The evolution of the X-ray luminosity functions of unabsorbed and absorbed AGNs out to z~ 5

36 Pages·2015·2.19 MB·English

Mon.Not.R.Astron.Soc.000,1–36(2015) Printed11May2015 (MNLATEXstylefilev2.2)
The evolution of the X-ray luminosity functions of unabsorbed and
absorbed AGNs out to z ∼ 5
5 J. Aird1,2⋆, A. L. Coil3, A. Georgakakis4,5, K. Nandra4, G. Barro6 and
1
0 P. G. Pe´rez-Gonza´lez7
2 1InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,Cambridge,CB30HA
y 2DepartmentofPhysics,DurhamUniversity,Durham,DH13LE
a 3CenterforAstrophysicsandSpaceSciences(CASS),DepartmentofPhysics,UniversityofCalifornia,SanDiego,CA92093,USA
M 4MaxPlanckInstitutefu¨rExtraterrestrischePhysik,Giessenbachstrasse,85748Garching,Germany
5IAASARS,NationalObservatoryofAthens,GR-15236Penteli,Greece
6UniversityofCalifornia,SantaCruz,1156HighStreet,SantaCruz,CA95064,USA
8
7DepartamentodeAstrof´ısica,FacultaddeCC.F´ısicas,UniversidadComplutensedeMadrid,E-28040Madrid,Spain

]
E
H Accepted2015May8.Received2015May8;inoriginalform2015February24
.
h
p
ABSTRACT
-
o We present new measurements of the evolution of the X-ray luminosity functions (XLFs)
r of unabsorbed and absorbed Active Galactic Nuclei (AGNs) out to z ∼ 5. We construct
t samplescontaining2957sourcesdetectedathard(2–7keV)X-rayenergiesand4351sources
s
a detectedatsoft(0.5–2keV)energiesfroma compilationof Chandrasurveyssupplemented
[ bywide-areasurveysfromASCAandROSAT.We considerthehardandsoftX-raysamples

separatelyandfindthattheXLFbasedoneither(initiallyneglectingabsorptioneffects)isbest
4
v describedbyanewflexiblemodelparametrizationwherethebreakluminosity,normalization
0 andfaint-endslopeallevolvewithredshift.Wethenincorporateabsorptioneffects,separately
2 modellingtheevolutionoftheXLFsofunabsorbed(20<logNH <22)andabsorbed(22<
1 logNH <24)AGNs,seekingamodelthatcanreconcileboththehard-andsoft-bandsamples.
1 We find that the absorbedAGN XLF has a lower break luminosity,a highernormalization,
0 andasteeperfaint-endslopethantheunabsorbedAGNXLFouttoz ∼ 2.Hence,absorbed
3. AGNsdominateatlowluminosities,withtheabsorbedfractionfallingrapidlyasluminosity
0 increases.Both XLFs undergostrongluminosityevolutionwhichshifts the transitionin the
5 absorbedfractiontohigherluminositiesathigherredshifts.Theevolutionintheshapeofthe
1 totalXLFisprimarilydrivenbythechangingmixofunabsorbedandabsorbedpopulations.
:
v
Keywords: galaxies:active–galaxies:evolution–galaxies:luminosityfunction,massfunc-
i
X tion–X-rays:galaxies
r
a
1 INTRODUCTION theluminosityfunction.QuantifyingAGNobscurationalsoreveals
whether SMBHsundergo significant periods of obscured growth,
TheluminosityfunctionofActiveGalacticNuclei(AGNs)repre-
whenthistakesplacewithinthelifetimesofAGNs,andhowitre-
sentsoneofthecrucialobservationalconstraintsonthegrowthof
latestothetriggeringandfuellingprocesses.
supermassiveblackhole(SMBHs)overthehistoryoftheUniverse.
Theshapeoftheluminosityfunctionreflectsacombinationofthe Obtainingaccuratemeasurements of theluminosityfunction
underlying distribution of the SMBH masses and the distribution and revealing the extent of obscuration requires large, unbiased
oftheiraccretionratesorEddingtonratios(e.g.Airdetal.2013a; samples of AGNsselected over thewidest possible range of red-
Shankaretal.2013;Schulzeetal.2015).Thus,accuratemeasure- shifts and luminosities. Optical surveys, combined with follow-
mentsoftheshapeandevolutionoftheluminosityfunctionprovide up spectroscopy, can efficiently cover wide areas (e.g. SDSS:
crucialinsightsintothephysicalprocessesthatdriveSMBHgrowth Yorketal.2000)butarebiasedtowardsthemostluminous,unob-
overcosmictime. scuredsources.Alternatively,AGNscanbeidentifiedinthemid-
ManyAGNsaresurroundedbygasanddustthatcanobscure infrared(mid-IR),whichprobesthereprocessedemissionfromthe
their emission at certain wavelengths. Thus, it is vital to under- dusty, obscuring material. Mid-IR selection should not be biased
standAGNobscurationinordertoobtainaccuratemeasurementsof againstobscuredsources,butthecontributionofthehostgalaxyis
oftensignificantatthesewavelengths, whichlimitsmid-IRselec-
tiontoluminoussourceswherethegalaxylightisoverwhelmedby
⋆ [email protected] theAGN(e.g.Donleyetal.2008;Mendezetal.2013).
(cid:13)c 2015RAS
2 J. Airdet al.
X-ray surveys can efficiently identify AGNs over a wide tionwasneededtodescribetheevolutionoftheXLF(withsome
luminosity range, including low-luminosity sources where the furthermodificationstodescribetheevolutionatz & 3,seealso
host galaxy dominates at optical or infrared wavelengths (e.g. Civanoetal.2011;Hiroietal.2012).
Bargeretal.2003).Nevertheless,softX-rayemission(atenergies Recently, the combination of extremely deep X-ray survey
.2keV)willbeabsorbedbythesamegasanddustthatobscures data and new approaches to X-ray spectral analysis have en-
the AGN at optical and UV wavelengths. Thus, soft X-ray sam- abled improved measurements of N at z ∼ 0.5 − 2 and
H
plesaregenerallydominatedbyunobscuredAGNs.Absorptionbi- have been used to identify sizable samples of Compton-thick
asesarereducedathardX-rayenergies(∼2−10keV),exceptin AGNs (e.g. Comastrietal. 2011; Georgantopoulosetal. 2013;
themostheavily-obscured,Compton-thickAGNs(equivalentline- Brightmanetal. 2014). Building on this work, Buchneretal.
of-sighthydrogencolumndensitiesN & 1024 cm−2).However, (2015) used a flexible, non-parametric method to estimate the
H
evenCompton-thicksourcesmaystillbeidentifiedatsoftorhard spacedensitiesofAGNsasafunctionofredshift,luminosityand
X-rayenergiesduetoscatteredemission,includingtheCompton- N , effectively measuring the XLF for different column densi-
H
scatteredemission(“reflection”)fromtheobscuringmaterialitself. ties. This work also recovered a luminosity and redshift depen-
AlargenumberofdeepandwideX-raysurveyshavebeencar- denceintheevolutionofthefractionofabsorbedAGNs(although
riedout,takingadvantageoftheefficiencyandpowerofX-rayse- the Compton-thick fraction was consistent with a constant value
lection(seearecentreviewbyBrandt&Alexander2015).Anum- of∼ 35percent).However, adetailedcomparison ofparametric
berofstudieshavemeasuredtheX-rayluminosityfunction(XLF) modelsfortheevolutionoftheXLFofAGNswasnotundertaken.
ofAGNsouttohighredshiftsusingthesesamples(e.g.Uedaetal. Inthispaperweaddresssomeremainingissuesinstudiesof
2003;Bargeretal.2005;Miyajietal.2015).Thesestudiesfindthat theevolutionoftheXLFofAGNs:theshapeoftheXLFandhow
AGNsareastronglyevolvingpopulation,withasharpdecreasein itevolves withredshift, theextent of anyluminosity and redshift
theirnumberdensitybetweenz ∼ 1−2andtoday.BrightX-ray- dependence oftheabsorbedfraction,andtheconnectionbetween
selectedAGNsarefoundtopeakinnumberdensityatz ≈2,sim- theabsorptionpropertiesandtheevolutionoftheAGNpopulation.
ilartooptically-selectedQSOs.FainterAGNspeaklaterinthehis- WecombinesamplesselectedatbothhardandsoftX-rayenergies
toryoftheUniverse(z ≈1)butwithamuchmilderdeclinetothe anddeterminetheunderlyingXLFanddistributionofNHthatad-
presentday(e.g.Hasingeretal.2005).Thesepatternshaveledsev- equatelydescribestheobservedfluxesinbothsamples(similarto
eral authors to propose a luminosity-dependent density evolution the approach of Uedaetal. 2014, cf. the X-ray spectral analysis
(LDDE) parametrization to describe the evolution of the XLF of usedinBuchneretal.2015).
AGNs(e.g.Miyajietal.2000;Uedaetal.2003).Inthismodelthe In Section 2 we describe our datasets that we use to define
XLFismodifiedbydifferingdegreesofdensityevolutionthatvary largesamplesofX-raysourcesselectedinthehard(2–7keV)and
withluminosityandredshift.ThisresultsinanXLFthatchanges soft(0.5–2keV)energybands.Wealsocompiledeepoptical,near-
shapeovercosmictime. infraredandmid-infraredimagingacrossourfieldsthatweuseto
In Airdetal. (2010, hereafter A10) we challenged this evo- robustly identify counterparts to our X-ray sources and calculate
lutionary model with a detailed study of the hard-band XLF that photometricredshifts.InSection3,wedescribeourBayesiansta-
carefully accounted for numerous uncertainties and biases that tistical technique that allows us to incorporate a range of X-ray
weregenerallynotincludedinpriormeasurements.Theseincluded spectralshapesandaccount fortheeffectsofabsorption.Wealso
fluxmeasurement errors, Eddingtonbias, incompleteness ofopti- introduce an approach to account for the contribution from nor-
calidentifications,andtheuncertaintyinphotometricredshiftesti- mal,X-raydetectedgalaxiesonourmeasurements.Wethenpresent
mates.Athighredshifts(z ∼ 2−3)weadoptedarest-frameUV measurementsoftheXLFbasedonourhardandsoftsamplesin-
colourpre-selectiontechnique(Airdetal.2008).Byperforminga dividually(Section4),introducing anew flexibleparametrization
robustmodelcomparisonbasedonBayesianstatisticaltechniques, of the XLF. We show that significant discrepancies between the
wefoundthattheevolutionoftheXLFcouldbedescribedbyasim- measurementsatallredshiftswarrant thefurtherconsideration of
plermodelinwhichtheXLFretainsthesameshapeatallredshifts absorption effects. In Section 5 we separately model the XLF of
but evolves in both luminosity and density (see also Assefetal. unabsorbed and absorbed AGNs (including a contribution from
2011;Rossetal.2013). Compton-thick sources) and show how the combination of these
While A10 presented a number of important advances, ab- populations can simulataneously account for both our hard- and
sorptioneffectswerenotexplored.Otherstudieshaveattemptedto soft-bandsamples. OurresultsplaceconstraintsonthetotalXLF
measurethedistributionofabsorptioncolumndensitiesandpresent ofAGNsandtheabsorbedfractionasafunctionofluminosityand
absorption-correctedmeasurementsoftheXLF.Uedaetal.(2003) redshift.InSection6wecompareourresultstopriorworkanddis-
foundthatthefractionofabsorbedAGNs(thosewithN > 1022 cussthewiderimplicationsofourfindings.Section7summarizes
H
cm−2)wasstronglydependentonluminosity,decreasingathigher ourpaperandoverallconclusions.
luminosities. Later studies found that the fraction of absorbed Giventhelengthofthispaper,acasualreadermaywishtoskip
AGNsdependsonbothluminosityand redshift,dropping athigh toSection4.4,Section5andthediscussioninSection6(andfocus
luminosities but increasing (at a given luminosity) to higher red- onFigures7,8,and9).WeadoptaflatcosmologywithΩΛ =0.7
shifts (e.g. LaFrancaetal. 2005; Hasinger 2008). The extent of andh=0.7throughoutthispaper.
anyredshiftevolutionhasbeenamatterofdebate(seeAkylasetal.
2006;Dwelly&Page2006),potentiallyduetodifficultiesregard-
ing the selection functions for absorbed and unabsorbed sources.
2 DATA
RecentworkbyUedaetal.(2014)re-examinedtheevolutionofthe
XLFandthedistributionofN (the“N -function”)usingalarge ToconstraintheevolutionoftheXLFwerequirelargesamplesof
H H
compilation of both soft and hard X-ray surveys and found that X-ray selected AGNs. By selecting samples in both the hard (>
both a luminosity and redshift dependence of the absorbed frac- 2keV) andsoft (0.5–2keV) observed energy bands, wecanalso
tion were required. They also found that an LDDE parametriza- constrainthedistributionofN andcorrectfortheseeffectsonthe
H
(cid:13)c 2015RAS,MNRAS000,1–36
The evolutionoftheXLFs ofunabsorbedand absorbedAGNs 3
XLF.InthispaperwecombinealargenumberofChandraX-ray conversion factor scalesdirectlywiththecount rate;inSection3
surveysalongwithlargerareasurveysfromASCAandROSAT.We belowwedescribeourproceduretoconvertbetweenthecountrate
givefurtherdetailsofourdatasetsbelow.Table1summarizesthe and intrinsic quantities (such as luminosity), which allows for a
differentsurveysandprovidesthenumber ofhardandsoftX-ray morecomplexX-rayspectrumandaccountsforuncertaintiesinthis
selectedsourcesfromeach. conversionfactor.Thesensitivitymapcalculationislimitedtothe
footprintofthemultiwavelengthphotometryforeachfield.Figure
1showsthecorrespondingareacurvesforeachofourX-rayfields.
2.1 ChandraX-raydata
We note that previously published X-ray source catalogues,
In this paper we use Chandra X-ray observations from five dis- oftenincludingmutiwavelengthcounterpartinformation,areavail-
tinctpartsofthesky:theChandraDeepField-South(CDFS),Chan- ablefor theall of our Chandra fields(e.g. Alexanderetal. 2003;
draDeepField-North(CDFN),ExtendedGrothStrip(EGS),COS- Gouldingetal.2012;Brandetal.2006).AdoptingourownX-ray
MOS,andBootesfields. reductions and source detection procedures ensures wecanaccu-
IntheCDFSfieldweidentifytwodifferent“surveys”:1)the rately determine the sensitivity in a consistent manner, which is
seriesofobservationsthathavetargetedthecentral∼0.07deg2of essential for our Bayesian analysis of the XLF. Our catalogues
thefieldandreachatotalcombinedexposure timeof ∼4Ms(the contain∼ 10−25per cent fewersources thanXueetal.(2011)
CDFS-4Mssurvey,Xueetal.2011);and2)theseriesoffour250ks and Puccettietal. (2009) in the CDFS-4Ms and C-COSMOS ar-
observations that surround the central area (the Extended-CDFS, eas,mainlyduetoourstricter(i.e.lower)falseprobabilitythresh-
orE-CDFSsurvey, Lehmeretal.2005).TheX-raydatareduction old.Thus,ourcataloguesaremoreconservative.
andsourcedetectionprocedureswerecarriedoutindependentlyfor
eachofthesesurveys.Tocombinethetwosurveys,wedefineacen-
2.2 Multiwavelengthcounterpartsandphotometry
tralregionwheretheCDFS-4Mssurveytakesprecedence,roughly
corresponding to the area within ∼ 9′ of the center of the field. IneachofourChandrafields,weidentifymultiwavelengthcoun-
OutsidethiscentralregionweadoptthesourcesdetectedintheE- terpartstoourX-raysourcesusingthelikelihoodratio(LR)method
CDFSsurveyonly.Thisprocedureensureswehaveawell-defined (e.g. Ciliegietal. 2003; Brusaetal. 2007; Civanoetal. 2012),
samplewherewecanaccuratelydeterminethesensitivity. matchingtomultipleoptical,near-IRandmid-IRbandstoensure
IntheEGSfieldwealsoidentifytwodistinctsurveys:1)the a high completeness and reliability. We also compile multiwave-
series of eight pointings that reach a nominal depth of ∼200ks lengthphotometryfromalargernumberofbands,whichweuseto
and were presented in Lairdetal. (2009), which we refer to as calculatephotometricredshifts(seeSection2.6below).
the AEGIS-XW(ide) survey; and 2) the AEGIS-XD(eep) survey
(Nandraetal. 2015) which took three of the original 200ks to a
depthof∼ 800ks. Weadopt thedeeper AEGIS-XDobservations 2.2.1 CDFS,CDFNandEGS
whenavailable.
In three of our fields—the CDFS, CDFN and EGS—we identify
In each of the remaining fields we adopt data from a sin-
counterparts and extract the multiwavelength photometry using a
gle Chandra survey: the 2Ms survey in CDFN (Alexanderetal. custom version of the Rainbow Cosmological Surveys Database1
2003); the ∼160ks C-COSMOS observations (Elvisetal. 2009;
(Pe´rez-Gonza´lezetal. 2005, 2008; Barroetal. 2011a,b), which
Puccettietal. 2009); and the 5ks XBootes survey (Murrayetal.
provides a compilation of the various photometric datasets. Ap-
2005).
pendix A lists all the different photometric imaging datasets for
TheX-raydatafromallofoursurveyswerereducedwithour
eachfieldthatareusedinthispaper.Wenotethatfullcoverageof
ownpipelineprocedure,whichisdescribedindetailbyLairdetal.
the entire field is not always available in each photometric band.
(2009)andNandraetal.(2015).Weperformedpointsourcedetec-
All the images are registered to a common astrometric reference
tion using the procedure described by Lairdetal. (2009) and ap-
frameandphotometryisperformedinconsistentaperturestopro-
pliedafalsePoissonprobabilitythresholdof< 4×10−6 togen-
duce spectral energy distributionsthat span fromthe UV tomid-
eratecatalogues ofdetected sourcesinthesoft(0.5–2keV), hard
IR.TheX-raysourcematchingprocedureisdescribedindetailin
(2–7 keV), full (0.5–7 keV) or ultrahard (4–7 keV) observed en-
Nandraetal.(2015),butwebrieflysummarisethemethodhere.
ergybands.Wecombinedthesourcelistsineachbandtocreatea
First,wererantheRainbow photometric code, extracting all
merged catalogue, which is used in the counterpart identification potentialcounterpartswithin3.5′′ oftheX-raypositionsinanyof
proceduredescribedinSection2.2below.
thebandscoveredbyRainbow(usinginitialSExtractorcatalogues
Forthe5ksXBootessurveyweappliedastricterfalseprob-
in each of the bands). The counterparts were then cross-matched
abilitycut(< 10−8)inadditiontoarequirementof> 5totalde- using a 2′′ search radius to create a single multiband catalogue.
tectedcountsineachband.Thiscutreducesthesamplesizebutap-
Weobtained consistent photometry by applying a singleaperture
pliesaneffectiveX-rayfluxlimitthathelpsraisethecompleteness
acrossallopticalandnear-IRbands.WealsoextractedIRACpho-
of the spectroscopic follow-up in this field. In this field, we also
tometry,applyingtheproceduredescribedinPe´rez-Gonza´lezetal.
restrictouranalysistothe∼7.1deg2 oftheBootesfieldthatcor-
(2008) and Barroetal. (2011a) to deblend the IRAC photometry
respondstothe15standardsub-fieldsoftheAGESspectroscopic
whenasingleIRACsourceisassociatedwithmultipleoptical/near-
survey(Kochaneketal.2012).Thiscutalsoensureswehaveahigh
IRcounterparts.
spectroscopiccompleteness(seeSection2.5below).
Next,wecalculatedtheLRforallcandidatecounterpartsde-
We determined X-ray sensitivity maps and area curves for
tected in the IRAC 3.6µm band and determined an LR threshold
each band as described in Georgakakisetal. (2008), accounting
that maximises the sum of the completeness and reliability (see
forthestricterfalseprobabilitycutandminimumcountsrequire-
Luoetal. 2010). A candidate counterpart that exceeded this LR
ment for the XBootes survey. We convert the sensitivity maps to
areacurvesasafunctionoffluxbyassumingafixedX-rayspectral
slopeofΓ = 1.4.Wenotethatthefluxcalculatedwiththisfixed 1 https://rainbowx.fis.ucm.es
(cid:13)c 2015RAS,MNRAS000,1–36
4 J. Airdet al.
Table1.DetailsoftheX-raysurveysusedinthispaper.
Field Survey RA Dec X-ray Survey Softband Hardband
exposure area NX Nctrprt Nspec−z NX Nctrprt Nspec−z
(J2000) (J2000) (deg2)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
CDFS CDFS-4Ms 03:32:27.2 -27:47:55 4Ms 0.075 413 397(96.1%) 240(58%) 283 273(97%) 155(55%)
CDFS ECDFS 03:32:27.2 -27:47:55 250ks 0.181 334 328(98.2%) 115(34%) 273 268(98%) 101(37%)
CDFN CDFN 12:36:49.3 +62:13:19 2Ms 0.112 384 363(94.5%) 242(63%) 286 273(96%) 176(62%)
EGS AEGIS-XD 14:19:20.8 +52:50:03 800ks 0.260 698 673(96.4%) 295(42%) 552 539(98%) 233(42%)
EGS AEGIS-XW 14:17:15.0 +52:25:31 200ks 0.204 334 332(99.4%) 130(39%) 274 274(100%) 110(40%)
COSMOS C-COSMOS 10:00:20.3 +02:11:20 160ks 0.984 1213 1195(98.5%) 694(57%) 889 877(99%) 530(60%)
Bootes XBootes 14:31:28.3 +34:28:07 5ks 7.124 754 744(98.7%) 566(75%) 257 255(99%) 196(76%)
... ALSS 13:14:00 +31:30:00 ... 5.800 ... ... ... 34 34(100%) 33(97%)
... AMSS ... ... ... 81.77 ... ... ... 109 109(100%) 107(98%)
... ROSAT ... ... ... 20391 221 221(100%) 221(100%) ... ... ...
Total 4351 4253 2503 2957 2902 1641
Column(1)nameofthefield;(2)nameofX-raysurveyprogrammewithinthisfield;(3,4)approximatecenterofthesurvey;(5)nominalX-rayexposure
time;(6)totalareacoveredbyboththeX-raydataandtheopticalorinfraredimaging,excludingareasclosetobrightstars;(7)numberofX-raysources
detectedinthesoft(0.5–2keV)energyband;(8)number(andfraction)ofthesoftX-raysourcesthatareassociatedwitharobustmultiwavelength
counterpart;(9)number(andfraction)ofthesoftX-raysourcesthathaveaspectroscopicredshift;(10)numberofX-raysourcesdetectedinthehard(2–7
keV)energyband;(11)number(andfraction)ofthehardX-raysourcesthatareassociatedwitharobustmultiwavelengthcounterpart;(12)number(and
fraction)ofthehardX-raysourcesthathaveaspectroscopicredshift.
thresholdwasdeemedasecurecounterpart(takingthecounterpart secure associations are considered. For 1499 of the 1526 secure
withthehighest LRvalueincasesof > 1securecandidate). We counterparts, we end up with both a Subaru i+ and S-COSMOS
then repeated the entire LR matching process for the bands indi- counterpart. For these sources we obtain photometry in up to 18
cated inthe tablein Appendix A, retainingany additional secure broad-bandfiltersspanningfromtheUVtonear-IR,aswellas15
counterparts identified in these bands. This procedure enables us intermediate- or narrow-band optical filters, from the Subaru i+
toidentifysecurecounterpartsforahighfraction(> 90%)ofthe catalogue(see Ilbertetal.2009;McCrackenetal.2010).Thepho-
X-raysourcesintheCDFS,CDFNandEGSfields(seeTable1). tometrywasextractedin3′′diameteraperturesfromPSF-matched
Thevastmajority(∼ 92%) ofthesecurecounterpartswereiden- images. Wealso adopt IRAC photometry in the 3.6, 4.5, 5.8 and
tifiedinthe(deblended) IRAC3.6µmcatalogue. Matchingtothe 8.0µmbands fromthe S-COSMOScatalogue, applying theaper-
additionalbandsallowsustoidentifycounterpartswhentheIRAC turecorrectionsgiveninIlbertetal.(2009).
candidate is faint, blended, or non-existent. No additional cross- In27caseswehaveani+ counterpart butdonot findanS-
matchingisrequiredasthefullmultibandphotometryisprovided COSMOScounterpart,eitherduetothelimiteddepthoftheIRAC
throughmatchedaperturesforallsourcesintheRainbowdatabase. imagingor because thei+ sourceisblended at theIRACresolu-
tion. For these sources we simply ignore the IRAC bands in our
photometricredshiftestimates(seeSection2.6below).
2.2.2 COSMOS In 23 cases, we identify an S-COSMOS counterpart, but no
Subarui+source.Forthesesourcesweextractedphotometryin3′′
IntheCOSMOSfield,whichisnotcurrentlyincludedintheRain-
diameteraperturesattheS-COSMOSpositioninthePSF-matched
bow surveys database, we matched directly between our X-ray
imagesfor all theUV tonear-IRbands, generally obtaining only
sourcelistsandtwomultiwavelengthcatalogues:1)theCOSMOS
upperlimitsfortheseopticallyfaintsources.
IntermediateandBroadBandPhotometryCatalogue20082,which
is based on detection in the deep Subaru i+ imaging of the en-
tire COSMOS field (Capaketal. 2007); and 2) the S-COSMOS
IRAC 3.6µm based catalogue (Sandersetal. 2007). Unlike the 2.2.3 Bootes
Rainbow catalogues,theS-COSMOSIRAC3.6µmcataloguehas
FortheBootesfield,wecompiledmultiwavelengthcataloguesfrom
notbeendeblended.Thus,wefirstidentifiedsecurematches(using
the NOAO Deep-Wide Field Survey (Jannuzi&Dey 1999) DR3,
theLRmethod)fromthehigher-resolutionSubarui+ catalogues.
SDSSDR9(Ahnetal.2012),GALEXGR73,FLAMINGOSEx-
Wefoundsecurecounterpartsfor1348ofthe1621X-raysources
tragalacticSurvey(Elstonetal.2006),andtheSpitzerDeep-Wide
(83 per cent) in our overall C-COSMOScatalogue. Next, weap-
FieldSurvey(Ashbyetal.2009).WeusetheLRmethodtomatch
pliedtheLRmethodtomatchbetweentheX-rayandS-COSMOS
ourX-raycataloguestotheappropriateselectionbandforeachof
catalogues.Weidentifiedsecurecounterpartsforanadditional178
these surveys, assigning secure matches from the surveys in the
sources,takingouroverallcompletenessto94percent.
order of priority indicated in the table in Appendix A. The vast
Finally, we cross-matched between our secure positions and
majority of our secure matches are identified in the NDWFS I
theoriginalcatalogues,againusingtheLRmethodtoensureonly
2 http://irsa.ipac.caltech.edu/data/COSMOS/datasets.html 3 http://galex.stsci.edu/GR6/
(cid:13)c 2015RAS,MNRAS000,1–36
The evolutionoftheXLFs ofunabsorbedand absorbedAGNs 5
brightendoftheXLFrequiressamplesofhigherluminosityX-ray
104 ROSAT sources identified from larger-area surveys. We thus supplement
our samplewithsources fromlarge-areasurveys carriedout with
Bootes
COSMOS ASCA(inthehardband)andROSAT(inthesoftband).
EGS For our large-area hard-band sample, we include the 34
102 CDFN sources from the ASCA Large Sky Survey (ALSS: Uedaetal.
2] CDFS 1999), which covers a contiguous area of 5.8 deg2 near the
eg north Galactic pole. We adopt the optical identifications from
d
[ Akiyamaetal.(2000):2sourcesareopticallyidentifiedasgalaxy
a
Are 100 clusters,1isastar,1sourceremainsunidentifiedandtheremain-
ing30areassociatedwithAGNs,allofwhichhavespectroscopic
redshifts.WealsoselectsourcesfromtheASCAMediumSensitiv-
itySurvey (AMSS, Uedaetal. 2001), which combines data from
10-2 a large number of ASCA observations at high Galactic latitudes
Soft (0.5-2 keV) overanarea∼82deg2.WeincludesourcesfromtheAMSSnsub-
sample,selectedinthehard(2–10keV)band,withopticalidentifi-
-17 -16 -15 -14 -13 -12 -11 cations presented by Akiyamaetal. (2003). The sample includes
logf0.5−2keV [erg s−1 cm−2] 87 X-ray sources and has 100 per cent spectroscopic complete-
ness. We include additional sources with from the AMSSs sub-
104 AMSS Hard (2-10 keV) sample(Ueda&Akiyama,privatecommunication),whichincludes
20 AGN;2 sources in thissample remainunidentified. Weadopt
ALSS
Bootes areacurvesfromtheALSSandAMSSfromAkiyamaetal.(2003)
COSMOS andUedaetal.(2003)respectively.
102 EGS For our soft band sample we combine samples from the
CDFN
2] CDFS ROSAT bright survey (Fischeretal. 1998; Schwopeetal. 2000)
g
e and the Selected-Area–North survey (SA–N: Appenzelleretal.
d
[ 1998), removing duplicate sources. We include sources with sig-
a
Are 100 nificantdetectionsinthe0.5–2keVbandandadopttheunabsorbed
fluxestimates(correctedforGalacticabsorption).Wecutoursam-
pleat fluxlimitsof f0.5−2keV > 3.6×10−12 ergs−1cm−2 for
the RBS sample and f0.5−2keV > 1×10−12 ergs−1cm−2 for
10-2 theSA–Nsample.Thesehighfluxlimitsensureoursourcesalllie
wellabovethesensitivitylimitsofthesurveys,allowingustoadopt
simplesensitivitycurvesthatcorrespondtotheentireareaofeach
-17 -16 -15 -14 -13 -12 -11 surveyandcutoffsharplyateachofthefluxlimits(seeFigure1).
logf2−10keV [erg s−1 cm−2] All thesources above these fluxlimitshave spectroscopic classi-
ficationsand weidentifyatotalof221 AGNswithspectroscopic
Figure1.X-rayareacurves(sensitiveareaversusX-rayflux)foreachof redshifts(excludingBLLactypeobjects).
oursurveysinthesoftandhardbands.Theblack lineindicates thetotal Wenotethat,incontrasttoourChandrafields,ourareacurves
areacurveforourstudy.Welimitoursensitivityanalysistotheareafalling
forourlarge-areasurveysdonotaccountforthePoissonnatureof
within the footprint of our multiwavelength photometry, excluding areas
thedetection. Aswerestrictthe samples fromthelarge-area sur-
closetobrightstars.TheROSATareacurveincludestheROSATbrightsur-
veys tohighly significant detections, thissimplificationwill have
veyandSA–Nsurvey(seeSection2.3).TheEGSareacurveincludesboth
aminimaleffectonourXLFmeasurements.However,differences
theAEGIS-XD800ksdataandtheadditionalareaat200ksfromAEGIS-
XW.TheCDFSareacurvecombinestheCDFS4Msdatawiththeflanking intheassumedspectralshapecanhaveasignificantimpactonthe
250ksdatafromtheE-CDFS.Theseareacurvesassumeasingle,fixedcon- estimate of a flux and thus the assumed sensitivity. Uncertainties
versionfactorbetweentheX-raycountrateandflux,correspondingtoan inthespectralshapeandtheresultingdifferencesinsensitivityare
X-rayspectrumwithaphotonindexΓ=1.4andGalacticabsorptiononly; accountedforbyourBayesianmethodologydescribedbelow.
theeffectofdifferentX-rayspectralshapes—andtheresultinguncertainties
intheconversionfactors—areaccountedforinourBayesianmethodology
describedinSection3. 2.4 Identificationandmaskingofstars
Bright stars can contaminate our photometry, leading to issues
band.Weidentifysecurecounterpartsfor95.8percent ofour X- withcounterpart identificationand photometric redshift estimates
raysources. Finally,wecross-matchedbetweentheoriginalcata- intheseregions.Wehavethereforemaskedoutareasclosetobright
loguesandoursecurecounterpartpositions,againapplyingtheLR stars from all of our Chandra fields in a consistent manner. We
method, toidentifycommon sources. Thecombined surveyspro- searchedforstarsbrighterthanV =15intheHSTGuideStarCat-
videphotometryinupto17differentbands(seeAppendixA). alog2.3(Laskeretal.2008).Wemaskedallareaswithinaradius,
r,givenby
2.3 Large-areasurveys r=(16−V)×6′′ (1)
CombiningourfiveChandrafieldsprovidesasampleofover4000 whereV istheV-bandmagnitudefromtheGuideStarCatalog.We
soft band detections and over 2800 hard band detections from setamaximummaskingradiusof40′′.WehaveremovedanyX-
a total area of ∼ 9 deg2. However, to accurately constrain the raysourceswithinthisradiusfromoursamples(whichcaninclude
(cid:13)c 2015RAS,MNRAS000,1–36
6 J. Airdet al.
thestaritselforanearbysource).Wealsoexcludedtheseregions 1 gives the number of X-ray sources in our hard- and soft-band
whencalculatingtheX-raysensitivityandareacurves. selectedsampleswithreliablespectroscopicredshifts.
Wehavealsoidentifiedstarswithfaintermagnitudesthatare
detected at X-ray wavelengths and removed them from our sam-
ples. In the fields with Rainbow coverage (CDFS, CDFN, EGS) 2.6 Photometricredshifts
starswereidentifiedbyarangeofcolourandmorphologycriteria,
The levels of spectroscopic completeness vary over our Chandra
asdescribed inBarroetal.(2011a).In theCOSMOSand Bootes
surveysfrom∼35percent(inourECDFSarea)to∼75percent
fieldswe applied a single colour criterion based on the region of
(intheBootesfield).FortheremainingX-raysourceswemustre-
colour-colourspaceoccupiedbystarsinIlbertetal.(2009),
sorttophotometricredshiftestimates,whicharedeterminedbyfit-
R−[3.6]<3.0×(R−I)−1.2 (2) tingasetoftemplatespectratotheobservedspectralenergydistri-
butions(SEDs)ofoursources.Suchredshiftscanbehighlyuncer-
where [3.6] is the magnitude in the IRAC 3.6µm imaging, R is
tain,particularlywhenconsideringfaintX-raysources.Akeyad-
themagnitudeintheSubarur+orNDWFSRfilter,andI isthe
vantageofourBayesiananalysis(seeSection3)isthatweareable
magnitudeintheSubarui+orNDWFSI filter.Forallfields,we
toaccountfortheuncertaintiesinphotometricredshiftsbyadopting
alsorequiredthattheX-raysourcesexhibitalowX-ray-to-optical
probabilitydistributionsfortheredshift,p(z),ratherthanasingle
fluxratio,logf /f <−1,wheretheratioiscalculatedas
X opt redshiftestimate.Wethusrequirethatourphoto-zapproachrecov-
f I ersap(z)distribution that accurately reflectstheuncertainties in
logfX =logf0.5−2keV+5.4+ 2.5. (3) ourredshiftestimates.
opt
We calculate photometric redshifts using the EaZY photo-z
ThiscutensuresthatwedonotexcludebrightQSOsfromoursam-
code(Brammeretal.2008).WeuseEaZY intwo-templatemode,
plethatmaysatisfytheotherstellarcriteria.Whenaspectroscopic
allowing for combinations of a galaxy and AGN template. For
classificationisavailable(seeSection2.5)thisover-ridesourpho-
the galaxy templates we adopt the “pegase13” template set pro-
tometricclassification.Ofthe50spectroscopicallyclassifiedstars
vided with EaZY. This template set consists of 259 synthetic
inourfiveChandrafields,40(80percent)werealsoidentifiedby
galaxy templates drawn from the range of parameters described
ourphotometricprocedure.
byGrazianetal.(2006).Additional“star-forminganddusty”tem-
plates are included by applying the Calzettietal. (2000) red-
2.5 Spectroscopicredshifts dening law for a range of different extinctions to a subset of
the galaxy templates. We adopt seven AGN templates from the
AllofourChandrasurveyshavebeenthesubjectofintensespec- Salvatoetal. (2009) template set4, namely the Sey 1.8, Sey 2,
troscopiccampaigns.These campaigns include large-scalefollow- Mrk231, pl TQSO1, pl QSOH, pl QSO and the S0-10 QSO2-90
up of the general galaxy population, in addition to those directly hybridtemplate.WealsoincludetheType-2“Torus”templatefrom
targetingX-raysources. the Pollettaetal. (2007) library5, which isnot included in the fi-
IntheCDF-Swefirstsearchedforspectroscopicredshiftsin nalSalvatoetal.(2009)set.Wenotethatsomeofthesetemplates
the catalogue of Xueetal. (2011). The majority of the spectro- will include host galaxy contributions (particularly the Sey 1.8,
scopicredshiftsforourCDFS-4Mssurveyaretakenfromthiscata- Sey2,Mrk231andS0-10 QSO2-90templates).Thisisnotama-
logue,aswellassomeofourECDFSsurvey(intheareathatover- jorissueaswewanttodeterminethedistributionofpossiblered-
laps withthe 4Ms data). Wealso searched for spectroscopic red- shifts, rather than perform an accurate host-AGN decomposition.
shiftsfromtheArizonaCDFSEnvironmentSurvey(Cooperetal. Thetwo-templatemodeinEaZY allowsanypossiblecombination
2012),thespectroscopicsub-sampleofsourcesfromtheMUSYC ofoneofourAGNtemplatesandoneofourgalaxytemplatesand
sample(Cardamoneetal.2010b),andPRIMUS(Coiletal.2011). thusallowsforalargeamount of flexibilityinthefittedtemplate
In the CDF-N we used spectroscopic redshifts from DEEP3 SEDs.
(Cooperetal.2011)aswellasthesurveysofTrouilleetal.(2008); AnotheradvantageoftheEaZYphoto-zcodeisthatitallows
Bargeretal. (2008); Reddyetal. (2006); Wirthetal. (2004); for the inclusion of a “template error function”. This feature ac-
Cowieetal.(2004)andSteideletal.(2003). counts for additional uncertainty in the template SED as a func-
IntheEGSwecompiledspectroscopicredshiftsfromanum- tionof(rest-frame)wavelengthandthusallowsforthefactthatour
ber of surveys including DEEP2, DEEP3, the Canada-France templatesetmaynotaccuratelyrepresentthetruediversityofSED
Redshift Survey and MMT follow-up of X-ray sources. See shapes.ThisuncertaintyinthetruerangeoftemplateSEDsispar-
Nandraetal.(2015)andreferencesthereinforfulldetails. ticularlyusefulasourobservedSEDsextendintotheUVandmid-
InCOSMOSweinitiallysearchedforspectroscopicredshifts IR,wherethetemplatesarepoorlycalibrated,especiallyforAGNs.
of X-ray sources in the C-COSMOS catalogue of Civanoetal. Inaddition,astheopticalemissionfroman(unobscured)AGNcan
(2012).Wealsosearchforadditionalspectroscopicredshiftsfrom varyontimescalesofmonths-to-years,ourobservedSEDsmaynot
the bright zCOSMOS survey catalogue (Lillyetal. 2009) and bewell-matchedbyasingleunderlyingtemplate.Thetemplateer-
PRIMUS(Coiletal.2011). rorfunctioncanalsoallowforanyoverallcalibrationuncertainties
InBootesweadoptspectroscopicredshiftsfromtheAGNand in the diverse sets of photometric observations used to construct
GalaxyEvolutionSurvey(Kochaneketal.2012).Forallfieldswe ourobservedSEDs.Wederiveatemplateerrorfunctiononafield-
alsosearchedforspectroscopicredshiftsfromtheSloanDigitalSky by-field basis—to ensure that it represents the calibration uncer-
Survey(SDSS:Yorketal.2000). taintiesinagiven dataset—usingthebasicprocedure laidout in
Wematchedthespectroscopiccataloguestothesecurecoun- Brammeretal.(2008).First,weattempttofittheobservedSEDs
terpartsofourX-raysourcesusinga2′′searchradius,correctedfor
anyoverallastrometricoffset,andrepeatedthematchingwitha1′′
radius.Weonlyadoptthosespectroscopicredshiftsthatareflagged 4 http://www.mpe.mpg.de/∼mara/PHOTOZ XCOSMOS/
ashigh-quality, reliableredshiftsintheoriginal catalogues.Table 5 http://www.iasf-milano.inaf.it/∼polletta/templates/swire templates.html
(cid:13)c 2015RAS,MNRAS000,1–36
The evolutionoftheXLFs ofunabsorbedand absorbedAGNs 7
5
CDFS CDFN EGS
4
3
t
o
h
p
z
2
n =405 n =280 n =491
1 zspec zspec zspec
σ =0.055 σ =0.064 σ =0.058
NMAD NMAD NMAD
f =14.8% f =12.5% f =15.9%
outlier outlier outlier
f =4.0% f =4.6% f =4.7%
0 catastrophic catastrophic catastrophic

5
COSMOS BOOTES
4
3

2
n =805 n =609
1 zspec zspec
σ =0.045 σ =0.150
NMAD NMAD
f =14.2% f =35.5%
outlier outlier
f =6.3% f =1.1%
0 catastrophic catastrophic
0 1 2 3 4 5 0 1 2 3 4 5
zspec
Figure2.Comparisonofphotometricredshifts(zphot)andspectroscopicredshifts(zspec)forourfiveChandrafields.Weplotthemeanofthep(z)distribution
asthebestestimateofthephotometricredshifts(blackcircles);errorbarsindicatethe95percentcentralconfidenceinterval.Thedashedlineindicatesa1:1
relation, whereas thedotted lines correspond to∆z/(1+zzspec) = ±0.15(sources wherethebestestimate ofthephoto-z lies outside this rangeare
flaggedasoutliers).InthelegendforeachpanelwegivethenumberofX-raysourceswithreliablespectroscopicredshifts(nzspec),theaccuracybasedon
thenormalizedmedianabsolutedeviation(σNMAD),thefractionofoutliers(foutlier)andthefractionofcatastrophicfailures(fcatastrophic);seetextfor
details.Wehighlightcatastrophicfailureswitharedtriangle.Overfourofourfields(CDFS,CDFN,EGSandCOSMOS)weobtainaconsistentaccuracyof
σNMAD ≈0.05,with∼15percentoutliersand∼5percentcatastrophicfailures.IntheBootesfield—ourlargestarea,shallowestfield—wehavepoorer
accuracyandahigheroutlierfraction,reflectingthemorelimitedphotometricimaginginthisfield.Whileourphoto-zhaveapooreraccuracy(σNMAD)and
ahigheroutlierratethaninsomepriorworks,wechoosetoadoptourestimatesastheyhavebeencalculated inaconsistentmanneracrossallfiveofour
Chandrafieldsandhaverepresentativeerrorsthatwecanfullytrackviathep(z)inourBayesianmethodology(seetextforfurtherdiscussion).
withour templates, fixing the redshift at the spectroscopic value, survey areas (AEGIS-XD,CDFS-4Ms), where thebest photome-
whereavailable.Wethencalculate tryisavailable,withthelarger-areashallowsurveys(AEGIS-XW,
∆fj = FjF−jTj (4) tErCosDcoFpSi)c.rWedeshinifctluidnethaellseXp-rlaoytssaonudrcdeos wnoitthapaphlyigha-nqyuacluittsybsapseecd-
ontheestimatedqualityofthephoto-z.Thus,weincludesources
where Fj indicates the observed flux in a filter for source j, and with extremely broad p(z) distributions, which are often flagged
Tj isthefluxfromthebest-fittingtemplate.Wecalculate∆fj as asunreliableandexcludedwhenassessingthesuccessofphoto-z
function of rest-frame wavelength for all sources and filters and
techniques.
takethemedianofevery400individual measurementsacrossthe
In each panel of Figure 2 we present a number of summary
rest-framewavelengthrange.Wesubtractthemedianphotometric
statistics:
error, in quadrature, to estimate the contribution from “template
error” to the uncertainty as a function of rest-frame wavelength. (i) σ : the accuracy based on the normalized me-
NMAD
Thevalueofthetemplateerroristypicallyaround10percent(in dian absolute deviation between the best photo-z and
flux)butvariesbetween∼4percentand∼20percentdepending the spectroscopic value, defined as σ = 1.48 ×
NMAD
onthewavelengthandthedatainagivenfield. median(|z −z |/(1+z )).
phot spec spec
In Figure 2 we compare our photo-z estimates for X-ray (ii) f : the fraction of outliers, defined as the fraction of
outlier
sources to secure spectroscopic redshifts across our 5 Chandra sourceswhere|z −z |/(1+z )>0.15;
phot spec spec
fields.ThepanelsfortheEGSandCDFSfieldscombinethedeep (iii) f :thecatastrophicoutlierrate,calculatedasthe
catastrophic
(cid:13)c 2015RAS,MNRAS000,1–36
8 J. Airdet al.
p(z)throughthefinalXLF)theremaybeapreferredredshiftso-
250 lution.Thelackofamultiwavelengthcounterpartcouldimplythat
Spec-z ahighredshiftsolutionshouldbegivenhigheraprioripreference
Photo-z best
forsuchsources, thusour approach isconservative. Thereisalso
Photo-z p(z)
200
apossibilitythattheseX-raysourceslackcounterpartsastheyare
spurious detections, corresponding to positive fluctuations in the
background count rate.Ouranalysisaccounts forthePoissonna-
150
er tureoftheX-raydetectionandthusallowsforthispossibility.
b
m Other estimates of photometric redshifts are available for
u
N 100 X-ray sources in many of our fields (e.g. Bargeretal. 2003;
Cardamoneetal. 2010a; Hsuetal. 2014). Many of these studies
take additional steps to improve the quality of the photo-z esti-
50 mates. These steps can include optimizing the template set (e.g.
Luoetal.2010),attemptingtocorrecttheobservedphotometryfor
variability (e.g. Salvatoetal. 2009), or applying priors based on
0 the source morphology and X-ray flux (e.g. Salvatoetal. 2011).
0.0 0.5 1 .0 2.0 3.0 5.0 1 0.0 These studies often achieve a higher accuracy and lower outlier
Redshift (z)
ratethanourownphoto-zanalysis.However,theseadditionalsteps
canleadtounderestimatesofthetrueuncertaintiesinthephoto-z.
Figure3.RedshiftdistributionofX-raysourcesinourfiveChandrafields Conversely,weretainalargesetofpossibletemplatestoensurewe
withhigh-qualityspectroscopicredshifts(blacksolidline)andthosewhere producep(z)distributionsthataccountforthelargeuncertaintiesin
weadoptphotometricredshifts.Thebluedashedlineindicatesthedistribu-
theredshiftandtemplatedegeneracies.Whilewehavehigherout-
tionofthe“best”photo-zestimates(meanofthep(z)distribution),whereas
lierrates,ourfractionofcatastrophicfailuresremains.5percent,
theorangedottedlineshowsthedistributionobtainedbycombiningthein-
indicatingthatourp(z)distributionsarerepresentingtheuncertain-
dividualp(z)distributions.
ties. Thenominalerrors(i.e.the68percentconfidenceintervals)
on our photo-z are also comparable to the residuals between our
bestphoto-z estimateandtheavailablespectroscopicredshifts,in
fractionofsourceswherelessthan5percentoftheintegrated
contrasttomostpreviousworkwhereerrorsmaybeunderestimated
p(z)lieswithin−0.15<(z−z )/z <+0.15.
spec spec byafactor∼2−6(e.g.Luoetal.2010;Hsuetal.2014).Further-
Over fourof ourfields(CDFS,CDFN,EGSandCOSMOS) more,werequirethefullp(z)distribution,whichmostpriorstudies
weobtainaconsistentaccuracyofσ ≈0.06,with∼15per donotprovide. Wethuschoosetouseourownphotometricred-
NMAD
cent outliers. Our approach ensures we assign anappropriate un- shifts:our poorer accuracy andhigher outlier ratesareaccounted
certainty, traced by the p(z),tothe bulk of our sources and only for and compensated by our Bayesian analysis that incorporates
∼ 5per cent of sources arethus flagged ascatastrophic failures. thefullp(z)information.
In the Bootes field—our largest area, shallowest field—we have
poorer accuracyandamuchhigher outlierfraction,reflectingthe
morelimitedphotometricimaginginthisfield.However,thecatas- 3 BAYESIANMETHODOLOGY
trophic outlier fraction is only ∼ 1 per cent, indicating that this
Inthispaper weexpand ontheBayesianmethodology developed
additionaluncertaintyisrepresentedbyourp(z)distributions.We
byA10,incorporatingthedistributionofX-rayabsorptionproper-
alsonotethatinthisfieldwehavethehighestspectroscopiccom-
tiesandaccounting for theeffectsontheinferredshape andevo-
pleteness(∼75percent)andsoonlyusephotometricredshiftsfor
lutionoftheXLF.Ourmethodalsoaccountsfortheuncertaintyin
arelativelysmallfractionofthesourcesinoureventualanalysisof
themeasuredX-rayflux(duetophotoncountingstatistics),uncer-
theXLF;whenwedoresorttoaphotometricredshiftweaccount
taintiesintheredshift(forsourceswithphotometricredshiftsorno
forthelargeuncertaintyintheredshift.
counterparts),uncertaintiesintheX-rayspectralshape,andthere-
In Figure 3 weplot the distributionof redshift estimatesfor
sultinguncertaintyintheX-rayluminosityforanindividualsource.
sourcesinourChandrafieldswherewehaveaspectroscopicred-
Ourmethodologyisdescribedbelow.
shiftandthosewhereweadopt thephotometricredshiftinforma-
tion.Generallythesourceswithphotometricredshiftslieathigher
redshifts, a consequence of spectroscopic follow-up programmes 3.1 Probabilitydistributionfunctionforasinglesource
beingbiasedtowardsopticallybrightsources.Wealsoshowthein-
For a single source in either our hard- or soft-band sample we
tegratedcontributionfromthep(z)ofallthephoto-zsources.The
canderivetheprobabilitydistributionfunctionforz,L andN
integratedp(z)isskewedtowardslowerredshifts.Thisskewisdue X H
based on our observed data for that source alone, which is given
to the possibility that many potential high-redshift sources could
actuallylieatlowerredshifts,whichisreflectedbytheirp(z)and byp(z,LX,NH | Di)whereDi indicatestheobserveddatafrom
sourceiinoursample.Thisfunctionisnormalizedsuchthat
mustbeaccountedforinmeasurementsoftheXLF.
A small fraction of our X-raysources (< 2 per cent) lacka
dz dlogLX dlogNH p(z,LX,NH |Di)=1. (5)
multiwavelengthcounterpart,precludingaphotometricredshiftes-
Z Z Z
timate.Weretainthesesourcesinouranalysis,ensuringcomplete- Wecanre-writetheprobabilitydistributionfunctionas
nessofoursample,butadoptap(z)thatisconstantinlog(1+z)
over our allowed redshift range (0 < z < 10). Thisreflects our p(z,LX,NH |Di)=p(z|di)p(LX,NH |z,Ti,bi) (6)
lack of a priori knowledge of the redshift; the X-ray flux infor- where di indicates the multiwavelength data used to estimatethe
mationisretainedandthusaposteriori(afterfoldingtheconstant redshiftandTiandbicorrespondtotheX-raydataforthissource:
(cid:13)c 2015RAS,MNRAS000,1–36
The evolutionoftheXLFs ofunabsorbedand absorbedAGNs 9
tion of this power-law, f , is allowed to emerge as an unab-
scatt
sorbedcomponent that isthought tobescattered intotheline-of-
sightbyionizedgasinthevicinityoftheAGN.Wealsoincludea
contributiondue toCompton reflectionfromcold, optically thick
matter, which gives rise to a characteristic “hump” in the X-ray
spectrum at ∼ 30 keV. Such a reflection component is expected
duetoreprocessingoftheprimaryX-rayemissionbyasurround-
ing, dusty torus or an accretion disc. Weadopt thepexrav model
(Magdziarz&Zdziarski 1995), which is based on Monte-Carlo
simulationsofComptonreflectionfromacold,opticallythickslab
ofmaterial.Weassumetheincidentpower-lawhasthesameshape
asthedirectlytransmittedcomponent.Wefixtheinclinationangle
to30◦asarepresentativevalueandallowtheintensitytobesetby
thenormalization,R,relativetothatexpectedfromaslabsubtend-
ing a solid angle of 2π (which is allowed to vary between 0 and
2, spanning the extreme cases of no reflection up to an effective
4π solidanglecoverage).Weabsorbthereflectioncomponent by
thesamecolumn density seenbythe primaryemission. Thisisa
Figure4.OurassumedX-rayspectralmodelforanAGN.Weassumethe
intrinsic X-ray spectrum is a power law with photon index Γ = 1.9± goodassumptionwhenthereflectionarisesfromtheaccretiondisc
0.2(purple line). The observed spectrum is absorbed bythe intervening andalsoprovidesreasonableagreementwiththeshapeandinten-
column density, fixed at NH = 5×1022 cm−2 for this example (red sityofthereflectioncomponent basedonsophisticatedmodelsof
dashed line). Wealso allow for a fraction (fscatt ≈ 2 per cent) of the toroidal obscurers (e.g Brightman&Nandra 2011a). All compo-
intrinsicpower-lawtobescattered,unabsorbed,intotheline-of-sight(blue nents aresubjected to Galacticabsorption, withcolumn densities
dot-dashed line). Inaddition, weallow for acomponent from Compton- determinedfromDickey&Lockman(1990)viatheHEASOFTNH
reflectionfromcold,opticallythickmatter(suchasatorusoraccretiondisc)
tool.InXSPECterminology,ourmodelisdescribedby
thatleads tothecharacteristic humpathighenergies (greendottedline).
Theblacklineindicatesthetotalobservedspectrum,whilethegreyregion wabs∗ (1−constant)∗zwabs∗cabs∗zpowerlw∗zhighect
indicatesthe95percentconfidenceintervalonthespectrum,allowingfor
+constant∗zpowerlw
therangeofpossiblespectralparameters(seeSection3.1,Table2). (cid:2)
+zwabs∗pexrav (8)
wheretheconstantcorrespondsto(cid:3)thescatteredfraction,f .We
thetotalobservedX-raycountsinthegivenbandandtheestimated scatt
note that more physically motivated models could be adopted to
backgroundrespectively.
describetheX-rayspectrum,self-consistentlymodelingtheemis-
Ourknowledgeofzisbasedoneitheraspectroscopicredshift,
sion, reflection and absorption due to the accretion disc or torus
inwhichcaseweassumep(z | di)isdescribedbyaδ-functionat (e.g.Ross&Fabian2005;Brightman&Nandra2011a).However,
thespectroscopicvalue,oraphotometricredshift,whenp(z | di) Buchneretal. (2014) found that more simplistic models such as
isgivenbythep(z)fromourphotometricredshiftfittingdescribed
ours are generally sufficient to reproduce the observed spectral
inSection 2.6above. For the small fraction of sources wherewe
shapeofindividual,distantAGNs,especiallyconsideringouranal-
were unable to identify amultiwavelength counterpart—and thus
ysisusesbroad-bandfluxesratherthanperformingadetailedX-ray
havenoredshiftinformation—weadoptap(z)distributionwitha
spectralanalysis.
constantdensityinlog(1+z)over0<z<10.
TodescribeourX-rayspectralmodelrequiresthreeadditional
TheobservedX-raydatacanbedescribedbyaPoissonpro-
parameters—thephotonindex,Γ,thescatteredfraction,f ,and
cess.Thus,thelikelihoodofobservingTi countsfromasourceis therelativenormalizationofthereflectioncomponent, Rs—catwthich
givenby
weintroduceas“nuisance”parameters(collectivelydesignatedby
L(Ti |ci,bi)= (ciT+i!bi)e−(ci+bi) (7) (ξξ))i,nzo,uLrXBaanydesNianH,anwaelycsains.dFeotreramgiinveenthseetexopfescpteecdtrcaolupnatraramtee,tecris,
andthuslinktheprobabilitydistributionfunctionforL ,N and
where ci is the X-ray count rate from source i in the observed ξtothePoissonlikelihoodgiveninEquation7above.TXhus,H
energy band and we have assumed that the expected background
countrate,bi,iswelldetermined.Theuncertaintyinciisfullyde- p(LX,NH,ξ|z,Ti,bi)∝L Ti|ci(z,LX,NH,ξ),bi π ξ
scribedbythePoissonlikelihoodgiveninEquation7.However,to (9)
(cid:0) (cid:1) (cid:0) (cid:1)
convertfromacountrate,ci,toanestimateofLX andNH (given whereci(z,LX,NH,ξ)istheexpectedcountrateforasourcewith
z)wemustassumeamodelfortheX-rayspectralshapeandfold redshiftz,luminosityL ,absorptioncolumn N ,andadditional
X H
thismodelthroughtheappropriateinstrumentalresponse. spectral parameters ξ based on our X-ray spectral model, folded
Figure4showsanexampleofourX-rayspectralmodel.We throughtheappropriateinstrumentalresponseforsourcei.
assumetheintrinsicX-raycontinuumisdescribedbyapowerlaw Apriori,thespectralparametersξforagivensourcearenot
with photon index Γ and a high energy cut-off (we fix the fold- wellknown;π ξ denotesthepriordistributionthatweadoptfor
ing energy at 300 keV, although this has a negligible impact on ourspectralparameters,whichdescribestherangeofpossibleval-
(cid:0) (cid:1)
thelowerenergiesweobserve).Theobservedspectrumisattenu- uesandthusencapsulatestheuncertaintyinX-rayspectralshape.
atedalongtheline-of-sightbytheinterveningcolumndensity,N . Weassumethephotonindex,Γ,isdrawnfromaGaussiandistribu-
H
We include both photoelectric absorption (using the wabs model tionwithameanof1.9andstandarddeviationof0.2(correspond-
in XSPEC)and Compton-scattering (via cabs), which suppresses ing to the observed distribution of intrinsic photon indices in X-
thecontinuumfurtherforCompton-thickcolumndensities.Afrac- rayspectralstudiesofnearbyAGNs,e.g.Nandraetal.2007).We
(cid:13)c 2015RAS,MNRAS000,1–36
10 J. Airdet al.
orsoft-bandsamplesasindependentdetections.Thus,theonlyX-
Table2.PriorsonthespectralparametersforanindividualX-rayAGN,ξ.
raydataweuseforanindividualsourceisthedetectedcounts(and
theexpected background), whichasdescribed above doesnot al-
Parameter Priortype Priorspecification
low usto constrain thevalue of N for anindividual source. In-
H
Γ Gaussian 1.9±0.2a stead,ourapproach(seeSections3.2below)involvesdetermining
logfscatt lognormal −1.73±0.8b the overall distribution of X-ray luminosities and absorption col-
R constant 0–2
umn densities (given by the XLAF) that correctly describes both
ourhard-andsoft-bandsamples.Usingthismethod,certainvalues
aBasedonobserveddistributionfromNandraetal.(2007).
of L and N may be disfavored a posteriori (after performing
bBasedonobserveddistributionfromWinteretal.(2009). X H
our full analysis of the overall sample). For example, higher val-
ues of L may be disfavored a posteriori based on the shape of
X
assume the scattered fraction, fscatt, is drawn from a lognormal theXLF(thatgenerallyshowshigherLXsourcesshouldberarer).
distributionwithmean of 2per cent and scatter of 0.8 dexbased Conversely, lower values of NH may be disfavoredif our overall
ontheobserved distributionofpartialcoveringfactorsofsources XLAFrequiresalargefractionofabsorbedsources.
intheSwift/BATsamplefromWinteretal.(2009).Forthereflec- Nevertheless,itisworthnotingthatamoresophisticatedanal-
tion strength, R, we assume a uniform distribution in the range ysiscouldplaceconstraintsonthevalueofNH (orindeedanyof
0 < R < 2.Wethusallowforalargeuncertaintyinthestrength theotherspectralparameters)foranindividualsourcebeforeper-
ofthereflectioncomponent,whichisreasonabletoencapsulateun- forming fits to the overall samples. We could combine the infor-
certaintiesinthegeometryoftheaccretiondiscand/ortoruswith mationonthecounts inboththehardandsoftbands foranindi-
oursimplifiedmodelingofthereflection.Table2summarizesthis vidual source to place constraints on the underlying X-ray spec-
priorinformation.ThecolouredlinesinFigure4showeachcom- trum,basedonthishardnessratioinformation(e.g.Hasinger2008;
ponent evaluatedatthepriormeanofthespectralparametersand Xueetal. 2010). Alternatively, the full X-ray spectrum could be
theblacklinecorrespondstothetotalobservedspectrumforthese extracted for a source and fitted with our spectral model or any
values.Thegreyregionindicatesthe95percentconfidenceinterval other well-motivated model (e.g. Tozzietal. 2006; Buchneretal.
onthetotalobservedspectrum,adoptingourpriordistributionsfor 2014).However,accuratelyincorporatingthisinformationintoour
thespectralparameters.Wenotethatthelargeuncertaintiesinthe Bayesian analysis—and fullypropagating theuncertainties inthe
scatteredfraction,fscatt,leadtolargeuncertaintiesinthespectrum estimated spectral parameters, LX and NH—isbeyond the scope
atsofterenergiesformoderatelyandheavilyabsorbedsourcesand ofthispaper.
thusleadstolargeuncertaintiesintheintrinsicL .
X
ToobtaintheprobabilitydistributionfunctionforL andN
X H
3.2 Thelikelihoodfunctionfortheoverallsample
only(foragivenzandourobservedX-raydata),wemustmarginal-
izeoverthenuisancespectralparameters.Thus, Here,wedescribehowwecombinetheindividualprobabilitydis-
tribution functions for each source in our sample with a given
p(LX,NH |z,Ti,bi)= dξp(LX,NH,ξ|z,Ti,bi). (10) model of the XLAF to construct the likelihood function for our
Z overallsample.
In Figure 5 we show an example of p(LX,NH | z,Ti,bi) for a FollowingA10(seealsoLoredo2004),weassumeourindi-
sourcedetectedinthehardband(left)andasourcedetectedinthe vidualsourcesareeffectivelyPoissonpointsdrawnfromadistribu-
softband(right)withChandra.Inbothcaseswefixz=1.0andas- tiondescribedbytheXLAFandtheoverallsampleselectionfunc-
sumeTi =30totalobservedcountswithanexpectedbackground tion.Theexpectednumber ofsourcesinour hard-band sampleis
of bi = 5.0 counts. We restrict the possible column densities to givenby
20<logN (cm−2)<26.Theshadingandcontoursindicatethe
H
dV
rangeofpossiblevaluesofLXandNHforeachsource.Detection Nhard(Θ) = dlogLX dlogNH dzdz dξ (11)
in a single, broad energy band does not place constraints on the Z Z Z Z
vpaolsuseibolefvNaHlu,ebsuotfwLeXaraendabhleowtothpilsacdeepceonndstsraoinntNsoHn.Fthoerrtahneghearodf ψ(LX,z,NH |Θ)π(ξ)NfieldsAj(LX,z,NH,ξ)
band example, we can constrain LX to within ∼ 0.25 dex, pro- (cid:20) Xj=1 (cid:21)
videdtheabsorptioncolumn isNH . 1023 cm−2.Ifthecolumn whereψ(LX,z,NH |Θ)istheXLAF—thedifferentialco-moving
densityishigher,thenthesameobservedcountsmustcorrespondto numberdensityofAGNsperlogarithmicintervalinL andN —
X H
ahighervalueofLX.Forasourcedetectedinthesoftband,absorp- andisdescribedbyamodelwithagivensetofparameters,Θ.We
tcimon−2ef)f.eActtscoarluemapnpdaernesnittifeosrNloHw&er2co×lu1m0n23dcemns−it2ie(sat(Nz=H &1.01)0th22e tnioatlecoth-matotvhiengXnLuFm,bφe(rLdXe,nzsity| oΘf)AG≡NsddΦpl(eoLgrXLlo,Xzg)ar(iit.hem. tihceindteifrfvearlenin-
observedfluxinthe0.5–2keVbandisdominatedbythescattered L ),canberecoveredfromthefullXLAFbyintegratingoverN .
X H
componentonly;theintrinsicluminosityispoorlyconstrainedbut Thus,
mustbeafactor∼30greaterthanifthesourcehadalowerN .
H
Wenotethattheeffectofabsorptionontheobservedcounts φ(L ,z|Θ)= dlogN ψ(L ,z,N |Θ). (12)
X H X H
in the hard or soft energy bands will vary significantly with red- Z
shift.Forexample,atz ∼3,wheretheobserved0.5–2keVenergy Weinvestigateand compare various different parametrizations of
band probes rest-frame energies ∼ 2−8keV, the inferred L is theXLAF(ortheXLFdirectly),whicharedescribedinSections4
X
onlyaffectedforcolumndensities& 1023 cm−2.Theseredshift- and5below.
dependent effectsarefullyaccountedforinourcalculationofthe The distribution of possible spectral parameters is given by
expectedcounts,ci(z,LX,NH,ξ),usingourX-rayspectralmodel. π(ξ),theprioronΓ,fscatt andRthatwedescribeinSection3.1
Fortheanalysisinthispaper,wetreateachsourceinourhard- above. dV isthedifferentialcomovingvolumeperunitarea,asa
dz
(cid:13)c 2015RAS,MNRAS000,1–36