The Fundamental Plane of the Broad-line Region in Active Galactic Nuclei

2.2 MB·

by  Pu Du

TOAPPEARINTheAstrophysicalJournalLetters.
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
THEFUNDAMENTALPLANEOFTHEBROAD-LINEREGIONINACTIVEGALACTICNUCLEI
PUDU1,JIAN-MINWANG1,2,*,CHENHU1,LUISC.HO3,4,YAN-RONGLI1 ANDJIN-MINGBAI5
Received2015November21;accepted2015December30
ABSTRACT
Broad emission lines in active galactic nuclei (AGNs) mainly arise from gas photoionized by continuum
radiation from an accretion disk around a central black hole. The shape of the broad-line profile, described
6
by D =FWHM/σ , the ratio of full width at half maximum to the dispersion of broad Hβ, reflects the
1 Hβ Hβ ˙
0 dynamicsofthebroad-lineregion(BLR)andcorrelateswiththedimensionlessaccretionrate(M)orEddington
˙
2 ratio (Lbol/LEdd). At the same time, M and Lbol/LEdd correlate with RFe, the ratio of optical Fe II to Hβ
n linefluxemission. AssemblingallAGNswithreverberationmappingmeasurementsofbroadHβ, bothfrom
a the literature and from new observations reported here, we find a strong bivariate correlation of the form
J log(M˙,L /L )=α+βD +γR ,whereα=(2.47,0.31),β=- (1.59,0.82)andγ=(1.34,0.80).Werefer
bol Edd Hβ Fe
8 tothisasthefundamentalplaneoftheBLR.Weapplytheplanetoasampleofz<0.8quasarstodemonstrate
theprevalenceofsuper-EddingtonaccretingAGNsarequitecommonatlowredshifts.

] Subjectheadings:blackholes:accretion–galaxies:active–galaxies:nuclei
A
G
. 1. INTRODUCTION plex (e.g., Baldwinetal. 2004). It may be influenced by
h different hydrogen density of BLR gas (Verneretal. 2004),
Broademissionlinesareahallmarkfeatureoftype1active
p or diverse contributionfrom microturbulence(Baldwinetal.
galactic nuclei (AGNs) and quasars (Osterbrock&Mathews
o- 1986). As pervasive as they are, many basic properties 2004). Inaddition,FeII lagsaregenerallylongerbyafactor
ofafewthanHβinbroad-lineSeyfert1galaxies(Barthetal.
r of the broad-line region (BLR), such as its basic geom-
t 2013; Cheloucheetal. 2014) and roughly equal to Hβ lags
s etry, dynamics, and physical connection to the accretion
a disk around the supermassive black hole (BH), remain ill- in narrow-line Seyfert 1s (Huetal. 2015), implying the po-
[ defined. AGN spectra exhibit both tremendous diversity as tentialconnectionofRFe withthedistributionorstructureof
well as discernable patterns of systematic regularity. Prin- line-emitting gas. The RFe- Lbol/LEdd correlation indicates
2
that Eddington ratios probably regulate all above mentioned
v cipalcomponentanalysishasisolatedseveraldominantrela-
properties of BLR. It should be noted that R also corre-
1 tionships among emission-line properties (Boroson&Green Fe
lates with some other properties like X-ray spectral slopes
9 1992;Sulenticetal. 2000). Themain varyingtrendof those
(e.g.,Wangetal.1996;Laoretal.1997;Sulenticetal.2000),
3 properties,whichisso-calledEigenvector1(EV1),hasbeen
but it likely originates from relation of those properties and
1 demonstrated to be driven by Eddington ratios, L /L ,
bol Edd Eddingtonratios (e.g., Wangetal. 2004; Risalitietal. 2009;
0 whereL isthebolometricluminosityandtheEddingtonlu-
bol Shemmeretal.2006;Brightmanetal.2013).
1. minosityLEdd=1.5×1038(M•/M⊙)(Boroson&Green1992; The overall breadth of the broad emission lines, notably
Sulenticetal. 2000; Shen&Ho 2014). As one of the most
0 Hβ, reflects both the virial velocity and inclination of the
6 prominentvariablesinEV1,therelativestrengthofbroadop- BLR (Kollatschny&Zetzl 2011; Shen&Ho 2014). The
1 ticalFeIIemission,expressedas
shape of the line profile may encode more information on
:
v F the detailed dynamics of the BLR (e.g., Collinetal. 2006;
i RFe= FeII, (1) Kollatschny&Zetzl2011), whichitself maydependonfun-
X FHβ damental properties such as the accretion or outflow rate.
r may correlate with L /L . Sources with high Edding- The broad Hβ lines of NLS1s tend to have more sharply
a bol Edd
tonratios(accretionrates),forinstanceso-callednarrow-line peaked (∼Lorentzian) profiles compared to type 1 AGNs
Seyfert 1 galaxies (Osterbrock&Pogge 1985), emit excep- withmorenormalEddingtonratios(Véron-Cettyetal.2001;
tionally strong Fe II lines compared with the normal ones Zamfiretal. 2010). As a non-parametric description of the
(Boroson&Green 1992; Huetal. 2008; Dongetal. 2011). lineprofile,onecandefine
However, the underlying physical mechanism that controls
RFe remains unclear, as the formation of Fe II is very com- D = FWHM, (2)
Hβ σ
1Key Laboratory for Particle Astrophysics, Institute of High Energy Hβ
Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing
where σ is the dispersion (second moment) of the Hβ
100049,China Hβ
2NationalAstronomicalObservatoriesofChina,ChineseAcademyof line. The value of D is 2.35, 3.46, 2.45, 2.83 and 0 for
Hβ
Sciences,20ADatunRoad,Beijing100020,China a Gaussian, a rectangular, a triangular, an edge-on rotating
3Kavli Institute for Astronomy and Astrophysics, Peking University, ring, anda Lorentzianprofiles(fora pureLorentzianprofile
Beijing100871,China σ →∞ and thus D =0), respectively (e.g., Collinetal.
4DepartmentofAstronomy,SchoolofPhysics,PekingUniversity,Bei- Hβ Hβ
2006). The quantity D correlates loosely with Edding-
jing100871,China Hβ
5Yunnan Observatories, Chinese Academy of Sciences, Kunming ton ratio (Collinetal. 2006) and, as the ratio of the rota-
650011,China tional and turbulent components of the line-emitting clouds
*Correspondingauthor,[email protected] (Kollatschny&Zetzl 2011), gives a simple, convenient pa-
2
rameterthatmayberelatedtothedynamicsoftheBLR. 1 galaxies (Czerny&Elvis 1987; Sun&Malkan 1989;
WhileR andD eachcorrelatesseparatelywithEdding- Laor&Netzer 1989; Collinetal. 2002; Brocksoppetal.
Fe Hβ
ton ratio, we demonstrate that both R and D combined 2006; Kishimotoetal. 2008; Davis&Laor 2011;
Fe Hβ
correlateevenmoretightlywithEddingtonratio(anddimen- Capellupoetal. 2015). The effective temperature dis-
sionlessaccretionrate).Thisbivariaterelation,whichwecall tribution is given by T = 6.2 × 104m˙1/4 m1/4R- 3/4K,
athbele“sf,upnldaaumsiebnlytarlepllaatnede”t7ootfhtehestBruLcRturlienkansdtwdoyndairmecictsobosfetrhve- where m˙•,0.1 = M˙•/0.1M⊙eyffr- 1, M˙• is mass•a,0c.1cre7tion14rates,
BLR, with the dimensionless accretion rate. Applying the m7 = M•/107M⊙, and R14 = R/1014cm (Franketal. 2002).
BLR fundamental plane to a large sample of Sloan Digital Here the effect of the inner boundary is neglected because
Sky Survey (SDSS) quasars, we find that a large fraction of theregionemittingopticalradiationisfarfromtheboundary.
quasarsatz<0.8havesuper-Eddingtonaccretionrates. Introducingx=hν/kTeff, we havethe spectralluminosityby
integratingovertheentiredisk,
2. MEASUREMENTS ∞ x5/3
2.1. TheReverberation-mappedAGNsample Lν=1.58×1028m˙2•/,03.1m27/3ν114/3cosiZ ex- 1dx ergs- 1Hz- 1,
WeselectallAGNswithreverberationmapping(RM)data xin (3)
(hereonlybroadHβ line), whichyieldrobustBH massesti- where i is the disk inclination relative to the observer and
mates needed for our analysis. All RM AGNs before 2013 ν =ν/1014Hz. Sincelong-wavelengthphotonsareradiated
14
are summarized by Bentzetal. (2013). We took all of 41 fromlargediskradii,theintegralterminEquation(3)canbe
AGNs from Bentzetal. (2013). Three additional sources well approximated by 1.93 for x =0 (Davis&Laor 2011).
in
(pMubrlkis1h5ed1.1,ONurGpCro5je2c7t3t,oKseAa1rc8h58f+or48su5p0e)rw-Eedrdeinsugbtosneqaucecnretlty- We thus have M˙• =0.53 ℓ44/cosi 3/2m-71 M⊙ yr- 1, and the
ing massive black holes (SEAMBHs) has monitored about dimensionlessaccretionr(cid:0)ate8 (cid:1)
A25GcNasndtoidadtaetsea(nDdusuetccael.ss2f0u1ll5y)manedasoutrheedrHfiβvelaogbsje(τcHtβs)minon1i4- M˙ =20.1 ℓ44 3/2m- 2, (4)
toredbetween2014-2015(tobe submitted). We measureFe (cid:18)cosi(cid:19) 7
(II20u1s5in).gFthoersraemveerbaeprpartiooanc-hmaaspHpeudeAtGalN. (s20w0i8th)oauntdpHubuliesthaeld. where ℓ44 is the 5100 Å luminosity in units of 1044ergs- 1.
Thisconvenientexpressioncaneasilyconvertluminosityand
measurements of Fe II and Hβ flux, we fit the mean spec-
BHmassintodimensionlessaccretionrates. Inthispaper,we
tra from the monitoringcampaigns, using the fitting scheme
describedin Huetal.(2015). Inshort, the spectrumisfitted take an average value of cosi=0.75, which corresponds to
theopeningangleofthedustytorus(e.g.,Davis&Laor2011;
withseveralcomponentssimultaneously:(1)apowerlawfor
continuum,(2)FeIItemplatefromBoroson&Green(1992), Duetal.2015). TheuncertaintiesofM˙ duetoi(∈[0,45◦])
(3)hostgalaxytemplateifnecessary,(4)broadHβ,(5)broad are∆logM˙=1.5∆logcosi.0.15fromEquation(4),where
HeIIλ4686emissionline,and(6)severalGaussiansfornar- we took ∆logcosi .0.1. This uncertainty is significantly
row lines such as [O III] λλ4959, 5007. The flux of broad smallerthantheaverageerrorbarsoflogM˙ (∼0.35),andis
opticalFeIIismeasuredbyintegrationfrom4434Åto4684 thusneglected.
Å.Table1liststhe63RMAGNsweconsider,alongwiththe The dimensionless accretion rate is related to the more
˙
BH mass, 5100 Å luminosity, dimensionless accretion rate, widelyusedEddingtonratioviaLbol/LEdd=ηM,whereη is
FWTHheMs,aσmHpβl,eRcFoevearnsdadawtaidseourarcnegse.of accretion rates, M˙ ≈ tThheeraudnicaetirvtaeineftifiecsieonfcEyd,danindgLtobonlr≈at1io0sLr5e1s00ul(tKfarospmiethtealf.a2c0t0th0a)t.
thebolometriccorrectiondependsonbothaccretionratesand
10- 3- 103, from the regime of a Shakura&Sunyaev (1973)
BH mass (Jinetal. 2012). In our following discussion, we
standard disk to a slim disk (Abramowiczetal. 1988). We ˙
takeR fromthepublishedliteratureifavailable;otherwise, willusebothM andLbol/LEdd.
Fe
we measureitfromtheaveragedspectrafollowingthespec-
3. FUNDAMENTALPLANEOFTHEBLR
tralfittingschemeofHuetal.(2008,2015). Asthevariabil-
ity of Hβ is unusuallymuchlargerthan thatof Fe II in sub- 3.1. Correlations
Eddington AGNs, the uncertainties of RFe are mainly gov- Figure1aand1c showthe R - (M˙,L /L ) plotsand
ernedbyHβ variability,whichonaverageis∼20%. yieldthefollowingcorrelations:Fe bol Edd
fBLWR eisesthtiemvaitreiathlefaBcHtomr,aVsFsWaHsMMi•s=HfβBLRFVWF2WHHMMc,τaHnβd/GG,wishethree (0.66±0.04)+(0.30±0.03)logM˙,
aggraavinitsattitohneaMlc•o-nsσtarnetl.aItniopnraocftiicnea,ctthiveefagcatloarxifeBsLR(Oisnckaelinbreattaeld. RFe= (1.20±0.07)+(0.55±0.06)log Lbol/LEdd . (5)
2004;Ho&Kim2014). Forconsistencywithourearlierse-
(cid:0) (cid:1)
riesofpapers,weadopt f =1. We define the scatter of a correlation as ∆X =
BLR
N (X- X)2/N, where N is the number of objects,
2.2. AccretionratesandEddingtonratios q i=1 i
P
We derived accretion rates from the disk model of 8 Theapplicability ofEq. (4)toSEAMBHscanbejustifiedbytheself-
Shakura&Sunyaev (1973), which has been exten- similarsolutionofslimdisks(Wangetal.1999;Wang&Zhou1999). The
sively applied to fit the spectra of quasars and Seyfert solutionshowsthatthe5100Å photonsareemittedfromR5100/RSch≈4.3×
103m-71/2,andthephotontrappingradiusRtrap/RSch≈144M˙100,whereRSch
7 Borrowing the terminology from galaxy formation (e.g., istheSchwartzschild radius. Eq. (4)holdsprovidedthatR5100&Rtrap,or
Djorgovski&Davis1987)andaccretingBHs(e.g.,Merlonietal.2003) M˙.3×103m- 1/2.NoSEAMBHsofarhasexceededthislimit.
7
3
TABLE1
THESAMPLEOFREVERBERATION-MAPPEDAGNS
Objects logL5100 log(cid:0)M•/M⊙(cid:1) logM˙ FWHM σline DHβ RFe Ref.
(ergs- 1) (kms- 1) (kms- 1)
Mrk335 4444433333.....7787666449±±±±±00000.....0000066667 67666.....9089832427++-+-+-+- 000000000.........111211111128514040 11111.....2232178957++-+-+-+- 000000000.........323232331090909108 12117076299746.29±±..±±21323760 11115433478720.01.±±.±±656860 11111.....2321470323±±±±±00000.....0011011635 00000.....7763677992 44441,,,,5572a,,,663aa,4
- 0.11 - 0.17
PPGG00002562++122591 4444..9871±±00..0023 88..1654+-+- 0000....01119314 -00..6559+-+-0000..22..328015 25504048±±5763 12713687±±13000 12..4361±±00..0095 00..3132 44,,55,,88aa
NOTE. —AllthevaluesoflogL5100,log(M•/M⊙)andlogM˙arecompiledfromDuetal. (2015). Valuesinboldfacearetheweightedaveragesofallthe
measurementsforthisobject.
Ref.:(1)Duetal.2014;(2)Wangetal.2014;(3)Huetal.2015;(4)Duetal.2015;(5)Collinetal.2006;(6)Petersonetal.1998;(7)Grieretal.2012;(8)
Kaspietal.2000.
ThesuperscriptaforreferencesindicatesthatRFeismeasuredinthispaper;bindicatesthatFWHMandσHβ aremeasuredfromSDSSspectra(theHβwidth
ofSEAMBHsissignificantlybroadenedbythe5′′longslitofourcampaign;seedetailsinRef. 4);cmeanstheMCMCBHmassisused(seeSection2.2);d
meansthatD istakenfromthelatestmeasurementsinKollatschny&Zetzl(2011).NGC5548markedwitheismeasuredfromitsmeanannualspectrainthe
Hβ
AGNwatchdatabase;theaveragevalueisprovidedhere.WefirstcalculateD foreachmeasurement,andthenaverage.Inthemaintext,weusetheseaveraged
Hβ
numbersfortheobjectswithmultipleRMmeasurements(treatedasonepointinallfigures). ForNGC7469,whichwasmappedtwiceCollieretal.(1998)
andPetersonetal.(2014),theHβlagsarenotverydifferentbuttheHβFWHMisverydifferent;takethevaluesofFWHMmeasuredbyKollatschny&Zetzl
(2011).NGC4051andPG1700+518haveverysmallvaluesofD inRef.5,butKollatschny&Zetzl(2011)providesnewmeasurements,whichareusedhere.
Hβ
Thistableisavailableinitsentiretyinamachine-readableformintheonlinejournal.Aportionisshownhereforguidanceregardingitsformandcontent.
andX representsR , D , M˙, orL /L . ThePearson’s and a standard R- L relation9. The RM AGNs overlap very
correlation coefficieFnet (rH)β, null-probabbolilityEdd(p), and scatters wellwiththeSDSSsample,onboththeR - (M˙,L /L )
(aare)iannddic(act)e,dwinetfihnedpltohtast.tBheycRomp- aMrin˙gc(orr,rpe,la∆tiRonFe)isinslpiganhetllys andthe DHβ- (M˙,Lbol/LEdd) plots. We noFete thatamboolngEtdhde
Fe mappedAGNsthereis asmallpopulation(.9%; Figure1a
stronger than that of RFe- Lbol/LEdd. In high-M˙ AGNs, andc) of AGNswith RFe >1.4 ofwhatappearto be super-
both Hβ and continuum variability are significantly smaller Eddingtonsources. Their values of M˙ are likely underesti-
thanthoseinsub-EddingtonAGNs. Ontheotherhand,Fe II matedbecausetheir blackholemasseswere estimatedusing
reverberatesinaverysimilarlyfashiontoHβ withrespectto thestandardR- Lrelation.
thecontinuum(Huetal.2015).Indeed,itcanbeseenthatthe
scatter of the correlation gets larger with decreasing M˙ or 3.2. FundamentalPlane
Lidbeoal/tLhEadtd.FTehIIeRstrFeen-g(tMhi˙s,Lnbootl/gLoEvdedr)nceodrrbeylamtioentasllsiucpitpyobrtusttbhye tioTnhsebe(RtwFeee,nDtHhβe)-B(LMR˙,sLtrbuocl/tuLrEedda)ndredlaytnioanmsicresflweictthcBoHnnaecc--
theionizingfluxandhydrogendensity(Verneretal.2004). cretion. Weinvestigatewhetherthesetwounivariatecorrela-
WeplottheD - (M˙,L /L )relationsinFigure1band tions can be unified into a single bivariate correlationof the
Hβ bol Edd
1dandfind form
log(M˙,L /L )=α +β D +γ R , (7)
bol Edd k k Hβ k Fe
(2.01±0.05)- (0.39±0.04)logM˙, where (α ,β ,γ ) are coefficients to be determined by data
k k k
D = (6) (k=1,2). Wedefine
Hβ (1.28±0.09)- (0.72±0.08)log L /L .
bol Edd
2
The above two correlations are similar, b(cid:0)ut the for(cid:1)mer is χ2k = N1 N (cid:16)logAσ2ik-+αβk-σ2βkD+Hiβγ- σγ2kRiFe(cid:17) , (8)
slightlystrongerthanthelatter. Collinetal.(2006)alsofound Xi=1 Ai k DHiβ k RiFe
lbdaiuukcteeotrtthoroeetlieharmterioeplasnhucabklstesiotzwfaerheteehignmahtDu-tcMhHhβe˙waDAneGdakNL-ebsr(oMlit/nhL˙at,EhnLdedoir(u/ssreLase.mtTph)leheiic.rsoWFirsriegemluwaratoeiionu6nll)yds, wbMahirnesrimoefiAzloikng=gAχ(,M2D,˙w,HLβeb,ooalb/ntLdaEindRd)F,eσoAfi,thσeDHiiβ- thanodbσjeRciFte, areresptehcetievrerloyr.
cannot be an artifact of the iHnβclusion ofboFlWEHddM in M˙. For α =2.47±0.k34; β =- 1.59±0.14; and γ =1.34±0.20,
1 1 1
a constant σ of RM AGNs, the accretion rates span over
about5dexwHβhereasluminositiesspanover4.5;however,the α2=0.31±0.30; β2=- 0.82±0.11; and γ2=0.80±0.20.
D - M˙ relation has a scatter of only ∆ =0.3- 0.4. The
Hβ D 9 This is an empirical relation between the BLR size and the con-
correlationsareintrinsic.
tinuum. From the recent work of Bentz et al. (2013), it has the form
Figure 1 also shows, as background,the SDSS DR5 sam- RBLR=33.65ℓ044.53ltd. However, Duetal.(2015)foundthatitonlyapplies
ple of Huetal. (2008). The sample comprises4037z.0.8 tosub-EddingtonAGNs;itdependsonM˙ forsuper-EddingtonAGNs. We
quasarswithcriteriaofS/N≥10andEW(Fe II)≥25Å (this donotconsider thedependence ofthe R- L relation onM˙ forthe SDSS
excludes Fe II-weak quasars). BH masses assume fBLR =1 sampleinthispaper.
4
y 0.4
t
i
l
i
b 0.2
a
b
o 0.0
r
P
2.0 (a) (c)
β
H 1.5
F
/
I
I
Fe 1.0
F
=
Fe 0.5
R
r=0.65 r=0.60
0.0 p=7.3×10−9 p=2.2×10−7
∆RFe=0.35 ∆RFe=0.38
3.5 r=−0.79 r=−0.74
(b) p=1.1×10−14 (d) p=6.6×10−12
∆DHβ=0.36 ∆DHβ=0.41
β 3.0
H
σ
/
M
2.5
H
W
F 2.0
=
β
H 1.5
D
SDSS SDSS
1.0
RM−AGN RM−AGN
−4 −3 −2 −1 0 1 2 3 −3 −2 −1 0 1
10 10 10 10 10 10 10 10 10 10 10 10 10 0.00.20.4
Accretion rate (M˙) Eddington ratio (LBol/LEdd) Probability
FIG.1.—Correlationsbetween(a)RFe- M˙and(b)DHβ- M˙.ThePearson’scoefficient,null-probability,andscatteroftheX- M˙correlationaregivenby
(r,p,∆X). Inpanel(a),theSDSSquasarsoverlapwiththeRMAGNsquitewell,exceptforAGNswithRFe&1.4. Thiscouldbebecausetheseobjectsare
super-Eddingtonaccretors,inwhichthenormalR- Lrelation(Bentzetal.2013)overestimatesR aswellasBHmass(Duetal.2015),andhenceM˙isgreatly
Hβ
underestimated(seedetailsinthetext).Inpanel(b),theSDSSsamplealsooverlapswellwiththeRMAGNs,butthelow- M˙AGNsliebeyondthelocusofthe
SDSSsample.TherearesomeSDSSquasarswithextremelyhighaccretionrates,M˙&102,suggestingthatweshouldmonitortheminthefutureofSEAMBH
project. ThehistogramsindicatethedistributionsofRFe,DHβ andM˙onanormalizedscale. WenotethatthereisnosignificantcorrelationbetweenRFeand
DHβ,eitherintheRMAGNorSDSSsample,indicatingthatDHβ andRFeareindependentfromeachother,althoughbothcorrelatewithM˙.Panels(c)and(d)
arethesameas(a)and(b),butforEddingtonratios.
Theerrorbarsof(α ,β ,γ )arederivedfrombootstrapsim- We apply the M˙- plane (Equation 7) to a sample of 4037
k k k
ulations. The bivariate correlations, plotted in Figure 2, are objectsHuetal.(2008),whichwereselectedfromtheSDSS
muchstrongerthanindividualcorrectionsofFigure1(seethe DR5 sample composed of N ≈ 15,000 quasars with z .
tot
correlation coefficients and null-probability). We call these 0.8. We calculate fractions of quasars with M˙ ≥M˙, δ =
c
ntweTwohcseiomrirmpellpealtiimcoanetasiosaunsrsethmoefefnuEtnsqduoaafmtiaeonnstian(lg7pl)lea-anerepeoocfehxthcseiptiBencLgtr.Ru.mForofma NcrMit˙icc/aNltaoct,cwrehtieornerNaMte˙cinisqtuheestniuomn.bFeorroofbqjuecatssawrsiathndMM˙≥˙c 3is,twhee
quasar—strength of Fe II and shape of broad Hβ—we can findδ3=N3/Ntot≈0.18. Similarly,wehaveδ10=N10/Ntot≈
deducethestatusofitsaccretionflow. Thiscanbeveryuse- 0.12 and δ100 =N100/Ntot ≈0.02. These numbersshow that
fulwhenappliedtolargesamplesofquasarstoinvestigatethe super-Eddington accreting AGNs are quite common in the
cosmologicalgrowthofBHs. Ourmethodcanbeusefullyap- Universeat z<0.8. We shouldnote that these fractionsare
plied to quasars with suitable spectroscopyin the rest-frame lower limits, as a result of the selection criteria imposed by
Hβregion,forwhichthestrengthofFeIIcanbemeasuredor Huetal. Detailedresultsoftheapplicationofourtechnique
constrained. tothelatestsampleofSDSSquasarswillbecarriedoutina
separatepaper.
3.3. ApplicationtoSDSSsample
5
1
3
2
0
)
1 d
d
E
˙M L
/ −1
g 0 Bol
o L
l
(
g
−1 lo
−2
−2 r=0.87 r=0.80
p=2.7×10−20 p=2.5×10−15
−3 ∆M˙ =0.70 −3 ∆LBol/LEdd =0.48
−3 −2 −1 0 1 2 3 −3 −2 −1 0 1
2.47−1.59DHβ +1.34RFe 0.31−0.82DHβ +0.80RFe
FIG.2.—ThefundamentalplaneofAGNBLRs,showingaphysicalconnectionbetweenaccretiondisksandBLRs. Thedependentvariableis(left)M˙and
(right)Eddingtonratio.ThetwoobservablesofRFeandDHβ canbereadilymeasuredfromsingle-epochspectra,allowingustoconstraintheaccretionstatusof
thecentralengine.
4. CONCLUSIONS plication of the BLR fundamental plane shows that super-
EddingtonaccretingAGNsarequitecommoninamonglow-
Thispaperstudiescorrelationsamongthreedimensionless
redshiftquasars.
AGN parameters: accretion rate (or Eddington ratio), shape
ofthebroadHβ line,andfluxratioofopticalFeII toHβ. A
strongcorrelationamongthemisfound,whichwedenoteas This research is supported by the Strategic Priority
thefundamentalplaneofAGNBLRs(Equation7). TheBLR Research Program - The Emergence of Cosmological
fundamentalplaneenablesustoconvenientlyexploretheac- Structures of the Chinese Academy of Sciences, Grant
cretion status of the AGN central engine using single-epoch No. XDB09000000, by NSFC grants NSFC-11173023, -
spectra, opening up many interesting avenues for exploring 11133006, -11373024, -11233003 and -11473002, and a
AGNs,includingtheircosmologicalevolution. Asimpleap- NSFC-CASjointkeygrantofU1431228.
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