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

18 Pages·2005·0.55 MB·English

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