The evolution of the hard X‐ray luminosity function of AGN

21 Pages·2010·1.21 MB·English

Mon.Not.R.Astron.Soc.401,2531–2551(2010) doi:10.1111/j.1365-2966.2009.15829.x
The evolution of the hard X-ray luminosity function of AGN
J. Aird,1(cid:2)† K. Nandra,1 E. S. Laird,1 A. Georgakakis,2 M. L. N. Ashby,3 P. Barmby,4
A. L. Coil,5 J.-S. Huang,3 A. M. Koekemoer,6 C. C. Steidel7 and C. N. A. Willmer8
1AstrophysicsGroup,ImperialCollegeLondon,BlackettLaboratory,PrinceConsortRoad,LondonSW72AZ
2NationalObservatoryofAthens,InstituteofAstronomy,V.Paulou&I.Metaxa,Athens15236,Greece
3Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA02138,USA
4DepartmentofPhysics&Astronomy,UniversityofWesternOntario,London,ONN6A3K7,Canada
5CenterforAstrophysicsandSpaceSciences(CASS),DepartmentofPhysics,UniversityofCalifornia,SanDiego,CA92093,USA
6SpaceTelescopeScienceInstitute,3700SanMartinDrive,BaltimoreMD21218,USA
7CaliforniaInstituteofTechnology,MS105-24,Pasadena,CA91125,USA
8StewardObservatory,UniversityofArizona,Tucson,AZ85721,USA
Accepted2009October5.Received2009September3;inoriginalform2009April29
ABSTRACT
Wepresentnewobservationaldeterminationsoftheevolutionofthe2–10keVX-rayluminos-
ityfunction(XLF)ofactivegalacticnuclei(AGN).Weutilizedatafromanumberofsurveys
includingboththe2MsChandraDeepFieldsandtheAEGIS-X200kssurvey,enablingac-
curate measurements of the evolution of the faint end of the XLF. We combine direct, hard
X-rayselectionandspectroscopicfollow-uporphotometricredshiftestimatesatz<1.2with
arest-frameUVcolourpre-selectionapproach athigherredshiftstoavoidbiasesassociated
withcatastrophicfailureofthephotometricredshifts.OnlyrobustopticalcounterpartstoX-ray
sourcesareconsideredusingalikelihoodratiomatchingtechnique.ABayesianmethodology
isdevelopedthatconsidersredshiftprobabilitydistributions,incorporatesselectionfunctions
forourhigh-redshiftsamplesandallowsrobustcomparisonofdifferentevolutionarymodels.
WestatisticallyaccountforX-raysourceswithoutopticalcounterpartstocorrectforincom-
pletenessinoursamples.WealsoaccountforPoissonianeffectsontheX-rayfluxestimates
and sensitivities and thus correct for the Eddington bias. We find that the XLF retains the
same shape at all redshifts, but undergoes strong luminosity evolution out to z ∼ 1, and an
overallnegativedensityevolutionwithincreasingredshift,whichthusdominatestheevolution
atearliertimes.Wedonotfindevidencethataluminosity-dependentdensityevolution,and
the associated flattening of the faint-end slope, is required to describe the evolution of the
XLF.Wefindsignificantlyhigherspacedensitiesoflow-luminosity,high-redshiftAGNthan
inpriorstudies,andasmallershiftinthepeakofthenumberdensitytolowerredshiftswith
decreasingluminosity.ThetotalluminositydensityofAGNpeaksatz=1.2±0.1,butthere
is a mild decline to higher redshifts. We find that >50 per cent of black hole growth takes
placeatz>1,witharoundhalfinL <1044ergs−1AGN.
X
Key words: galaxies: active – galaxies: evolution – galaxies: luminosity function, mass
function–X-rays:galaxies.
activitythroughoutthehistoryoftheUniverse,tracedbythelumi-
1 INTRODUCTION
nosity function, is essential to constrain models of super-massive
Active galactic nuclei (AGN) are an important constituent of the blackholeformationandgrowth,thetriggeringandfuellingofAGN
Universe, playing a vital role in the formation and evolution of andtheirco-evolutionwithgalaxies.Thisrequireslargesamplesof
galaxiesandhavingawiderinfluenceonthestructureoftheUni- objectsspanningawiderangeofredshiftsandluminositiestoaccu-
verse.DeterminingthedistributionandevolutionofAGNaccretion ratelydeterminetheshapeoftheluminosityfunctionandhowthis
evolvesovercosmictime.
(cid:2)E-mail:[email protected] X-ray surveys provide a highly efficient method of selecting
†Present address: Center for Astrophysics and Space Sciences (CASS), AGN,includingunobscuredandmoderatelyobscuredsourcesand
Department of Physics, University of California, San Diego, CA 92093, low-luminositysourcesthatmaynotbeidentifiedasAGNatoptical
USA. wavelengths.X-rayemissionisrelativelyunaffectedbyabsorption,
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS
2532 J.Airdetal.
particularlyathardX-rayenergies((cid:2)2keV)formoderatecolumn small number of fields with sufficiently high spectroscopic com-
densities(N (cid:3)1023cm−2),andthusprovidesadirectprobeofthe pleteness also means that most results are susceptible to cosmic
H
accretionactivity.Largeeffortshavebeenmadetoobtainfollow-up variance.
observations of X-ray sources in various X-ray surveys to deter- Analternativeapproachtotheincompletenessissuewasadopted
minetheirredshifts,andthusallowtheX-rayluminosityfunction by Aird et al. (2008) (see also Nandra et al. 2005) to determine
(XLF)tobedetermined(e.g.Bargeretal.2003;Szokolyetal.2004; the XLF at high redshift, where the effects can be most severe.
Trouille et al. 2008). Such studies of the XLF have revealed that TheLyman-breaktechnique(e.g.Steidel&Hamilton1993;Steidel
AGNareastronglyevolvingpopulation,withtheoveralldistribu- et al. 2003) was used to pre-select a sample of objects at z ∼ 3
tionshiftingtolowerluminositiesbetweenz∼1andthepresent basedontheirbroad-bandcoloursinthreefilters,anddeepX-ray
day.Thisevolutioncanbedescribedbyapureluminosityevolution observationswereusedtoidentifyAGN.Thistechniqueprovidesan
(PLE) parametrization (Boyle et al. 1993; Barger et al. 2005) in incompletesample(missingheavilyreddenedsourcesinparticular),
which the XLF retains the same shape (a double power law with buttheopticalselectionfunctionsarewelldefinedandwerederived
a break at a characteristic luminosity, L∗), but shifts to lower lu- usingsimulationsoftheopticaldata.Thisallowedcorrectionsfor
minositiesasredshiftdecreases.However,recentdataindicatethat theincompletenesstobeapplied,andthusthefaintendoftheXLF
amorecomplex,luminosity-dependentdensityevolution(LDDE) at z ∼ 3 could be accurately measured. The number density of
parametrization is required to describe the evolution of the XLF low-luminosity AGN was at least as high as previous estimates,
atbothlow(z(cid:3)1)andhigh(z≈1–4)redshifts(e.g.Uedaetal. andtherewasnoevidencefortheflatteningofthefaint-endslopeat
2003; La Franca et al. 2005; Silverman et al. 2008; Ebrero et al. z>1thatischaracteristicofLDDEparametrizations.However,this
2009; Yencho et al. 2009). In this scheme the shape of the XLF workdidnotaccountfortheuncertaintiesintheredshiftestimates
changes with redshift, with the faint-end slope flattening as red- forsourceswithoutspectroscopicconfirmationanddidnotpresent
shiftincreases.Thisevolutionisalsocharacterizedbyashiftinthe anevolutionarymodel.
peakofthespacedensityofAGNtowardslowerredshiftsforlower Inadditiontouncertaintiesintheopticalfollow-upandredshift
luminosities. estimates,anumberofissuesarisingfromtheX-rayobservations
However,thereareremaininguncertaintiesastotheexactform mayalsoaffectthedeterminationoftheevolutionoftheXLF.The
oftheevolution,especiallyathighredshifts.Inpart,thisisdueto faintest sources in Chandra surveys are detected with very small
the difficulties of accurately measuring the faint end of the XLF, numbersofcounts,andthusPoissonianeffectscanbesignificant.
where incomplete and uncertain redshift information is a serious Derived X-ray fluxes can thus be highly uncertain, and may be
issue.TheChandraDeepFields-North(CDF-N;Alexanderetal. underestimatedbyupto50percentduetotheEddingtonbias(Laird
2003) and Chandra Deep Fields-South (CDF-S; Giacconi et al. etal.2009),leadingtouncertaintiesintheluminosity.Georgakakis
2002)havebeenkeyinstudiesoftheXLF,providingthedeepest etal.(2008)presentedanewmethodofdeterminingthesensitivity
availableX-raydataandsubstantialprogrammesofspectroscopic ofChandraobservations,whichfullyaccountsforthePoissonian
follow-up of the X-ray sources to determine redshifts. However, natureofthedetectionlimitsandaccountedforthefluxuncertainties
even in these fields a high fraction (∼50 per cent) of the X-ray andEddingtonbiasinthedeterminationoftheX-raynumbercounts.
sourcesremainsspectroscopicallyunidentified,mainlybecausethe However,thesetechniqueshavenotbeenincorporatedinprevious
opticalcounterpartsofthefaintestX-raysourcesarealsofaint(R(cid:2) studiesoftheXLF.
24),andthusbeyondthelimitsofcurrentinstrumentation.Thiscan In this paper we present a new study of the evolution of the
severelybiasdeterminationsoftheXLF,especiallyathighredshifts XLF, in which we incorporate new deep X-ray observations and
(e.g.Bargeretal.2005). developimprovedmethodologiestoaddresssomeoftheissuesre-
Onegeneralapproachtoaddressthisissueistodeterminepho- garding optical counterparts, completeness, photometric redshifts
tometricredshiftsfortheX-raysourcesthataretoofaintforoptical and X-ray fluxes described above. Section 2 describes our data,
spectroscopicfollow-up.Thissignificantlyimprovesthecomplete- including our samples of hard X-ray-selected AGN and the data
nessofthesamples,althoughmanyX-raysourceswhichlackde- used to perform high-redshift colour pre-selection of AGN. We
tectable optical counterparts remain unidentified. However, there adopt a likelihood ratio method to ensure that we assign secure
are considerable uncertainties in such redshift estimates, particu- opticalcounterpartstothefaintestX-raysources.InSection3we
larlyforthefaintestopticalcounterparts,andariskofcatastrophic developaBayesianmethodologytodeterminetheevolutionofthe
failuresintheredshiftdeterminations,whichisparticularlyacute XLF, which accounts for uncertainties in redshift estimates and
for sources at z ∼ 1–3. It is also necessary to correct for the re- X-rayfluxes,incorporatestheimprovedsensitivitycalculationsof
mainingincompletenessinsuchsamples,whichcanprovedifficult. Georgakakisetal.(2008),correctsfortheremainingincomplete-
Additionally,thereisasignificantriskofassociatingtheincorrect nessoftheopticalidentificationsandallowsarobustcomparison
optical counterpart with an X-ray source, due to the high surface ofdifferentevolutionarymodels.Section3.3describeshowhigh-
density of optical sources at these faint magnitudes, and thus an redshift rest-frame UV colour-selected samples are incorporated
X-raysourcemaybeassignedcompletelyincorrectredshiftinfor- intothismethodology(buildingontheworkofAirdetal.2008),to
mation.Forexample,Bargeretal.(2003)wereabletoassignoptical provideamorerobustdeterminationoftheevolutionatz(cid:2)1.2.Our
counterpartsto∼85percentoftheX-raysourcesintheCDF-N,but resultsarepresentedinSection4anddiscussedfurtherinSection5.
notedthat∼25percentoftheopticalidentificationsatR=24–26 Aflatcosmologywith(cid:3) =0.7andh=0.7isadoptedthrough-
(cid:4)
areexpectedtobespurious.SuchfalseidentificationsoffaintX-ray out.
sourcescouldsignificantlybiasdeterminationsoftheXLF.Tore-
ducetheseeffectsmanyauthors(e.g.Uedaetal.2003;Bargeretal.
2 DATA AND SAMPLES
2005;Silvermanetal.2008)setrelativelyhighX-rayfluxlimits,
thusincreasingthespectroscopicallyidentifiedfractionandreduc- To determine the evolution of the XLF requires large samples of
ingthenumbersofopticallyfaintorunidentifiedsources,butthis AGNspanningawiderangeofluminositiesandredshifts.Forour
also reduces the sensitivity to the key low-luminosity AGN. The initial investigation of the evolution of the XLF, our approach is
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551
Theevolution ofthehardXLFofAGN 2533
Table1. DetailsofthehardX-ray-selectedsamples/fields.
Field RA Dec. X-rayexposure Surveyareaa NXb Foptc Fspecd
(J2000) (J2000) (ks) (arcmin2) (percent) (percent)
CDF-S 03:32:28 −27:48:30 1933.4 436.2 248 68 44
CDF-N 12:36:55 +62:14:18 1862.9 436.0 303 67 55
AEGIS-X 14:17:43 +52:28:25 188.7 1155.6 397 86 40
ALSS 13:14:00 +31:30:00 – 20880.0 34 97 97
AMSS – – – 294386.0 109 98 98
aAreacoveredbybothX-raydataandrequiredopticalimaging;btotalnumberofhardX-ray-selectedsources
intheareacovered;cfractionofhardX-raysourceswithsecureopticalcounterparts;dfractionofhardX-ray
sourceswithsecureopticalcounterpartsandspectroscopicredshifts.
similartomostpreviousstudiesoftheXLF(e.g.Uedaetal.2003; Telescope (HST). We have searched for optical counterparts us-
Barger et al. 2005; Silverman et al. 2008; Ebrero et al. 2009) ing the COMBO-17 survey (Wolf et al. 2004) source catalogue,
in that we attempt to assign redshifts to all sources in a purely in which sources are detected in deep R-band images (10σ lim-
X-ray-selectedcatalogue,utilizingphotometricredshiftstoimprove itingABmagnitudeof∼25.6)obtainedwiththeWFIinstrument
the completeness. Thus AGN are detected over a wide redshift on the European Southern Observatory (ESO) 2.2 m telescope at
range, which is essential for probing the evolution. Our method- LaSilla.Counterpartswerefoundusingtheimplementationofthe
ology (see Section 3) requires probability distributions that de- likelihoodratiomethod(Sutherland&Saunders1992;Ciliegietal.
scribe the uncertainties in the photometric redshift estimates. We 2003) described in Laird et al. (2009). This method allows us to
thereforeadoptthebestavailablephotometricredshiftswithsuit- assign secure optical counterparts to the X-ray source, account-
ableprobabilitydistributionsorgenerateourownfromtheavail- ingfortheX-rayandopticalpositionaluncertainties,theapriori
abledata.ToobtainthebestconstraintsontheXLF,ahighfrac- probabilityofacounterpartwithagivenmagnitudeandtheprob-
tionofspectroscopicidentificationsisalsorequired.Additionally, abilityofaspuriousopticalcounterpart.Werestrictoursampleto
we require hard X-ray coverage to reduce biases against mod- objectswithlikelihoodratiosof>0.5,whichprovidesopticalcoun-
erately absorbed sources. Three deep Chandra surveys have the terparts for 169 (≈68 per cent) of the hard-band-selected X-ray
necessary spectroscopic follow-up, combined with the deep mul- sources.
tiwavelength imaging required for photometric redshifts: the two A number of spectroscopic programmes have been carried out
CDF and the AEGIS-X survey. We supplement this sample with in the CDF-S. Following Luo et al. (2008), we have combined
two larger area ASCA surveys with near complete spectroscopic spectroscopic surveys from Szokoly et al. (2004), Le Fe`vre et al.
follow-up,whichareneededtoconstrainthebrightendoftheXLF. (2004), Mignoli et al. (2005), Ravikumar et al. (2007), Popesso
Table1summarizesthenumbersofsourcesandfractionwithop- etal.(2009)andVanzellaetal.(2008).Thisprovidesspectroscopic
tical counterparts and spectroscopic redshifts. Further details and redshifts for 110 sources (65 per cent of the optical counterparts
a description of the photometric redshift estimates are given in and44percentoftheentirehardX-ray-selectedsample).
Section2.1. Avarietyofphotometricredshiftestimateshavebeenpublished
Forthehigh-redshiftcolourpre-selectionapproach,therequire- in the CDF-S area, focused on both the X-ray source population
ments are different. Deep X-ray data are again required, but the (e.g.Zhengetal.2004)andlargerpopulationsofopticallyselected
soft(0.5–2keV)band,wherethesensitivityofChandraishighest, sources(e.g.Mobasheretal.2004;Wolfetal.2004).However,we
maybeusedforselectionasthisprobesrelativelyhardrest-frame have chosen to use our own photometric redshift estimates using
energiesatz(cid:2)2,andthusshouldnotbeseverelybiasedbyabsorp- theBayesianphotometricredshiftcodeBPZ(Ben´ıtez2000),which
tioneffects.DeepopticalimagingdatainU GRoracomparable allowsustousethefullredshiftprobabilitydistributionoutputby
n
filtersetarerequiredforthecolourpre-selection,withdeepdataat the BPZ code and thus account for the significant uncertainties in
U-bandwavelengthsbeingthemajorrequirement.Adescriptionof photo-zestimatesinourdeterminationoftheXLF(seeSection3).
thedataforthehigh-redshiftworkisgiveninSection2.2. Such probability distributions are not available for the published
catalogues.
Our photo-z estimates were determined using the full 17-band
2.1 HardX-ray-selectedsamplesofAGN photometryfortheX-raysources(withsecureopticalcounterparts)
fromtheCOMBO-17catalogues(Wolfetal.2004).TheBPZcode
2.1.1 ChandraDeepField-South
usesaχ2minimizationtemplatefittingapproach.Asetofsixtem-
Theoriginal∼1MsobservationoftheCDF-S(Giacconietal.2002) platespectraareused,consistingofthefourstandardtemplatesfrom
hasrecentlybeensupplementedwithadditionalDirector’sDiscre- Coleman,Wu&Weedman(1980)(E/S0,Sbc,ScdandIrr)andtwo
tionaryTimetoprovideatotalof∼2Msexposure(Luoetal.2008), starburstinggalaxytemplatesfromKinneyetal.(1996).Additional
whichweuseinthispaper.Datareductionandsourcedetectionwere pointsincolourspacearecalculatedbyinterpolatingbetweenthe
carried out using the procedures described in Laird et al. (2009). templates.TheBPZcodealsoadoptsaBayesianapproach,applying
For our investigation of the XLF, we use the hard (2–7keV) se- priorsbasedontheexpectedfractionsandredshiftdistributionsfor
lectedsourcecatalogueofobjectsdetectedwiththefalsePoisson differenttemplatesandmarginalizingoverthetemplatestoproduce
probabilityof<4×10−6,whichprovidesasampleof248X-ray thefinalredshiftprobabilitydistribution,p(z).Thesedistributions
sources.TheX-raysensitivity(areacurve)isdeterminedusingthe describetheuncertaintiesintheredshiftestimateduetobothphoto-
proceduredescribedinGeorgakakisetal.(2008). metricerrorsandcolour,redshiftandtemplatedegeneracies,which
DeepopticaldatahavebeenobtainedinseveralbandsintheCDF- often result in multimodal probability distributions. We note that
S using both ground-based observatories and the Hubble Space BPZdoesnotincludeAGNorquasi-stellarobject(QSO)templates.
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551
2534 J.Airdetal.
5.0 2.1.2 ChandraDeepField-North
TheCDF-Nprovidesasecond2MsX-rayfield.Apointsourcecat-
aloguebasedonthefull2Msexposureobtainedhasbeenpresented
2.0
by Alexander et al. (2003); however we use our own reduction
andsourcecatalogue,againusingtheproceduredescribedinLaird
1.0 etal.(2009).Ourcatalogueprobestolowersignificancesthanthe
zphot Aselnesxiatinvditeyrceatlaclu.l(a2ti0o0n3s)(wGoerokrgaankdakalilsoewtsalu.s2t0o0a8d).oIpntothuirsipmappreorvwede
0.5
useobjectswithsignificantdetections(falsePoissonprobabilityof
<4 × 10−6) in the hard band, providing a sample of 303 X-ray
sources.
0.2
Avastquantityofmultiwavelengthdataareavailableinthisthor-
oughlyobservedfield(e.g.Dickinsonetal.2003).Tofindoptical
0.1 counterpartstoourX-raysources,weusetheHawaiiHDF-Ndata
0.1 0.2 0.5 1.0 2.0 5.0 (Capak et al. 2004), which fully covers the X-ray data with deep
zspec observations in U, B, V, R, I, z(cid:6) and HK(cid:6) bandpasses. Optical
counterpartswerefoundusingthelikelihoodratiomethod,asinthe
Figure 1. Comparison of spectroscopic and template fitting photometric CDF-S. This yields secure optical counterparts for 204 (≈67 per
redshiftestimatesintheCDF-S(circles),CDF-N(triangles)andAEGIS
cent)ofourhard-band-selectedX-raysources.
(squares).Errorbarsare95percentcentralconfidenceintervalsderived
fromtheredshiftprobabilitydistributions.Atz(cid:2)1.0,thephotometricand We searched for spectroscopic redshifts for our secure optical
counterparts in a variety of spectroscopic surveys that have been
spectroscopicredshiftsaregenerallyingoodagreement.Athigherredshifts
the photo-zs are less reliable, reflected by the larger error bars. A high carried out in the region (Steidel et al. 2003; Reddy et al. 2006;
fractionoftheoutliersisassociatedwithbroad-lineQSOs(opensymbols), Weiner et al. 2006; Barger, Cowie & Wang 2008; Trouille et al.
whicharepoorlyfittedbythetemplates.However,thereisasystematicbias 2008). This provided spectroscopic redshifts of 166 sources (81
toassignz(cid:3)1.2sourcestolowerredshifts. percentoftheX-raysourceswithsecureopticalcounterpartsand
55percentofthetotalhardX-ray-selectedsample).Thespectro-
scopiccompletenessismuchhigher(∼80percent)forthebrightest
X-raysources(f >10−14ergs−1cm−2;seeTrouilleetal.2008).
Broad-lineQSOsarelikelytobeopticallybright,andmaybemore X
As for the CDF-S, we have recalculated photometric redshift
easilyidentifiedspectroscopicallyduetotheirclearspectroscopic
features.TheremainingAGNpopulationisexpectedtobefainter, estimateswithBPZ,usingtheCapaketal.(2004)U,B,V,R,I,z(cid:6)and
HK(cid:6) photometry.Acomparisonofphotometricandspectroscopic
withasignificantfractionoftheopticallightcomingfromthehost
redshiftsisshowninFig.1.Again,alargenumberoftheoutliersare
galaxy,thusimprovingthematchtothegalaxytemplates.Uncer-
associatedwithbroad-lineAGN,inadditiontohigh-redshiftsources
tainties due to the mismatch between the observed AGN spectral
whichareassignedlargeerrors.ExcludingQSOs,theaccuracyof
energydistributions(SEDs)andthegalaxytemplatesmaybepar-
ourphoto-zsisδz≈0.11.Asystematicbiasatz (cid:2)1.2,assigning
tially reflected in the redshift probability distributions, although spec
sourcestolowerredshifts,ispresent,asfoundfortheCDF-S.
the lack of a representative template may result in catastrophic
failures,andanunrepresentativep(z).Additionally,thepriorsare
basedonobservationsofthegalaxypopulationintheHubbleDeep
2.1.3 AEGIS
Field-North(HDF-N),andthusmaynottrulyrepresenttheAGN
population. AEGIS(Davisetal.2007)isaninternationalmultiwavelengthsur-
InFig.1wecomparetheavailablespectroscopicredshiftswith veyoftheExtendedGrothStrip,coveringan∼0.25by2◦ stripof
thebestphoto-zestimates,givenbythemodeofthep(z)distribution. thesky.Deep(∼200ks)X-raydatahavebeenobtainedalongthe
Errorbarsonthephoto-zrepresent95percentcentralconfidence entirelengthofthestrip.Lairdetal.(2009)describedthereduc-
intervals determined from the p(z) distribution, although will not tionofthesedataandpresentedacatalogueof1325uniquepoint
fullyrepresentmorecomplicatedmultimodaldistributions.Thees- sources,mergedoverallbands.Inthispaperwerestrictouranaly-
timatesgenerallyagreewellatz <1.5andhaveaδz=|(z − sistohard-band-detectedsources(falsePoissonprobabilityof<4
spec phot
z )|/(1+z )≈0.18.Therearehoweveranumberofoutliers. ×10−6)andthosewhichalsofallwithintheareawithverydeep
spec spec
A high fraction of these are associated with broad-line QSOs, in u∗g(cid:6)r(cid:6)i(cid:6)z optical data from the Canada–France–Hawaii Telescope
whichtheopticallightisdominatedbytheAGN,andthuscannot LegacySurvey(CFHTLS).1Thisreducesthesampleto397X-ray
beaccuratelydescribedwiththeBPZgalaxytemplates.Excluding sources, of which 343 (86 per cent) have secure i(cid:6)-band optical
these sources reduces the error to δz ≈ 0.13. The remaining out- counterparts(likelihoodratioof>0.5).
liersaregenerallyathighredshifts(z (cid:2)1.2),andareassigned Significant spectroscopic follow-up is available in the AEGIS
spec
largeerrors,indicatingbroadp(z)distributions.However,wenote field,includingredshiftsfromtheDEEP2survey(Davisetal.2007)
asystematicbiasthatassignsz (cid:2)1.2sourcestolowerredshifts. andadditionaltargetedfollow-upofX-raysourceswithMMT(Coil
spec
Thep(z)distributionsareequallyaffectedbysuchbias;accounting etal.2009).Thisprovidesspectroscopicredshiftsfor157sources
fortheredshiftuncertainty,howeverbroad,willnotcorrectforthis (40percent).
effect. Indeed, the systematic bias indicates a catastrophic failure Inthisfield,wehavechosentousephotometricredshiftsfrom
of the BPZ code to correctly fit the observed SEDs with realistic twodifferentsources.Huangetal.(inpreparation)useanArtificial
templates at the higher redshifts. This failure may severely bias
any determination of the XLF. We explore this in more detail in
Section3.3. 1http://www.cfht.hawaii.edu/Science/CFHTLS
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551
Theevolution ofthehardXLFofAGN 2535
1.5 Fortheremainingsourcesinoursamplewithsecureopticalcoun-
terparts we adopt photometric redshifts from Ilbert et al. (2006),
whicharebasedontheCFHTLSu∗g(cid:6)r(cid:6)i(cid:6)zdata.Theredshiftsare
basedontemplatefittingandaBayesianapproach,andthususethe
1.0 samemethodastheBPZcode.Thepriorsarecalibratedusingspec-
troscopicidentificationsofgalaxiesintheD1fieldoftheCFHTLS.
z
N TheestimatesarelessreliablethantheANNzresults(δz≈0.16),
N
butdoprovideredshiftinformationfortheremainingopticallyiden-
A
tifiedX-raysources.Howeverthereisasystematicbiasforsources
0.5
withz (cid:2)1.2tobeplacedatlowerredshifts,aswasfoundforthe
spec
CDF-SandCDF-N.Theauthorshavemadeavailablethefullp(z)
redshiftprobabilitydistributionsforeverysource,whichwehave
adoptedtoaccountfortheuncertainties,thoughonceagainwillnot
0.0
accountforthesystematicbias.
0.0 0.5 1.0 1.5
z
spec
2.1.4 ASCALargeSkySurvey
The ASCA Large Sky Survey (ALSS; Ueda et al. 1999) covers
1.0
a contiguous area of ∼5deg2 near the North Galactic Pole, and
contains34sourcesdetectedinthehard(2–7keV)bandwiththe
0.8
Solid-State Imaging Spectrometer (SIS) detector, down to a flux
limit∼10−13ergs−1cm−2(2–10keV).Opticalidentificationshave
0.6
)
z been presented by Akiyama et al. (2000). Two of these sources
(
p areopticallyidentifiedasgalaxyclusters:oneisastarand30are
0.4
associated with AGN, all of which have spectroscopic redshifts.
0.2 One source remains unidentified. An area curve for this survey
was presented by Akiyama et al. (2003), which we adopt forour
0.0 work. We note that this area curve does not fully account for the
PoissoniannatureoftheX-raysourcedetection,butasarelatively
-0.4 -0.2 0.0 0.2 0.4
highfluxlimitwassetforthecatalogueandtheX-rayfluxeswill
(z-z )/(1+z)
phot beaccuratelymeasuredthisisunlikelytohaveanadverseaffecton
ourbright-enddetermination.
Figure 2. Top panel: comparison of ANNz and spectroscopic redshifts
in AEGIS, shown for all sources (red circles) and X-ray sources (black
squares).TheANNzredshiftsgenerallyprovideextremelygoodestimates,
2.1.5 ASCAMediumSensitivitySurvey
althoughareavailableforalimitedsubsetofobjects,andarerestrictedto
z<1.5wheretherearesufficientspectroscopictrainingdata.Theprobability ThelargestareasurveyinourstudyistheASCAMediumSensitiv-
distributionforanANNzestimateisdeterminedfromthedistributionof
itySurvey(AMSS;Uedaetal.2001).Weincludesourcesfromthe
spectroscopicredshiftsforasmallsliceofphotometricredshifts(e.g.blue
AMSSnsub-sample,selectedinthehard(2–10keV)band,withop-
dashedlines).Bottompanel):thedistributionof(z−zphot)/(1+z)forthe ticalidentificationspresentedbyAkiyamaetal.(2003).Thesample
ANNzredshiftrangeindicatedinthetopfigure.Thetruedistribution(black
includes87X-raysources,76ofwhichareAGN,toafluxlimitof
histogram)issmoothed(redcurve)toprovideanestimateofprobability
distributionoftrueredshiftsassociatedwithagivenANNzestimate. ∼3 × 10−13ergs−1cm−2, and is 100 per cent optically identified
withspectroscopicredshiftsavailableforalltheAGN.Weinclude
Neural Network/training set approach (ANNz; Collister & Lahav additional sources with redshift identifications from the AMSSs
2004). This approach effectively fits an arbitrary function to the sub-sample(Ueda&Akiyama,privatecommunication),whichin-
redshift–colour relation, using a set of spectroscopic redshifts to cludes 20 AGN; two sources in this sample remain unidentified.
train the neural network. As such the redshifts are only expected TheareacurveforthecombinedAMSSnandAMSSssampleswas
to be valid for sources with the same range of properties as the presentedbyUedaetal.(2003).
training set. The Huang et al. work uses a 3.6μm InfraredArray
Camera (IRAC)-selected catalogue (Barmby et al. 2008), further
2.2 High-redshiftsample
subjectedtoanumberofcolourcuts,andutilizesphotometryfrom
MMT (Megacam)aswellasIRAC,MultibandImagingPhotome- Duetothecatastrophicfailureofourphotometricredshiftestimates
ter and DEEP2. The neural network was then trained using the at z (cid:2) 1.2, we have also investigated an alternative colour pre-
DEEP2spectroscopicdataandphotometricredshiftsestimatedfor selectionapproachforidentifyingAGNathigh-redshift,building
allsourceswhichsatisfytheselectioncriteria.Thisprovideshighly ontheworkofAirdetal.(2008).Weincludefourofthefieldsused
accuratephoto-zs(δz≈0.04),albeitforarestrictedsample.ANNz in Aird et al. (2008): HDF-N (fully encompassed by the CDF-N
redshiftsareadoptedfor38X-raysourcesinoursample(without X-rayfielddescribedabove),LALACETUS,LynxandEGS1.We
spectroscopicredshifts).Toaccountfortheerror,wemustdetermine additionally include the large area covered by both the AEGIS-
aprobabilitydistributionforeachredshift.FortheANNzestimates X survey and the CFHTLS field D3 optical imaging. This fully
wehavebasedthisonthedistributionofspectroscopicredshifts,for encompasses the Groth-Westphal Strip (GWS) field used in Aird
agivenANNzestimate,usingallobjectsintheHuangetal.work et al. (2008), and thus supersedes those data. Our high-redshift
withspectroscopicidentification,asdemonstratedinFig.2. data overlap with our hard X-ray-selected samples described in
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551
2536 J.Airdetal.
Section 2.1; in Section 3.3, we explain how data from our hard of uncertain colour corrections. The differences in the filters will
X-raysurveysatz<1.2andourhigh-redshiftcolourpre-selected lead to different selection functions, which we determine in Sec-
samplesarecombinedtodeterminetheevolutionoftheXLF. tion3.3.1.
2.2.1 Opticaldata 2.2.2 X-raydata
The reduction of the optical data for HDF-N, LALA CETUS, AllofourfieldshavebeenobservedwithChandra,andhaveex-
Lynx and EGS1 and the source detection and photometry with posure times of (cid:2)200ks. The data have been reduced using our
SEXTRACTORhasbeendescribedinAirdetal.(2008)andReddyetal. pipelineprocedure(Lairdetal.2009).Forourhigh-redshiftsam-
(2006),andwereferthereadertothosepapersforfurtherdetails. ples we use sources detected in the soft band with a significance
For the CFHTLS we have used the publicly released images and of<4×10−6.Ourcolourpre-selectionlimitsustosourcesatz(cid:2)
cataloguesavailablefromCanadaAstronomicalDataCenter,22008 2,andattheseredshiftsthesoftbandwillproberest-frameener-
Marchrelease.ThecataloguesweregeneratedusingSEXTRACTOR, giesof∼2–8keV.Thusourselectionshouldberelativelyunbiased
althoughwithaslightlydifferentconfigurationtoAirdetal.(2008). fortheselectionofmoderatelyabsorbedAGN(N (cid:3)1023cm−2),
H
Initialdetectionwasperformedinthei(cid:6)band(whichisthedeepest andiscomparablewiththehard-bandselectionemployedatlower
band), and magnitudes were determined in the other bands using redshifts(Cowieetal.2003;Bargeretal.2005).
theKron(1980)styleaperture(determinedfromthei(cid:6)-banddata).
Thedatawerenotsmoothedtomatchtheseeingindifferentbands.
Thesedifferenceswillaffectthedetectionofobjectsandmeasure- 2.2.3 MatchingtheX-rayandopticalsamples
mentsoftheircolours,althoughgiventhedepthandqualityofthe
Wedeterminedwhichofourcolourpre-selectedhigh-redshiftob-
CFHTLSdatatheyareunlikelytoadverselyaffectthecolourselec-
jectshostAGNbymatchingtheopticalandX-raysourcelists.The
tionofcandidates.Nevertheless,anyerrors,biasesandscatterdue matchingisperformedwiththeentireR-(ori(cid:6)-)selectedoptical
tothesourcedetectionandphotometryprocedurewillbeaccounted
cataloguesusingthelikelihoodratiomethod.Thecolourselection
forbyoursimulationstoderivetheopticalselectionfunctions(Sec-
criteriaarethenappliedtothematches.Matchingtheentireoptical
tion3.3.1).
catalogueensuresthatX-raysourcesarematchedtothemostlikely
Samplesofz∼3Lyman-breakgalaxies(LBGs)wereextracted
optical counterparts and prevents colour pre-selected objects be-
from the optical catalogues using the standard selection criteria
ingerroneouslyassociatedwithnearbybrightX-raysources,which
fromSteideletal.(2003):
have correspondingly bright, secure optical counterparts (cf. the
G−R≤1.2 directextractionmethodusedinAirdetal.2008).
In Table 2, we list the total numbers of X-ray-detected objects
U −G≥G−R+1.0
n withineachofourcolour-selectedsamples.Wesearchedforspec-
19.0≤R≤25.5 (1) troscopic redshifts for our sources as described in Sections 2.1.2
withthefaintlimitofR≤25.0forEGS1.Anadditionalsampleof and 2.1.3 for the HDF-N and AEGIS-X fields respectively, and
fromSternetal.(2002)fortheLynxfield.Theremaininguniden-
objectsatslightlylowerredshiftsisselectedusingtheBXselection
tifiedsourceswereassignedredshiftprobabilitydistributions,p(z),
criteria(Adelbergeretal.2004):
basedontheopticalselectionfunctions(seeSection3.3.1).
G−R ≥ −0.2
U −G≥ G−R+0.2
n 2.2.4 Low-redshiftinterlopers
G−R ≤ 0.2(U −G)+0.4
n U GR LBG selection at z ∼ 3 is known to be extremely clean
U −G<G−R+1.0. (2) n
n andcontainsveryfewlow-redshiftinterlopers(Steideletal.2003).
Theseobjectsare‘sub-Udropouts’,fallinginathinsliceofcolour The majority of interlopers are Galactic stars, which are not ex-
spacebelowtheLyman-breakcriteria,withaselectionfunctionthat pectedtobebrightX-raysourcesandthuswillnotcontaminateour
peaksaroundz∼2.5(seeSection3.3.1). sample. However, the BX selection, which does not rely on very
ObjectswereselectedfromtheCFHTLSopticaldatausingthe strong features such as the Lyman break to identify candidates,
same criteria. However, there are significant differences between is more susceptible to contamination from low-redshift sources,
theCFHTLSfiltersetandourU GRfiltersusedintheotherfields. mainlyfromlow-redshift(z(cid:3)0.3)star-forminggalaxiesinwhich
n
TheRbandfallsbetweenther(cid:6)andi(cid:6)filters;thus,thetotalR-band theBalmerbreakisconfusedwiththeLymanα forestabsorption
magnitudeswerecalculatedforeveryobjectusinganapproximate at z (cid:2) 2 (Adelberger et al. 2004; Reddy et al. 2006). Indeed, a
colourcorrection,givenby significant number of low-redshift (z < 1.2) interlopers are iden-
tified within our spectroscopically observed, X-ray-detected BX
R=r(cid:6)+0.05−1.08(r(cid:6)−i(cid:6)), (3)
sample (see Table 2 and Fig. 3). By examining the positions of
which was determined from our model colour distributions de- these sources in the fX–fopt plane (see Fig. 4) it is clear that
scribedinSection3.3.1.TheseestimatedRmagnitudeswereused five of these low-redshift interlopers occupy a distinct position,
toapplythetotalmagnitudelimits,consistentwithourotherfields. associated with optically bright objects (R < 23), but with rel-
However, for the selection in colour space we used the original atively low X-ray fluxes; thus, log(fX/fopt) < −1.5. These ob-
u∗g(cid:6)r(cid:6) magnitudes in place of U GR, thus avoiding the effects jects are the expected bright, low-redshift star-forming galaxies,
n
withX-rayemissionassociatedwithstarformationprocesses.We
exclude two more X-ray-detected BX sources from our analysis
2http://www4.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/community/CFHTLS-SG/ which fall in the same region and are thus also suspected to be
docs/cfhtls.html low-redshiftcontaminants.ThefaintBXsourcewithR≈23.5and
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551
Theevolution ofthehardXLFofAGN 2537
Table2. Summaryofthefieldsusedtodeterminethehigh-redshiftXLFusingrest-frameUVcolourpre-selection.
Field RA Dec NHa X-ray Survey Selection Ncandd NXe Nspecf Nlowzg Nsamph
name exposureb areac z<1.4
(J2000) (J2000) (1020cm−2) (ks) (arcmin2)
HDF-N 12:36:55 +62:14:18 1.5 1862.9 149.1 BX 1192 9 8 2 7
LBG 292 3 2 0 3
AEGIS-X/CFHTLS 14:17:43 +52:28:25 1.2 188.7 1155.6 BX 17050 77 26 10 66
LBG 6933 30 10 0 30
Lynx 08:48:56 +44:54:50 1.0 186.5 243.4 BX 647 2 0 0 2
LBG 223 1 1 0 1
EGS1 14:22:43 +53:25:25 1.2 177.8 358.9 BX 809 8 0 0 7
LBG 329 7 0 0 7
LALACETUS 02:04:44 −05:05:34 2.2 173.1 233.3 BX 660 4 0 0 4
LBG 144 3 0 0 3
aGalacticcolumndensityfromDickey&Lockman(1990);bX-rayexposuretimeaftergoodtimeintervalandbackgroundfiltering(averageoftheindividual
pointingsforAEGIS-X);ctotalsurveyareacoveredbyX-rayandopticaldata;dnumberofcandidatesfromtheopticalimagingsatisfyingthecolourselection
criteria;enumberofthecolour-selectedcandidateswithsecureX-raycounterparts;fnumberoftheX-ray-detectedcandidateswithspectroscopicredshifts;
gnumberofthespectroscopicallyidentifiedsamplewhicharelow-redshiftinterlopers(z <1.4);hfinalnumberofsourcesinoursampleafterexcluding
spectroscopicallyidentifiedlow-redshiftinterlopersandadditionalsuspectedlow-redshiftinterlopersaccordingtotheirpositioninthefX–fopt plane(see
Section2.2.4,Fig.4).
88 26
66 24
ber nitude 22 log(fX/fopt)=+1.0
m 44 ag
Nu R m 0.0

20
22 -1.0
-1.5
18
00 10-17 10-16 10-15 10-14 10-13
Soft flux / erg s-1 cm-2
00 11 22 33 44
Redshift Figure4. X-rayflux(0.5–2keV)versusRmagnitudefortheBX(green
triangles)andLBG(redcircles)X-ray-detectedsamples.Blackcirclesin-
Figure3. DistributionofavailablespectroscopicredshiftsfortheX-ray- dicateobjectswithspectroscopicredshifts,zspec >1.4;purplediamonds
detectedcolour-selectedobjects.Green:BX,red:LBGandblack:total.The indicate low-redshift interlopers with zspec < 1.4. As discussed in Sec-
BX sample is contaminated by low-redshift interlopers, although around tion2.2.4anumberoftheinterlopersareassociatedwithlow-redshiftstar-
halfmaybeidentifiedaslow-redshiftstar-forminggalaxiesandonthebasis forminggalaxies,whichareopticallybrightbutveryfaintinX-rays.We
oftheirfX/foptratio(seeFig.4,Section2.2.4). thusexcludeallsourceswithlog(fX/fopt)<−1.5.Thiswillexcludethe
low-redshiftinterlopers,inadditiontobrighthigh-redshiftstarburstgalax-
iesthatmayalsocontaminatetheAGNXLFatthefaintestfluxes(seeAird
log(fX/fopt) < −1.5, which has a spectroscopic redshift in the etal.2008).Objectswithzspec<1.4arealsoexcludedfromouranalysis,but
correctrange,isalsoexcludedaswesuspectastarburstorigin(see interlopersassociatedwithlow-zAGNmaystillcontaminatetheremaining
alsoAirdetal.2008). spectroscopicallyunidentifiedBX-selectedsample.
The six remaining interlopers, however, are associated with
low-redshift AGN, and thus fall within the AGN region −1.0 (cid:3)
log(f /f ) (cid:3) +1.0. While any AGN which have been spec- AGN(includingQSOsandnarrow-lineAGN),thecontamination
X opt
troscopically identified as low-redshift interlopers are excluded fractionwasonly∼12percentandapproximatelyconsistentover
fromouranalysis,additionalcontaminantsmayremainwithinour theentiremagnituderange.Clearlyamuchlarger,nearcomplete
unidentified BX sample. Based on our spectroscopic sample the sampleofspectroscopicredshiftsforBX/X-ray-selectedAGNisre-
fraction of low-redshift AGN contaminants may be as high as quiredtotrulydeterminetheinterloperfractionwithinoursample,
∼25percent,althoughoursampleisbiasedinthesensethatahigher andcouldalsoallowimprovementstotheselectioncriteria(suchas
fractionofbrightobjectshasspectroscopicidentifications.Indeed, introducingdatafromredderwavebands)tobedevelopedtohelp
in the large sample of BX-selected galaxies with spectroscopic reducethecontamination.However,giventhecurrentuncertainties,
redshiftsusedbyReddyetal.(2008)thelow-redshiftcontamina- wehavechosennottomakefurthercorrectionstoaccountforthe
tioninthegalaxysamplewas∼59percentforbrightcandidates interloper fraction within our sample. We thus note that the faint
(R<23.5),whereasforfaintercandidatesitwasonly∼9percent. endofourXLFbasedontheBXsamplemaybeoverestimateddue
Conversely,inthesampleofobjectsspectroscopicallyidentifiedas tolow-redshiftcontamination.
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551
2538 J.Airdetal.
2.2.5 High-luminositysample where{d}representsthesetofobserveddatafromallsources,and
i
theproductinthesecondpartoftheequationisoverM-detected
The total area coverage for our high-redshift sample remains rel-
sources.Fortheidealizedsituationwheretheredshiftandluminos-
atively small, and thus we require an additional sample of high-
ityareperfectlydetermined,p(d |L ,z)willbeadeltafunction
luminosityAGNtoconstrainthebrightendoftheXLF.Wehave i X
at the true values, and equation (6) will generalize to the stan-
chosentousebrightobjects(f >5×10−15ergs−1cm−2)from
X dardmaximumlikelihoodestimator.Foroursamplep(d |L ,z)is
theHasinger,Miyaji&Schmidt(2005)compilationofsurveys(ex- i X
theconvolutionoftheredshiftprobabilitydistributionp(z)andthe
cludingtheCDF-Ntoavoidoverlapwithourownanalysis).These
PoissonlikelihoodofobtainingtheobservedX-raydata,Ncounts:
samplesprovideasoft-bandselected,highlycomplete,spectroscop-
icallyconfirmedsample.Wehaveincludedobjectswith1.9<z≤ (s+b)N
L(N |s,b)= e−(s+b), (6)
3.5,providing30high-luminosityAGNinourhigh-redshiftsample. N!
These bright, complete, spectroscopic surveys may be combined
where s is calculated from the hard-band (2–10keV) flux for a
withourcolourpre-selectedsamplesbyassumingatop-hatselec-
source of luminosity L and redshift z, assuming (cid:12) = 1.9 and
tionfunctionoverthechosenredshiftrange(seeSection3.3.2). X
Galactic N . Thus, the Poissonian nature of the counts from the
H
X-ray sources, the associated uncertainty in the flux and the Ed-
3 A BAYESIAN APPROACH TO DETERMINING dington bias are naturally accounted for in our determination of
THE XLF theXLF.Assuming(cid:12)=1.9approximatelycorrectsforabsorption
effectsduetointrinsiccolumndensitiesN (cid:3)1023cm−2atz∼1,al-
OurcompilationofX-raysurveysprovideslargesamplesofAGN H
thoughwehavenotchosentomakeamoresophisticatedcorrection
overarangeofredshiftswithwell-definedcompleteness,requiredto
onasource-by-sourcebasis(seefurtherdiscussioninSection5.2).
determinetheevolutionoftheXLF.However,thefaintsourcesfrom
OurapproachbuildsonthelogN–logSworkofGeorgakakisetal.
the Chandra fields are subject to uncertainty in both the redshift
(2008),extendedtoincluderedshiftinformation,andallowsusto
determination(forthosesourceswithphotometricredshiftsorinthe
usetheimprovedmethodofcalculatingtheX-raysensitivity.For
high-zcolourpre-selectedsamples)andtheX-rayfluxmeasurement
sourceswithspectroscopicredshifts,weassumedeltafunctionsfor
(duetothesmallnumbersofcountsfromthefaintestsources).This
p(z).Wealsoassumedeltafunctionsfortheluminositiesofsources
has led us to develop a Bayesian methodology to make accurate
inboththehardandsoftX-ray-selected,largearea,brightsamples
inferencesabouttheformandevolutionoftheXLF,accountingfor
(Sections2.1.4,2.1.5and2.2.5).
theuncertaintiesinindividualsources.
3.1 Thelikelihoodfunction 3.2 Correctingforincompleteness
Thefirststepistodeterminethelikelihoodfunction,L,forwhich Theabovelikelihoodfunctiondoesnotaccountfortheincomplete-
wehavefollowedtheworkofLoredo(2004).Ourindividualsources nessofoursamples.InourhardX-ray-selectedsamples,between
areeffectivelyPoissonianpoints,drawnfromthedistributiongiven ∼14percent(AEGIS)and∼32percent(CDF-N,CDF-S)ofthe
bytheXLF.Thus,foragivenmodelXLF,theexpectednumberof sourceslacksecureopticalcounterparts,andthushaveneitherspec-
detectablesources,λ,isgivenby troscopicnorphotometricredshifts.However,wecanderiveacom-
(cid:2) (cid:2) pletenesscorrectiontermtoaccountfortheincompletenessinthe
dV
λ= dlogL dzA(L ,z)φ(L ,z|θ), (4) likelihoodfunction.
X dz X X Fig. 5(a)shows the distribution of the hard X-ray flux and op-
wheretheintegralsaretakenovertheentirerangeofpossiblevalues. ticalmagnitudesofour(opticallyidentified)sources.Sourcesare
A(L ,z)istheareaofthesurveysensitivetoasourceofaparticular scatteredoverarangeofopticaltoX-rayfluxratios,approximately
X
luminosity, L , and redshift, z, and thus a particular flux if we overtherange−1<logf /f <1althoughasmallproportionis
X X opt
assume a single spectral shape (power law with a photon index atlowerratiosandasignificantnumberofthishardX-ray-selected
of (cid:12) = 1.9). A(L , z) effectively describes the probability of a sampleexhibitlogf /f >1.AtfaintX-rayfluxes,alargefrac-
X X opt
sourcebeingdetected.Theluminosityfunction,φ(L ,z|θ),isthe tion will be unidentified due to their faint optical magnitudes. In
X
differentialnumber densityofsources perunitcomoving volume Fig.5(b),weshowthelogf /f distributionofoursources.A
X opt
asafunctionofL andz,givenanassumedmodeldescribedbythe Gaussianapproximation,takingthesamplemean,μ,andstandard
X
setofparameters,θ.dV isthedifferentialcomovingvolumeperunit deviation,σ,isshowninred,andprovidesareasonabledescription
area,asafunctionofdzz. ofthisdistribution.IfweapplyastrictmagnitudelimitofR=25.5
AsdescribedinLoredo(2004),thelikelihoodfunctionmaybe (sourcesfainterthanthislimitarenowdeemedunidentified),and
constructed from the product of the probabilities of the observed assumethatalltheunidentifiedsourceswouldhaveopticalcounter-
datafromtheindividualsources,giventhemodel,andtheproba- partsfainterthanthislimit(reasonablegiventheverydeepoptical
bility that no other objects were detected. For a Poisson process, datawehaveusedtosearchforcounterparts),thenwecanintro-
the probability of no objects being detected is simply e−λ. In the duceacorrectiontotheexpectednumberofsources,λ,givenby
presenceofindividualsourceuncertainties,theprobabilityofthe equation(4),basedonthefractionofthelogf /f distribution
X opt
observeddata,d,fromanindividualsourcei,giventhemodelXLF probedatagivenflux.Thus,
i
isfoundbymarginalizingp(d |L ,z)overthemodeldistribution
i X λ
ofLXandz.Thus, (cid:2) (cid:2) (cid:2)
dV
L({di}|θ)= = dlogLX dzdz dRA(LX,z)φ(LX,z|θ)g(LX,z,R|μ,σ)
(cid:2) (cid:2) (cid:2) (cid:2)
(cid:3)M dV dV
e−λ× dlogLX dzdzp(di |LX,z)φ(LX,z|θ), (5) = dlogLX dzdzA(LX,z)φ(LX,z|θ)C(LX,z|μ,σ),
i=1 (7)
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551
Theevolution ofthehardXLFofAGN 2539
30 sourceswithfaintX-rayfluxeswheretheproblemarises.Therefore,
(a)
toimproveourcompletenesscorrectionthelogf /f distribution
X opt
shouldbedeterminedsimultaneouslywiththeXLF,accountingfor
R=25.5
25 theincompleteness,usingtheobserveddata(theR-magnitudesof
B) thedetectedsources).Wethereforeintroduceg(LX,z,R)intothe
A
secondterminequation(6),modifyingthelikelihoodto
ude ( 20 (cid:3)M (cid:2)
magnit +1.0 L((cid:2){di}|θ,μ,σ)=e−λi=1 dlogLX
R 15 log(fX/fopt)=0-1.0.0 w×hereddVwzedznepg(ldeic|tLaXn,yzu)φn(cLerXta,izn|tyθ)ign(LthXe,zm,eRaisu|μre,mσe)n,t of the(R9-)
magnitudeofanindividualsource,R,whichisaminorsimplifica-
10 i
tion.Theparametersμandσareintroducedasnuisanceparameters,
-16 -15 -14 -13 -12 -11
log(f / erg s-1 cm-2) andwillbedeterminedalongwiththeXLF,integratingovertheir
X
uncertaintieswhenmakinginferencesregardingtheXLFparame-
120 ters,θ.InFig.5(b),thegreendashedlineindicatesthebest-fitting
(b) (mode)values ofμ=0.24±0.01andσ =0.68±0.01forour
100 luminosityanddensityevolution(LADE)evolutionarymodel(Sec-
tion4.2).Thepeakofthedistributionisclearlyshiftedtoahigher
f /f ,indicatingthebiasinthesimpleestimates.
80 X opt
er
b 3.3 Incorporatingthehigh-zcolourpre-selectedsamples
m 60
u
N InSection4,wepresentresultsfortheevolutionoftheXLFover
40 thefullavailableredshiftrangebasedonourhardX-ray-selected
sampleonly(usingspectroscopicandphotometricredshifts).How-
20 ever, due to the systematic bias in photo-z estimates at z (cid:2) 1.2,
wealsowishtoderivetheevolutionusingourhigh-redshiftcolour
0 pre-selected samples. Due to the a priori colour selection, these
-2 -1 0 1 2 samples will suffer from large, but well-defined, incompleteness.
log(f /f ) Accountingforthisincompletenessandcombiningoursoft-band-
X opt
selected high-z sample with the hard X-ray-selected samples at
Figure 5. (a) Hard (2–10keV) flux against R magnitude (AB) for our lower redshifts require a number of further modifications to our
entire hard X-ray-selected sample (black circles). Black dashed lines: methodology.
logfX/fopt =−1.0,0.0and+1.0,indicatingthetypicalrangeofAGN.
Green lines: mean (dashed) and ±1σ (dotted) of the best-fitting Gaus-
sianlogfX/foptdistribution(seeSection4.2).Bluedottedline:R=25.5 3.3.1 Opticalselectionfunctions
limitforincludingopticalcounterparts.(b)Histogramofthedistribution
The first step is to determine the optical selection functions for
oflogfX/fopt(black)andtheGaussiandistributioncorrespondingtothe thecolourselectioncriteria.Theseweredeterminedusingthesim-
samplemeanandstandarddeviation(redcurve).Thisdistributionwillbe
ulation method described in Aird et al. (2008) (see also Steidel
biasedduetoincompleteopticalidentifications,aswellasthedistribution
ofX-rayfluxes.Weaccountfortheseeffectswhenfittingourevolutionary et al. 1999; Hunt et al. 2004; Reddy et al. 2008). Three sets of
models (see Sections 3.2 and 4) and derive the logfX/fopt distribution templatespectraweredeterminedfordifferentspectroscopicclas-
(greendashedcurve),whichisshiftedtohigherfX/foptratios. sifications (QSO, NLAGN or GAL; see Steidel et al. 2003), and
used to generate model U GR and u∗g(cid:6)r(cid:6) colour distributions.
n
whereg(LX,z,R|μ,σ)describestheR-magnitudedistributionof GALandNLAGNcoloursweregeneratedusingaBruzual&Char-
sourcesatagivenflux,fX(LX,z),andisderivedfromtheGaussian lot(2003)modeltemplatespectrumforagalaxywithcontinuous
distributionoflogfX/fopt .g(LX,z,R|μ,σ)isnormalizedsuch star formation and an age of 1Gyr. This template spectrum was
t(cid:2)hat reddenedusingtheCalzettietal.(2000)relationforobscurationby
∞
dust,withvariousextinctioncoefficientsdrawnfromthedistribu-
dRg(L ,z,R|μ,σ)=1.
X tionsbasedontheobservedrangeofUVspectralslopesforGAL
−∞
andNLAGNsourcesinLBGsamples(Adelberger&Steidel2000;
Thus,thefactor
(cid:2) Steidel et al. 2002, 2003). Such modelling is not a full physical
25.5
C(L ,z|μ,σ)= dRg(L ,z,R|μ,σ) (8) descriptionfortheNLAGN,beingbasedonlyonatemplatespec-
X X
−∞ trum for star-forming processes, but is sufficient to simulate the
isacompletenesscorrection,reducingtheexpectednumberofde- observedrangeofspectralshapesandredderdistributionofbroad-
tectablesourceswithlowX-rayfluxes. bandcoloursforNLAGN.ForQSOs,wehavefollowedtheworkof
However,theobserveddistribution(theredcurveinFig.5)will Huntetal.(2004).Thetemplatespectraweregeneratedbyvarying
bebiasedbytheveryincompletenesswearetryingtocorrectfor, thecontinuumslopeandLyα-equivalentwidthsofacompositeof59
assourceswithR(cid:2)25.5willbemissed.Theextentofthebiaswill QSOspectra(correctedforintergalacticabsorption)fromSargent,
dependonthefluxdistributionoftheX-raysources(andthusthe Steidel&Boksenberg(1989),basedontheGaussiandistributions
XLF,andtheX-raysensitivity),whichdeterminesthenumberof giveninHuntetal.(2004).Thesemodelspectraforallthreetypes
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551
2540 J.Airdetal.
3 3
2 2
LBG LBG
G BX ’ BX
U-n 1 *u-g 1
0 QSO 0
GAL
NLAGN
-1 -1
-0.5 0.0 0.5 1.0 1.5 -0.5 0.0 0.5 1.0 1.5
G- R g’-r’
Figure6. ExamplemodelcolourdistributionsforourGAL(blackcircles),NLAGN(greensquares)andQSO(redtriangles)classifications.Thesamemodel
foreachtypeisshowninUnGR(left-handpanel)andu∗g(cid:6)r(cid:6)(right-handpanel)colour-space.Themodelisredshiftedover1.0<z<4.0.Marksshowthe
coloursat(cid:13)z=0.1intervals,withlargersymbolsindicating2.5<z<3.5.Thevariationbetweencoloursthroughdifferentfiltersetsleadstodifferencesin
theopticalselectionfunctions(seeFig.7,Section3.3.1).
GAL NLAGN QSO
1.0
0.8
’
0.6 ’i
P(z) 0.4 *ug’r
0.2
0.0

BX L BG BX L BG BX L BG

0.8
0.6 R
P(z) UG
0.4
0.2
0.0
1 2 3 1 2 3 1 2 3 4
Redshift (z)
Figure7. OpticalselectionfunctionsforourBX(greensolidlines)andLBG(reddashedlines)colourselectioncriteria.Thetoprowshowstheselection
functionsfortheCFHTLS-D3opticaldataandu∗g(cid:6)r(cid:6)i(cid:6)filtersets.ThebottomrowshowsselectionfunctionsintheHDF-N(withopticaldataofcomparable
depth)usingUnGRfilters.Eachcolumnisforadifferentspectroscopicclassificationasindicated.Significantdifferencesinefficiencyandredshiftcoverage
existbetweentheselectionfunctionsfordifferentopticaltypesandfiltersets(seediscussioninSection3.3.1).
were then redshifted over the range z = 1 − 4 and intergalactic generatethereleasedcataloguesforCFHTLSisavailableon-line;3
absorptionwasappliedbysimulatingarandomlineofsighttoeach thus,weusedthisconfigurationforthosedata.Objectswereselected
objectwithinterveningLyman-limitabsorptionsystemsdistributed inthei(cid:6)-bandimage,andflexibleKron(1980)styleapertureswere
accordingtotheMC-NHmodelofBershady,Charlton&Geoffroy used to measure the magnitudes in other bands and calculate the
(1999), as described by Hunt et al. (2004). The final spectra are output colours. Our selection functions will thus account for the
multiplied by the filter transmission curves to produce the model differentsourcedetectionandphotometrytechnique,andtheeffects
colour distributions. Fig. 6 compares colours for a single model ofthedifferentfiltersets.
spectrum(foreachclassification)atdifferentredshiftsinbothU Fig.7comparesourfinalselectionfunctions(derivedfromthe
n
GRandu∗g(cid:6)r(cid:6)colourspace. simulations)forthedifferentcolourcriteria,filtersetsandoptical
Thefullcolourdistributionswereusedtoaddartificialobjectsto classifications.TherearecleardifferencesbetweentheU GRand
n
theopticalimagingdata.Selectionfunctionsarethendetermined u∗g(cid:6)r(cid:6) selections, which we expect given the varying wavelength
astheprobabilityofrecoveringanobjectwithagivenRmagnitude
witheithertheLBGorBXselectionasafunctionofredshift.Objects
wererecoveredusingourSEXTRACTORroutines(seeAirdetal.2008) 3http://www1.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/community/CFHTLS-SG/
in the Un GR fields. The SEXTRACTOR configuration file used to docs/cfhtlscat.sex
(cid:3)C 2009TheAuthors.Journalcompilation(cid:3)C 2009RAS,MNRAS401,2531–2551