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

36 Pages·2015·4.06 MB·English

MNRAS451,1892–1927(2015) doi:10.1093/mnras/stv1062
The evolution of the X-ray luminosity functions of unabsorbed and
∼
absorbed AGNs out to z 5
J. Aird,1,2‹ A. L. Coil,3 A. Georgakakis,4,5 K. Nandra,4 G. Barro6
and P. G. Pe´rez-Gonza´lez7
1InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,CambridgeCB30HA,UK
2DepartmentofPhysics,DurhamUniversity,DurhamDH13LE,UK
3CenterforAstrophysicsandSpaceSciences(CASS),DepartmentofPhysics,UniversityofCalifornia,SanDiego,CA92093,USA
4MaxPlanckInstitutefu¨rExtraterrestrischePhysik,Giessenbachstrasse,D-85748Garching,Germany
5IAASARS,NationalObservatoryofAthens,GR-15236Penteli,Greece
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6UniversityofCalifornia,SantaCruz,1156HighStreet,SantaCruz,CA95064,USA o
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7DepartamentodeAstrof´ısica,FacultaddeCC.F´ısicas,UniversidadComplutensedeMadrid,E-28040Madrid,Spain n
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Accepted2015May8.Received2015May8;inoriginalform2015February24 fro
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ABSTRACT ://a
WepresentnewmeasurementsoftheevolutionoftheX-rayluminosityfunctions(XLFs)of ca
d
unabsorbed and absorbed active galactic nuclei (AGNs) out to z ∼ 5. We construct samples em
containing2957sourcesdetectedathard(2–7keV)X-rayenergiesand4351sourcesdetected ic.o
u
atsoft(0.5–2keV)energiesfromacompilationofChandrasurveyssupplementedbywide- p
.c
areasurveysfromASCAandROSAT.WeconsiderthehardandsoftX-raysamplesseparately o
m
andfindthattheXLFbasedoneither(initiallyneglectingabsorptioneffects)isbestdescribed /m
n
byanewflexiblemodelparametrizationwherethebreakluminosity,normalization,andfaint- ra
s
endslopeallevolvewithredshift.Wethenincorporateabsorptioneffects,separatelymodelling /a
theevolutionoftheXLFsofunabsorbed(20<logNH<22)andabsorbed(22<logNH<24) rticle
AGNs,seekingamodelthatcanreconcileboththehard-andsoft-bandsamples.Wefindthat /45
1
theabsorbedAGNXLFhasalowerbreakluminosity,ahighernormalization,andasteeper /2
faint-endslopethantheunabsorbedAGNXLFouttoz∼2.Hence,absorbedAGNsdominate /18
9
2
at low luminosities, with the absorbed fraction falling rapidly as luminosity increases. Both /1
7
XLFsundergostrongluminosityevolutionwhichshiftsthetransitionintheabsorbedfraction 4
7
7
to higher luminosities at higher redshifts. The evolution in the shape of the total XLF is 8
4
primarilydrivenbythechangingmixofunabsorbedandabsorbedpopulations. b
y
g
u
Key words: galaxies: active–galaxies: evolution–galaxies: luminosity function, mass e
s
function–X-rays:galaxies. t o
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M
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2
0
ManyAGNsaresurroundedbygasanddustthatcanobscuretheir 2
1 INTRODUCTION 3
emissionatcertainwavelengths.Thus,itisvitaltounderstandAGN
Theluminosityfunctionofactivegalacticnuclei(AGNs)represents obscurationinordertoobtainaccuratemeasurementsofthelumi-
oneofthecrucialobservationalconstraintsonthegrowthofsuper- nosityfunction.QuantifyingAGNobscurationalsorevealswhether
massiveblackholes(SMBHs)overthehistoryoftheUniverse.The SMBHsundergosignificantperiodsofobscuredgrowth,whenthis
shapeoftheluminosityfunctionreflectsacombinationoftheunder- takesplacewithinthelifetimesofAGNs,andhowitrelatestothe
lyingdistributionoftheSMBHmassesandthedistributionoftheir triggeringandfuellingprocesses.
accretionratesorEddingtonratios(e.g.Airdetal.2013a;Shankar, Obtainingaccuratemeasurementsoftheluminosityfunctionand
Weinberg&Miralda-Escude´2013;Schulzeetal.2015).Thus,ac- revealingtheextentofobscurationrequireslarge,unbiasedsamples
curatemeasurementsoftheshapeandevolutionoftheluminosity ofAGNsselectedoverthewidestpossiblerangeofredshiftsandlu-
function provide crucial insights into the physical processes that minosities.Opticalsurveys,combinedwithfollow-upspectroscopy,
driveSMBHgrowthovercosmictime. canefficientlycoverwideareas(e.g.SDSS:Yorketal.2000)but
arebiasedtowardsthemostluminous,unobscuredsources.Alterna-
tively,AGNscanbeidentifiedinthemid-infrared(mid-IR),which
(cid:2)E-mail:[email protected] probesthereprocessedemissionfromthedusty,obscuringmaterial.
(cid:3)C 2015TheAuthors
PublishedbyOxfordUniversityPressonbehalfoftheRoyalAstronomicalSociety
TheXLFsofunabsorbedandabsorbedAGNs 1893
Mid-IRselectionshouldnotbebiasedagainstobscuredsources,but bate (see Akylas et al. 2006; Dwelly & Page 2006), potentially
thecontributionofthehostgalaxyisoftensignificantatthesewave- due to difficulties regarding the selection functions for absorbed
lengths,whichlimitsmid-IRselectiontoluminoussourceswhere and unabsorbed sources. Recent work by Ueda et al. (2014) re-
the galaxy light is overwhelmed by the AGN (e.g. Donley et al. examinedtheevolutionoftheXLFandthedistributionofN (the
H
2008;Mendezetal.2013). ‘N -function’) using a large compilation of both soft and hard
H
X-raysurveyscanefficientlyidentifyAGNsoverawideluminos- X-ray surveys and found that both a luminosity and redshift de-
ityrange,includinglow-luminositysourceswherethehostgalaxy pendenceoftheabsorbedfractionwererequired.Theyalsofound
dominates at optical or infrared wavelengths (e.g. Barger et al. that an LDDE parametrization was needed to describe the evo-
2003). Nevertheless, soft X-ray emission (at energies (cid:2) 2 keV) lution of the XLF (with some further modifications to describe
will be absorbed by the same gas and dust that obscures the the evolution at z (cid:3) 3, see also Civano et al. 2011; Hiroi et al.
AGN at optical and UV wavelengths. Thus, soft X-ray samples 2012).
aregenerallydominatedbyunobscuredAGNs.Absorptionbiases Recently,thecombinationofextremelydeepX-raysurveydata
are reduced at hard X-ray energies (∼2–10 keV), except in the and new approaches to X-ray spectral analysis have enabled im-
mostheavily-obscured,Compton-thickAGNs(equivalentline-of- proved measurements of N at z ∼ 0.5–2 and have been used to
H D
sighthydrogencolumndensitiesNH(cid:3)1024cm−2).However,even identify sizable samples of Compton-thick AGNs (e.g. Comastri ow
Compton-thick sources may still be identified at soft or hard X- etal.2011;Georgantopoulosetal.2013;Brightmanetal.2014). nlo
a
ray energies due to scattered emission, including the Compton- Buildingonthiswork,Buchneretal.(2015)usedaflexible,non- d
e
scattered emission (‘reflection’) from the obscuring material parametric method to estimate the space densities of AGNs as a d
itself. functionofredshift,luminosity,andN ,effectivelymeasuringthe fro
H m
AlargenumberofdeepandwideX-raysurveyshavebeencar- XLFfordifferentcolumndensities.Thisworkalsorecoveredalu- h
ried out, taking advantage of the efficiency and power of X-ray minosity and redshift dependence in the evolution of the fraction ttp
s
selection (see a recent review by Brandt & Alexander 2015). A ofabsorbedAGNs(althoughtheCompton-thickfractionwascon- ://a
number of studies have measured the X-ray luminosity function sistentwithaconstantvalueof∼35percent).However,adetailed ca
d
(XLF) of AGNs out to high redshifts using these samples (e.g. comparisonofparametricmodelsfortheevolutionoftheXLFof e
m
Ueda et al. 2003; Barger et al. 2005; Miyaji et al. 2015). These AGNswasnotundertaken. ic
.o
studiesfindthatAGNsareastronglyevolvingpopulation,witha Inthispaperweaddresssomeremainingissuesinstudiesofthe u
p
sharpdecreaseintheirnumberdensitybetweenz∼1–2andtoday. evolution of the XLF of AGNs: the shape of the XLF and how .c
o
BrightX-ray-selectedAGNsarefoundtopeakinnumberdensity itevolves withredshift,theextent ofanyluminosityand redshift m
at z ≈ 2, similar to optically selected QSOs. Fainter AGNs peak dependenceoftheabsorbedfraction,andtheconnectionbetween /m
n
laterinthehistoryoftheUniverse(z≈1)butwithamuchmilder theabsorptionpropertiesandtheevolutionoftheAGNpopulation. ra
s
declinetothepresentday(e.g.Hasinger,Miyaji&Schmidt2005). WecombinesamplesselectedatbothhardandsoftX-rayenergies /a
These patterns have led several authors to propose a luminosity- anddeterminetheunderlyingXLFanddistributionofN thatad- rtic
H le
dependent density evolution (LDDE) parametrization to describe equatelydescribestheobservedfluxesinbothsamples(similarto /4
5
theevolutionoftheXLFofAGNs(e.g.Miyaji,Hasinger&Schmidt the approach of Ueda et al. 2014, cf. the X-ray spectral analysis 1
/2
2000;Uedaetal.2003).InthismodeltheXLFismodifiedbydif- usedinBuchneretal.2015). /1
8
fering degrees of density evolution that vary with luminosity and InSection2wedescribeourdatasetsthatweusetodefinelarge 9
2
redshift. This results in an XLF that changes shape over cosmic samplesofX-raysourcesselectedinthehard(2–7keV)andsoft /1
7
time. (0.5–2 keV) energy bands. We also compile deep optical, near- 47
7
InAirdetal.(2010,hereafterA10)wechallengedthisevolution- IR, and mid-IR imaging across our fields that we use to robustly 8
4
arymodelwithadetailedstudyofthehard-bandXLFthatcarefully identify counterparts to our X-ray sources and calculate photo- b
y
accountedfornumerousuncertaintiesandbiasesthatweregenerally metricredshifts.InSection3,wedescribeourBayesianstatistical g
u
notincludedinpriormeasurements.Theseincludedfluxmeasure- technique that allows us to incorporate a range of X-ray spectral es
menterrors,Eddingtonbias,incompletenessofopticalidentifica- shapesandaccountfortheeffectsofabsorption.Wealsointroduce t o
n
tions,andtheuncertaintyinphotometricredshiftestimates.Athigh an approach to account for the contribution from normal, X-ray- 0
9
redshifts(z∼2–3)weadoptedarest-frameUVcolourpre-selection detectedgalaxiesonourmeasurements.Wethenpresentmeasure- M
a
technique(Airdetal.2008).Byperformingarobustmodelcom- mentsoftheXLFbasedonourhardandsoftsamplesindividually rc
h
parisonbasedonBayesianstatisticaltechniques,wefoundthatthe (Section4),introducinganewflexibleparametrizationoftheXLF. 2
0
evolution of the XLF could be described by a simpler model in Weshowthatsignificantdiscrepanciesbetweenthemeasurements 2
3
whichtheXLFretainsthesameshapeatallredshiftsbutevolvesin atallredshiftswarrantthefurtherconsiderationofabsorptionef-
bothluminosityanddensity(seealsoAssefetal.2011;Rossetal. fects. In Section 5 we separately model the XLF of unabsorbed
2013). andabsorbedAGNs(includingacontributionfromCompton-thick
While A10 presented a number of important advances, ab- sources)andshowhowthecombinationofthesepopulationscan
sorption effects were not explored. Other studies have attempted simultaneouslyaccountforbothourhard-andsoft-bandsamples.
to measure the distribution of absorption column densities and OurresultsplaceconstraintsonthetotalXLFofAGNsandtheab-
presentabsorption-correctedmeasurementsoftheXLF.Uedaetal. sorbedfractionasafunctionofluminosityandredshift.InSection6
(2003) found that the fraction of absorbed AGNs (those with wecompareourresultstopriorworkanddiscussthewiderimpli-
N >1022 cm−2)wasstronglydependentonluminosity,decreas- cationsofourfindings.Section7summarizesourpaperandoverall
H
ingathigherluminosities.Laterstudiesfoundthatthefractionof conclusions.
absorbed AGNs depends on both luminosity and redshift, drop- Giventhelengthofthispaper,acasualreadermaywishtoskip
ping at high luminosities but increasing (at a given luminosity) toSection4.4,Section5,andthediscussioninSection6(andfocus
to higher redshifts (e.g. La Franca et al. 2005; Hasinger 2008). onFigs7–9).Weadoptaflatcosmologywith(cid:3)(cid:4)=0.7andh=
The extent of any redshift evolution has been a matter of de- 0.7throughoutthispaper.
MNRAS451,1892–1927(2015)
1894 J.Airdetal.
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 E-CDFS 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%)
D
– AMSS – – – 81.77 – – – 109 109(100%) 107(98%) o
– ROSAT – – – 20391 221 221(100%) 221(100%) – – – wn
lo
Total 4351 4253 2503 2957 2902 1641 ad
e
d
Nexoptoess.urCeotliummen;s(:6)(1t)otnaalmareeaofcothveerfieedldb;y(b2o)tnhatmheeXof-rXay-rdayatasuarnvdeythperoogprtaicmalmoerwiniftrhairnedthiimsfiageilndg;,(3ex,4c)luadpipnrgoxairmeaasteclcoesnetrteoobfrigthhetsstuarrvse;y(;7)(5n)unmobmeirnoaflXX--rraayy from
sourcesdetectedinthesoft(0.5–2keV)energyband;(8)number(andfraction)ofthesoftX-raysourcesthatareassociatedwitharobustmultiwavelength h
counterpart;(9)number(andfraction)ofthesoftX-raysourcesthathaveaspectroscopicredshift;(10)numberofX-raysourcesdetectedinthehard(2–7keV) ttp
s
energyband;(11)number(andfraction)ofthehardX-raysourcesthatareassociatedwitharobustmultiwavelengthcounterpart;(12)number(andfraction) ://a
ofthehardX-raysourcesthathaveaspectroscopicredshift. c
a
d
e
m
2 DATA In each of the remaining fields we adopt data from a single ic
Chandrasurvey:the2MssurveyinCDFN(Alexanderetal.2003); .ou
To constrain the evolution of the XLF we require large samples the∼160-ksC-COSMOSobservations(Elvisetal.2009;Puccetti p.c
of X-ray-selected AGNs. By selecting samples in both the hard o
etal.2009);andthe5-ksXBootessurvey(Murrayetal.2005). m
(>2keV)andsoft(0.5–2keV)observedenergybands,wecanalso TheX-raydatafromallofoursurveyswerereducedwithourown /m
constrainthedistributionofNHandcorrectfortheseeffectsonthe pipelineprocedure,whichisdescribedindetailbyLairdetal.(2009) nra
XLF.InthispaperwecombinealargenumberofChandraX-ray andNandraetal.(2015).Weperformedpointsourcedetectionusing s/a
surveysalongwithlargerareasurveysfromASCAandROSAT.We theproceduredescribedbyLairdetal.(2009)andappliedafalse rtic
givefurtherdetailsofourdatasetsbelow.Table1summarizesthe le
Poissonprobabilitythresholdof<4×10−6togeneratecatalogues /4
differentsurveysandprovidesthenumberofhardandsoftX-ray- 5
of detected sources in the soft (0.5–2 keV), hard (2–7 keV), full 1
selectedsourcesfromeach. /2
(0.5–7 keV) or ultrahard (4–7 keV) observed energy bands. We /1
8
combinedthesourcelistsineachbandtocreateamergedcatalogue, 9
2
whichisusedinthecounterpartidentificationproceduredescribed /1
2.1 ChandraX-raydata inSection2.2below. 747
7
InthispaperweuseChandraX-rayobservationsfromfivedistinct Forthe5-ksXBootessurveyweappliedastricterfalseprobabil- 8
4
partsofthesky:theChandraDeepField-South(CDFS),Chandra ity cut (<10−8) in addition to a requirement of ≥5 total detected b
y
Deep Field-North (CDFN), Extended Groth Strip (EGS), COS- countsineachband.Thiscutreducesthesamplesizebutapplies g
u
MOS,andBootesfields. aneffectiveX-rayfluxlimitthathelpsraisethecompletenessofthe es
In the CDFS field we identify two different ‘surveys’: (1) the spectroscopicfollow-upinthisfield.Inthisfield,wealsorestrict t o
n
seriesofobservationsthathavetargetedthecentral∼0.07deg2 of ouranalysistothe∼7.1deg2 oftheBootesfieldthatcorresponds 0
9
thefieldandreachatotalcombinedexposuretimeof∼4Ms(the to the 15 standard sub-fields of the AGES spectroscopic survey M
a
CDFS-4Mssurvey;Xueetal.2011);and(2)theseriesoffour250ks (Kochaneketal.2012).Thiscutalsoensureswehaveahighspec- rc
h
observationsthatsurroundthecentralarea(theExtended-CDFS,or troscopiccompleteness(seeSection2.5below). 2
0
E-CDFS survey; Lehmer et al. 2005). The X-ray data reduction WedeterminedX-raysensitivitymapsandareacurvesforeach 2
3
and source detection procedures were carried out independently bandasdescribedinGeorgakakisetal.(2008),accountingforthe
foreachofthesesurveys.Tocombinethetwosurveys,wedefine stricterfalseprobabilitycutandminimumcountsrequirementfor
a central region where the CDFS-4Ms survey takes precedence, theXBootessurvey.Weconvertthesensitivitymapstoareacurves
roughlycorrespondingtotheareawithin∼9arcminofthecentreof as a function of flux by assuming a fixed X-ray spectral slope of
thefield.Outsidethiscentralregionweadoptthesourcesdetected (cid:5)=1.4.Wenotethatthefluxcalculatedwiththisfixedconversion
intheE-CDFSsurveyonly.Thisprocedureensureswehaveawell- factorscalesdirectlywiththecountrate;inSection3belowwede-
definedsamplewherewecanaccuratelydeterminethesensitivity. scribeourproceduretoconvertbetweenthecountrateandintrinsic
In the EGS field we also identify two distinct surveys: (1) the quantities(suchasluminosity),whichallowsforamorecomplex
series of eight pointings that reach a nominal depth of ∼200 ks X-ray spectrum and accounts for uncertainties in this conversion
and were presented in Laird et al. (2009), which we refer to as factor.Thesensitivitymapcalculationislimitedtothefootprintof
the AEGIS-XW(ide) survey; and (2) the AEGIS-XD(eep) survey the multiwavelength photometry for each field. Fig. 1 shows the
(Nandra et al. 2015) which took three of the original 200 ks to a correspondingareacurvesforeachofourX-rayfields.
depth of ∼800 ks. We adopt the deeper AEGIS-XD observations WenotethatpreviouslypublishedX-raysourcecatalogues,often
whenavailable. includingmutiwavelengthcounterpartinformation,areavailablefor
MNRAS451,1892–1927(2015)
TheXLFsofunabsorbedandabsorbedAGNs 1895
stricter(i.e.lower)falseprobabilitythreshold.Thus,ourcatalogues
aremoreconservative.
2.2 Multiwavelengthcounterpartsandphotometry
IneachofourChandrafields,weidentifymultiwavelengthcoun-
terpartstoourX-raysourcesusingthelikelihoodratio(LR)method
(e.g. Ciliegi et al. 2003; Brusa et al. 2007; Civano et al. 2012),
matchingtomultipleoptical,near-IR,andmid-IRbandstoensure
a high completeness and reliability. We also compile multiwave-
lengthphotometryfromalargernumberofbands,whichweuseto
calculatephotometricredshifts(seeSection2.6below).
D
o
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2.2.1 CDFS,CDFN,andEGS n
lo
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In three of our fields – the CDFS, CDFN, and EGS – we iden- e
d
tify counterparts and extract the multiwavelength photometry us- fro
ing a custom version of the Rainbow Cosmological Surveys m
. Database1(Pe´rez-Gonza´lezetal.2005,2008;Barroetal.2011a,b), http
whichprovidesacompilationofthevariousphotometricdatasets. s
AppendixAlistsallthedifferentphotometricimagingdatasetsfor ://a
c
eachfieldthatareusedinthispaper.Wenotethatfullcoverageof ad
e
the entire field is not always available in each photometric band. m
ic
All the images are registered to a common astrometric reference .o
u
frameandphotometryisperformedinconsistentaperturestopro- p
.c
duce spectral energy distributions (SEDs) that span from the UV o
m
to mid-IR. The X-ray source matching procedure is described in /m
detailinNandraetal.(2015),butwebrieflysummarizethemethod n
ra
here. s
/a
First,wererantheRainbowphotometriccode,extractingallpo- rtic
tentialcounterpartswithin3.5arcsecoftheX-raypositionsinanyof le
/4
thebandscoveredbyRainbow(usinginitialSEXTRACTORcatalogues 5
1
ineachofthebands).Thecounterpartswerethencross-matchedus- /2
/1
inga2-arcsecsearchradiustocreateasinglemultibandcatalogue. 8
9
We obtained consistent photometry by applying a single aperture 2
/1
acrossallopticalandnear-IRbands.WealsoextractedIRACpho- 7
4
tometry,applyingtheproceduredescribedinPe´rez-Gonza´lezetal. 77
8
(2008) and Barroet al. (2011a) to deblend the IRAC photometry 4
b
whenasingleIRACsourceisassociatedwithmultipleoptical/near- y
g
IRcounterparts. u
e
Figure1. X-rayareacurves(sensitiveareaversusX-rayflux)foreachof Next, we calculated the LR for all candidate counterparts de- st o
oursurveysinthesoftandhardbands.Theblacklineindicatesthetotalarea tectedintheIRAC3.6μmbandanddeterminedanLRthreshold n
0
curveforourstudy.Welimitoursensitivityanalysistotheareafallingwithin that maximizes the sum of the completeness and reliability (see 9
thefootprintofourmultiwavelengthphotometry,excludingareascloseto Luo et al. 2010). A candidate counterpart that exceeded this LR Ma
brightstars.TheROSATareacurveincludestheROSATbrightsurveyand thresholdwasdeemedasecurecounterpart(takingthecounterpart rch
SA–N survey (see Section 2.3). The EGS area curve includes both the withthehighestLRvalueincasesof>1securecandidate).Wethen 20
AEGIS-XD800ksdataandtheadditionalareaat200ksfromAEGIS-XW. 2
repeatedtheentireLRmatchingprocessforthebandsindicatedin 3
TheCDFSareacurvecombinestheCDFS4Msdatawiththeflanking250ks
thetableinAppendixA,retaininganyadditionalsecurecounter-
datafromtheE-CDFS.Theseareacurvesassumeasingle,fixedconversion
factorbetweentheX-raycountrateandflux,correspondingtoanX-ray partsidentifiedinthesebands.Thisprocedureenablesustoidentify
spectrumwithaphotonindex(cid:5) =1.4andGalacticabsorptiononly;the securecounterpartsforahighfraction(>90percent)oftheX-ray
effectofdifferentX-rayspectralshapes–andtheresultinguncertainties sources in the CDFS, CDFN, and EGS fields (see Table 1). The
intheconversionfactors–areaccountedforinourBayesianmethodology vastmajority(∼92percent)ofthesecurecounterpartswereiden-
describedinSection3. tifiedinthe(deblended)IRAC3.6μmcatalogue.Matchingtothe
additionalbandsallowsustoidentifycounterpartswhentheIRAC
theallofourChandrafields(e.g.Alexanderetal.2003;Brandetal.
candidate is faint, blended, or non-existent. No additional cross-
2006; Goulding et al. 2012). Adopting our own X-ray reductions
matchingisrequiredasthefullmultibandphotometryisprovided
andsourcedetectionproceduresensureswecanaccuratelydeter-
throughmatchedaperturesforallsourcesintheRainbowdatabase.
minethesensitivityinaconsistentmanner,whichisessentialfor
our Bayesian analysis of the XLF. Our catalogues contain ∼10–
25percentfewersourcesthanXueetal.(2011)andPuccettietal.
(2009)intheCDFS-4MsandC-COSMOSareas,mainlyduetoour 1https://rainbowx.fis.ucm.es
MNRAS451,1892–1927(2015)
1896 J.Airdetal.
2.2.2 COSMOS 2.3 Large-areasurveys
IntheCOSMOSfield,whichisnotcurrentlyincludedintheRain- CombiningourfiveChandrafieldsprovidesasampleofover4000
bow surveys data base, we matched directly between our X-ray soft-band detections and over 2800 hard-band detections from a
source lists and two multiwavelength catalogues: (1) the COS- totalareaof∼9deg2.However,toaccuratelyconstrainthebright
MOSIntermediateandBroadBandPhotometryCatalogue2008,2 endoftheXLFrequiressamplesofhigherluminosityX-raysources
which is based on detection in the deep Subaru i+ imaging of identifiedfromlarger-areasurveys.Wethussupplementoursample
the entire COSMOS field (Capak et al. 2007); and (2) the S- withsourcesfromlarge-areasurveyscarriedoutwithASCA(inthe
COSMOS IRAC 3.6 μm based catalogue (Sanders et al. 2007). hardband)andROSAT(inthesoftband).
Unlike the Rainbow catalogues, the S-COSMOS IRAC 3.6 μm Forourlarge-areahard-bandsample,weincludethe34sources
cataloguehasnotbeendeblended.Thus,wefirstidentifiedsecure fromtheASCALargeSkySurvey(ALSS:Uedaetal.1999),which
matches (using the LR method) from the higher-resolution Sub- coversacontiguousareaof5.8deg2 nearthenorthGalacticpole.
aru i+ catalogues. We found secure counterparts for 1348 of the We adopt the optical identifications from Akiyama et al. (2000):
1621X-raysources(83percent)inouroverallC-COSMOScata- 2 sources are optically identified as galaxy clusters, 1 is a star, 1
logue.Next,weappliedtheLRmethodtomatchbetweentheX- source remains unidentified, and the remaining 30 are associated Do
w
rayandS-COSMOScatalogues.Weidentifiedsecurecounterparts withAGNs,allofwhichhavespectroscopicredshifts.Wealsose- n
for an additional 178 sources, taking our overall completeness to lect sources from the ASCA Medium Sensitivity Survey (AMSS; loa
d
94percent. Ueda et al. 2001), which combines data from a large number of e
d
Finally,wecross-matchedbetweenoursecurepositionsandthe ASCAobservationsathighGalacticlatitudesoveranarea∼82deg2. fro
originalcatalogues,againusingtheLRmethodtoensureonlysecure We includesourcesfromtheAMSSnsub-sample,selectedinthe m
h
associationsareconsidered.For1499ofthe1526securecounter- hard (2–10 keV) band, with optical identifications presented by ttp
pFaorrtsth,weseeesnodurucpewswitheboobtthaianSpuhboatroumi+etaryndinSu-CpOtoS1M8ObSrocaodu-nbtaenrdpafirlt-. Ahaksiy1a0m0paeertcaeln.t(s2p0e0c3t)r.osTchoepiscamcopmleplientcelnuedsess.W87eXin-craluydseoaudrdceitsioannadl s://ac
a
tersspanningfromtheUVtonear-IR,aswellas15intermediate-or sources from the AMSSs sub-sample (Ueda & Akiyama, private d
e
narrow-bandopticalfilters,fromtheSubarui+catalogue(seeIlbert communication),whichincludes20AGN;twosourcesinthissam- m
ic
etal.2009;McCrackenetal.2010).Thephotometrywasextracted pleremainunidentified.WeadoptareacurvesfromtheALSSand .o
u
in3-arcsecdiameteraperturesfromPSF-matchedimages.Wealso AMSSfromAkiyamaetal.(2003)andUedaetal.(2003),respec- p
adoptIRACphotometryinthe3.6,4.5,5.8,and8.0μmbandsfrom tively. .co
m
theS-COSMOScatalogue,applyingtheaperturecorrectionsgiven Foroursoft-bandsamplewecombinesamplesfromtheROSAT /m
inIlbertetal.(2009). BrightSurvey(RBS;Fischeretal.1998;Schwopeetal.2000)and nra
In 27 cases we have an i+ counterpart but do not find an S- theSelected-Area–Northsurvey(SA–N:Appenzelleretal.1998), s/a
COSMOScounterpart,eitherduetothelimiteddepthoftheIRAC removing duplicate sources. We include sources with significant rtic
imaging or because the i+ source is blended at the IRAC resolu- detections in the 0.5–2 keV band and adopt the unabsorbed flux le
/4
tion. For these sources we simply ignore the IRAC bands in our estimates(correctedforGalacticabsorption).Wecutoursampleat 5
1
photometricredshiftestimates(seeSection2.6below). fluxlimitsoff >3.6×10−12ergs−1cm−2fortheRBSsample /2
In23cases,weidentifyanS-COSMOScounterpart,butnoSub- andf >0.51-2×keV10−12ergs−1cm−2fortheSA–Nsample.These /18
0.5-2keV 9
arui+source.Forthesesourcesweextractedphotometryin3-arcsec highfluxlimitsensureoursourcesallliewellabovethesensitivity 2/1
diameteraperturesattheS-COSMOSpositioninthePSF-matched limitsofthesurveys,allowingustoadoptsimplesensitivitycurves 74
7
imagesforalltheUVtonear-IRbands,generallyobtainingonly thatcorrespondtotheentireareaofeachsurveyandcutoffsharply 7
8
upperlimitsfortheseopticallyfaintsources. ateachofthefluxlimits(seeFig.1).Allthesourcesabovethese 4 b
fluxlimitshavespectroscopicclassificationsandweidentifyatotal y g
of221AGNswithspectroscopicredshifts(excludingBLLactype u
e
s
2.2.3 Bootes objects). t o
FortheBootesfield,wecompiledmultiwavelengthcataloguesfrom Wenotethat,incontrasttoourChandrafields,ourareacurves n 0
forourlarge-areasurveysdonotaccountforthePoissonnatureof 9
the NOAO Deep Wide-Field Survey (NDWFS; Jannuzi & Dey M
the detection. As we restrict the samples from the large-area sur- a
1999) DR3, Sloan Digital Sky Survey (SDSS) DR9 (Ahn et al. veys to highly significant detections, this simplification will have rch
2012),GALEXGR7,3FLAMINGOSExtragalacticSurvey(Elston 2
aminimaleffectonourXLFmeasurements.However,differences 0
etal.2006),andtheSpitzerDeep-WideFieldSurvey(Ashbyetal. 2
in the assumed spectral shape can have a significant impact on 3
2009). We use the LR method to match our X-ray catalogues to
theestimateofafluxandthustheassumedsensitivity.Uncertain-
theappropriateselectionbandforeachofthesesurveys,assigning
ties in the spectral shape and the resulting differences in sensi-
securematchesfromthesurveysintheorderofpriorityindicated
tivity are accounted for by our Bayesian methodology described
inthetableinAppendixA.Thevastmajorityofoursecurematches
below.
areidentifiedintheNDWFSIband.Weidentifysecurecounterparts
for 95.8percent of our X-ray sources. Finally, we cross-matched
between the original catalogues and our secure counterpart posi-
2.4 Identificationandmaskingofstars
tions,againapplyingtheLRmethod,toidentifycommonsources.
The combined surveys provide photometry in up to 17 different Bright stars can contaminate our photometry, leading to issues
bands(seeAppendixA). withcounterpart identificationand photometricredshiftestimates
intheseregions.Wehavethereforemaskedoutareasclosetobright
stars from all of our Chandra fields in a consistent manner. We
2http://irsa.ipac.caltech.edu/data/COSMOS/datasets.html searchedforstarsbrighterthanV=15intheHSTGuideStarCat-
3http://galex.stsci.edu/GR6/ alog2.3(Laskeretal.2008).Wemaskedallareaswithinaradius,
MNRAS451,1892–1927(2015)
TheXLFsofunabsorbedandabsorbedAGNs 1897
r,givenby alsosearchedforspectroscopicredshiftsfromtheSDSS(Yorketal.
2000).
r =(16−V)×6arcsec, (1)
Wematchedthespectroscopiccataloguestothesecurecounter-
whereVistheV-bandmagnitudefromtheGuideStarCatalog.We partsofourX-raysourcesusinga2-arcsecsearchradius,corrected
set a maximum masking radius of 40 arcsec. We have removed foranyoverallastrometricoffset,andrepeatedthematchingwith
anyX-raysourceswithinthisradiusfromoursamples(whichcan a1arcsecradius.Weonlyadoptthosespectroscopicredshiftsthat
includethestaritselforanearbysource).Wealsoexcludedthese are flagged as high-quality, reliable redshifts in the original cata-
regionswhencalculatingtheX-raysensitivityandareacurves. logues.Table1givesthenumberofX-raysourcesinourhard-and
We have also identified stars with fainter magnitudes that are soft-band-selectedsampleswithreliablespectroscopicredshifts.
detectedatX-raywavelengthsandremovedthemfromoursamples.
In the fields with Rainbow coverage (CDFS, CDFN, EGS) stars
2.6 Photometricredshifts
were identified by a range of colour and morphology criteria, as
described in Barro et al. (2011a). In the COSMOS and Bootes The levels of spectroscopic completeness vary over our Chandra
fields we applied a single colour criterion based on the region of surveysfrom∼35percent(inourE-CDFSarea)to∼75percent(in D
o
colour–colourspaceoccupiedbystarsinIlbertetal.(2009), theBootesfield).FortheremainingX-raysourceswemustresort w
n
tophotometricredshiftestimates,whicharedeterminedbyfittinga lo
R−[3.6]<3.0×(R−I)−1.2, (2) a
setoftemplatespectratotheobservedSEDsofoursources.Such d
e
wthheemreag[3n.i6tu]dies itnhethmeaSgunbitaurduerin+thoerNIRDAWCF3S.6Rμfimlteirm,aangdinIg,isRthies rfaeidnsthXift-sracyasnoubrecehsi.gAhlykeuynacdevratanitna,gepaorftiocuurlaBrlayyewsihaennacnoanlyssidiser(isnege d from
malsaognreitquudiereidntthhaetSthuebaXru-raiy+soourrNceDsWexFhSibIitfialtleorw.FXor-raalyl-fitoe-lodpst,iwcael Sphecottioomne3tr)icisrethdashtiwftsebayreaadbolpetitnogapcrcoobuanbtilfitoyrdthisetruibnucteiortnasinftoiersthine https
fluxratio,logf /f <−1,wheretheratioiscalculatedas redshift,p(z),ratherthanasingleredshiftestimate.Wethusrequire ://a
X opt thatourphoto-zapproachrecoversap(z)distributionthataccurately ca
logffoXpt =logf0.5−2keV+5.4+ 2I.5. (3) reflWecetscathlceuulantceeprthaointotimesetirnicourerdrsehdisfhtsifutseisntgimthateesE.AZYphoto-zcode demic.o
ThiscutensuresthatwedonotexcludebrightQSOsfromoursam- (Brammer, van Dokkum & Coppi 2008). We use EAZY in two- up
template mode, allowing for combinations of a galaxy and AGN .c
plethatmaysatisfytheotherstellarcriteria.Whenaspectroscopic o
template. For the galaxy templates we adopt the ‘pegase13’ tem- m
classificationisavailable(seeSection2.5)thisoverridesourpho- /m
tioonumroeuptrhroifictvocemlaCesthsriaificncdparrtaoiocfinee.dluOdrsfe,.t4h0e(5800sppeercctreonstc)owpeicrealalylscolaidsseinfiteifidesdtabrys psddyleuansstcttehyrie’sbtteeiectdmpgbpraylolavatGxiedsyreaadztreieamwniniptcelhaltutEeadAsle.ZddY(r2.ba0yTw0ahn6pi)sp.frltAyoeimmdndgpitlthtaihoeteenraCaslane‘ltgzsetecatortoni-ffseoitpsraamtsrl.aino(m2gfe02ta0e5n0r9ds) nras/article
reddeninglawforarangeofdifferentextinctionstoasub-setofthe /4
5
2.5 Spectroscopicredshifts galaxytemplates.WeadoptsevenAGNtemplatesfromtheSalvato 1/2
et al. (2009) template set,4 namely the Sey 1.8, Sey 2, Mrk231, /1
8
AllofourChandrasurveyshavebeenthesubjectofintensespectro- pl_TQSO1, pl_QSOH, pl_QSO, and the S0-10_QSO2-90 hybrid 92
scopiccampaigns.Thesecampaignsincludelarge-scalefollow-up template. We also include the Type-2 ‘Torus’ template from the /17
ofthegeneralgalaxypopulation,inadditiontothosedirectlytar- Polletta et al. (2007) library,5 which is not included in the final 47
7
getingX-raysources. Salvatoetal.(2009)set.Wenotethatsomeofthesetemplateswill 84
IntheCDF-Swefirstsearchedforspectroscopicredshiftsinthe includehostgalaxycontributions(particularlytheSey1.8,Sey2, by
catalogueofXueetal.(2011).Themajorityofthespectroscopic Mrk231, and S0-10_QSO2-90 templates). This is not a major is- gu
redshiftsforourCDFS-4Mssurveyaretakenfromthiscatalogue, sueaswewanttodeterminethedistributionofpossibleredshifts, es
as well as some of our E-CDFS survey (in the area that overlaps ratherthanperformanaccuratehost-AGNdecomposition.Thetwo- t on
withthe4Msdata).Wealsosearchedforspectroscopicredshifts templatemodeinEAZYallowsanypossiblecombinationofoneof 09
fromtheArizonaCDFSEnvironmentSurvey(Cooperetal.2012), ourAGNtemplatesandoneofourgalaxytemplatesandthusallows M
a
thespectroscopicsub-sampleofsourcesfromtheMUSYCsample foralargeamountofflexibilityinthefittedtemplateSEDs. rc
h
(Cardamoneetal.2010a),andPRIMUS(Coiletal.2011). AnotheradvantageoftheEAZYphoto-zcodeisthatitallowsfor 20
In the CDFN we used spectroscopic redshifts from DEEP3 theinclusionofa‘templateerrorfunction’.Thisfeatureaccounts 23
(Cooperetal.2011)aswellasthesurveysofTrouilleetal.(2008), foradditionaluncertaintyinthetemplateSEDasafunctionof(rest-
Barger, Cowie & Wang (2008), Reddy et al. (2006), Wirth et al. frame)wavelengthandthusallowsforthefactthatourtemplateset
(2004),Cowieetal.(2004),andSteideletal.(2003). maynotaccuratelyrepresentthetruediversityofSEDshapes.This
IntheEGSwecompiledspectroscopicredshiftsfromanumber uncertaintyinthetruerangeoftemplateSEDsisparticularlyuse-
ofsurveysincludingDEEP2,DEEP3,theCanada–FranceRedshift fulasourobservedSEDsextendintotheUVandmid-IR,where
Survey, and MMT follow-up of X-ray sources. See Nandra et al. thetemplatesarepoorlycalibrated,especiallyforAGNs.Inaddi-
(2015)andreferencesthereinforfulldetails. tion,astheopticalemissionfroman(unobscured)AGNcanvary
InCOSMOSweinitiallysearchedforspectroscopicredshiftsof ontime-scalesofmonths-to-years,ourobservedSEDsmaynotbe
X-raysourcesintheC-COSMOScatalogueofCivanoetal.(2012). well-matchedbyasingleunderlyingtemplate.Thetemplateerror
Wealsosearchforadditionalspectroscopicredshiftsfromthebright functioncanalsoallowforanyoverallcalibrationuncertaintiesin
zCOSMOSsurveycatalogue(Lillyetal.2009)andPRIMUS(Coil
etal.2011).
In Bootes we adopt spectroscopic redshifts from the AGN and 4http://www.mpe.mpg.de/∼mara/PHOTOZ_XCOSMOS/
GalaxyEvolutionSurvey(Kochaneketal.2012).Forallfieldswe 5http://www.iasf-milano.inaf.it/∼polletta/templates/swire_templates.html
MNRAS451,1892–1927(2015)
1898 J.Airdetal.
D
o
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lo
a
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e
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fro
m
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ttp
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://a
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ic
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ra
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aFsigthuereb2es.tCesotmimpaatreisoofnthoefpphhoottoommeettrriiccrreeddsshhiiffttss((zbplhaoct)kacnidrcslepse)c;terorrsocropbiacrsreidnsdhicifattse(tzhsepec9)5fpoerrocuernfitvceenCtrhaalncdornafifideelndcse.Wineteprvloatl.thTehemdeaasnhoefdthlienep(izn)ddiciasttreisbuati1o:n1 /artic
relation,whereasthedottedlinescorrespondto(cid:6)z/(1+zzspec)=±0.15(sourceswherethebestestimateofthephoto-zliesoutsidethisrangeareflaggedas le/4
outliers).InthelegendforeachpanelwegivethenumberofX-raysourceswithreliablespectroscopicredshifts(nzspec),theaccuracybasedonthenormalized 51
mcaetadsitarnopahbiscofluaitleurdeesvwiaittihona(rσedNMtrAiaDn)g,lteh.eOfvrearctfioounrooffoouutrlifieersld(sfo(uCtlDierF),Sa,nCdDtFhNe,frEaGctSio,nanodfCcaOtaSsMtroOpSh)icwfeaiolubrteasin(facactaosntrsoipshtiecn);tsaececuteraxctyfoorfdσeNtaMilAsD.W≈e0h.0ig5h,lwigithht /2/189
∼15percentoutliersand∼5percentcatastrophicfailures.IntheBootesfield–ourlargestarea,shallowestfield–wehavepooreraccuracyandahigheroutlier 2
fraction,reflectingthemorelimitedphotometricimaginginthisfield.Whileourphoto-zhaveapooreraccuracy(σNMAD)andahigheroutlierratethaninsome /174
priorworks,wechoosetoadoptourestimatesastheyhavebeencalculatedinaconsistentmanneracrossallfiveofourChandrafieldsandhaverepresentative 7
7
errorsthatwecanfullytrackviathep(z)inourBayesianmethodology(seetextforfurtherdiscussion). 84
b
y
thediversesetsofphotometricobservationsusedtoconstructour panelsfortheEGSandCDFSfieldscombinethedeepsurveyareas gu
e
observedSEDs.Wederiveatemplateerrorfunctiononafield-by- (AEGIS-XD,CDFS-4Ms),wherethebestphotometryisavailable, s
fieldbasis–toensurethatitrepresentsthecalibrationuncertainties with the larger-area shallow surveys (AEGIS-XW, E-CDFS). We t on
in a given data set – using the basic procedure laid out in Bram- includeallX-raysourceswithahigh-qualityspectroscopicredshift 09
meretal.(2008).First,weattempttofittheobservedSEDswith in these plots and do not apply any cuts based on the estimated M
a
ourtemplates,fixingtheredshiftatthespectroscopicvalue,where quality of the photo-z. Thus, we include sources with extremely rc
h
available.Wethencalculate broadp(z)distributions,whichareoftenflaggedasunreliableand 2
0
(cid:6)fj = FjF−Tj, (4) excInluedaecdhwpahneenlaosfsFeisgs.in2gwtheeprseuscecnetsasnoufmphboertoo-fzstuemchmnaiqryuessta.tistics: 23
j
whereFjindicatestheobservedfluxinafilterforsourcej,andTjis (i) σNMAD:theaccuracybasedonthenormalizedmedianabsolute
thefluxfromthebest-fittingtemplate.Wecalculate(cid:6)fjasfunction deviation between the best photo-z and the spectroscopic value,
of rest-frame wavelength for all sources and filters and take the definedasσ =1.48×median(|z −z |/(1+z )).
NMAD phot spec spec
medianofevery400individualmeasurementsacrosstherest-frame (ii) f : the fraction of outliers, defined as the fraction of
outlier
wavelength range. We subtract the median photometric error, in sourceswhere|z −z |/(1+z )>0.15;
phot spec spec
quadrature,toestimatethecontributionfrom‘templateerror’tothe (iii) f :thecatastrophicoutlierrate,calculatedasthefrac-
catastrophic
uncertainty as a function of rest-frame wavelength. The value of tionofsourceswherelessthan5percentoftheintegratedp(z)lies
thetemplateerroristypicallyaround10percent(influx)butvaries within−0.15<(z−z )/z <+0.15.
spec spec
between∼4and∼20percentdependingonthewavelengthandthe
datainagivenfield. Inoverfourofourfields(CDFS,CDFN,EGS,andCOSMOS)we
InFig.2wecompareourphoto-zestimatesforX-raysourcesto obtainaconsistentaccuracyofσ ≈0.06,with∼15percent
NMAD
securespectroscopicredshiftsacrossourfiveChandrafields.The outliers.Ourapproachensuresweassignanappropriateuncertainty,
MNRAS451,1892–1927(2015)
TheXLFsofunabsorbedandabsorbedAGNs 1899
etal.2010b;Hsuetal.2014).Manyofthesestudiestakeadditional
stepstoimprovethequalityofthephoto-zestimates.Thesestepscan
includeoptimizingthetemplateset(e.g.Luoetal.2010),attempting
tocorrecttheobservedphotometryforvariability(e.g.Salvatoetal.
2009), or applying priors based on the source morphology and
X-ray flux (e.g. Salvato et al. 2011). These studies often achieve
a higher accuracy and lower outlier rate than our own photo-z
analysis.However,theseadditionalstepscanleadtounderestimates
ofthetrueuncertaintiesinthephoto-z.Conversely,weretainalarge
set of possible templates to ensure we produce p(z) distributions
thataccountforthelargeuncertaintiesintheredshiftandtemplate
degeneracies. While we have higher outlier rates, our fraction of
catastrophicfailuresremains(cid:2)5percent,indicatingthatourp(z)
distributionsarerepresentingtheuncertainties.Thenominalerrors
D
(i.e. the 68percent confidence intervals) on our photo-z are also ow
Figure3. RedshiftdistributionofX-raysourcesinourfiveChandrafields comparabletotheresidualsbetweenourbestphoto-zestimateand nlo
a
withhigh-qualityspectroscopicredshifts(blacksolidline)andthosewhere theavailablespectroscopicredshifts,incontrasttomostprevious d
e
wtioenaodfopthtep‘hboetsotm’pethroictor-ezdeshstiifmtsa.tTehse(mbleuaendoafshtheedpli(nze)dinisdtircibatuetsiotnh)e,dwishterribeaus- wLuoorketwahle.r2e0e1r0r;oHrssmuaeytabl.e2u0n1d4e)r.eFstuirmthaetermdobrye,awfeacrteoqru∼ire2–th6e(efu.gll. d fro
m
the orange dotted line shows the distribution obtained by combining the p(z)distribution,whichmostpriorstudiesdonotprovide.Wethus h
individualp(z)distributions. choosetouseourownphotometricredshifts:ourpooreraccuracy ttp
s
andhigheroutlierratesareaccountedforandcompensatedbyour ://a
tracedbythep(z),tothebulkofoursourcesandonly∼5percentof Bayesiananalysisthatincorporatesthefullp(z)information. ca
d
sourcesarethusflaggedascatastrophicfailures.IntheBootesfield e
m
–ourlargestarea,shallowestfield–wehavepooreraccuracyanda ic
muchhigheroutlierfraction,reflectingthemorelimitedphotomet- 3 BAYESIAN METHODOLOGY .ou
p
ricimaginginthisfield.However,thecatastrophicoutlierfraction .c
InthispaperweexpandontheBayesianmethodologydevelopedby o
isonly∼1percent,indicatingthatthisadditionaluncertaintyisrep- m
resentedbyourp(z)distributions.Wealsonotethatinthisfieldwe A10,incorporatingthedistributionofX-rayabsorptionproperties /m
andaccountingfortheeffectsontheinferredshapeandevolutionof n
havethehighestspectroscopiccompleteness(∼75percent)andso ra
theXLF.Ourmethodalsoaccountsfortheuncertaintyinthemea- s
onlyusephotometricredshiftsforarelativelysmallfractionofthe /a
sourcesinoureventualanalysisoftheXLF;whenwedoresortto suredX-rayflux(duetophotoncountingstatistics),uncertaintiesin rtic
theredshift(forsourceswithphotometricredshiftsornocounter- le
aphotometricredshiftweaccountforthelargeuncertaintyinthe /4
parts),uncertaintiesintheX-rayspectralshape,andtheresulting 5
redshift. 1
uncertainty intheX-rayluminosityforanindividualsource.Our /2
InFig.3weplotthedistributionofredshiftestimatesforsources /1
methodologyisdescribedbelow. 8
inourChandrafieldswherewehaveaspectroscopicredshiftand 9
2
thosewhereweadoptthephotometricredshiftinformation.Gener- /1
7
allythesourceswithphotometricredshiftslieathigherredshifts,a 3.1 Probabilitydistributionfunctionforasinglesource 477
consequenceofspectroscopicfollow-upprogrammesbeingbiased 8
4
towardsopticallybrightsources.Wealsoshowtheintegratedcon- Forasinglesourceineitherourhard-orsoft-bandsamplewecan b
tpr(izb)utiisonskferwomedthtoewpa(rzd)solfowalelrthreedpshhoifttos-.zTshoiusrcskese.wTihsediunetegtoratthede odneriovuertohbesperrovbeadbdilaittayfdoisrttrhibauttsioonurfcuenacltoionne,fowrhzi,chLXis,agnivdeNnHbybaps(ezd, y gues
possibilitythatmanypotentialhigh-redshiftsourcescouldactually LX,NH|Di)whereDi indicatestheobserveddatafromsourceiin t on
lieatlowerredshifts,whichisreflectedbytheirp(z)andmustbe oursample.Thisfunctionisnormalizedsuchthat 0
accountedforinmeasurementsoftheXLF. (cid:2) (cid:2) (cid:2) 9 M
AsmallfractionofourX-raysources(<2percent)lackamulti- dz dlogLX dlogNHp(z,LX,NH|Di)=1. (5) arc
h
wavelengthcounterpart,precludingaphotometricredshiftestimate. 2
Weretainthesesourcesinouranalysis,ensuringcompletenessof Wecanrewritetheprobabilitydistributionfunctionas 02
3
oalulrowsaemdpreled,sbhuifttardanogpeta(0p<(z)zt<ha1t0is).cTohnisstarenflteinctlsoogu(r1la+ckz)ofoaveprrioourri p(z,LX,NH|Di)=p(z|di)p(LX,NH|z,Ti,bi), (6)
knowledgeoftheredshift;theX-rayfluxinformationisretainedand where d indicates the multiwavelength data used to estimate the
i
thus a posteriori (after folding the constant p(z) through the final redshiftandT andb correspondtotheX-raydataforthissource:
i i
XLF)theremaybeapreferredredshiftsolution.Thelackofamul- thetotalobservedX-raycountsinthegivenbandandtheestimated
tiwavelengthcounterpartcouldimplythatahigh-redshiftsolution background,respectively.
should be given higher a priori preference for such sources, thus Ourknowledgeofzisbasedoneitheraspectroscopicredshift,
ourapproachisconservative.Thereisalsoapossibilitythatthese in which case we assume p(z|d) is described by a δ-function at
i
X-ray sources lack counterparts as they are spurious detections, thespectroscopicvalue,oraphotometricredshift,whenp(z|d)is
i
correspondingtopositivefluctuationsinthebackgroundcountrate. givenbythep(z)fromourphotometricredshiftfittingdescribedin
OuranalysisaccountsforthePoissonnatureoftheX-raydetection Section2.6above.Forthesmallfractionofsourceswherewewere
andthusallowsforthispossibility. unabletoidentifyamultiwavelengthcounterpart–andthushaveno
OtherestimatesofphotometricredshiftsareavailableforX-ray redshiftinformation–weadoptap(z)distributionwithaconstant
sourcesinmanyofourfields(e.g.Bargeretal.2003;Cardamone densityinlog(1+z)over0<z<10.
MNRAS451,1892–1927(2015)
1900 J.Airdetal.
fixtheinclinationangleto30◦ asarepresentativevalueandallow
theintensitytobesetbythenormalization,R,relativetothatex-
pectedfromaslabsubtendingasolidangleof2π(whichisallowed
tovarybetween0and2,spanningtheextremecasesofnoreflection
uptoaneffective4πsolidanglecoverage).Weabsorbthereflec-
tioncomponentbythesamecolumn densityseenbytheprimary
emission.Thisisagoodassumptionwhenthereflectionarisesfrom
the accretion disc and also provides reasonable agreement with
the shape and intensity of the reflection component based on so-
phisticatedmodelsoftoroidalobscurers(e.g.Brightman&Nandra
2011a).AllcomponentsaresubjectedtoGalacticabsorption,with
columndensitiesdeterminedfromDickey&Lockman(1990)via
theHEASOFTNHtool.InXSPECterminology,ourmodelisdescribed
by
D
(cid:3) ow
wabs∗ (1−constant)∗zwabs∗cabs∗zpowerlw∗zhighect nlo
Figure4. OurassumedX-rayspectralmodelforanAGN.Weassumethe (cid:4) a
d
intrinsicX-rayspectrumisapowerlawwithphotonindex(cid:5)=1.9±0.2 +constant∗zpowerlw+zwabs∗pexrav , (8) ed
(dWtopeuenbrsaepiltlsyseoc,laifiantxlteleeo)rd.weTda,hftoeuNrnoHaabbsf=seroarvc5rbtei×edodns,1p(i0efns2ctc2toartucttmmh≈e−i2s2liapnfbeoesrrooctrfehbnisestid)gehobxtfyam(ttbhhpleeuleieinn(tdtrreoeirntdv–seiddncaaissnphhgoeewcddoellrliiunnlmaeew))n.. nwohteerethtahtemcoonrestpanhtysciocrarlelsypomnodtsivtaotetdhemsocdatetlesrecdoufrldacbtieona,dfoscpattte.dWtoe from https
Inaddition,weallowforacomponentfromComptonreflectionfromcold, describetheX-rayspectrum,self-consistentlymodellingtheemis- ://a
opticallythickmatter(suchasatorusoraccretiondisc)thatleadstothe sion, reflection, and absorption due to the accretion disc or torus ca
d
characteristic hump at high energies (green dotted line). The black line (e.g.Ross&Fabian2005;Brightman&Nandra2011a).However, e
m
indicatesthetotalobservedspectrum,whilethegreyregionindicatesthe Buchneretal.(2014)foundthatmoresimplisticmodelssuchasours ic
95percentconfidenceintervalonthespectrum,allowingfortherangeof aregenerallysufficienttoreproducetheobservedspectralshapeof .ou
possiblespectralparameters(seeSection3.1,Table2). individual,distantAGNs,especiallyconsideringouranalysisuses p.c
o
broad-bandfluxesratherthanperformingadetailedX-rayspectral m
analysis. /m
n
TheobservedX-raydatacanbedescribedbyaPoissonprocess. To describe our X-ray spectral model requires three additional ra
s
bTyhus,thelikelihoodofobservingTi countsfromasourceisgiven tphaerarmeleatteivrse–nothrmeaplhizoatotinoninodfexth,e(cid:5)r,etflheecsticoanttecroemdpforancetniot,nR,fs–cawtt,hainchd /artic
le
L(Ti |ci,bi)= (ciT+i!bi)e−(ci+bi), (7) wξ(ξ)e)i,ninzo,truLordXBu,caaeynedassiNa‘Hnn,uaiwnsaaenlyccsaein’s.pdFaeortaermramegtienivresent(hcseoeltelxeocpfteisvcpteeelcdytrcdaoeluspingatnraraamtteeed,tebcryis, /451/2/1
whereciistheX-raycountratefromsourceiintheobservedenergy andthuslinktheprobabilitydistributionfunctionforLX,NH,andξ 892
bandandwehaveassumedthattheexpectedbackgroundcountrate, tothePoissonlikelihoodgiveninequation(7)above.Thus, /1
7
tbhi,eiPsowiseslolndelitkeermlihinoeodd.gTihveenuninceerqtauianttiyonin(7c)i.iHsofuwlleyvedre,stcoricboendvebryt p(LX,NH,ξ |z,Ti,bi)∝L(Ti |ci(z,LX,NH,ξ),bi)π(ξ), (9) 4778
4
fromacountrate,c,toanestimateofL andN (givenz),wemust b
assumeamodelfoirtheX-rayspectralXshapeHandfoldthismodel whereci(z,LX,NH,ξ)istheexpectedcountrateforasourcewith y g
thrFoiugg.h4thsehoawppsroanpreiaxtaeminpslteruomfeonutralXre-rsapyonsspee.ctral model. We as- srepdeschtriaftl zp,arlaummeinteorssitξybLaXs,edabosnoroputironX-croalyumspnecNtrHa,lamndodaedl,diftoioldneadl uest o
sume the intrinsic X-ray continuum is described by a power law throughtheappropriateinstrumentalresponseforsourcei. n 0
withphotonindex(cid:5)andahighenergycut-off(wefixthefolding Apriori(cid:5),th(cid:6)espectralparametersξforagivensourcearenotwell 9 M
energyat300keV,althoughthishasanegligibleimpactonthelower known;π ξ denotesthepriordistributionthatweadoptforour arc
h
energies we observe). The observed spectrum is attenuated along spectralparameters, whichdescribes therangeofpossiblevalues 2
0
theline-of-sightbytheinterveningcolumndensity,N .Weinclude andthusencapsulatestheuncertaintyinX-rayspectralshape.We 2
H 3
bothphotoelectricabsorption(usingthewabsmodelinXSPEC)and assumethephotonindex,(cid:5),isdrawnfromaGaussiandistribution
Comptonscattering(viacabs),whichsuppressesthecontinuumfur- withameanof1.9andstandarddeviationof0.2(correspondingto
therforCompton-thickcolumndensities.Afractionofthispower theobserveddistributionofintrinsicphotonindicesinX-rayspec-
law,f ,isallowedtoemergeasanunabsorbedcomponentthatis tralstudiesofnearbyAGNs,e.g.Nandraetal.2007).Weassume
scatt
thoughttobescatteredintothelineofsightbyionizedgasinthe thescatteredfraction,f ,isdrawnfromalognormaldistribution
scatt
vicinityoftheAGN.WealsoincludeacontributionduetoComp- withmeanof2percentandscatterof0.8dexbasedontheobserved
tonreflectionfromcold,opticallythickmatter,whichgivesriseto distributionofpartialcoveringfactorsofsourcesintheSwift/BAT
acharacteristic‘hump’intheX-rayspectrumat∼30keV.Sucha samplefromWinteretal.(2009).Forthereflectionstrength,R,we
reflectioncomponentisexpectedduetoreprocessingoftheprimary assumeauniformdistributionintherange0<R<2.Wethusallow
X-rayemissionbyasurrounding,dustytorusoranaccretiondisc. foralargeuncertaintyinthestrengthofthereflectioncomponent,
Weadoptthepexravmodel(Magdziarz&Zdziarski1995),which which is reasonable to encapsulate uncertainties in the geometry
isbasedonMonteCarlosimulationsofComptonreflectionfroma of the accretion disc and/or torus with our simplified modelling
cold,opticallythickslabofmaterial.Weassumetheincidentpower of the reflection. Table 2 summarizes this prior information. The
lawhasthesameshapeasthedirectlytransmittedcomponent.We colouredlinesinFig.4showeachcomponentevaluatedattheprior
MNRAS451,1892–1927(2015)
TheXLFsofunabsorbedandabsorbedAGNs 1901
Table2. Priorsonthespectralparametersfor ofN ,butweareabletoplaceconstraintsontherangeofpossi-
H
anindividualX-rayAGN,ξ. blevaluesofL andhowthisdepends onN .Forthehard-band
X H
example,wecanconstrainL towithin∼0.25dex,providedtheab-
X
Parameter Priortype Priorspecification sorptioncolumnisN (cid:2)1023cm−2.Ifthecolumndensityishigher,
H
thenthesameobservedcountsmustcorrespondtoahighervalue
(cid:5) Gaussian 1.9±0.2a
logfscatt Lognormal −1.73±0.8b aopfpLaXr.enFtofroarsloowurecrecdoeltuemctneddeinnstihteiesso(fNtba(cid:3)nd1,0a2b2socmrp−ti2o)n.Aeftfeccotlsumarne
R Constant 0–2 H
densitiesN (cid:3)2×1023cm−2(atz=1.0)theobservedfluxinthe
Notes. aBased on observed distribution from H
0.5–2keVbandisdominatedbythescatteredcomponentonly;the
Nandraetal.(2007).
intrinsicluminosityispoorlyconstrainedbutmustbeafactor∼30
bBased on observed distribution from Winter
greaterthanifthesourcehadalowerN .
etal.(2009). H
Wenotethattheeffectofabsorptionontheobservedcountsinthe
mean of the spectral parameters and the black line corresponds hardorsoftenergybandswillvarysignificantlywithredshift.For
to the total observed spectrum for these values. The grey region example,atz∼3,wheretheobserved0.5–2keVenergybandprobes
D
indicatesthe95percentconfidenceintervalonthetotalobserved rest-frameenergies∼2–8keV,theinferredLX isonlyaffectedfor ow
spectrum,adoptingourpriordistributionsforthespectralparame- column densities (cid:3) 1023 cm−2. These redshift-dependent effects nlo
a
ters.Wenotethatthelargeuncertaintiesinthescatteredfraction, are fully accounted for in our calculation of the expected counts, d
e
ffsocrattm,oledaedrattoellyaragneduhnecaevritlayinatbiseosribnedthseousrpceecstraunmdtahtussolfetaedrsetnoelragrigees ci(Fz,oLrtXh,eNanHa,lξy)s,isusinintghiosupraXpe-rr,awyesptreecatrtaelamchodsoeul.rceinourhard-or d fro
m
uncertaintiesintheintrinsicLX. soft-bandsamplesasindependentdetections.Thus,theonlyX-ray h
ToobtaintheprobabilitydistributionfunctionforL andN only dataweuseforanindividualsourceisthedetectedcounts(andthe ttp
X H s
(foragivenzandourobservedX-raydata),wemustmarginalize expectedbackground),whichasdescribedabovedoesnotallowus ://a
overthenuisancespectra(cid:2)lparameters.Thus, toconstrainthevalueofNH foranindividualsource.Instead,our cad
approach(seeSections3.2below)involvesdeterminingtheoverall e
m
p(LX,NH|z,Ti,bi)= dξ p(LX,NH,ξ |z,Ti,bi). (10) distributionofX-rayluminositiesandabsorptioncolumndensities ic
.o
(given by the X-ray luminosity and absorption-distribution func- u
InFig.5weshowanexampleofp(LX,NH|z,Ti,bi)forasource tion–XLAF)thatcorrectlydescribesbothourhard-andsoft-band p.c
o
detected in the hard band (left) and a source detected in the soft samples.Usingthismethod,certainvaluesofL andN maybe m
band (right) with Chandra. In both cases we fix z = 1.0 and as- disfavoured a posteriori (after performing our fuXll analyHsis of the /m
n
s2ou0fmb<ei =Tloig=5N.0H30(ccotmuont−at2ls).o<Wbsee2r6vr.eesTdtrhciecotushtnhatesdiwpnoigtshsainabdnleecxocponeltuocmuternds ibdnaedcnikscigatrtieeosutnhtdoe fsoahvvoeowruaslrlehdsigaahmpeprolsLet)Xe.rsiFoooruirrbceeaxssaesmdhopoulneld,thhbeiegsrhhaaerpreerv)o.afClutohensevXoerfLseFLlXy(,thmloaawtygeerbnveearldaulielsys- ras/article
rangeofpossiblevaluesofLXandNHforeachsource.Detectionin of NH may be disfavoured if our overall XLAF requires a large /45
asingle,broadenergybanddoesnotplaceconstraintsonthevalue fractionofabsorbedsources. 1
/2
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8
9
2
/1
7
4
7
7
8
4
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y
g
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9
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a
rc
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0
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Figure5. Exampleconstraintsontherest-frame2–10keVluminosity,LX,andtheline-of-sightabsorptioncolumndensity,NH,forsourcesdetectedinthe
observedhardband(2–7keV,left)andsoftband(0.5–2keV,right)inatypicaldeepChandraobservation.Inbothcases,weassume30totalcountsdetected
intheobservedenergybandwithanexpectedbackgroundof5counts,typicalofoursampleintheAEGIS-XDsurveyregion.Wefixtheredshiftatz=1.0.
ThegreyshadingindicatestheprobabilitydistributionfunctionforLXandNH,allowingforthePoissonuncertaintyfromtheobservedcountsandassuming
theX-rayspectralmodelshowninFig.4,marginalizedovertheuncertaintyinthe‘nuisance’spectralparameters((cid:5),fscatt,andR).Thesolidanddashedlines
indicatethe68.3and95.4percent(i.e.1σ and2σ equivalent)confidenceintervalsonthejointparameterspace.Detectioninasinglebanddoesnotconstrain
thevalueofNHbutdoesplaceconstraintsontherangeofpossiblevaluesofLX.AtlowvaluesofNH,theX-rayluminosityisconstrainedtowithin∼0.25
dex.However,forhigherNHvaluestheX-rayluminositymustbecorrespondinglyhighertoproducethesamenumberofobservedcounts.Absorptionaffects
theX-rayspectrum(andthustheconstraintsonLX)forlowercolumndensitiesinthesoftband(NH(cid:2)1022cm−2)thanthehardband(NH(cid:2)1023cm−2)
atz=1.0.
MNRAS451,1892–1927(2015)