We q(m) f (r) LR = (1) also defined for each OIR source a represen- n(m) tative band, which is the first one available In this definition, f (r) is the radial distribu- and with an error smaller than 0.1m proceed- tion function of the separations between OIR ingfromshortertolongerwavelengths,start- andX-raypairsasafunctionofthepositional ing from the r band. In the optical bands we error: used preferentially the OSIRIS photometry. The IPHAS photometry has been used when 1 −r2 f (r) = exp (2) OSIRIS data are not available, and SDSS 2πσ2 2σ2 ! pos pos photometry when there are no other optical data. Ourmain catalog in the near infrared is Here, r is the positional offset between OIR UKIDSS, while 2MASS data are used when and X-ray sources, and σ the positional pos UKIDSSdataarenotavailableorofbadqual- uncertainties, calculated adding in quadra- ity. This priority among the available bands turetheOIRandX-raypositionaluncertainty. has been arbitrary chosen, after having ver- The quantities q(m) and n(m), i.e. the mag- ified that the chosen order was not affect- nitude probability distributions of the corre- 6 ing our results, since it was possible to de- where nearby(m) is the magnitude distri- fine a representative band for almost all the bution of the nearby sources, N is the total x bands. Forthevastmajorityofsourcesinour numberofX-ray sources(7924),∆ isthe match OIR catalog, the representative bands are the matchingareawitharadiusof10′′,∆ isthe tot OSIRIS r ortheUKIDSS J bands. totalareaofoursurvey(1squaredegree),and Toobtainn(m),wefirstcalculated theob- N(m) is the observed magnitude distribution served magnitude distributions in each band n(m) × ∆tot. By using this formula, we are of our catalog, sampled in bins of 0.25m of also assuming that the uncorrelated sources width. The probability n(m) for a given OIR are uniformly distributed in the survey area, sourceisthengivenbythefractionofsources whichmaybeincorrectincaseofnotuniform observed in our OIR catalog in the represen- extinctionsuchas in Cyg OB2. tative band in the same magnitude bin, nor- Fig. 1 shows the magnitude distributions malizedby thetotalareaofthesurvey. in the OSIRIS r and UKIDSS J bands for the entire OIR catalog, the nearby sources, 4.1.2. The correlated magnitude distribu- andtheexpectedcorrelatedpopulation. Inthe tions optical band there is not much difference be- tweenthesedistributions,noteveninthefaint The calculation of q(m) for each OIR part. This may indicate that this method is source is more complicated, since it requires not very effective in removing fortuitous co- thecomputationofthemagnitudedistribution incidences between X-ray sources and faint of the expected correlated population, after background optical sources. The correction considering and removing the contribution used to remove the uncorrelated population from the uncorrelated population. Follow- has been more effective in the J band, as ingSmithetal.(2011),theinitialapproxima- demonstrated by the difference between the tion of the expected magnitude distribution total distribution, centered at J = 19.5m, and of the correlated population is obtained from the expected correlated distribution, centered all the OIR sources closer than 10′′ to the X- intherange16m < J < 17m. raysources(hereafterthenearbypopulation). Even at large off-axis angles, this matching 4.1.3. ReliabilityassociatedwithanOIR+X- radius is significantly larger than the propa- raypair gatedpositionaluncertainty,resultinginase- lection of 78182 nearby OIR sources for the Once we have calculated f (r), q(m), and 7924 X-ray sources. The expected magni- n(m), we can obtain LR for each pair of X- tude distribution of the correlated population ray and OIR sources from Eq 1. Using the is obtained from that of the nearby popula- valueofLR,wecanassignaprobabilitythata tion, by subtracting in each magnitude bin givenOIRsourceistherealcounterpartofthe the number of uncorrelated sources expected nearby X-ray source, and compare it with a to match the positions the X-ray sources and chosenthreshold(seeSect. 4.1.4). Thisprob- fallinginthegivenbin ofmagnitude: ability is calculated comparing the observed LR valuewitha distributionof LR valuesob- tained from 200000 test X-ray sources uni- ∆ q(m) = nearby(m)−N(m)×N × match, (3) formly distributed across the field. The use x ∆ tot 7 Fig. 1.— Magnitudedistributionsin the OSIRIS r (left panel) and UKIDSS J (right panel) bands for the entire OIR catalog (solid histogram), the nearby sources (dotted histogram), and the ex- pected correlated distributions(dashed histograms)usingEq. 3(SM method) of uniform spatial distribution of the X-ray whereR isthereliabilitythattheOIRsource ij sources is an acceptable approximation since i is the real counterpart of the X-ray source the OIR catalog, dominated by background j; N is the number of simulated LR val- sim NIR sources, has a nearly uniform spatial ues; N isthenumberofsimulatedLRvalues gt density. These test sources were matched larger than the one observed between the ij with the OIR catalog, obtaining a distribu- pair: tion of simulated LR values from more than N = N LR > LR (5) gt simul ij 70000 pairs (the exponential form in f (r) (cid:16) (cid:17) In this way each ij pair (i.e. each pair of X- cuts any match between sources more dis- ray and OIRsources)hasan associatedprob- tant than few arcseconds). The reliability as- abilitythattheOIRsourceistherealcounter- sociated with each match between the X-ray part oftheX-ray source. and OIR sources in our catalog, which is, by definition, the probability that the given OIR 4.1.4. Matchresults source is the real counterpart of the nearby X-ray source, isthen calculated as: The last step consists in assigning a prob- abilitycut-off,i.e. todecidewhatisthemini- N R = 1− gt (4) mum reliability that identifies real matches. ij N sim 8 This was performed by studying how the number of spurious matches out of the total numberofmatchesincreaseswithdecreasing the cut-off. To obtain the numberof spurious matches, we repeated the matching proce- dure after “randomizing” our X-ray catalog, i.e. applying rigid translations of 1′ to the X-ray sources four times, each time with a different combination of positive and nega- tive rigid translations in RA and DEC. The number of expected spurious matches corre- sponding to given test values of the cut-off is the mean of the number of matches obtained withthesefour“randomized”X-raycatalogs. Wethen fixed ourcut-off valueas theonefor whichtheratioofspurioustototalmatchesis ∼ 10% (correspondingtoR = 0.95). cut−off Fig. 2.—Numberofreal(solidline)andspu- Fig. 2 shows how the number of total and rious(dashed line)matches obtainedwithin- spurious matches, together with their ratio, creasing the reliability threshold in the SM varywiththetestthresholds. Withthechosen method. The numbers over the solid line cut-off of 0.95, we matched 5180 pairs, with show how the fraction of spurious matches 4946 single matches. Hereafter, this method decreases withincreasingthethreshold iscalled theSM method. 4.2. Matching procedure with the corre- the nearby population the expected contribu- lated population from an accurate tion of the uncorrelated OIR sources. This positionmatch. correction was necessary, as proved by the very large number of nearby sources found The second matching procedure is based (78182)andtheriskthattheSMmethodmay onadifferentdefinitionofthecorrelatedpop- not be very effective in removing spurious ulation. The definitions of LR (Eq. 1), of coincidencesbetween X-ray andfaint optical the observed magnitude distributions n(m), sources in the background. However, since as well as that of the reliability (Eqs. 4 and the chances that OIR sources nearby X-ray 5) and the procedure to define the threshold positions are real counterparts decrease with (Sect. 4.1.4)arethesameasthoseadoptedin increasing separation, a different estimate of theprevioussections. thecorrelatedpopulationcanbefoundwitha In Sect. 4.1.2 we calculated the magni- nearest-neighbor match using suitable small tude distribution of the expected correlated matching radii estimated with a detailed sta- population starting from a position match tisticalanalysisofreal andspuriousmatches. between the X-ray and OIR catalog with a large matching radius (10′′), and then we used a statistical approach to remove from 9 4.2.1. Thecorrelatedpopulationfromaccu- i.e. by comparing the ratio of the numbers ratenearest-neighbormatch of spurious coincidences to that of the to- tal matches obtained with increasing test val- In this procedure, we obtained a corre- ues of A and r . The spurious coincidences min latedpopulationfromwhichwederivedq(m) are calculated by matching the OIR catalogs from an accurate nearest-neighbor match. with“randomized”X-raycatalogs(asinSect. The matching radius used in this procedure 4.1.4); while the total number of matches by must takeinto account the degradationof the combining the OIR catalogs with the “real” PSF in the X-ray images at increasing off- X-ray catalog (i.e. with no positional offset axis angles and the photon statistics of the added). We first evaluated A and then r , in min X-ray source. In order to do that, we used both cases as the largest test values at which an individualmatching radius for each X-ray the spurious matches reached ∼ 10% of the sourcewhichisproportionalto theX-ray po- realmatches. Table1liststhevaluesofAand sitionaluncertainty,thelattercalculated asin r found for the optical, JHK and Spitzer min Kimet al. (2007): catalogs, together with the total number of r = A×σ (6) matches. The catalog of the expected corre- match pos latedsourcesobtainedbymergingtheresults log σ = 0.1137Θ−0.46log(C)−0.2398 pos ofthesethreenearest-neighbormatchesnum- (cid:16) (cid:17) (7) bers 5820sources, manylessthanthenearby log σ = 0.1031Θ−0.1945log(C)−0.8034 pos sources defined in Sect. 4.1.2 and compa- (cid:16) (cid:17) (8) rable to the final number of the OIR+X-ray wherer istheindividualmatchingradius, match pairs matched in the merged catalog (Sect. A is a coefficient to be evaluated, σ is the pos 5). This catalog has been used to define the positional uncertainty, Θ is the off-axis angle magnitudedistributionq(m)usedinEq. 1. of the X-ray sources and C is the net num- Fig. 3 shows the distributions of the ber of counts. Following Kimet al. (2007), OSIRIS r and UKIDSS J magnitudes for Eq. 7 is applied to sources with less than 133 all the OIR sources and for the expected counts;Eq. 8 tobrightersources. correlated population found with the accu- Given the different depth and spatial dis- rate nearest-neighbor match described here. tribution of the optical, JHK (UKIDSS and Comparison with Fig. 1 reveals that the 2MASS),andSpitzercatalogs,wedecidedto magnitude distributions obtained with this perform the nearest-neighbor match for each of these three catalogs separately and then to merge the results. The crucial step here Table 1: Results of the close-neighbor is to estimate the coefficients A for the three matches catalogs, together with a minimum allowed matchingradius(r ). Theuseofr isnec- OIR catalog r A N.matches min min min essarysincethepositionalerrorsinthecenter Optical 0.6′′ 1.4 4917 of the ACIS field are very small, resulting in JHK 0.5′′ 0.9 5025 unacceptably lowmatchingradii. Spitzer 0.5′′ 1.3 5278 The procedure adopted to calculate these parametersissimilartothatdefinedinSect.4.1.4, 10