The Covering Factor of Warm Dust in Quasars: View from WISE All-Sky Data Release

1.6 MB·English

by  Xiang-Cheng Ma

Mon.Not.R.Astron.Soc.000,1–8(2013) Printed17January2013 (MNLATEXstylefilev2.2)
The Covering Factor of Warm Dust in Quasars: View from WISE
All-Sky Data Release
Xiang-Cheng Ma,1,2⋆ Ting-Gui Wang1,2
3
1 1DepartmentofAstronomy,SchoolofPhysicalScience,TheUniversityofScienceandTechnologyofChina(USTC),Hefei,Anhui230026,P.R.China
0 2KeyLaboratoryforResearchinGalaxiesandCosmology,ChineseAcademyofScience
2

n
17January2013
a
J

6
ABSTRACT
1
By combining the newly infrared photometric data from the All-Sky Data Release of the

] Wide-field Infrared Survey Explorer with the spectroscopicdata from the Seventh Data Re-
O leaseoftheSloanDigitalSkySurvey,westudythecoveringfactorofwarmdust(CFWD)fora
C largequasarsample,aswellastherelationsbetweenCFWDandotherphysicalparametersof
quasars.Wefindastrongcorrelationbetweenthefluxratioofmid-infraredtonear-ultraviolet
.
h and the slope of near-ultraviolet spectra, which is interpreted as the dust extinction effect.
p After correcting for the dust extinction utilizing the above correlation, we examine the re-
o- lationsbetweenCFWD andAGNproperties:bolometricluminosity(Lbol),blackholemass
r (MBH)andEddingtonratio(L/LEdd).We confirmtheanti-correlationbetween CFWD and
st Lbol.FurtherwefindthatCFWDisanti-correlatedwithMBH,butisindependentofL/LEdd.
a Radio-loudquasarsarefoundtofollowthesamecorrelationsasforradio-quietquasars.Monte
[ CarlosimulationsshowthattheanisotropyofUV-opticalcontinuumoftheaccretiondisccan

2 significantlyaffect,butislesslikelytodominatetheCFWD–Lbolcorrelation.
v
Keywords: catalogues–galaxies:active–quasars:general–infrared:galaxies
5
4
2
4
2. 1 INTRODUCTION scaleandthemoreextendednucleardisc(e.g.Krolik&Begelman
1 1986; Hopkinsetal. 2005; DiMatteoetal. 2005). It has been ar-
Theterminology ‘activegalacticnucleus’ (AGN)generally refers
2 gued that the torus is a smooth continuation of the BLR and the
toenergeticphenomenainthecentralregionsofgalaxiesthatcan
1 boundary between them is determined only by dust sublimation
beattributedtotheaccretionofgasontosupermassiveblackholes.
: (e.g.Elitzur2008).SothetorusmaydefinetheextensionofBLR
v Due to its angular momentum, the in-falling gas forms a disc
i (Netzer&Laor1993).Also,dustytorusmaybethesourceofout-
X aroundtheblackholeandslowlyspiralsinwardsasfrictiontorque flowsonthescalesofparsecs.Theanisotropicobscurationofion-
transportstheangularmomentumout.Duringthisprocess,gasin
ar thediscisheatedtoafew105 K andproduces strongUV toop- izing continuum causes an ionization cone structure in the nar-
rowlineregion,whichhasbeendetectedinmanyobscurednearby
ticalcontinuum. StrongUVradiationionizesgassurrounding the
Seyfertgalaxies.
blackhole,givingrisetoprominentbroademissionlineswithinone
parsecandnarrowemissionlinesfurtherout.Theseemissioncom- Due to its great importance, the geometry, column density
ponents are further modified by dust in a torus outside the broad distribution and the composition of dusty torus have been sub-
lineregion(BLR)andintheinterstellarmediumofgalaxies.Dust jectsof intensive study in thepast thirtyyears. The average cov-
absorbsandscattersUVandopticallightandre-emitsatinfrared ering fraction of torus could be constrained from the number ra-
(IR)bands, altering spectral energy distribution(SED)as wellas tios of obscured to unobscured AGNs in the local universe. For
causinganisotropicobscuration.Inthepastthirtyyears,ithasbeen nearby Seyfert galaxies and radio galaxies, Luetal. (2010) re-
establishedthatalargeportionofobserveddiversities,suchaspres- ported a Type 2 to Type 1 ratio around 2:1 to 3:1. This suggests
ence or absence of broad lines and prominent non-stellar contin- thatanaverageopeningangleofthedusttorusisabout45degree,
uum,canbeattributedtotheanisotropicobscuration ofthe dusty which is basically consistent with that derived from quasi-steller
torus(seeAntonucci1993forareview). radiosources(Barthel1989)anddirectimagingofionizingconein
The study of dusty torus is of great significance in our un- manynearbySeyfertgalaxies(e.g.Wilson&Ulvestad1983;Pogge
derstanding of physical processes of AGNs. The torus is a natu- 1988;Sakoetal.2000).Whileintheliterature,Lawrence&Elvis
ralreservoirofgassupplytotheaccretiondisc,andthusprovides (2010) suggested this ratio to be ∼1:1, and so did Reyesetal.
a possible connection between the accretion disc at sub-parsec (2008) by reporting approximately equal space densities of ob-
scured and unobscured quasars. Yet a consensus has still to be
reachedonwhetherand how theopening angledepends onother
⋆ [email protected] properties of AGNs. Lawrence (1991) suggested that the fraction
(cid:13)c 2013RAS
2 Ma &Wang
of type I AGNs increases with the increase of the nuclear lu- 2 THESAMPLEANDMEASUREMENTOFFLUX
minosity. Similar results were obtained by Simpson (2005) and
2.1 SampleDescription
Hao&Strauss (2004) for a large sample of AGNs derived from
Sloan Digital Sky Survey (SDSS), and by Hasinger (2008) from We construct our quasar sample by cross-correlating the SDSS
deepX-raysurveys.However,Luetal.(2010)didnotfindsucha DR7quasarcatalog(Schneideretal.2010)withtheWISEAll-Sky
correlationforradioloudAGNsbytakingintoaccountofvarious Data Release catalog. This leads to a sample of 101639 quasars
selection effects, and nor did Lawrence&Elvis (2010) for radio withreliableWISEdetectionsinatleastoneband(96%ofwhole
quietAGNs.Thisinconsistencyislargelyduetothecorrectionof SDSSDR7quasarcatalog).Togetamorereliableestimateofthe
complicatedselectioneffectsindealingwiththeAGNsineachlu- bolometricluminosityandmid-infraredluminosity,werequirethat
minositybin. the SDSS spectra cover the rest-frame wavelengths from 2000–
4000A˚A˚ andthattheWISEbandsaccesstoatleast10µminthe
Theinfraredemissionisapowerfulprobeofthedustytorus. quasarrest frame.Thisleadstoaredshift cut 0.76 6 z 6 1.17.
17639quasarsfallinthisredshiftrange.
Withamaximumtemperaturearound ∼ 2000K,theemissionof
Wefittherest-frameSDSSspectra,corrected fortheGalac-
dusty torus is mainly at IR bands. The total IR luminosity from
tic extinction using the dust map of Schlegeletal. (1998) and
the torus is a measurement of the amount of optical to UV light
the extinction curve of Fitzpatrick (1999), in three relative line-
absorbedbythetorus,whileindividualfeaturesareusedto probe
free windows 2150–2200, 3030–3100 & 4150–4250 A˚A˚ (see
thecompositionofgrainsandtheirdistribution.TheSpitzerSpace
VandenBerketal.2001)withapower-lawfunction
Telescope and more recent Herschel provide very rich data-sets,
which allow us to study different features and parameters of the Fλ =c(λ/3000)α, (1)
dustytorus.Meanwhile,largeunbiasedmid-infraredsurveysallow
tostudythestatisticalpropertiesofthedusttorus.Oneoftheprob- wherenormalizationfactorcandspectralslopeαaretwofreepa-
lems that we are primarily concerned is the dust covering factor rameterstobedeterminedbystandardχ2minimizationapproach1.
(CF)anditscorrelationswithAGNproperties,suchasbolometric Bad pixels are removed using the mask bits in the SDSS spec-
luminosity, black hole mass and accretion rates. In the literature, trum.Toachieve reliablefitting,wefurtherrequirethat thenum-
severalauthorshavesuggestedthattheCFdecreaseswithincreas- ber of good pixels must be greater than 50, and that the median
ing bolometric luminosity (Lbol) (see, e.g. Maiolinoetal. 2007; signal-to-noiseratio(S/N)shouldbegreaterthan3ineachwin-
Treisteretal.2008).However, thesestudies usedeitherarelative dow. 1220 sources (7%) fail to meet these criteria and are thus
small sample, oracombination of alow-redshift, low-luminosity dropped.Another71sourceswithbroadabsorptionlines(accord-
samplewithahigh-redshift, high-luminosity sample. Inthelatter ingtoShenetal.2011)werealsoexcluded.Furthermore,wedis-
caseevolutioneffectcannotbeexcluded. count another69sourceswithfittedspectral slope αgreaterthan
0becausetheircontinuaareseverelyreddenedandarelikelycon-
taminatedbystarlight.Bythisstage,16275sources(92%)areleft.
Recently, the Wide-field Infrared Survey Explorer (WISE;
According to Shenetal. (2011), 15279 of these sources lie
Wrightetal. 2010) provided a large amount of photometric data
in the footprint of the Faint Images of the Radio Sky at Twenty-
at near- and mid-infrared bands that can be used to study the
Centimeters(FIRST;Whiteetal.1997)survey.And1568ofthem
IR emission as well as dust CF of AGNs for a quite large sam-
are classified as ‘radio-loud quasars’. In the following analysis,
ple.Forexample,recentworksofMor&Trakhtenbrot(2011)and
wewillexaminethepotentialdifferencesbetweenradio-loudand
Calderoneetal.(2012)reportedthatCFanti-correlateswithLbol radio-quiet quasars on the properties we are discussing. Further-
bystudyinglargemagnitude-limitedsamples.Inthispaper,wewill
more, since our purpose is to study the mid-infrared emission of
utilizethemostrecentWISEAll-SkyDataRelease,combinedwith
warmdust,wewillfirstrestrictouranalysistotheprimarysample
thespectroscopicdatafromtheSeventhDataReleaseoftheSloan
of12483outof16275quasarsthathavereliabledetectionsinALL
Digital Sky Survey (SDSS/DR7; Abazajianetal. 2009), to study
fourWISEbands,andthenexaminethepropertiesoftherest3792
the warm dust emission of 16275 quasars in a redshift range of
quasars which only have upper limits of W3 or/and W4 magni-
0.76<z<1.17(including∼10%radioloudquasars).Thesam-
tudes.Allinformationfortheentiresamplerelevanttothispaperis
pleisdescribedin§2.1.WefittheSDSSspectrawithpower-law
availableonlineasthesupplementarymaterial(seeAppendixand
function toderivethefluxinthenear-ultraviolet(NUV) rangeof
Table1foradescription).
restframewavelengthfrom2000A˚ to4000A˚ (FNUV).ThisNUV
bandisclosetothepeakSEDofthebigbluebump(Zhengetal.
1997;Shangetal.2011).Wealsocalculatethefluxinnear-tomid- 2.2 Near-UVandMid-Infraredflux
infrared(MIR)rangeofrestframewavelengthfrom3µmto10µm
(FMIR,§2.2),whichisdominatedbywarm,andasmallportionof We calculate the integrated NUV continuum flux, FNUV, in the
rest-frame wavelength range of 2000–4000 A˚A˚ by simply inte-
hot, dust.Wefindastrongcorrelation between FMIR/FNUV and
gratingthebestfittedpower-lawmodel.Itexcludesthereprocessed
NUV spectral slope α, which can be best explained as dust ex-
componentssuchasBalmerandpseudoFeIIcontinua,andbroad
tinctionandreddeninginNUV(§3).Aftercorrectingforthedust
extinction, weestimate thecovering factorof warmdust CFWD, emission lines. The errors of FNUV come from two sources: the
andexamineitsrelationswithotherAGNproperties(§4).Inthe uncertaintiesoffittingparameters candα,andtheuncertaintyof
SDSSspectrophotometriccalibration.Usingerrorpropagation,we
end, we compare our resultswithprevious works and investigate
estimate that the former introduces only a small error, typically
how anisotropic continuum can affect the observed CFWD–Lbol
correlation(§5). 0.5%.Weexpectthelattertobethedominantsource.Toquantify
this,wenoticethatthedifferencebetweenspectrophotometricand
In this paper, we use a flat cosmology with H0 =
70kms−1Mpc−1,ΩM =0.3andΩΛ =0.7. 1 WeusetheMPFITpackageforallnonlinearfittinginthiswork.
(cid:13)c 2013RAS,MNRAS000,1–8
Covering Factorof WarmDustinQuasars 3
photometricmagnitudes hasa1σ scatterof 0.05magat r band2,
whichismostlyattributedtotheuncertaintyinspectroscopiccali-
bration.Thisindicatesthespectralfluxatrbandhasarelativeun-
certaintyof∼0.047.Wewillquote5%inFNUVasthecalibration
uncertaintyhereafter.
For mid-infrared (MIR) emission, we will focus on the in-
tegrated flux in the quasar’s rest-frame wavelength range of 3–
10µm.ThisregimeiscoveredbytheWISEW2,W3&W4bands
forour chosen redshift range. Furthermore, theinfrared emission
in this regime is primarily dominated by the warm and hot dust
heatedbyquasars.Finally,themeanquasarSEDinthiswavelength
rangeisrelativelysmoothaccordingtoRichardsetal.(2006)and
Shangetal.(2011).Therefore,itisrelativelystraightforwardtoob-
tain the integrated flux from the WISE photometric data without
invokingdetaileddustmodelling.
Inpractice,weapproximatetheMIRSEDasabrokenpower-
lawwithbrokenwavelengthattheeffectivewavelengthofW3band
Figure 1. Correlation between FMIR/FNUV and spectra slope α. The
attherestframeofthequasar.Thenweintegratethemodelfrom
blackdotsrepresentthe12483objectsinourprimarysampleandreddots
rest-frame3µmto10µm,toobtaintheintegratedMIRfluxFMIR. representthe3792objectswithonlyupperlimitsofW3or/andW4magni-
Toestimate theuncertainty of this measured MIR flux, weapply tudes.ThegreenlinedisplaysthetendencypredictedbySMC-likeextinc-
the same approach to every object in the sample of Shangetal. tion,onlyforthoseα>−1.7.Thegreendashlinedenotesthemeanvalue
(2011),whichhavetheSpitzer MIRspectra.Wefindthatourap- ofFMIR/FNUVforquasarswithα<−1.7.
proachgivesFMIR3%higheronaveragethanthedirectintegration
ofIRspectraoverthecorrespondentwavelengthrange,withascat-
terof8%.Hereafter,weadopt 3%astheglobaloffsetand8%as mostbluequasarsarelikelynotdustreddened,wecheckhowthe
theuncertaintyintroducedbyourmethod.Finally,wecombinethis parameterkchangeswithdifferentαranges.Forthe7700sources
uncertaintywithstatisticaluncertaintycomesfromtheuncertainty withα > −1.7,weobtaink1.7 = 0.29±0.02,andforthe4505
ofWISEmagnitudesasthefinaluncertaintyofFMIR.Thespectra sourceswithα>−1.5,theresultisk1.5 =0.33±0.02.
slopeα,NUVfluxFNUVandMIRfluxFMIRfortheentiresample By comparing the behaviours of radio-loud and radio-quiet
canbefoundintheonlinetable(seeTable1forareference). quasarsinoursample,wefindthatthisFMIR/FNUV–αrelationis
independentofradioactivities.Also,forthe3792sourcesthatare
removedfromourprimarysample,wecalculatetheir FMIR using
thesameapproachdescribedin§2.2withtheupperlimitsofW3
3 EXTINCTIONCORRECTION
&W4magnitudesprovidedintheWISEcatalog,andfindthatthey
3.1 CorrelationbetweenFMIR/FNUVandSpectralSlopeα sharethesamebehaviourasfortheprimarysample(thereddotsin
Fig.1).Therefore,wewillnotdistinguishthesedifferentcategories
The observed near-ultraviolet spectral slopes of quasars in our
ofquasarswhenanalyzingextinctioneffectbelow.
sample lie in a quite wide range from −2.9 for the bluest one
Previous studies suggested that dust extinction to quasars
to 0 for the reddest one, with a median value of −1.7. We plot
can be characterized by an SMC-like extinction curve (e.g.
FMIR/FNUVversasαinFig.1.Thereisafairlystrongcorrelation Richardsetal.2003;Hopkinsetal.2004;Gaskelletal.2004).To
betweenFMIR/FNUV andαwithaSpearmanrankingcorrelation illustratetheextinctioneffectonFMIR/FNUV–αrelationquantita-
coefficient Rs = 0.41, corresponding to a chance probability of tively,weapplySMC-likeextinction(Pei1992)ofdifferentvalues
Pr <10−6.Wefitthisrelationwithalinearfunction3 of E(B −V) to an intrinsic blue QSO continuum, which is de-
log(FMIR/FNUV)=k·α+b, (2) scribed by an intrinsic spectral slope β (Fλ ∝ λβ) in the NUV
range and a certain fraction of reprocessed infrared emission, to
wherekandbarefreeparameters.Forall12483quasarsincluding
getasetoffakedquasarcontinuua.WemeasuretheNUVspectral
in our primary sample, the best fit yields k = 0.24 ±0.02 and
slope(α) and FNUV foreach faked continuum inexact thesame
b=0.45±0.05.
wayasthatdescribedaboveforrealQSOs.Itturnsoutthatthere-
This correlation can be naturally interpreted as wavelength-
lationshipbetween αand E(B−V)can bewell described bya
dependent dust extinction. For example, Richardsetal. (2001)
linearfunction,
showed that SDSS colors of quasars can be well represented by
powerlawsof spectral indexes α = −1.5±0.65 witharedtail E(B−V)=c(α−β), (3)
possibly due to dust extinctions. Because extinction is larger at
for E(B − V) < 0.3. Particularly, for β = −2.0, we have
shorter wavelengths, it makes the observed optical-UV spectrum
c=0.127.ForsuchaE(B−V)range,thedustextinctionhaslittle
flatter(redder),andsimultaneouslyraisesobserved FMIR/FNUV.
The large intrinsic scatters of α and FMIR/FNUV dominate the effectontheFMIR,whichcanthusbeconsideredasaconstant.The
variations at small αand small FMIR/FNUV, thusmake the cor- relation between log(FMIR/FNUV) and α for the mock quasars
canbewelldescribedbyalinearfunctionwithaslopeof0.322,in-
relation weaker for blue sources as seen in Figure 1. Given that
dependentofthevalueofβforawiderangeof−2.2<β <−1.8.
Thisslope isalso veryclosetotheobserved one k1.7 = 0.29 or
2 seehttp://www.sdss.org/dr7/products/spectra/spectrophotometry.html k1.5 = 0.33. Therefore, our analysis supports that the observed
3 WeusetheIDLprocedure robust linefit.proforallthelinear fittingin FMIR/FNUV–αrelationisstatisticallyattributedtothedustextinc-
thiswork. tion.Andthescatteringofthiscorrelationisdominatedbyintrinsic
(cid:13)c 2013RAS,MNRAS000,1–8
4 Ma &Wang
dispersionsofthecontinuumslopeandFMIR/FNUV (greenlines denoting by FMIR, should beconsidered asthe MIR emissionof
inFig.1). thewarmdust.
Assuming that theNUV and MIR are isotropic, wecan cal-
culatetheNUVluminosityLNUVandMIRluminosityLMIRfrom
3.2 ExtinctionCorrectionforFNUV FNUV and FMIR, respectively. Next, we consider the bolometric
correction (BC) for the total luminosity from optical to X-ray.
In this subsection, we will correct FNUV for dust extinction in a
Sincewehavealreadycorrectedforextinctioneffect,wewilluse
statisticalwayusingtherelationderivedinthelastsection. First,
the mean SED of optically blue quasars in Richardsetal. (2006)
we estimate the intrinsic distribution of log(FMIR/FNUV) using
tocalculatethiscorrection.WecalculatetheLNUVusingthesame
bluequasarswithα< −1.7.Asmentionedabove,inthisregime,
extinctionissmall,andvariationsoflog(FMIR/FNUV)andαare 1meµtmhotdod1e0sckreibVedtoinob§t2ai.n2,tahnedtointatelgluramteinloosgi(tyνfinν)thoivserralnogge5ν.fTrohmis
dominatedbyintrinsicscatters,ratherthanreddeningeffect,albeit
yieldsBC =4.34.Thusbolometricluminositiescanbecalculated
the latter must be present. The distribution of log(FMIR/FNUV)
by Lbol = BC ×LNUV. Finally, we define the covering factor
forbluequasarscanbewelldescribedbyaGaussianfunctionwith
ofwarmdustasCFWD =LMIR/Lbol.Ourdefinitionofcovering
ameanvalueof0.010(FMIR/FNUV = 1.02),andadispersionof
factorissimilartothatofCalderoneetal.(2012),butdifferentfrom
σ=0.144.
theirsinthesensethatweconsidertheIRfluxinafixedMIRrange
Aswehaveshown inthelast subsection, thedependence of
dominatedbywarmdustratherthanthewholeIRbandscoveredby
FMIR/FNUVonobservedspectralslopeαcanbeexplainedbydust
WISE.Besides,wedonot takeintoaccount anisotropicemission
extinction.Therefore,itispossibletocorrectFNUVinastatistical
intentionallybythisstage,whilewewillexamineorientationeffect
wayfortheextinctionusingthederived FMIR/FNUV–αrelation,
inthelastsection.
withfittedspectralslopeαasanextinctionindicator.Assumingthe
meanFMIR/FNUVatdifferentαisthesame(1.02)asthatforblue
quasars,andfollowingtheFMIR/FNUV–αrelationderivedinthe
lastsubsection,wecalculatethecorrectionfactorforFNUV: 4.2 DependenceofCFWDonAGNProperties
3.5×100.322×α ifα>−1.7 Inthissubsection, we consider therelations between CFWD and
C =(cid:26) 1 ifα<−1.7. (4) AGN properties: bolometric luminosity Lbol, black hole mass
MBH,andEddingtonratioL/LEdd.Wepresenttheserelationsfor
Inthefollowinganalysis,westillusethenotationFNUVtodenote oursampleinFig.2.Weadoptthevirialblackholemassesinthe
the NUV flux, while it has already been corrected for extinction catalogofShenetal.(2011)withanadditional extinctioncorrec-
effect. Itshould be pointed out that thiscorrection isonly insta- tion. These massesare estimated using thewidth of MgII λ2798
tisticalsensefortheentiresampleratherthanforindividualobject andUVcontinuumluminosityat2800A˚ (Eqn.(2)inShenetal.
sincethe intrinsicUV continuum slope β and FMIR/FNUV have 2011).
fairly broad distributions. Nevertheless, by applying different cut
onαasthestandardforbluequasars,weestimatetheuncertainty log(MBH,vir) = a+b log( λLλ )
ofthiscorrectionforindividualobjectislessthan10%. M⊙ 1044ergs−1
FWHM
+2 log( ), (5)
kms−1
witha = 0.740andb = 0.62.Shenetal.(2011)didnotconsider
4 WARMDUSTCOVERINGFACTORANDITS
intrinsicextinctionontheUVluminosity.Inthefollowinganalysis,
RELATIONWITHAGNPROPERTIES
wewillapplyacorrectionbyadding
4.1 CoveringFactorofWarmDust
∆=1.588∗E(B−V) (6)
TheobservedMIRfluxFMIRcomesfromthreecomponents:emis-
tothevalueprovidedbyShenetal.(2011).Thiscorrectioniscalcu-
sion of the warm and hot dust heated by AGN, young-star emis-
latedaccordingtoSMCreddeningcurveat2800A˚.AndE(B−V)
sionatMIRband,andtheemissionoftheaccretiondiscextending
can be calculated from spectra slope (α) using Eqn. (3) in § 3.1.
toMIRbands.Star-formationgalaxiesarecharacterizedbystrong
Bolometricluminositiesandblackholemassesfortheentiresam-
PAHemissioninMIR.Previousinfraredspectroscopicstudiessug-
plearealsoprovidedintheonlinetable.
gestthatPAHfeaturesareveryweakinquasarspectra.Therefore,
First,CFWDisanti-correlatedwithLbol.TheSpearmanrank
thiscomponent isnot statisticallyimportant inourMIR range of
rWeset-efsratimmeat3e–t1h0eaµcmcr.eWtioenwdiilslcnceogmlepcotnietnitnbtyheexatnraaplyosliastihoenreoaffttehre. tchoerraenlattii-ocnorcreoleaftfiiocnienist(vRersy)osifgtnhiifisccaonrtre(lPatrio<nis1−0−06.3).6A,inldiniceaatrinfigt
yields
optical/UVpower-lawcorrectedforreddeningeffect.Thiscouldbe
consideredasanupperlimitconsideringspectralflatteninginthe logCFWD = (−0.23±0.02)logLbol/(erg·s−1)
near-infraredduetostarlightcontributionintheSDSSspectrum4.
+(9.79±0.04). (7)
Numerically, the disc contribution to FMIR is5.2% of FNUV for
β = −2.2,9.3%ofFNUV forβ = −2.0and16.6%ofFNUV for There is a significant anti-correlation between CFWD and
β=−1.8.SincewefocusontheMIRemissionofthedusttori,we blackholemassMBHwithaSpearmanrankcorrelationcoefficient
willsubtract0.093FNUVfromFMIRtoremovethecontributionof
theaccretiondiscandtheslightstarlight.Theremainedvalue,also
5 We discount the IR luminosity here since most mid- and far-infrared
emissionisthere-radiationoftheabsorbedcontinuum(Shangetal.2011).
4 Starlightcontributioninourcontinuumwindowsisgeneralsmallforlu- Butthis still includes asmall contribution fromemission lines, which is
minousquasarsinthispaper(e.g.Stern&Laor2012). doublycounted.
(cid:13)c 2013RAS,MNRAS000,1–8
Covering Factorof WarmDustinQuasars 5
(Rs =−0.27,Pr <10−6).Alinearfityields CFWD withincreasingLbol.Ourresultsareinqualitativeconsis-
tencywithpreviousworks.
logCFWD = (−0.13±0.02)log(MBH/M⊙) Maiolinoetal. (2007) estimated the dust covering factor for
+(0.50±0.02). (8) a few tens of QSOsusing monochromatic flux ratio of 6.7µm to
Finally,noapparentcorrelationisfoundbetween CFWD andEd- 5100A˚,whichissimilartoourmethodinthespirit.However,their
dingtonratio, samplewasconstructedbymergingtwogroupsofQSOsfromto-
tallyseparateredshiftranges.Moreover,theiranalogous CF–Lbol
L = Lbol (9) correlationisfarlesssignificantwhenonlyconsideringeitherone
LEdd 1.5×1038MBH groupofobjectswithcloseredshifts.Therefore,theirresultmight
(ρ=−0.008andPr =0.34). behamperedbypossibleevolutioneffect.Asimilartrendwasob-
Wecompareradio-quietandradio-loudquasarsonthesethree tainedbyTreisteretal.(2008),whomadeuseofnearlyonehun-
diagrams,andfindthattheyareindistinguishable.Particularly,we dredobjectsconstructedfromdifferentsurveys.Incomparisonwith
have fitted related parametres separately for the radio-loud sub- theseworks,oursampleismuchlarger,andisuniformlyselected
sample. First, the median value of CFWD is consistent with that inarelativelysmallredshiftrange.
of the radio-quiet subsample within 10%. Second, the slopes of More recently, Mor&Trakhtenbrot (2011) used the prelim-
CFWD–Lbol and CFWD–MBH relations are −0.21 ± 0.02 and inary data release of WISE to study the hot dust component for
−0.15±0.02,respectively.ThedistributionofCFWD,andthese a large and uniformly selected sample. Their definition of hot
fittingslopesareconsistentwiththeir1σuncertainties.Therefore, dustcoveringfactorisquitesimilartoours,andtheirresultsalso
weconcludethatnoneofthesethreerelationsareaffectedbyradio revealed a dependence of hot dust CF on bolometric luminos-
activities. ity. Their sample covers a very wide redshift range and their hot
Next,weconsiderthe3792sourcesthatonlyhaveupperlim- dust luminosities were estimated using a certain dust model. In-
itsofW3and/orW4magnitudes. Fromtheleftpanel of Fig2,it stead, wetake amodel-independent approach in our work. Simi-
isobviousthattheseobjectshavesystematicallylowerLbol,while larly,Calderoneetal.(2012)studiedthedustcoveringfactorforall
at the same time their CFWD (upper limits) are similar to those radio-quietAGNsconstructedfromWISEandSDSSwithinasmall
of quasars in our primary sample, so they shift to the left on the redshiftrange.TheseauthorsreportedasimilartrendofCF–Lbol
CFWD–Lbol diagram. In other words, they show systematically relationbydividingthewholesampleintothreebins.Comparing
lowerCFWD,comparingtothequasarsofsimilarluminositiesin with these studies, our work has taken the extinction effect into
theprimarysample.Becausethefractionofthesesourcesissmall, account.Also,weusedtheextinction-correctedbroadband NUV
weget almostanidentical slopeforCFWD–Lbol relationforthe luminosity,whichisabetterestimationofbolometricluminosity.
entire sample. From the middle and right panels of Fig. 2, these Furthermore,wefindthatCFissignificantlycorrelatedwithblack
quasarshavesimilardistributionofblackholemasses,butsystem- holemass,butisindependentofEddingtonratio.Thelatterresults
aticallylowerL/LEddthantheprimarysample.However,theyfol- areconsistentwiththosereachedbyCao(2005)forPGquasars.
lowthesameCFWD–MBH andCFWD–L/LEdd relationsasthe Intheliterature,manyauthorsusedthefractionoftype2ob-
primarysample. jectsasanindicatoroftotaldustcoveringfactorandreachedasim-
ilarconclusion. Forinstance, Simpson (2005) and Hao&Strauss
(2004) found a similar dependence of type 2 fraction on the
5 DISCUSSIONANDCONCLUSION [O III] luminosity using a magnitude-limited sample from the
SDSSspectroscopicsurvey.Similarresultswerereportedbyother
5.1 OnRadio-loudQuasars
authors using sample constructed from flux-limited X-ray sur-
Approximately10%objectsinoursampleareradio-loudquasars. vey (e.g. Hasinger 2008) or a combination of multi-band survey
As we have discussed earlier, they exhibit the same correlations (Hatziminaoglouetal. 2009). However, some other authors have
as radio-quiet quasars. Therefore, the majority of the radio-loud reportedthe opposite results.Lawrence&Elvis(2010) suggested
quasarshavetheverysimilarstructureofaccretiondiscanddusty thatthereisnocorrelationbetweentype2fractionand[OIII]lu-
torus.ThisisconsistentwithRichardsetal.(2006)andShangetal. minosityafterremovingLINERsfromthedefinitionoftype2ob-
(2011) that mean SEDs of radio-quiet and radio-loud quasars in jects,andsodidLuetal.(2010)bytakingintoaccountofvarious
NUVandMIRarequitesimilar.However,itisofnecessitytopoint selectioneffects. A caution should betaken when comparing our
outthatasmallfractionoftheradio-loudquasarswithinoursam- results withthose derived from the fraction of type 2 AGNs. We
ple are blazars, in which the relativistic jets are beamed toward only consider the covering factor of warm dust, which is merely
us. Inthiscase, therelativisticjetswould contributesignificantly aportionoftheobscuringmaterial.Furthermore,afractionofthe
or even dominate the observed flux at near-ultraviolet and mid- type2objectsareobscuredbydustintheirhostgalaxiesratherthan
infrared bands. Therefore, NUV and MIR emission in these ob- dusttorithemselves(Goulding&Alexander2009).
jectswillnolongerrepresenttheprimaryemissionoftheaccretion
discsandre-emissionofthedustytori.Thusourdefinitionofwarm
5.3 EffectsofAnisotropicContinuum
dustcoveringfactorisnolongappropriatefortheseblazars.Nev-
ertheless,thefractionofblazarsinourwholesampleisquitesmall Itshouldbeemphasizedthatuptonow,ourwholeanalysisisbased
(∼ 1% of type 1 quasars according to the argument of Padovani ontheassumptionthattheNUVandMIRemissionofquasarsare
2007),theywilldefinitelynotaffectourconclusion. isotropic. However, the NUV emission from a geometrically thin
butopticallythickaccretiondiscispredictedtobestrongeratpo-
lardirectionsthanatequatorialdirections(e.g.Shakura&Sunyaev
5.2 ComparisonwithPreviousStudies
1973; Laor&Netzer1989; Fukue&Akizuki 2006). If thisisthe
Inthiswork,weusethemid-infraredtonear-UVluminosityratio case,ourestimationofbolometricluminositywouldbebiasedde-
toestimatethecoveringfactorofwarmdust,andfindadecreaseof pending on the viewing angle (cf. Nemmen&Brotherton 2010;
(cid:13)c 2013RAS,MNRAS000,1–8
6 Ma &Wang
Figure2.RelationsbetweenwarmdustcoveringfactorCFWDandAGNproperties:bolometricluminosityLbol(leftpanel),blackholemassMBH(middle
panel),andaccretionrateLbol/LEdd(rightpanel).Themeaningsofblackandreddotsareexactlythesameasinfigure1.Thebluedotsrepresentradio-loud
quasarsintheprimarysample.Thegreendashlinesrepresentthelinearfitfortheserelations.
Runnoeetal. 2012) and our definition of covering factor would
certainly be inaccurate. For example, if an object is viewing rel-
atively edge-on, we will underestimate its bolometric luminosity
Lbol while overestimate its covering factor CFWD. In a statisti-
calview,thiscanresultinananti-correlationbetweenCFWD and
Lbol,thesametendencyaswehavediscoveredfromoursample.
To illustrate this more clearly, we construct a simple model
tosimulatetheeffect of different viewingangles. Thesimulation
involves the same number of faked quasars as for our sample.
We adopt three assumptions: (1) The intrinsic CFWD and Lbol
are independent, and obey log-normal distributions respectively.
(2) The inclinations are random in a range of 1/2 < µ < 1,
where µ = cosθ (the viewing angle). A lower limit on µ is set,
since we require the line-of-sight must lie in the open angle of
thetorus,otherwisetheNUVemissionwouldbetotallyabsorbed.
Thevalue1/2iscorresponding toatype2totype1ratioof1:16
(Lawrence&Elvis2010;Reyesetal.2008).(3)TheobservedLbol
andCFWDforeachobjectarecalculatedfromobservedNUVflux
andNIR/NUVfluxratioviewingfromacertaindirection.Thede-
pendenceofNUVfluxonviewingangleusedinourmodelis
2
f(µ)=f0×µ(µ+ ), (10)
3
following the results of Fukue&Akizuki (2006) who have taken
intoaccount limbdarkening effect.Moreover, werequirethatthe
observedLbolandCFWDhaveexactlythesamedistributionasfor
oursample.
WeplotoursimulatedCFWD–LbolrelationinFig.3,incom-
parison with the same relation of the sample. It turns out that
Figure3.Above:theCFWD–Lbolrelationfortheprimarysample.Bot-
our simulation obtains a similar but more compact relation. This
tom:thesamerelationforthesimulatedsample.
seemstoindicatethattheobserved CFWD–Lbol mayresultfrom
anisotropicNUVcontinuum.
However,westressthatoursimulationisinitialandneedsto
Inotherwords,thesampleisbiasedagainstleastluminousquasars
berefinedinseveralaspects.First,theassumptionthattheviewing
atlargeinclinations.Wenotethatthecontinuumfluxdecreasesby
angles are uniformly distributed is not satisfied by a flux-limited
a factor of 2.9 from µ = 1 to µ = 1/2, so this selection effect
sample,suchastheSDSSquasarsampleusedhere.Forexample,a
willsignificantlyaffecttheinclinationdistributionofquasarswith
quasarclosetothefluxlimitmaymoveoutofthislimitifitisob-
luminositiesofafactorof2.9abovetheminimumvalue.Thenetef-
servedatahigherinclination.Thusitwillbemissedinthesample.
fectwillweakentheCFWD–Lbolcorrelation.Inprincipal,wecan
incorporate this selection effect into the simulation by using the
6 Wesetthelowestµtothevaluefortheaveragetorusoppeningangle, quasar luminosity function. However, we should understand that
ratherthanthatgivingbythewarmdustcoveringfactorofeachobjectbe- dustextinctionisalsocoupledwiththeselectioneffectinthereal
causethecoveringfactorofthickcoldandhotdustisnotknown. case. Furthermore,dust extinctionmayormaynot correlate with
(cid:13)c 2013RAS,MNRAS000,1–8
Covering Factorof WarmDustinQuasars 7
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APPENDIX
2360
We present the primary data of all 16275 sources in our sample SimpsonC.,2005,MNRAS,360,565
with an ASCII table as the supplementary material of this paper. ShakuraN.I.,&SunyaevR.A.,1973,A&A,24,337
Theentiretableisavailableonline.Hereweofferasmallportion ShangZ.,BrothertonM.S.,WillsB.J.,etal.,2011,ApJS,196,2
ofthetableforaguidance(Table1). ShenY.,RichardsG.T.,StraussM.A.,etal.,2011,ApJS,194,45
(cid:13)c 2013RAS,MNRAS000,1–8
8 Ma &Wang
Table1.Primarydataofoursample.
Name Redshift Spectraslope NUVflux MIRflux CFWD Bolometricluminosity Blackholemass Flagb FIRST
(SDSSJ) (z) (−α) (FNUVa) (FMIRa) log(Lbol/(ergs−1)) log(MBH/M⊙) flagc
000013.14+141034.6 0.958 1.657 2.773e-13 2.617e-13 0.217 45.757 8.800 0 -1
000024.02+152005.4 0.989 1.744 2.820e-13 2.044e-13 0.167 45.798 9.181 1 -1
000025.21+291609.2 0.924 1.718 8.433e-14 9.096e-14 0.249 45.201 8.216 0 -1
000025.93+242417.5 1.156 1.296 1.487e-13 2.077e-13 0.322 45.688 9.310 1 -1
000026.29+134604.6 0.768 1.691 3.206e-13 1.291e-13 0.093 45.582 8.670 1 -1
000028.82-102755.7 1.152 1.277 4.372e-13 2.150e-13 0.113 46.152 9.449 0 1
000031.86+010305.2 1.093 1.086 2.274e-13 3.818e-13 0.387 45.812 8.552 0 0
000042.89+005539.5 0.951 1.805 9.408e-13 1.033e-12 0.253 46.279 8.844 0 0
000057.67-085617.0 1.095 1.460 8.727e-13 8.643e-13 0.228 46.397 8.778 0 0
000123.96-102458.1 1.058 1.616 6.734e-13 6.254e-13 0.214 46.248 9.338 0 0
000123.98+284249.4 0.936 0.269 2.419e-13 2.935e-13 0.280 45.672 9.255 0 -1
000140.70+260425.5 0.765 1.385 3.656e-13 3.700e-13 0.233 45.636 8.670 0 -1
Thefulltableincludingall16275sourcesisavailableonlineassupplementarymaterial.Aportionisshownhereforguidanceofitscontent.
aThefluxisinunitofergs−1cm−2A˚−1.
HereFNUVreferstothevalueafterextinctioncorrection(see§3)andFMIRreferstothevalueafterdiscountingthedisccontribution(see§4.1).
bFlag:0=12483sourceinourprimarysample;1=therest3792sourceswhichonlyhaveupperlimitsforW3orW4magnitudes.
cFirstflag:thesameascolumn15inthecatalogofShenetal.(2011).-1=notinFIRSTprint;0=FIRSTundetected;1=coredominant;2=lobedominant.
Stern,J.,&Laor,A.2012,MNRAS,423,600
TreisterE.,KrolikJ.H.,&DullemondC.,2008,ApJ,679,140
VandenBerkD.E.,RichardsG.T.,BauerA.,etal.,2001,AJ,122,
549
White,R.L.,Becker,R.H.,Helfand,D.J.,&Gregg,M.D.,1997,
ApJ,475,479
WilsonA.S.,&UlvestadJ.S.,1983,ApJ,275,8
WrightE.L.,EisenhardtP.R.M.,MainzerA.K.,etal.,2010,AJ,
140,1868
Zheng W., Kriss G. A., Telfer R. C., Grimes J. P., & Davidsen
A.F.,1997,ApJ,475,469
(cid:13)c 2013RAS,MNRAS000,1–8