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Luminosity-dependent evolution of soft X-ray selected AGN-New Chandra and XMM-Newton surveys PDF

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Preview Luminosity-dependent evolution of soft X-ray selected AGN-New Chandra and XMM-Newton surveys

A&A441,417–434(2005) Astronomy DOI:10.1051/0004-6361:20042134 & (cid:1)c ESO2005 Astrophysics Luminosity-dependent evolution of soft X-ray selected AGN New Chandra and XMM-Newton surveys G.Hasinger1,T.Miyaji2,andM.Schmidt3 1 Max-Planck-InstitutfürextraterrestrischePhysik,Postf.1312,85741Garching,Germany e-mail:[email protected] 2 DepartmentofPhysics,CarnegieMellonUniversity,5000ForbesAvenue,Pittsburg,PA15213,USA e-mail:[email protected] 3 CaliforniaInstituteofTechnology,Pasadena,CA91125,USA e-mail:[email protected] Received7October2004/Accepted10June2005 Abstract. We present new results on the cosmological evolution of unabsorbed (type-1) active galactic nuclei (AGN) se- lectedinthesoft(0.5−2keV)X-rayband.FromavarietyofROSAT,XMM-NewtonandChandrasurveysweselectedatotal of∼1000AGNwithanunprecedentedspectroscopicandphotometricoptical/NIRidentificationcompleteness.Forthefirsttime weareabletoderivereliablespacedensitiesforlow-luminosity(Seyfert-type)X-raysourcesatcosmological redshifts.The evolutionarybehaviourofAGNshowsastrongdependenceonX-rayluminosity:whilethespacedensityofhigh-luminosity AGNreachesapeakaroundz∼2,similartothatofopticallyselectedQSO,thespacedensityoflow-luminosityAGNspeaks atredshiftsbelowz=1.ThisconfirmspreviousROSATfindingsofaluminosity-dependentdensityevolution.Usingarigorous treatmentoftheopticalidentificationcompletenessweareabletoshowthatthespacedensityofAGNwithX-rayluminosities L <1045ergs−1declinessignificantlytowardshighredshifts. x Keywords.galaxies:active–X-rays:general 1. Introduction the origin of and accretion history onto supermassive black holes, which are now believed to occupy the centers of most InrecentyearsthebulkoftheextragalacticX-raybackground galaxies.X-raysurveysarepracticallythemostefficientmeans inthe0.1−10keVbandhasbeenresolvedintodiscretesources of findingactivegalactic nuclei(AGNs)overa wide rangeof withthedeepestROSAT,ChandraandXMM-Newtonobserva- luminosityand redshift.Enormouseffortshavebeenmadeby tions (Hasinger et al. 1998; Mushotzky et al. 2000; Giacconi several groups to follow up X-ray sources with major opti- et al. 2001, 2002; Hasinger et al. 2001; Alexander et al. cal telescopes around the globe, so that now we have fairly 2003; Worsley et al. 2004, 2005). Optical identification pro- complete samples of X-ray selected AGNs. In this work we grammes with Keck (Schmidt et al. 1998; Lehmann et al. concentrate on unabsorbed (type-1) AGN selected in the soft 2001;Bargeretal.2001,2003)andVLT(Szokolyetal.2004; (0.5−2 keV) X-ray band, where due to the previous ROSAT Fiore et al. 2003) find predominantly unobscured AGN–1 at work (see Miyaji et al. 2000, 2001, hereafter PapersI and II) X-rayfluxesSX > 10−14 ergcm−2s−1,andamixtureofunob- completesamplesexist,withsensitivitylimitsvaryingoverfive scured AGN–1and obscuredAGN–2at fluxes10−14 > SX > orders of magnitude in flux, and survey solid angles ranging 10−15.5 ergcm−2s−1 witheverfainterandredderopticalcoun- fromthewholehighgalacticlatitudeskytothedeepestpencil- terparts, while at even lower X-ray fluxes a new population beam fields. These samples enable us to construct and probe of star forminggalaxiesemerges(Hornschemeieret al. 2003; luminosityfunctionsovercosmologicaltimescales,withanun- Rosatietal.2002;Normanetal.2004).Atopticalmagnitudes precedentedaccuracyandparameterspace. R > 24 these surveys suffer from large spectroscopic incom- Conceptually,spacedensitiesandluminosityfunctionsare pleteness, but deep optical/NIR photometry can improve the simplyderivedby dividingthe observednumberofobjects N identification completeness significantly, even for the faintest bythevolumeV,inwhichtheyhavebeensurveyed.Thebinned opticalcounterparts(Zhengetal.2004;Mainierietal.2005). luminosityfunctionderivedin thisfashion generallydoesnot TheAGN/QSOluminosityfunctionanditsevolutionwith represent the center of the bin. In Paper II, we introduced cosmictimearekeyobservationalquantitiesforunderstanding the estimator N /N , where N is the number of objects obs mdl mdl Article published by EDP Sciences and available at http://www.edpsciences.org/aaor http://dx.doi.org/10.1051/0004-6361:20042134 418 G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN expected from an analytical representation of the luminosity andGalacticabsorption.TypicalvaluesoftheGalacticneutral function. Scaling the model value of the analytical function hydrogencolumndensityare(0.5−1)×1020cm−2forthedeep at the bin center bythe estimator removesthe binningbias to surveysandamaximumof16×1020cm−2forasmallportionof firstorder.ThismethodisappliedinSect.4.Aquitedifferent theskycoveredbytheROSATBrightSurvey(RBS). Because methodbasedon1/V values(Schmidt1968)forindividual theband,inwhichtheAGNareselected,isthesameastheone max objectsis usedin Sect. 5. It involvesa derivationofthe zero- forwhichwecalculatethefluxes,systematicdifferencesinthe redshift luminosity function that is free of binning bias. The trueAGNpowerlawindiceshaveanegligibleeffectonthede- luminosityfunctionathigherredshiftsisagainderivedbyem- rivedfluxes.AssumingspectralindicesintherangeΓ = 1−3, ployingananalyticalrepresentationoftheluminosityfunction the conversion between the observed 0.5−2 keV count rates andscalingitbytheratioofobservedoverexpectednumbers. and the X-ray flux S (here and hereafter, S represents the x x Theuseofindividual1/V valuesinthiscaseallowsaccount- 0.5−2keVfluxandS isthesamequantitymeasuredinunits max X14 ingforaneffectiveopticalmagnitudelimitbeyondwhichred- of10−14ergs−1cm−2)variesbylessthan10%. shiftshavegenerallynotbeenobtainedinsomesurveys. The surveys we have used are summarized in Table 1. A Throughout this work we use a Hubble constant H0 = total of 944 X-ray selected type-1 AGN were compiled from 70h70kms−1Mpc−1andcosmologicalparameters(Ωm,ΩΛ)= eightindependentsamplescontainingatotalof2566softX-ray (0.3,0.7)consistentwiththeWMAPcosmology(Spergeletal. sources. The number of unidentified sources1 in these sam- 2003). ples is only 86 (of which 57 could be AGN–1), yielding an unprecedented identification fraction of 97%. Due to the ex- treme faintness of the optical counterparts, the lowest iden- 2. TheX-rayselectedAGN–1sample tification fractions are achieved in the recent deepest sam- ForthederivationoftheX-rayluminosityfunctionandcosmo- ples: 87% for the XMM-Newton survey in the LockmanHole logical evolution of AGN we have chosen well-defined flux- and88%intheCDF–N.Asurprisinglyhighidentificationfrac- limited samples of active galactic nuclei, with flux limits and tion of 98% has been achieved in the CDF–S through the survey solid angles ranging over five and six orders of mag- utilization of photometric redshifts based on extremely faint nitude, respectively. To be able to utilize the massive amount optical/NIRphotometry. ofopticalidentificationworkperformedpreviouslyona large For thecomputationofthe softX-rayluminosityfunction number of shallow to deep ROSAT surveys, we restricted the SXLF,itisimportanttodefinetheavailablesurveysolidangle analysistosamplesselectedinthe0.5−2keVband.Inaddition as a function of limiting flux. In case there is incompleteness to the ROSATsurveys already used in Papers I and II, we in- in the spectroscopicidentifications in the ROSATsurveys, we cludeddatafromtherecentlypublishedROSATNorthEcliptic havemadetheusualassumptionthattheredshift/classification PoleSurvey(NEPS,Gioiaetal.2003;Mullisetal.2004),from distribution of these unidentified sources is the same as the an XMM-Newton observationof the Lockman Hole (Mainieri identified sources at similar fluxes by defining the “effective” et al. 2002) and the Chandra Deep Fields South (CDF–S, surveysolid angle as the geometricalsurveysolid angle mul- Szokoly et al. 2004; Zheng et al. 2004; Mainieri et al. 2005) tipliedbythecompletenessoftheidentifications(seePaperI). andNorth(CDF–N,Bargeretal.2001,2003).Inordertoavoid Thisassumptionisnotcorrectwhenthesourceisunidentified systematicuncertaintiesintroducedbythevaryingandapriori due to non-random causes, in particular its optical faintness. unknown AGN absorption column densities we selected only Thetreatmentofthisidentificationincompletenessandtheef- unabsorbed (type-1) AGN, classified by optical and/or X-ray fect of the optical limit on the derived space densities is dis- methods.Weareusinghereadefinitionoftype-1AGN,which cussedindetailinSect.5. is largely based on the presence of broad Balmer emission In several surveyswe had to choose an X-ray flux limit a lines and small Balmer decrement in the optical spectrum of posteriori,basedonopticalcompletenesscriteria,i.e.maximis- the source (optical type-1 AGN, e.g. the ID classes a, b, and ing the number of optically identified sources, while simulta- partlycinSchmidtetal.1998),whichlargelyoverlapstheclass neously minimising the number of unidentified objects. This of X-ray type-1 AGN defined by their X-ray luminosity and procedurecanintroducea biasagainstopticallyfaintsources, unabsorbedX-rayspectrum(Szokolyetal.2004).However,as if the reason for the missing redshift is the optical faintness Szokolyet al. show,at low X-rayluminositiesandintermedi- of the source and in fields with relatively few objects. We ateredshiftstheopticalAGNclassificationoftenbreaksdown havetriedtominimisetheimpactofthis“gerrymandering”ef- because of the dilution of the AGN excess light by the stars fect, e.g. by allowing a number of unidentified sourcesto en- in the host galaxy (see e.g. Moran et al. 2002), so that only terthesampleandthendefiningthecorrespondingX-rayflux an X-ray classification scheme can be utilized. Schmidt et al. limits as the geometric mean between the last identified and (1998) have already introduced the X-ray luminosity in their the next unidentified source. In addition, the wide range for classification.ForthedeepXMM-NewtonandChandrasurveys X-ray and thus optical flux limits in our survey tends to re- weinadditionusetheX-rayhardnessratiotodiscriminatebe- ducebiases,whichoccuratthefluxlimitofindividualsurveys. tweenX-raytype-1andtype-2AGN,followingSzokolyetal. (2004). 1 Wecallunidentified sourcesthose, whichdonot haveareliable In order to convert the count rates observed in the redshift determination, either through spectroscopy or through pho- 0.5−2keVbandtounabsorbed0.5−2keVfluxes,weassumed tometric redshifts; however practically all of these have optical or a power law AGN spectrum with a photon index of Γ = 2.0 NIRcounterparts. G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN 419 Table1.ThesoftX-raysample. Surveya Solidangle SX14,lim Ntot NAGN−1b Nucnid [deg2] [cgs] RBS 20391 ≈250 901 203 0 SA–N 684.0–36.0 47.4–13.0 380 134 5 NEPS 80.8–70.5 12.4–10.1 252 101 1 RIXOS 19.5–15.0 10.2–3.0 340 194 14 RMS 0.74–0.32 1.0–0.5 124 84 7 RDS/XMM 0.126–0.087 0.38–0.13 81 48 8 CDF–S 0.087–0.023 0.022–0.0053 293 113 1 CDF–N 0.048–0.0064 0.030–0.0046 195 67 21 Total 2566 944 57 aAbbreviations–RBS:theROSATBrightSurvey(Schwopeetal.2000);SA–N:ROSATSelectedAreasNorth(Appenzelleretal.1998);NEPS: ROSATNorthEclipticPoleSurvey(Gioiaetal.2003);RIXOS:ROSATInternationalX-rayOpticalSurvey(Masonetal.2000),RMS:ROSAT Medium Deep Survey, consisting of deep PSPC pointings at the North Ecliptic Pole (Bower et al. 1996), the UK Deep Survey (McHardy et al.1998),theMarano field(Zamorani etal.1999)andtheouter partsof theLockman Hole(Schmidtetal.1998;Lehmannetal.2000); RDS/XMM:ROSATDeepSurveyinthecentralpartoftheLockmanHole,observedwithXMM-Newton(Lehmannetal.2001;Mainierietal. 2002;Faddaetal.2002);CDF–S:theChandraDeepFieldSouth(Szokolyetal.2004;Zhengetal.2004;Mainierietal.2005);CDF–N:the ChandraDeepFieldNorth(Bargeretal.2001,2003). bExcludingAGNswithz<0.015. cObjectswithoutredshifts,buthardnessratiosconsistentwithtype-1AGN. Fig.2.ThesurveysolidangleofthecombinedsoftX-raysampleas a function of flux. The solid line shows the case where the CDF–N sampleisexcludedasusedinSect.4.ThedottedlineincludesCDF−N Fig.1.TheAGN–1softX-raysampleinthez-logL plane. andisusedinSect.5. x 2.1.TheROSATBrightSurvey(RBS) Theproblemofmissingredshiftsinthefaintestsurveysisad- TheRBSidentifiedthebrightest∼2000X-raysourcesdetected dressedspecificallyinSects.4and5. in the ROSAT All–Sky Survey (RASS, Voges et al. 1999) at Below we summarize our sample selection and complete- high galactic latitude, |b| > 30◦, excluding the Magellanic ness for each survey. Figure 1 shows the AGN–1 sample in Clouds and the Virgo cluster, with ROSAT PSPC count rates the redshift – luminosity plane. Figure 2 gives the combined above 0.2s−1. This program achieved a spectroscopic com- solid angle versus flux curve. Both the sample and the solid pleteness of 99.5% (Schwope et al. 2000). We selected the anglecoverageareavailableincomputerreadableformunder sub-sample of 931 sources with count rates above 0.2 s−1 in http://mpe.mpg.de/˜ghasinger. the ROSAT0.5−2 keV band (PSPC channels52−201),which 420 G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN is 100% identified. Since the absorption in our galaxy varies high Galactic latitude fields (|b| > 28deg) and observed with from place to place, the same count rate limit correspondsto the Position Sensitive Proportional Counter (PSPC) detector different0.5−2keV flux limits based on the differentgalactic withaminimumexposuretimeof8ks.Thesurveycomprises N values. The N value ranges from (0.5−16)× 1020 cm−2 82ROSATPSPCfieldsandmadeuseofthecentral17arcmin H H intheRBSsurveyarea.Correspondingly,thesurveysolidan- ofeachfield,however,excludingthetargetregionforpointings gle varies steeply with flux from about 3000 deg2 at a flux onknownX-raysources.Thetotalsurveycontains395X-ray limit of S = 246 to a total of 20391 deg2 at a flux limit sources,selectedinthePSPC0.5−2keVband.Afluxlimitof X14 ofS =360. S =3.0wasadoptedforthesurvey,substantiallyabovethe X14 X14 detectionthreshold of each field, however,the actual spectro- scopic completeness limit varies from field to field. We have 2.2.TheRASSSelected-AreaSurveyNorth(SA–N) chosenastrategy,whichononehandmaximisesthesampleof identifiedAGN–1andontheotherhandminimisesthenumber This survey gives optical identifications of a representative sample of northern (δ > −9◦) RASS sources in six study ofunidentifiedsources.Thereare51fields(12.3deg2)identi- areas outside the Galactic plane (|b| > 19.6◦) with a total fiedcompletelydowntothesurveyfluxlimit.Threefieldshave of 685deg2. A count rate limited complete RASS subsam- suchalowidentificationfraction,thatweignorethem.Forthe remaining28fieldswe allowatmostoneunidentifiedsource. ple comprising 674 sources has been identified (Appenzeller Ifan unidentifiedsource hasthe lowestfluxof the subsample etal.1998).ThefieldsselectedforthesurveyhaveaGalactic column density in the range N = (2−11) × 1020 cm−2. We of a particular field, we excludethis sourceand raise the flux H limit for this field to the geometric average between the flux have further selected our sample such that each of the six fields has a complete ROSAT hard-band (0.5−2 keV; chan- of this source and that of the last identified source. This way nels 52−201) countrate-limited sample with complete identi- we can define a clean RIXOS sample comprising340objects fications (CR0.5−2keV > 0.01−0.05 ctss−1). To avoid overlap andonly14unidentifiedsources,i.e.anidentificationfraction of 95.9%.The surveysolid angle,correctedfor spectroscopic withtheRBS,thosesourcescommoninbothsampleswerere- incompleteness,risesfrom15.0deg2atS =3.0to19.5deg2 movedfromSA–N,yieldingatotalof406sourceswith98.5% X14 atS =10.2. spectroscopiccompleteness. X14 2.3.TheROSATNorthEclipticPoleSurvey(NEPS) 2.5.TheROSATMediumSurvey(RMS) The RASS data in a contiguousarea of 80.7 deg2 around the For this work we have grouped a number of medium-deep North Ecliptic Pole (Galactic latitude b > 29.8◦) have been ROSAT surveys with flux limits in the range SX14 = 0.5−1 usedtoconstructasurveyconsistingof445X-raysourcesde- intotherms.Inparticularthesecomprisepointedobservations tected above a 4σ threshold. Gioia et al. (2003) and Mullis at the North Ecliptic Pole (Bower et al. 1996), the UK Deep et al. (2004) have identified 99.6% of these sources and de- Survey (McHardy et al. 1998), the Marano field (Zamorani termined redshifts for the extragalactic objects. Since the ex- etal.1999)andtheouterpartsoftheLockmanHole(Schmidt posure in the ROSAT All-Sky Survey increases significantly et al. 1998; Lehmann et al. 2000). The North Ecliptic pole towardstheNorth-EclipticPole,theactualsurveysensitivityis pointingcoversthe same sky area as the center of the NEPS, a strongfunctionofeclipticlatitude.TheoriginalNEPSsam- however, to a flux limit of SX14 = 1.0. Again, we remove ple is selected in the full ROSATPSPC band.Forconsistency the overlapping sources between the two surveys. For the with the other surveys used in our work, we selected sources UK DeepSurveyandthe MaranoField we definea flux limit detectedsignificantlyinthePSPChardband(0.5−2keV;chan- of SX14 = 0.5, following Paper I. For the ROSAT PSPC sur- nels52−201)byspecifyingahardcountratelimitasafunction vey of the Lockman Hole we only chose the region not cov- ofeclipticlatitude.New0.5−2keVfluxeswerecalculatedfrom eredbythe deeperRDS/XMM survey(see Sect. 2.6)butoth- thehardPSPCcountratesinthesamewayasfortheRBSand erwiseselectedthecompletelyidentifiedsamplewiththesame SA–Nobjects,takingintoaccounttheGalacticneutralhydro- flux limits as those chosen for the ROSAT Ultradeep Survey gencolumndensityvaryingintherange2.6−6.2×1020 cm−2 UDSbyLehmannetal. 2001:SX14 > 0.96forPSPC off-axis acrosstheNEPSregion.Duetothelargegradientinexposure angles in the range 12.5−18.5 arcmin and SX14 > 0.55 for times,wehavecutthesampleto252sourceswithfluxesabove off-axisanglessmallerthan12.5arcmin.Overall,thermscon- S = 10.1,wherethesolidangleofthissurveyis70.5deg2, tains124sources,atan identificationcompletenessof94.4%. X14 increasing to 80.8 deg2 at S = 12.4. Only one of these Correspondingly,thecorrectedsurveysolidanglevariesinthe X14 sourcesremainsunidentifiedintheNEPSsample. range0.30−0.70deg2forfluxlimitsSX14 =0.5−1. 2.4.TheROSATInternationalX-ray/OpticalSurvey 2.6.DeepXMM-NewtonsurveyoftheLockmanHole (RIXOS) (XMM/RDS) The ROSAT International X-ray/Optical Survey (RIXOS, The Lockmam Hole (XMM/RDS) has been observed by Masonetal.2000) isamedium-sensitivitysurveyandoptical XMM-Newton a total of 17 times during the PV, AO−1 identification programof X-raysourcesdiscoveredin ROSAT and AO−2 phases of the mission, with total good exposure G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN 421 times in the range 680−880 ks in the PN and MOS instru- either from broad permitted Balmer lines or from the X-ray ments(seeHasingeretal.2001,2004andWorsleyetal.2004 luminosity and hardness, using HR < −0.2. We set our flux fordetails).SpectroscopicopticalidentificationsoftheROSAT limits such that we also have sufficient hard (2−8 keV) sen- sourcesintheLHhavebeenpresentedbySchmidtetal.(1998) sitivity to exclude objects with HR > −0.2 and to include as and Lehmann et al. (2000, 2001) and a new catalogue from manysourcesaspossiblewhichmeetthesecriteria.Unlikethe theXMM-NewtonPVphaseisgiveninMainierietal.(2002). CDF–S, the CDF–N exposure map has a complicated struc- SomephotometricredshiftshavebeendiscussedinFaddaetal. ture and a simple off-axis dependence of the limiting flux is (2002). Here we selected sources from the 770 ks dataset nota goodapproximation.Thuswe haveusedtherectangular (Brunner et al. 2005, in prep.) with additional spectroscopic regionof170arcmin2, whichhasthe deepestcoverageandis identificationsobtainedwiththeDEIMOSspectrographonthe mostlyco-spatialwiththeregioncoveredbyHSTACSinthe Keck telescope in spring 2003 and 2004 by M. Schmidt and GOODS project (Giavalisco et al. 2004; Cowie et al. 2004). P. Henry(Szokolyetal. 2005,in prep.).Inordertomaximise Within this region, the exposure and background are smooth thespectroscopic/photometriccompletenessofthesample,we enough that the photon counts limit of the detected sources selectedobjectsintwooff-axisintervals:S = 0.38foroff- can be approximated by a simple function of off-axis angle. X14 axisanglesintherange10.0−12.5arcminandS =0.13for In practice, due to statistical fluctuations, three sources have X14 off-axisanglessmaller than 10.0arcmin.The totalnumberof upper limits to HR between −0.1 and −0.2 and those have sourcesin theXMM/RDSis81,with8 potentialAGN–1still been considered to meet our hardness ratio criterion. Among unidentified. the128sourcesmeetingthesoftcountslimitandhardnessra- tiocriteria,20areunidentifiedand5arestars(85%complete- ness). Only one broad-line AGN had a harder hardness ratio 2.7.ChandraDeepFieldSouth(CDF–S) thanourlimit;thiswasalsoincludedinourtype-1AGNsam- ple.Theflux-solidanglerelationhasbeencalculatedfromthe We have used the catalogue of Giacconi et al. (2002) based “limiting flux map”, where the counts limit is divided by the on the 1 Ms observation of the CDF–S (Rosati et al. 2002). soft-bandexposuremap(inseconds)andmultipliedbythecon- SpectroscopicidentificationswiththeFORSinstrumentsatthe versionfactorof5×10−12ergs−1cm−2(Alexanderetal.2003). ESOVLThavebeenobtainedbySzokolyetal.(2004),yielding Duetotheincompletenessinthisfield,wheremostunidentified a spectroscopic completeness around 60%. Additional spec- sources are optically faint, this sample has not been included troscopic redshifts of CDF–S X-ray sources have been ob- in the analysis in Sect. 4, but considered in Sect. 5, where a tainedwiththeVIMOSspectrographattheESOVLT(Lefevre methodisdevelopedtoaccountfortheopticalmagnitudelimit et al. 2004). The field is also included in the COMBO-17 incalculatingthesurveyvolume. intermediate–band optical survey, which gives very reliable photometric redshifts for the brighter sources (Wolf et al. 2004). VerydeepNIRphotometryhasbeenobtainedwith the 3. Numbercountsfordifferentsourceclasses ISAAC camera at the VLT in conjunction with deep optical The combination of a large number of surveys with a wide imaging with the HST ACS as part of the GOODS project range of sensitivity limits and solid angle coverage presents (Dickinson & Giavalisco 2003; Mobasher et al. 2004). The a unique resource. On one hand, the surveys presented here CDF–S therefore offers the highest quality photometric red- resolve the soft X-ray backgroundalmost completely. On the shifts of faint X-ray sources, which are discussed in Zheng otherhand,we have an almostcompleteopticalidentification etal.(2004)andMainierietal.(2005).UsingtheISAACim- andredshiftdeterminationforallconstituents.Forthefirsttime ages, tentative photometric redshifts could even be assigned in any astrophysical waveband we are thus in the position to to several of the extreme X-ray/optical sources (EXOs) dis- study the complete contribution of different object classes to cussed by Koekemoer et al. (2004). We selected all sources the X-ray background and their evolution with cosmic time. from the Giacconi et al. 2002 catalogue within 10 arcmin Using the solid angle versus flux limit curve given in Fig. 2 fromtheChandrapointingcentersignificantlydetectedinthe wecompilednumbercountsforthetotalsampleincludingall 0.5−2 keV band. The sample thus containsa total of 293 ob- classes of sources and for the subclass of AGN–1. Figure 3 jects. Combining all spectroscopic and photometric redshifts, (top)showsthe cumulativesourcecounts. For clarity we also only2sourcesintheCDFSremainunidentified,ofwhichone show normalized differential source counts dN/dS S2.5 in couldbeanAGN–1.ThesurveysolidanglefortheCDF–Shas X14 X14 thebottompanelofFig.3.Euclideansourcecountswouldcor- been estimated using a simple off–axis dependent flux limit. respondtohorizontallinesinthisgraph. The solid angle increases from 0.023 deg2 at S = 0.0053 X14 For the totalsource counts,the well-knownbrokenpower to0.087deg2atS =0.027. X14 law behaviour is confirmed with high precision. We fitted a brokenpower law to the differentialsource countsand obtain 2.8.ChandraDeepFieldNorth(CDF–N) powerlaw indices of αb = 2.34±0.01and αf = 1.55±0.04 forthebrightandfaintend,respectively,abreakfluxofS = X14 We have used selected X-ray sources from the 2 Ms CDF–N 0.65±0.10andanormalisationofdN/dS =103.5±5.3deg−2 X14 source catalogue by Alexander et al. (2003) along with op- at S = 1.0 with a reduced χ2 = 1.51. The total dif- X14 tical identifications by Barger et al. (2003) for our AGN–1 ferential source counts, normalized to a Euclidean behaviour sample.FollowingSzokolyetal. (2004),weselectedAGN−1 (dN/dS ×S2.5 )isshownwith opensymbolsinFig.3.We X14 X14 422 G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN they compete with type-2 AGN and normal galaxies. We fit- ted a broken power law to the differential AGN–1 source counts and obtain power law indices of α = 2.55 ± 0.02 b and α = 1.15 ± 0.05 for the bright and faint end, respec- f tively,abreakfluxofS = 0.53±0.05,consistentwiththat X14 of the total source counts within errors, and a normalisation ofdN/dS = 83.2±5.5deg−2 atS = 1.0withareduced X14 X14 χ2 = 1.26.TheAGN–1differentialsourcecounts,normalized toaEuclideanbehaviour(dN/dS ×S2.5 )isshownwithfilled X14 X14 symbolsin Fig.3. Also shownisthe predictionofthe best-fit SXLFmodeldiscussedinSect.5. 4. TheSXLFandthespacedensityfunction 4.1.Basicmethod In this section, we present the binned Soft X-ray Luminosity Function(SXLF)oftype-1AGNs.Thebasicapproachistouse theNobs/NmdlestimatordescribedinPaperII.Theprocedureis outlinedbelow: 1. Dividethecombinedsampleintoseveralredshiftshells.For each redshift shell, fit the AGN XLF with a smooth ana- lyticalfunctionusinga Maximum-likelihoodfit overeach object(i.e.,withoutbinning;seePaperIfordetails). 2. For the fitted model in each redshift shell, check the absolute goodness of fit with one- and two- dimensionalKolmogorov–Smirnovtests(hereafter,1D–KS and2D−KStestsrespectively;Pressetal.1992;Fassano& Franceschini1987).TheK–Stestsarealsofortheunbinned datasetsandthusarefreefromartefactsandbiasesdueto binning. 3. Foreachredshiftshell,bintheobjectsinluminositybinsto Fig.3.a)CumulativenumbercountsN(>S)forthetotalsample(upper determinetheobservednumberofobjects(Nobs). thinline)andtheAGN–1subsample(lowerthickline).b)Differential 4. For each luminosity bin, evaluate the analytical fit at the numbercountsofthetotalsampleofX-raysources(opensquares)and centralluminosity/redshift(dΦmdl/dlogL ). theAGN–1subsample(filledsquares).Thedot-dashedlinesreferto x brokenpowerlawfitstothedifferentialsourcecounts(seetext).The 5. CalculatethepredictednumberofAGNsinthebin(Nmdl). dashed red line shows the prediction for type-1 AGN based on the 6. Thefinalresultis modeldescribedininSect.5. dΦ/dlogL =dΦmdl/dlogL · Nobs/Nmdl. (1) x x FortheanalyticalexpressionoftheSXLFineachredshiftshell, see thatthe totalsourcecountsatbrightfluxes,asdetermined weusethesmoothedtwopowerlawformula.Becausethered- by the ROSAT All-Sky Survey data, are significantly flatter shift shells have a finite widths, the fit results depend on the thanEuclidean,consistentwiththediscussioninHasingeretal. evolutionoftheSXLFwithinthem: (1993).Morettietal.(2003),ontheotherhand,havederiveda dΦ(L ,z) (cid:1)(cid:2) L (cid:3)γ1 (cid:2) L (cid:3)γ2(cid:4)−1 significantlysteeperbrightfluxslope(αb ≈ 2.8)fromROSAT x ∝ x + x ·ed(z,Lx), (2) HRIpointedobservations.Thisdiscrepancycanprobablybeat- dlogLx Lx,∗ Lx,∗ tributedtotheselectionbiasagainstbrightsources,whenusing where e (z,L ) is the density evolution factor. While the fi- d x pointedobservationswherethetargetareahastobeexcised. nal results are insensitive to the detailed behavior of e (z,L ) d x Type-1 AGN are the most abundant population of soft withintheshellatmostlocationsinthe(L ,z)space,wehave x X-ray sources. For the determination of the AGN–1 number takenourbest-estimatebyusingtheluminosity-dependentden- countsweincludethoseunidentifiedsources,whichhavehard- sityevolution(LDDE)modelderivedlaterinSect.4.4.Thelu- nessratiosconsistentwithAGN–1(acontributionof∼6%,see minosityrangeofthefitisfromlogL =42.0tothemaximum x Table 1). Figure 3 shows, that the break in the total source availableluminosityinthesample. counts at intermediate fluxes is produced by type-1 AGN, In this section, we tried to make the sample as complete whicharethedominantpopulationthere.Bothatbrightfluxes as possible, and we excluded the CDF–N from the analysis, and at the faintest fluxes, type-1 AGN contribute about 30% where the incompleteness fraction is significant and most of of the X-raysource population.At brightfluxes, they have to the unidentifiedsourcesare optically faint. All of the uniden- share with clusters, stars and BL-Lac objects, at faint fluxes tified sources in the ROSAT samples are optically bright and G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN 423 Table2.Best-fitparametersforeachredshiftshell. z-range z N Aa log La γ γ KS-probb c 44 x,∗ 1 2 0.0–0.2 0.1 268 (3.64±0.22)×10−7 43.45+0.32 0.35+0.31 2.1+0.4 0.84,0.17,0.14 −0.27 −0.40 −0.3 0.2–0.4 0.3 139 (9.76±0.83)×10−7 43.91+0.38 0.70+0.31 2.5+0.5 0.97,0.71,0.65 −0.36 −0.45 −0.3 0.4–0.8 0.6 143 (1.84±0.15)×10−6 43.91+0.41 0.84+0.23 2.3+0.3 1.00,0.03,0.08 −0.41 −0.32 −0.2 0.8–1.6 1.2 187 (1.19±0.09)×10−5 43.97+0.13 0.10+0.17 2.3+0.2 0.91,0.68,0.88 −0.13 −0.19 −0.1 1.6–3.2 2.4 110 (1.03±0.10)×10−5 44.39+0.16 0.15+0.16 2.3+0.2 0.91,0.55,0.44 −0.17 −0.18 −0.2 3.2–4.8 4.0 17 (4.53±1.10)×10−6 44.43+0.40 −0.26+0.56 1.9+0.4 0.95,0.21,0.39 −0.37 −0.75 −0.3 Parametervalueswhichhavebeenfixedduringthefitarelabelledby(*).aUnits–A44:h370 Mpc−3, Lx,∗:1044 h−702ergs−1.bThethreevaluesare probabilitiesintwo1D–KStestforthedistribution,L ,1D–KStestforthezdistributionandthe2D–KStestforthe(L ,z)spacerespectively. x x the reasons for them to be unidentified are mostly by ran- parameters. In any case, Eq. (2) gives a statistically satisfac- dom causes, i.e., are not correlated with the intrinsic proper- toryexpressionforallredshiftshellsasshowninTable2. ties ofthe source.Forthe CDF–S, extensivephotometricred- We have made luminosity bins starting with a minimum shift studies including COMBO-17 (Wolf et al. 2004) and a luminosity of log L = 42.0 with a smallest bin size of x carefulindividualphotometricredshiftdeterminationofX-ray ∆log L = 0.25 in each redshift shell. If there are fewer x sources by Zheng et al. (2004) and Mainieriet al. (2005) has than 10 AGNs in a bin, we have further rebinned up to a left only one potential AGN–1 without redshift information. maximum bin size of ∆logL = 1.0. Table 3 shows the full x ForRDS/XMM,2ofthe8unidentifiedsourceswhichcouldbe binnedresultsforthenominalcase,alongwithobservednum- type-1AGNsfromX-rayhardness/spectracriteriaareoptically berofAGNs(Nobs),model(Table2)predictednumber(Nmdl) bright and they have remained unidentifiedso far for random andfinalestimatedvaluesoftheSXLFatthecenterofeachbin. reasons.Theremaining6areopticallyfaint(R≥24.0)andthe Forreference,theadditionalnumberNf ofAGNsforthecase reasonforremainingunidentifiedmaywellbecorrelatedwith where all the optically-faintunidentified sources are assigned redshift. thecentralredshiftofthebin(induplicate,asdescribedabove) Asournominalcase,wetookthefirst-orderapproachand are also shown in the last column of Table 3. The full SXLF defined “effective” survey solid angle (as a function of flux), in the 6 redshift shells is plotted in Fig. 4 in separate panels. which is the geometricalsurvey solid angle multiplied by the Inallbuttheclosestredshiftshellpanel,thebest-fittwopower completeness, i.e. the fraction of identified X-ray sources in law functionto the 0.015 < z < 0.2 SXLF (Table 2) are also the survey, whether or not they are optically faint or bright. overplottedforreference.Threeoverallanalyticalexpressions The correctionhas beenmadein eachsurvey.In addition,we discussed in Sect. 4.4 are also overplotted for comparison as have also considered the upper bounds on the binned SXLF discussedthere.Becauseofthehighcompletenessofoursam- and the space density function from the sample where all the ple,theredshiftdistributionoftheopticallyfaintsourcesaffects unidentified optically faint (R ≥ 24.0) sources in turn are as- thefinalSXLFresultsverylittleexceptforthecasewhereallof signedthecentralredshiftofeachredshiftshell. themhappentofallintothehighestredshiftshell.Inthiscase, In the latter case, we used the geometrical solid an- the SXLF in the 3.2 < z < 4.8,44 < log L bin almostdou- x gle for the CDF–S and the incompleteness correction to the ble. This is also verified by a comparisonwith the alternative RDS/XMMsolidanglewasonlyfortheopticallybrightR<24 approachoutlinedinSect.5. unidentifiedsources. 4.3.Evolutionofthespacedensity 4.2.ThebinnedSXLF Inthissection,weinvestigatetheevolutionofthetype-1AGN The best fit parameters of Eq. (2) for each redshift shell space density in different luminosity classes as a function of are shown in Table 2 along with the results of the 1D– and redshift. The estimator of the space density is the Nobs/Nmdl. 2D−KStests(seethenotesofthetable).Thenormalizationis ThefitwithEq.(2)hasbeenmadeinfinerredshiftshellsthanin definedby: Sect.4.2.Thespacedensitiesasafunctionofredshiftwerecal- dΦ(L =1044 ergs−1,z=z ) culatedinfiveluminosityclasseswithlogLxof42−43,43−44, A = x c , (3) 44−45,45−46,and>46aswellas thesum overallluminosi- 44 dlogL x tieswithlogL >42.TheresultingcurvesareshowninFig.5a x wherez isthecentralredshiftoftheshell.Theparametererrors forthenominalcalculations.Theincompletenessupperbounds c inTable2correspondtoalikelihoodchangeof2.7(90%con- havealsobeencalculated,buthavenotbeenshownhereforthe fidenceerrors),exceptforthenormalizationA ,whichcannot visibilityofthefigure.TheseupperboundsareshowninSect.6 44 beafitparameterinthemaximum-likelihoodmethod.Theer- (Figs.11and13).SincetheBlackHolegrowthfunctionismore rors of A are simply taken as the 90%Poisson errorsof the closelylinkedtotheemissivitypercomovingvolume,wealso 44 number of the sources. Defining the normalization at a fixed showtheemissivityasafunctionofredshiftinthesamelumi- luminosity (logL = 44) minimizes its dependence on other nosityclassesinFig.5b. x 424 G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN Table3.ThefullbinnedSXLFvalues. Figure5aclearlyshowsashiftofthenumberdensitypeak withluminosity,inthesensethatmoreluminousAGNs(QSOs) z logL a Nobs Nmdl dΦ b (Nf) peakearlierinthehistoryoftheuniverse,whilethelowlumi- x dlogLx nosityonesariselater.Also,thereisacleardeclineofthede- 00..001155––00..22 4422..0500––4422..5705 1105 1115..53 ((11..30+−+000...543))××1100−−55 rivedspace densitiesat least for luminositiesof log Lx < 44, −0.3 evenwhentheopticalincompletenessupperboundsaretaken 0.015–0.2 42.75–43.00 20 25.2 (6.4+1.7)×10−6 0.015–0.2 43.00–43.25 48 38.6 (7.1−+11..41)×10−6 intoaccount.Thecountingstatisticsandspectroscopicincom- 0.015–0.2 43.25–43.50 45 44.9 (3.4−+10..06)×10−6 pletenessfor the more luminousAGNs do notallow to deter- −0.5 0.015–0.2 43.50–43.75 38 45.7 (1.4+0.2)×10−6 mineadecline,butdoalsonotexcludeit.Thisissueisfurther −0.2 0.015–0.2 43.75–44.00 36 34.6 (6.5+1.2)×10−7 discussedinSects.5and6. −1.1 0.015–0.2 44.00–44.25 27 23.7 (2.4+−00..55)×10−7 In order to show the behaviour of the luminosity depen- 0.015–0.2 44.25–44.50 22 16.9 (8.5+−21..18)×10−8 denceoftheevolutionmorequantitatively,wehavealsomade 0.015–0.2 44.50–45.50 7 11.2 (2.1+1.1)×10−9 −0.8 a maximum-likelihood fit of the evolution curve in each of 00..22––00..44 4423..2050––4433..0205 129 191..62 ((120..00+−+−0032..97..68))××1100−−56 4th4e−4lu5m,ainndos4it5y−4b6in.sW, ewuisthedltowgoLpxorwaenrgleaswocfom42p−o4n3en,ts43o−f4th4e, 0.2–0.4 43.25–43.50 23 19.1 (7.0+−11..75)×10−6 (1+z)evolutionwithacutoffredshift: 0.2–0.4 43.50–43.75 22 24.1 (3.0+−00..86)×10−6 (cid:5) 000...222–––000...444 444344...702505–––444444...025050 211551 211580...716 (((141...578+−+−+00110.....43527)))×××111000−−−677 ed(z,Lxc)= (e1d(+zcz)[)(p11+z)/(1+zc)]p2 ((zz≤>zzcc)) , (4) −0.5 00..22––00..44 4444..5705––4445..7550 1111 171..68 ((62..45+−+210...499))××1100−−89 whereLxcisthecentral(logarithmic)luminosityofthebin.As −0.7 was the case for Eq. (2), the fit depends on the shape of the 0.2–0.4 45.50–46.50 0 0.4 <9.9×10−11 luminosityfunction(alongtheluminositydirection)withinthe 0.4–0.8 42.00–42.75 18 17.1 (1.1+−00..32)×10−4 (6) luminositybin.Again,wehavefixedthebehaviorinthelumi- 0.4–0.8 42.75–43.50 23 22.0 (2.3+0.6)×10−5 −0.5 nositydirectionusingthosefromtheLDDEmodel(Sect.4.4) 0.4–0.8 43.50–43.75 13 15.4 (5.5+1.9)×10−6 0.4–0.8 43.75–44.00 21 23.4 (2.6−+10..57)×10−6 asatemplate.Wealsoshowthenormalization: −0.6 00..44––00..88 4444..0205––4444..2550 2163 2126..70 ((12..39+−+001...320))××1100−−67 A0 ≡dΦ(Lx = Lxc,z=0)/dlogLx. (5) −0.8 0.4–0.8 44.50–44.75 11 11.1 (1.0+−00..43)×10−7 The best-fit results are shown in Table 4 together with the 00..44––00..88 4454..2755––4465..2255 135 68..28 ((22..22++−100.4..76))××1100−−180 K−S probabilities. In the logLx = 45−46 bin, the fit for p2 −1.0 wasunconstrained.Thuswehavefixedthevaluesof p tothat 0.4–0.8 46.25–47.25 0 0.2 <1.8×10−11 2 fromLDDE(seebelow)forthisluminositybin. 0.8–1.6 42.00–42.50 12 11.0 (4.2+1.5)×10−5 (1) −1.2 0.8–1.6 42.50–43.00 13 12.4 (3.6+1.2)×10−5 −1.0 0.8–1.6 43.00–43.50 14 17.7 (2.4+−00..86)×10−5 (6) 4.4.Globalrepresentationsbyanalyticalfunctions 0.8–1.6 43.50–43.75 12 12.9 (2.2+0.8)×10−5 −0.6 0.8–1.6 43.75–44.00 20 16.4 (2.0+0.5)×10−5 Itissometimesusefultoprovideasimpleanalyticalfitforthe −0.4 0.8–1.6 44.00–44.25 27 25.5 (8.2+1.8)×10−6 SXLFoverthewholeredshift-luminosityrange.We firstused −1.6 0.8–1.6 44.25–44.50 27 25.0 (2.8+−00..65)×10−6 thepure-luminosityevolution(PLE)form,inordertoenablea 0.8–1.6 44.50–44.75 26 25.7 (7.5+1.7)×10−7 −1.5 comparisonwithpreviouswork: 0.8–1.6 44.75–45.00 13 16.7 (1.5+0.5)×10−7 −0.4 00..88––11..66 4455..7050––4465..7755 158 148..45 ((21..21++−100.0..33))××1100−−180 dΦ(Lx,z) = dΦ(Lx/el(z),0), (6) −0.8 dlogL dlogL 0.8–1.6 46.75–47.75 0 0.3 <4.0×10−12 x x 1.6–3.2 42.00–42.75 10 9.5 (2.2+0.9)×10−5 withtheluminosityevolutionfactor: −0.7 1.6–3.2 42.75–43.25 11 13.1 (1.4+0.5)×10−5 (1) (cid:5) 11..66––33..22 4434..2050––4444..0500 2237 2223..00 ((18..44−+−+−00011.....43396))××1100−−56 (6) el(z)= (e1(z+c)[z()1p1+z)/(1+zc)]p2 ((zz≤>zzcc)) . (7) 1.6–3.2 44.50–45.00 16 16.9 (1.2+0.4)×10−6 1.6–3.2 45.00–45.25 12 8.4 (2.9−+01..30)×10−7 We again used the smoothed two power law form (Eq. (2), 1.6–3.2 45.25–46.00 8 13.1 (9.1−+04..82)×10−9 excluding the z-dependent factor) for the z = 0 SXLF. The −3.1 1.6–3.2 46.00–47.00 0 2.9 <1.2×10−10 best-fit PLE parametersare shown in Table 5 with the results 1.6–3.2 47.00–48.00 3 0.5 (4.6+−42..25)×10−12 of the K−S tests. The best-fit PLE model is overplotted with 3.2–4.8 43.00–44.00 5 4.9 (3.8+2.4)×10−6 (1) the binnedSXLF in Figs. 4 and 5 as dotted lines. It is appar- −1.6 3.2–4.8 44.00–45.00 8 6.9 (3.2+−11..51)×10−6 (6) entfromthe comparisoninthese figures,especiallythelatter, 3.2–4.8 45.00–46.00 1 3.2 (1.7+−31..54)×10−8 PLE does not represent the behaviour of the low-luminosity 33..22––44..88 4467..0000––4478..0000 30 10..96 (9<.82+−.859..83×)×101−01−110 (logLx <∼ 44), intermediate redshift (0.5 <∼ z <∼ 1.8) regime, duetotheratherrestrictivenatureofthePLEform. Notes:a Lxh−702ergs−1inthe0.5–2keVband.b h370Mpc−3;thequoted As a more general analytical form for a refined repre- errorsare68%PoissonerrorsusingapproximationsbyGehrels(1986) sentation of the SXLF, we have explored the luminosity- ofthenumberofAGNs. dependent density evolution form (LDDE) form, originally G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN 425 Fig.4. Thesoft X-ray luminosity function of the type-1 AGN sample indifferent redshift shellsfor thenominal case as labeled. Theerror barscorrespondto68%PoissonerrorsofthenumberofAGNsinthebin.Thebest-fittwopowerlawmodelforthe0.015<z<0.2shellare overplottedinthehigherredshiftpanelsforreference.Thedottedandlong-dashedlinesgivethebest-fitPLEandLDDEmodelsdiscussedin Sect.4.4respectively. suggestedbySchmidt&Green(1983)fordescribingoptically- We use zc,44 ≡ zc(Lx = 1044ergs−1) as a model parameter. selectedQSOs: The results of the analysis in the previous section shown in Table4suggestthatconsideringthedependenceof p1and p2 dΦ(L ,z) dΦ(L ,0) x = x ·e (z,L ), (8) on luminosity would still improve the fit. Thus we have also d x dlogL dlogL x x includedthefollowingforourfullLDDEexpression: whereed(z,Lx)isthedensityfunctionnormalizedtoz=0.The p1(L )= p1 +β (logL −44) (11) x 44 1 x resultsfromSect.4.3showthatthepeaknumberdensityshifts p2(L )= p2 +β (logL −44). (12) from z ∼ 0.7 at log L ∼ 42.5 to z > 2 at high luminosities. x 44 2 x x Based onasimilar observationofahardX-ray–selectedsam- Thebest-fitparametersandtheresultsoftheK–Stestsforthe ple,Uedaetal.(2003)usedanexpressionwherez isasimple PLEandLDDEmodelsaresummarizedinTable5.Thebest-fit c functionofL : PLE and LDDE modelsare overplottedin Figs. 4 and 5 with x (cid:5) dotted and dashed lines respectively.A detailed discussion of (1+z)p1 (z≤z ) e (z,L )= c (9) thecomparisonofmodelanddataisgiveninSect.6. d x e (z )[(1+z)/(1+z )]p2 (z>z ) d c c c alongwith 5. AnalternateapproachusingtheV method max (cid:5) z (L )= zc,0(Lx/Lx,c)α (Lx ≤ Lx,c) . (10) As described in the Introduction, the luminosity function de- c x zc,0 (Lx > Lx,c) rivedfromsurveydatabinnedin luminosityandredshiftdoes 426 G.Hasingeretal.:Luminosity-dependentevolutionofsoftX-rayselectedAGN Fig.5.a)ThespacedensityofAGNsasafunctionofredshiftindifferentluminosityclassesandthesumoverallluminositieswithlogL ≥42. x DensitiesfromthePLEandLDDEmodels(Sect.4.4)areoverplottedwithsolidlines.b)Thesameasa),exceptthatthesoftX-rayemissivities areplottedinsteadofnumberdensities.Theuppermostcurve(black)showsthesumofemissivitiesinallluminosityclassesplotted. Table4.Best-fitevolutionparametersforeachluminositybin. logL -range logL N A p z p KS–probb x xc 0 1 c 2 42.0–43.0 42.5 117 (7.67±1.28)×10−6 4.90+1.21 0.65+0.12 −2.4+1.0 0.47,0.77,0.64 −1.12 −0.12 −1.1 43.0–44.0 43.5 381 (1.59±0.15)×10−6 3.89+0.43 1.11+0.22 −1.8+0.7 0.55,0.25,0.39 −0.50 −0.11 −1.1 44.0–45.0 44.5 303 (1.83±0.19)×10−8 5.51+0.38 1.78+0.14 −1.8+1.3 0.05,0.47,0.07 −0.37 −0.16 −1.4 45.0–46.0 45.5 53 (4.90±1.21)×10−11 6.06+1.18 1.79+0.59 −0.4(*) 0.81,0.98,0.62 −1.22 −0.26 Parametervalueswhichhavebeenfixedduringthefitarelabelledby(*).aUnits–A0:h370 Mpc−3, Lx,∗:1044 h−702ergs−1.bThethreevaluesare probabilitiesintwo1D–KStestforthedistribution,L ,1D–KStestforthezdistributionandthe2D–KStestforthe(L ,z)spacerespectively. x x notnecessarilyapplytothecentersofthe(L ,z)bins.Thisbin- luminosity function of radio quasars from a sample in which x ningbiastendstobeespeciallyaproblemifdataarescarce(of- only the optically brightest objects had redshifts (Schmidt tenathigherredshifts)andgradientsacrossbinsarelarge.The 1968). previoussectiondescribesaprocedurethatcorrectsthebinned spacedensitiestofirstorder. 5.1.UsingV toderivetheluminosityfunction max In this section, we avoid deriving densities from binned Thederivationofaluminosityfunctionfromobjectsinawell survey data. Instead, we use the V values of individual max defined sample usually involves binning the observations in RBSsourcestoderivethezeroredshiftluminosityfunction.We redshiftand luminosity. If we make the bins in luminosity so then derivebyiteration an analyticaldensitytemplate at vari- small that each contains only one or zero objects then the lu- ous L values that, together with the zero redshift luminosity x minosity function is composed of contributions from each of function,accountsfortheobservedcountsandredshiftsofthe theindividualsampleobjects.Inthelimit,eachoftheobjects deepersurveys.Theendresultoftheprocedureisasetofob- contributesto the luminosity functiona delta functionof am- servedvaluesoftheluminosityfunctionthatapplytothecen- plitude1/V atthe object’sluminosity L, whereV is the tersofthe(L ,z)bins,andthatisquiteinsensitivetotheprecise max max x co-moving,density-weightedvolumeoverwhichtheobjectcan templateemployed.AfurtheradvantageofemployingV of max be observed within the sample limits in flux and solid angle. individualsourcesisthatitcanbederivedfortwoormorese- This luminosity function will reproduce the source counts of lection variables.This allows us to accountfor the effect of a theinputsampleexactly. spectroscopic magnitude limit in some of the deeper surveys Wewritetheluminosityfunctionas beyondwhichtheredshiftisunknownformostofthesources. In the first use of V , this feature was used to derive the Φ(L ,z)=Φ(L ,0)ρ(z,L ) (13) max x x x

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Fiore et al. 2003) find predominantly unobscured from the whole high galactic latitude sky to the deepest pencil- beam fields c Objects without redshifts, but hardness ratios consistent with type-1 AGN. Fig. 1. The AGN–1 soft
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