Locating positions of γ-ray--emitting regions in blazars

1.4 MB·English

by  H. T. Liu

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed17January2011 (MNLATEXstylefilev2.2)
Locating positions of γ-ray–emitting regions in blazars
H. T. Liu1,2⋆, J. M. Bai1,2⋆ and J. M. Wang3,4⋆
1 1National Astronomical Observatories/Yunnan Astronomical Observatory, Chinese Academy of Sciences,
1 Kunming, Yunnan 650011, China
0 2Key Laboratory for the Structure and Evolution of CelestialObjects, Chinese Academy of Sciences,
2 Kunming, Yunnan 650011, China
3Key Laboratory for Particle Astrophysics, Institute of HighEnergy Physics, Chinese Academy of Sciences,
n
19B Yuquan Road, Beijing 100049, China
a
J 4Theoretical Physics Centerfor Science Facilities, Chinese Academy of Sciences, Beijing 100049, China

4
1
Accepted .Received

]
O
C ABSTRACT
Weproposeanewmethodtolocatetheγ-ray–emittingpositionsR fromthemeasured
. γ
h time lags τob of γ-ray emission relative to broad emission lines. The method is also
p applicabletolowerfrequencies.Rγ dependsonparametersτob,RBLR,vd andθ,where
-
o RBLR is the size of broad-line region, vd is the travelling speed of disturbances down
r the jet and θ is the viewing angle of the jet axis to the line of sight. As τob = 0,
st τob < 0 or τob > 0, the broad lines zero-lag, lag or lead the γ-rays, respectively. It
a is applied to 3C 273, in which the lines and the radio emission have enough data,
[ but the γ-rays have not. We find τob < 0 and τob > 0 for the 5, 8, 15, 22 and 37
GHz emission relative to the broad lines Hα, Hβ and Hγ. The lag may be positive or
1
v negative, however current data do not allow to discriminate between the two cases.
4 The measured lags are on the order of years. For a given line, τob generally decreases
2 as radio frequency increases. This trend most likely results from the radiative cooling
8 ofrelativisticelectrons.Thenegativelagshaveanaverageofτob =−2.86yearsforthe
2 37 GHz emission, which represents that the lines lag the radio emission. The positive
1. lags have τob = 3.20 years, which represents that the lines lead the radio emission.
0 We obtainthe radio emitting positions Rradio =0.40–2.62pc and Rradio =9.43–62.31
1 pc forthe negative andpositive lags,respectively.Fromthe constraintofRγ .Rradio
1 (e.g. Dermer & Schlickeiser 1994; Jorstad et al. 2001), we have R . 0.40–2.62 pc
γ
: for the negative lags. For the positive lags, 4.67–30.81 < R . 9.43–62.31 pc. These
v γ
estimatedR are consistentwith those of otherresearches.These agreementsconfirm
i γ
X the reliability of the method andassumptions. The method may be also applicable to
r BL Lacertae objects, in which broad lines were detected.
a
Key words: γ-rays:theory–galaxies:active–galaxies:jets–quasars:emissionlines
– quasars: individual: 3C 273.
1 INTRODUCTION The first component is from the synchrotron process, and
the second one, generally peaking at the γ-ray regime, is
Theγ-raysofblazarsaregenerally believedtobegenerated
generated by the IC emission of the same electron pop-
byinverseCompton(IC)emissionfromarelativisticjetori-
ulation responsible for the synchrotron emission (see e.g.
entedatasmallangletothelineofsight(Blandford & Rees
Ghisellini et al. 1998; B¨ottcher 1999). However, the posi-
1978). Two of the most accepted scenarios for broad-band
tionsofγ-ray–emittingregionsarestillanopenandcontro-
emission from radio to γ-rays are the synchrotron self-
versial issue in the researches on blazars. It was suggested
Compton (SSC) and external Compton (EC) models (see
that γ-rays are produced within broad-line region (BLR)
e.g. Ghisellini et al. 1998). The broad-band spectral en-
andthattheγ-ray–emittingpositionsR rangeroughlybe-
ergy distributions (SEDs) of blazars consist of two broad γ
tween 0.03 and 0.3 parsec (pc) (Ghisellini & Madau 1996).
bumps (see e.g. Fossati et al. 1998; Ghisellini et al. 1998).
Blandford & Levinson(1995)alsosuggestedasub-pcγ-ray–
emitting region. It was argued that the radiative plasma
in relativistic jets of powerful blazars are inside the BLR
⋆ E-mail: [email protected]; [email protected]; (Georganopoulos, Kirk & Mastichiadis 2001). On the con-
[email protected]
2 H. T. Liu, J. M. Bai and J. M. Wang
trary, it was also argued that the γ-ray–emitting regions jets of AGNs and microquasars (e.g. Marscher et al. 2002;
are outside the BLR (Lindfors, Valtaoja & Tu¨rler 2005; Chaterjee et al. 2009; Arshakian et al. 2010). The events
Sokolov & Marscher2005).Internalabsorptionfor10GeV– in the central engine, where the X-rays are produced, will
1 TeV γ-rays were used to constrain R (Liu & Bai 2006; have a direct effect on the events in the radio jets (e.g.
γ
Liu, Bai & Ma2008;Bai, Liu & Ma2009).Variabilityofthe Marscher et al. 2002; Chaterjee et al. 2009). The disc-jet
highenergyfluxindicatesthattheγ-ray–emittingpositions connectionwassuggestedbycorrelationsofemissionlinelu-
cannot be too distant from the central supermassive black minosityandradiopowerofjetsforvarioussamplesofAGNs
hole (Ghisellini & Madau 1996; Ghisellini & Tavecchio (Rawlings & Saunders 1991; Falcke, Malkan & Biermann
2009),whilethephoton-photonabsorption implies that the 1995; Celotti, Padovani & Ghisellini 1997; Serjeant et al.
emittingpositionscannotbetooclosetotheblackholeand 1998; Cao & Jiang 1999, 2001; Wang & Ho 2003;
its accretion disc (Ghisellini & Madau 1996; Wang 2000; Gu, Cao & Jiang 2009). The relativistic jets can be
Liu & Bai 2006; Liu, Bai & Ma 2008; Sitarek & Bednarek ejected from inner accretion disc in the vicinity of the cen-
2008; Bai, Liu & Ma 2009; Ghisellini & Tavecchio 2009; tral black hole (see e.g. Penrose 1969; Blandford & Znajek
Tavecchio & Mazin 2009). Bracketed by thetwolimits, one 1977; Blandford & Payne 1982; Meier, Koide & Uchida
obtains a few hundreds of Schwarzschild radii as the pre- 2001). The close connection between accretion disc and
ferred jet location where most of the dissipation occurs jets indicates that the central disturbances are likely trans-
(Ghisellini & Tavecchio 2009). Jorstad et al. (2001) estab- porteddownthejets.Forexample,thecentraldisturbances
lished a connection between ejections of superluminal ra- that drive variations of the central ionizing continuum
dio knots and γ-ray outbursts observed by EGRET. They may be transported with the outward Alfv´en waves (see
concluded that the radio and γ-ray events are originating e.g. Meier, Koide & Uchida 2001; Koide et al. 2002). By
from the same region of a relativistic jet. Wagner (2008) magnetohydrodynamic mechanisms (Kudoh & Shibata
found that the blazar γ-ray emission might depend on the 1999), the transported disturbances may be converted into
mass of the central black hole and that very high energy thelocal energies of plasma far from thecentralblack hole.
(VHE) γ-ray–emitting active galactic nuclei (AGNs) have Thusthedisturbancesinthecentralenginewould influence
the black hole masses larger than 108 solar masses. Bloom the γ-rays emitted by the relativistic jet aligned with the
(2008)confirmedtheradioandγ-raycorrelationofEGRET line of sight. At the same time, these disturbances can lead
blazars.Thompson(2008)reportedthatacentralfeatureof to the variations of the central ionizing continuum that
the EGRET results is the high degree of variability seen in drives broad emission lines from BLR. Hence, the broad
many γ-ray sources, indicative of the powerful central en- lines from the BLR and the γ-rays from the relativistic jet
gines at work in objects visible to γ-ray telescopes. may be both coupled to the disturbances in the central
The operation of Fermi Gamma Ray Space Telescope engine.
(Fermi)–Large Area Telescope (LAT) (see e.g. Abdoet al. Based on the photoionization assumption and the
2009,2010a)presentsanexceptionalopportunityforunder- time lags between broad lines and continuum, rever-
standingthecentralenginesoperating inblazars. TheFirst beration mapping observations are able to determine
LAT AGN Catalog includes 709 AGNs, comprising 300 BL the sizes of the BLRs for type 1 AGNs (see e.g.
Lacertaeobjects(BLLacs),296flatspectrumradioquasars Kaspi & Netzer 1999; Wandel, Peterson & Malkan 1999;
(FSRQs),41AGNsofothertypesand72AGNsofunknown Kaspi et al. 2000, 2005, 2007; Peterson et al. 2000, 2004,
types (Abdoet al. 2010a). The distribution of γ-ray pho- 2005; Vestergaard & Peterson 2006). According to the re-
tonspectralindexisfoundtocorrelatestronglywithblazar verberationmappingmodel(e.g.Blandford & McKee1982),
subclass (Abdoet al. 2010a,c). Abdoet al. (2010b) found the variations of broad lines can reflect the disturbances in
for Fermi blazars that variation amplitudes are larger for thecentralenginesofblazars,eventhoughthebeamedemis-
FSRQsandlow/intermediatesynchrotronfrequencypeaked sionfromtherelativisticjetstronglyaffectstherealionizing
BLLacs.Ghisellini, Tavecchio & Ghirlanda(2009)obtained continuum from accretion disc so that no appropriate con-
a few hundreds of Schwarzschild radii as the preferred jet tinuum could be used as the reference to estimate the time
dissipation region. Ghisellini et al. (2010) found for bright lags relative to the broad lines. If the broad lines from the
Fermi blazars that the jet dissipation region is within the BLRandtheγ-raysfromtherelativisticjetarebothcoupled
BLRforFSRQs.Kovalev et al.(2009)identifiedthepc-scale to the disturbances in the central engine, the disturbances
radio core as a likely location for both the γ-ray and radio should similarly influenceboth variations of the γ-rays and
flares. Sikora et al. (2009) suggested that the blazar emis- thebroad lines. Thusthereshould becorrelations and time
sion zone is located at pc-scale distances from the nucleus, lags between the broad lines and the γ-rays. The time lags
andtheyalsoproposedthatthepc-scaleblazaractivitycan shouldberelated toRγ.Inthepaper,weattempttolocate
be occasionally accompanied by dissipative events taking Rγ from thetimelagsbetweenbothvariationsofthebroad
place at sub-pcdistances. Ghisellini, Maraschi & Tavecchio lines from theBLR and theγ-raysfrom therelativistic jet.
(2009) argued that the bulk of the most luminous blazars
already detectedbyFermi shouldbecharacterized bylarge
black hole masses, around 109 solar masses. Kovalev et al.
2 METHOD
(2009) found for Fermi blazars that the γ-ray photon flux
correlates with the compact radio density flux. The broad lines from the BLR and the γ-rays from the
Disturbances in the central engine are likely trans- relativistic jet may be both coupled to the disturbances
ported down the relativistic jets. This was supported by in the central engine. Thus the disturbances could sim-
observations that dips in the X-ray emission are followed ilarly influence both variations of the broad lines and
by ejections of bright superluminal knots in the radio the γ-rays emitted by the jet aligned with the line of
Locating positions of γ-ray–emitting regions 3
sight. The outbursts seen in light curves are physically thetimelagofthelinesrelativetotheγ-rays(seeFig.1a).In
linked to the ejections of superluminal radio knots (e.g. thiscase(hereafterCaseB),wehaveR +R R c/v =
γ BLR γ d
−
Tu¨rler, Courvoisier & Paltani 2000).Theeventsin thecen- cτ /(1+z),and then
ob
tral engine will have a direct effect on the events in the
R cτob
radio jets (e.g. Marscher et al. 2002; Chaterjee et al. 2009). R = BLR− 1+z , (2)
Thus it is likely that the γ-ray outbursts are caused by the γ c 1
vd −
disturbances from the central engine, but not the local dis-
where z is the redshift of source, τ > 0 and τ is the
turbancesproduced in thejets. Hence,there should becor- ob ob
observed time lag of the broad lines relative to theγ-rays.
relations between the γ-ray outbursts and the variations of
Outside segment AG, the γ-rays will lag the lines. As
broadlines.Itispossiblethattherearetimelagsinthecor-
the disturbances reach point H, where the γ-rays are pro-
relations and the time lags are related to the positions R .
γ duced, i.e. R = AH, the line photons reach point L. The
ThusR couldbelocatedbythetimelagsbetweentheγ-ray γ
γ lighttravellingtimeeffectsfortheγ-rayphotonsfrompoint
outburstsandthevariationsofbroadlines.Inthefuture,the
J toL,i.e.from pointH toM,resultinthetimelagofthe
quasi-simultaneous observations of γ-rays with Fermi/LAT
γ-rays relative to the lines (see Fig. 1a). In this case (here-
andbroadlineswithopticaltelescopesontheorderofyears
afterCaseC),wehaveR c/v =R +R +cτ /(1+z),
may be employed to test this expectation. The method of γ d γ BLR ob
and then
locating R is also applicable to infrared, optical and radio
γ
emission. R = RBLR+ c1τ+ozb, (3)
First,itisassumedthatthedisturbancesinthecentral γ c 1
vd −
engine are transported outward by some process, and the
disturbancescouldsimilarlyinfluencebothvariationsofthe whereτob >0andτob istheobservedtimelagoftheγ-rays
broadlinesfrom theBLRandtheγ-raysfromtherelativis- relative to the broad lines. Equations (1), (2) and (3) can
tic jet aligned with the line of sight. Second, we assume a beunified into
simplegeometry(seeFig.1a)thatissimilartotheschemes R + cτob
in the classical reverberation mapping of the broad lines Rγ = BLcR 11+z , (4)
(see e.g. Kaspi & Netzer 1999; Wandel,Peterson & Malkan vd −
1999; Kaspi et al. 2000, 2005, 2007; Peterson et al. 2000, whereτ is theobserved timelags of theγ-raysrelative to
ob
2004, 2005; Vestergaard & Peterson 2006). The differences the broad lines and is zero, negative or positive. As τ =
ob
between this method and the classical mapping are as fol- 0 (Case A), equation (4) becomes equation (1). As τ <
ob
lows.Intheclassical mapping,apartofionizingcontinuum 0 (Case B), equation (4) becomes equation (2). As τ >
ob
drives the broad lines from the BLR, and another directly 0 (Case C), equation (4) becomes equation (3). Once τ ,
ob
reaches observers. Thus the broad lines lag the continuum R andv areknown,R canbeobtainedfromequations
BLR d γ
due to light travelling time effects, and the time lag corre- (1)–(4).
spondstothesizeoftheBLR.Inthemethodproposedhere, Thecalculationsaboveareundertheconditionofθ=0,
the ionizing photon signals directly detected by telescopes whereθistheanglebetweenthejetaxisandthelineofsight.
in the classical mapping are replaced with the transporting In fact, the approaching relativistic jets of blazars are ori-
disturbancesfrom thecentralenginedown thejet and then entedatasmallangletothelineofsight(Blandford & Rees
withthejetemissionsignalsatRγ.Thusthemethodwould 1978).Thusθ=0.Consideringtheactualinclinationofthe
be valid even if the BLR has a complex configuration, such jetaxiswithre6specttothelineofsight(seeFig. 1b),were-
as a spherical shell. For simplicity for graphic illustration, deducetheexpression ofCase C. Asthedisturbancesreach
we choose the BLR to be a ring (see Fig. 1a). The trans- point H, where the γ-rays are produced, the line photons
porting speed of disturbances down the jet cannot exceed reachpointL.Thelighttravellingtimeeffectsfortheγ-ray
thespeed of light. photonsfrompointO toL,i.e.frompointH toS,resultin
Because Rγ is unknown, the γ-rays may lag, lead or thetimelagoftheγ-raysrelativetothelines(seeFig.1b).In
zero-lag the broad lines. First, we try to find the position thiscase,wehaveR c/v =R +R cosθ+cτ /(1+z),
γ d BLR γ ob
wheretheγ-raysareproducedandzero-lagthebroadlines. and then
As the disturbances reach point G (see Fig. 1a), where the
R + cτob
γph-roatyosnasrterapvreoldfruocmedp,oi.ien.tRAγt=oBAGan,dththeeiolinniezipnhgoctoonntsitnruauvmel Rγ = BcLR cos1+θz . (5)
vd −
frompointBtoI intimeintervalR /v .Inthecaseofzero-
γ d
Itisobviousthatequation(5)containsCasesA,BandC.As
lag (hereafter Case A), we have (R +R )/c = R /v ,
BLR γ γ d
θ=0,equation(5)becomesequation(4).Theobservedline
and then
photonsarefromtheBLRofring,andthentheobservedlag
R =R vd , (1) isan ensembleaverage overall pointsof thering.Forpoint
γ BLRc−vd T,wehaveRγc/vd =RBLR+TW+Rγcosθ+cτob/(1+z)
and TW =R sinαsinθ (see Fig. 1b), and then
wherev isthetravellingspeedofdisturbancesdownthejet BLR
d
and c is the speed of light. For Case A,Rγ >RBLR. R = RBLR(1+sinαsinθ)+ c1τ+ozb, (6)
WithinsegmentAG,thelineswilllagtheγ-rays.Asthe γ c cosθ
disturbancesreach pointF,wheretheγ-raysare produced, vd −
i.e. R = AF, the ionizing continuum photons reach point where α is the angle between AB and AT and varies from
γ
E. The light travelling time effects for theionizing photons 0 to 2π. For a given source, i.e. given R , R , v , θ and
γ BLR d
frompointEtoBandthelinephotonsfromBtoKresultin z,τ varieswith α,i.e. τ =τ (α).Calculating ensemble
ob ob ob
4 H. T. Liu, J. M. Bai and J. M. Wang
(cid:1)(cid:2)(cid:3) (cid:2) (cid:5) (cid:12) (cid:9) (cid:7) (cid:3) The blue-bump of 3C 273 is thermal continuum emission
fromtheinneraccretiondisc(Shields1978).FeKαlinesob-
(cid:11) served in 3C 273 were shown to be from an accretion disc
around a supermassive black hole (Yaqoob & Serlemitsos
(cid:4) 2000; Torres et al. 2003). If the assumptions in the method
(cid:12)(cid:13)(cid:4)
arecorrect,itisexpectedfor3C273thatthereshouldexist
(cid:10) (cid:8) (cid:4)
(cid:12)(cid:1)(cid:13)(cid:4) (cid:1) (cid:6) (cid:13) time lags between the broad lines from the BLR and the
(cid:14)(cid:5)(cid:7)(cid:11)(cid:2)(cid:15)(cid:16)(cid:17)
γ-raysfrom the relativistic jet.
(cid:4)(cid:5)(cid:6)(cid:7)(cid:2)(cid:8)(cid:9)(cid:10)(cid:5)(cid:11)(cid:1)(cid:2)(cid:5)(cid:6)
(cid:4)(cid:5)(cid:6)(cid:7)(cid:2)(cid:8)(cid:9)(cid:10)(cid:5)(cid:11)(cid:1)(cid:2)(cid:12)(cid:13)
(cid:4)(cid:5)(cid:6)(cid:7)(cid:2)(cid:8)(cid:9)(cid:10)(cid:5)(cid:11)(cid:1)(cid:2)(cid:9)(cid:10)
(cid:4)(cid:5)(cid:6)(cid:7)(cid:2)(cid:8)(cid:9)(cid:10)(cid:5)(cid:11)(cid:1)(cid:2)(cid:7)(cid:8) 3.1 Data of 3C 273
(cid:4)(cid:5)(cid:6)(cid:7)(cid:2)(cid:8)(cid:9)(cid:10)(cid:5)(cid:11)(cid:1)(cid:2)(cid:3)(cid:4)
(cid:1)
(cid:1) (cid:1)
This paper makes use of the 3C 273 database hosted by
the ISDC (Tu¨rler et al. 1999). This database is one of the
most complete multi-wavelength databases currently avail-
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:2)(cid:9)(cid:9)(cid:11)(cid:5)(cid:10) (cid:9)(cid:10)(cid:9)(cid:15)(cid:9)(cid:9)(cid:4)(cid:9)(cid:3)(cid:16)(cid:17)q(cid:9)qqq
(cid:12)(cid:13)(cid:14) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:2)(cid:9)(cid:9)(cid:11)(cid:12)(cid:4) (cid:11)(cid:5)(cid:9)(cid:15)(cid:9)(cid:11)(cid:12)(cid:9)(cid:3)(cid:16)(cid:17)q(cid:9)qqq able for one AGN. For 3C 273, the γ-ray light curves are
(cid:10)(cid:11)(cid:1) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:2)(cid:9)(cid:4)(cid:10)(cid:5)(cid:12) (cid:9)(cid:4)(cid:9)(cid:15)(cid:9)(cid:11)(cid:12) very sparsely sampled and/or the error bars of γ-ray fluxes
(cid:1) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:2)(cid:9)(cid:4)(cid:5)(cid:6)(cid:7) (cid:9)(cid:10)(cid:9)(cid:15)(cid:9)(cid:11)(cid:5) are also very large. Of course with Fermi taking data since
(cid:10)(cid:11)(cid:1)
June 2008 this is no longer the case (see e.g. Abdoet al.
(cid:9) (cid:4) (cid:18)(cid:2)(cid:4)(cid:9)(cid:5)(cid:19)(cid:20)(cid:17)
(cid:3) qqqq 2010b). However, the sampling over the dates of interest,
(cid:7) and, in general over the timescales of interest is still sparse
a aaa (cid:10) (seethelinelight curvesinthefollowing paragraphs).Thus
it should be unreliable to employ the γ-ray light curves
(cid:2)
(cid:8) (cid:1) (cid:12) to estimate the time lags. Hence for these blazars lacking
qqqq adequate γ-ray light curves, the synchrotron emission, es-
(cid:11)
(cid:6) pecially the radio emission, could be used to derive the
(cid:5)
timelags relative tothebroad lines. Thesynchrotron flares
from the relativistic jet dominate energy output from ra-
Figure 1. Sketch of the geometry assumed, and it is similar to
dio to millimeter and extend up to the infrared–optical
that used in the reverberation mapping method of broad emis-
regimes (Robson et al. 1993; Tu¨rler, Courvoisier & Paltani
sion lines. RBLR is the size of BLR. (a) the angle between the
2000; Soldi et al. 2008). Radio light curves are better than
line of sight and the jet axis θ = 0. (b) θ 6= 0. The jet axis
is perpendicular to the plane of BLR. (b) the planes ABU and millimeter ones in the samplings and the features of syn-
HNOP are perpendicular to the line of sight. ∵ TV ⊥ AV, ∴ chrotron flares. Gamma-ray detections correspond to rising
TV = ATsinα = RBLRsinα. ∵ TW k BL, ∴ TW ⊥ WV and radio fluxes (e.g. Ulrich, Maraschi & Urry 1997). Thus the
TW ⊥ AV. TW ⊥ AV and TV ⊥ AV give WV ⊥ AV. ∵ radio light curves are adopted to be analyzed. Though the
TV ⊥ AV and WV ⊥ AV, ∴ ∠TVW = θ. ∵ ∠TVW = θ and synchrotronflaresextenduptotheinfrared–opticalregimes,
∠TWV =π/2,∴TW =TV sinθ=RBLRsinαsinθ. the flares are sparse (denoted by red color in the 3C 273
database).Intheintervalsamongtheseflares,theinfrared–
opticallightcurvesmaybecontaminatedbyotheremission
average over α in equation (6), we have
components.Thusitisexpectedthatthereshouldbenosig-
R + chτobi nificant features in the cross correlation functions between
Rγ = BcLR cos1+θz , (7) the broad lines and the light curves. Considering that the
vd − synchrotronemissionpeaksaroundtheinfraredbandfor3C
where τ is the ensemble average of τ (α) and is the 273(seee.g.Ghisellini et al.1998),theinfraredlightcurves
ob ob
h i
measured time lag between the γ-ray and line light curves are also adopted to be analyzed and to test the expecta-
(and 1+sinαsinθ = 2π(1+sinαsinθ)dα/2π =1). It is tionabove.Inthelightcurvesadoptedhere,onlygooddata
h i R0
obvious that equation (7) contains Cases A, B and C. As (Flag>=0) are adopted.
θ = 0, equation (7) becomes equation (4). In the following Light curvesof 5, 8, 15, 22 and 37 GHz aretaken from
sections, we will calculate R based on equation (7). the3C273database,fortheselightcurveshaveenoughdata
γ
(Tu¨rler et al. 1999). These radio light curves are presented
in Fig. 2. There are four distinct outbursts in each radio
light curve after 1980 (see Fig. 2). The data of 22 and
3 APPLICATION TO 3C 273 ∼
37 GHzare adoptedfrom 1980, for observations are very
∼
3C 273 was first identified as aquasar at redshift z=0.158 sharply sampled before 1980 (see Fig. 2). From 1973 to
∼
bySchmidt(1963).ItisoneofthebeststudiedAGNsinall 1978, there is a gap of 5 years without observations of 5
bands(see e.g. Lichti et al. 1995; von Montigny et al. 1997; GHz. Considering the four distinct outbursts in each radio
Tu¨rler et al. 1999; Soldi et al. 2008). The database site1 of light curve, the data from 1980 are adopted for the light
∼
3C 273 provides a series of about 70 light curves as well as curveof5GHz.Also,thedatafrom 1980areadoptedfor
∼
some spectra. The jet of 3C 273 is one-sided, with no signs the light curves of 8 and 15 GHz. The sampling rates of 5,
of emission from the counterjet side (Unwin et al. 1985). 8, 15, 22 and 37 GHz are 29, 40, 40, 44 and 46 times per
yearfor theadopted data, respectively.
Light curves of broad lines Hα, Hβ and Hγ are taken
1 http://isdc.unige.ch/3c273/ fromKaspi et al.(2000),andallthedatainthelightcurves
Locating positions of γ-ray–emitting regions 5
(cid:18) (cid:18)
(cid:4)(cid:6) (cid:4)(cid:4)
(cid:13) (cid:4)(cid:6) (cid:13) (cid:12)
(cid:9)(cid:4) (cid:4)(cid:15)(cid:16)(cid:17) (cid:14) (cid:12) (cid:9)(cid:4) (cid:5)(cid:15)(cid:16)(cid:17) (cid:14)
(cid:22) (cid:9)(cid:6) (cid:11) (cid:9)(cid:6) (cid:11)
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(cid:3)(cid:6) (cid:3)(cid:6)
(cid:4)(cid:10)(cid:6)(cid:6) (cid:1)(cid:4)(cid:15)(cid:16)(cid:17) (cid:14) (cid:13) (cid:12) (cid:4)(cid:10)(cid:6)(cid:6) (cid:7)(cid:7)(cid:15)(cid:16)(cid:17) (cid:14) (cid:13) (cid:12)
(cid:19)(cid:20)(cid:21)(cid:22) (cid:8)(cid:9)(cid:6)(cid:6) (cid:11) (cid:18)(cid:8)(cid:9)(cid:6)(cid:6) (cid:11) (cid:18)
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(cid:1)(cid:2)(cid:3)(cid:4) (cid:1)(cid:2)(cid:5)(cid:6) (cid:1)(cid:2)(cid:5)(cid:4) (cid:1)(cid:2)(cid:2)(cid:6) (cid:1)(cid:2)(cid:2)(cid:4) (cid:7)(cid:6)(cid:6)(cid:6) (cid:7)(cid:6)(cid:6)(cid:4) (cid:1)(cid:2)(cid:3)(cid:4) (cid:1)(cid:2)(cid:5)(cid:6) (cid:1)(cid:2)(cid:5)(cid:4) (cid:1)(cid:2)(cid:2)(cid:6) (cid:1)(cid:2)(cid:2)(cid:4) (cid:7)(cid:6)(cid:6)(cid:6) (cid:7)(cid:6)(cid:6)(cid:4)
(cid:18) (cid:18)
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(cid:4)(cid:10)(cid:6)(cid:6) (cid:8)(cid:3)(cid:15)(cid:16)(cid:17) (cid:14) (cid:13)(cid:18) (cid:12) (cid:10)(cid:4)(cid:6) (cid:16)a
(cid:10)(cid:6)(cid:6)
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(cid:19)(cid:20) (cid:7)(cid:6) (cid:4)(cid:6)(cid:6)
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(cid:19)(cid:20)(cid:21)(cid:1)(cid:1)(cid:4)(cid:10)(cid:6)(cid:6) (cid:18)(cid:4)(cid:4)(cid:10)(cid:6)(cid:4)(cid:6) (cid:18)
(cid:1)(cid:9)(cid:6) (cid:9)(cid:4)
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(cid:1)(cid:2)(cid:3)(cid:4) (cid:1)(cid:2)(cid:5)(cid:6) (cid:1)(cid:2)(cid:5)(cid:4) (cid:1)(cid:2)(cid:2)(cid:6) (cid:1)(cid:2)(cid:2)(cid:4) (cid:7)(cid:6)(cid:6)(cid:6) (cid:7)(cid:6)(cid:6)(cid:4) (cid:1)(cid:2)(cid:3)(cid:4) (cid:1)(cid:2)(cid:5)(cid:6) (cid:1)(cid:2)(cid:5)(cid:4) (cid:1)(cid:2)(cid:2)(cid:6) (cid:1)(cid:2)(cid:2)(cid:4) (cid:7)(cid:6)(cid:6)(cid:6) (cid:7)(cid:6)(cid:6)(cid:4)
(cid:11)(cid:23)(cid:24)(cid:25)(cid:18)(cid:26)(cid:27)(cid:28)(cid:29)(cid:30) (cid:11)(cid:23)(cid:24)(cid:25)(cid:18)(cid:26)(cid:27)(cid:28)(cid:29)(cid:30)
Figure 2. Light curves of the radio emission and the Balmer lines. The y-axis is in units of Jy. For lines, the y-axis is in units of
10−14 ergcm−2 s−1.A,B,CandDdenotethefourdistinctoutburstsafter∼1980.
are adopted to calculate the time lags relative to the ra- DCF,thereisanothermethodofestimatingtheCCFinthe
dio emission. The sampling rates of the lines are around 5 caseofnonuniformlysampledlightcurves,thez-transformed
times per year. The line light curves are also presented in discrete correlation function (ZDCF; Alexander 1997). The
Fig. 2, wherein all the light curves show the same time in- ZDCF is a binning type of method as an improvement of
terval.It can beseen in Fig. 2that thelinelight curvesare the DCF technique, but it has a notable feature in that
sharply sampled relative to the radio light curves adopted. the data are binned by equal population rather than equal
Especially, there is only one data point in each of several bin width as in the DCF. It has been shown in practice
valley-bottomsintheHαandHβlightcurves,andthetrend thattheZDCFismorerobustthantheICCFandtheDCF
of variations can be changed if the points in these valley- whenappliedtosparselyandunequallysampledlightcurves
bottomsareexcludedfromtheHαandHβ lightcurves(see (see e.g. Edelson et al. 1996; Giveon et al. 1999; Roy et al.
Fig. 2).Thesharp samplings will affect thechoiceof analy- 2000). Liu et al. (2008) analyzed the ZDCFs between un-
sismethodforthecrosscorrelation betweenthebroad lines equally sampled light curves of AGNs, and they obtained
and the radio emission. The infrared light curves of J, H, inter-band time lags. In practice, the ZDCF is applicable
K and L bandsarealso adopted from the3C 273 database. and reliable to analyze the unequally sampled light curves.
The data before 1998 are adopted for the J, H and L light Thus the ZDCF will be calculated in the paper because of
curves. The data before 2000 are adopted for the K light thesharp samplings of theBalmer lines.
curve. In general, it seems to be true that the time lag is
better characterized by the centroid τ of the DCF and
cent
the ICCF than by the peak value τ , namely, the time
3.2 Analysis of time lags peak
lagwherethelinearcorrelation coefficienthasitsmaximum
Cross-correlation function (CCF) analysis is a standard valuer (see e.g. Peterson et al. 2004,2005).In both the
max
technique in time series analysis for finding time lags be- DCF and the ICCF, τ is much less stable than τ ,
peak cent
tween light curves at different wavelengths, and the defi- but τ is much less stable in the DCF than in the ICCF
peak
nition of the CCF assumes that the light curves are uni- (Peterson et al. 2005). Thus we prefer the time lag to be
formlysampled.However,inmostcasesthesamplingisnot characterized by the centroid τ of the ZDCF. The cen-
cent
uniform.Theinterpolatedcrosscorrelationfunction(ICCF) troidtimelagτ iscomputedusingallthepointswithcor-
cent
method of Gaskell & Peterson (1987) uses a linear interpo- relation coefficients r >0.8r in the ZDCF bumps closer
max
lation scheme to determine the missing data in the light tothezero-lag (see Fig. 3). Thecalculated ZDCFsbetween
curves.Ontheotherhand,thediscretecorrelation function the radio and broad-line light curves are presented in Fig.
(DCF;Edelson & Krolik1988)canutilizeabinningscheme 3.The horizontal and verticalerror bars in Fig. 3represent
toapproximatethemissingdata.ApartfromtheICCFand the68.3% confidenceintervalsinthetimelagsandtherele-
6 H. T. Liu, J. M. Bai and J. M. Wang
Table 1. Time lags between emission lines and radio emission. The sign of
thetimelagisdefinedasτcent=tradio−tline.Timelagsareinunitsofyrs.
Lines 5GHz 8GHz 15GHz 22GHz 37GHz
Hα −1.23+0.02 −1.99+0.06 −2.77+0.02 −3.14+0.02 −3.30+0.02
−0.07 −0.01 −0.08 −0.09 −0.08
Hβ −0.19+0.03 −1.06+0.08 −2.40+0.02 −2.27+0.03 −3.27+0.02
−0.09 −0.02 −0.07 −0.09 −0.08
Hγ −0.35+0.03 −1.13+0.07 −1.57+0.02 −1.82+0.02 −2.01+0.02
−0.09 −0.01 −0.07 −0.08 −0.07
Hα 4.72+0.08 4.20+0.06 3.43+0.08 3.21+0.07 3.06+0.08
−0.02 −0.02 −0.02 −0.02 −0.03
Hβ 4.31+0.07 4.13+0.07 3.72+0.07 3.45+0.07 3.26+0.09
−0.02 −0.01 −0.02 −0.02 −0.03
Hγ 6.19+0.10 4.13+0.06 3.73+0.07 3.78+0.08 3.29+0.08
−0.04 −0.01 −0.02 −0.03 −0.03
vantcorrelationcoefficients,respectively.TheZDCFbumps Semenov,Dyadechin & Punsly 2004). In most cases, the
closer to the zero-lag have a good profile in Fig. 3. The bulk velocity of jet v is close to the escape speed
j
measured time lags are listed in Table 1. Thecentroid τ (Kudohet al. 1998). The escape speed is around 0.9c
cent
is calculated by τ = τ(i)r(i)/ r(i), where τ(i) and near the ergosphere of the rapidly spinning black hole
cent
P P
r(i) are the values of i-th data pair with r > 0.8r . The (Meier, Koide& Uchida 2001). Most supermassive black
max
errors of τ are calculated by ∆τ± = [∆τ±(i)r(i)+ holes are spinning rapidly (Elvis, Risaliti & Zamorani
τ(i)∆r±(i)c]ent r(i) τ(i)r(i) ∆cren±t(i){/P[ r(i)]2,where 2002). Thus v 0.9c. If the disturbances in the cental en-
j
∆τ±(i) andP∆r±(i−) aPre the relePvant error}s oPf τ(i) and r(i), ginearetranspo∼rtedwiththejetitself,v =v 0.9c.Thus
d j
∼
respectively. we would haveR 9R from equation (1).
γ BLR
∼
Our results show two possibilities that the broad-line For 3C 273, the jet has v =0.95c and cosθ = 0.95 on
j
variations lag or lead the radio ones (see Fig. 3). The mea- 100 pc scales (Davis, Unwin,Muxlow 1991). The pc-scale
suredtimelagsareontheorderofyears(seeTable1).Fora jet was constrained to have θ < 15◦ and the bulk Lorentz
givenline,therelevanttimelagsgenerallydecreaseasradio factor Γ > 10 (Unwin et al. 1985). The actual value of θ
frequency increases from 5 to 37 GHz (see Table 1). The cannot be too small, unlike better aligned blazars, because
calculatedZDCFsbetweentheinfraredandHαlightcurves it has a strong big blue bump (Shields 1978; Courvoisier
are presented in Fig. 4 for illustration. For the ZDCFs in 1998). Thus it is likely that θ be larger than 10◦. The ratio
Fig. 4, there are no significant common features closer to of the jet to counterjet flux is R = [(1+v cosθ/c)/(1
j
−
thezero-lag. Also, thereare nosignificant common features v cosθ/c)]3+α for discretemovingblobs (Lind & Blandford
j
closertothezero-lagfortheZDCFsoftheHβ andHγ lines 1985).R>104 wasobservedfor3C273andv canbeupto
j
relative to the infrared emission. On the contrary, the ZD- 0.995c (see e.g. Georganopoulos et al. 2006). The observed
CFs in Fig. 3 have significant common features closer to spectralindexα=0.8(Unwin et al.1985).Itisobviousthat
the zero-lag. The absence of significant features tests the θ.21◦ and0.9c6v 60.995careallowedbyR>104.The
j
expectation in subsection 3.1. This test indicates that the disturbances are transported from the central engine down
infraredsynchrotronemissiondoesnotdominatetheenergy the jet, and then it is possible that v = v = 0.9–0.995c
d j
outputintheintervalsbetweenthesynchrotronflaresinthe and θ = 12◦–21◦. For a given line, the relevant time lags
infrared–opticalbands.Thelagτob isthelagτcent measured generally decreaseasradiofrequencyincreases from 5to37
here. Hereafter, τcent is equivalent to τob and τob . GHz(seeTable1).Weadopt themeasured timelags of the
h i
linesrelativetothe37GHzemission.Thenegativelagshave
an average of τ− = 2.86 years. The positive lags have an
3.3 Calculations average of τ+ o=b 3.2−0 years. There is no zero-lag. In the
ob
For 3C 273, Kaspi et al. (2000) determined the Hα, Hβ following calculations, vd =0.9–0.995c and θ=12◦–21◦ are
and Hγ lags τ relative to the optical continuum, and adopted, and these values estimated from τob are denoted
Paltani & Tu¨rler (2005) determined their lags relative to byRradio.
tthameiUnVatecdonbtyinnuounm-t.hTerhmeaolpetmicaislsicoonn,tipnoususimblyisrsetlraotnedglytoctohne- 0.995Fcr,omθ =τ−ob12=◦–2−12◦.8a6ndyeeaqrus,atRioBnLR(7=), w2.e70calyn,ovbdta=in0t.9h–e
relativisticjet,andthereforeitappearsunsuitableforstudy- radioemittingpositionRradio =0.40–2.62pc(CaseB).The
ing the lags between the ionizing continuum and the lines typicalsizeof RBLR =2.70 ly=0.83 pcis within therange
(Paltani, Courvoisier & Walter 1998). The Hα, Hβ and Hγ of Rradio estimated in Case B. The radio emitting regions
lags relative to the UV continuum are more reliable than in Case B are at distances of pc-scale from the central en-
those relative to the optical continuum (Paltani & Tu¨rler gineandarearoundtheBLR,i.e.likelyinsidetheBLR,co-
2005). Thus we adopt the Hα, Hβ and Hγ lags determined located withtheBLRoroutsidetheBLR.Fromτ+ =3.20
ob
byPaltani & Tu¨rler (2005).Here,theaverage ofrest-frame years, RBLR = 2.70 ly, vd = 0.9–0.995c, θ = 12◦–21◦ and
lags of these lines, τ = 2.70 years, is adopted as a char- equation (7), we can obtain Rradio = 9.43–62.31 pc (Case
acteristic value of τ. Thus the BLR has a typical size of C). The estimated sizes are much larger than the typical
RBLR =2.70 ly. size of RBLR =0.83 pc. The radio emitting regions in Case
Simulations show that the relativistic jets can C are at distances of tens of pc from the central black hole
be driven from a region just outside the ergosphere and are far away from theBLR.
of a Kerr black hole (see e.g. Meier, Koide& Uchida Kovalev et al. (2009) identified the pc-scale radio core
2001; Koide et al. 2002; Koide 2004; Komissarov 2004; as a likely location for both the γ-ray and radio flares.
Locating positions of γ-ray–emitting regions 7
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(cid:12)
(cid:19)(cid:9)(cid:10) (cid:6)(cid:7)(cid:5) (cid:6)(cid:7)(cid:5) (cid:6)(cid:7)(cid:5) (cid:6)(cid:7)(cid:5) (cid:6)(cid:7)(cid:5)
(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:12)(cid:1)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:1)(cid:9)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:9)(cid:1)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:9)(cid:1)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:9)(cid:1)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:9)
(cid:12)(cid:11)(cid:11)(cid:1)(cid:6)(cid:7)(cid:4) (cid:1)(cid:6)(cid:7)(cid:4) (cid:1)(cid:6)(cid:7)(cid:4) (cid:1)(cid:6)(cid:7)(cid:4) (cid:1)(cid:6)(cid:7)(cid:4)
(cid:10)
(cid:13)(cid:9)(cid:1)(cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:7)(cid:3)
(cid:13)
(cid:12)(cid:1)(cid:6)(cid:7)(cid:2) (cid:1)(cid:6)(cid:7)(cid:2) (cid:1)(cid:6)(cid:7)(cid:2) (cid:1)(cid:6)(cid:7)(cid:2) (cid:1)(cid:6)(cid:7)(cid:2)
(cid:10)(cid:11) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2)
(cid:22)(cid:16)(cid:23)(cid:24)(cid:25)(cid:26)(cid:27)(cid:9)(cid:28)(cid:29)(cid:1)(cid:28)b(cid:30) (cid:22)(cid:16)(cid:23)(cid:24)(cid:5)(cid:5)(cid:27)(cid:9)(cid:28)(cid:29)(cid:1)(cid:28)b(cid:30) (cid:22)(cid:16)(cid:23)(cid:24)(cid:8)(cid:31)(cid:27)(cid:9)(cid:28)(cid:29)(cid:1)(cid:28)b(cid:30) (cid:22)(cid:16)(cid:23)(cid:24)(cid:2)(cid:27)(cid:9)(cid:28)(cid:29)(cid:1)(cid:28)b(cid:30) (cid:22)(cid:16)(cid:23)(cid:24)(cid:31)(cid:27)(cid:9)(cid:28)(cid:29)(cid:1)(cid:28)b(cid:30)
(cid:19)(cid:17) (cid:6)(cid:7)(cid:2) (cid:6)(cid:7)(cid:2) (cid:6)(cid:7)(cid:2) (cid:6)(cid:7)(cid:2) (cid:6)(cid:7)(cid:2)
(cid:14)
(cid:21)(cid:18) (cid:6)(cid:7)(cid:3) (cid:1)(cid:5)(cid:3) (cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:3) (cid:6)(cid:7)(cid:3) (cid:1)(cid:10)(cid:3) (cid:6)(cid:7)(cid:3) (cid:1)(cid:13)(cid:3) (cid:6)(cid:7)(cid:3) (cid:1)(cid:16)(cid:3)
(cid:14)(cid:20)(cid:20)(cid:18) (cid:6)(cid:7)(cid:4) (cid:6)(cid:7)(cid:4) (cid:6)(cid:7)(cid:4) (cid:6)(cid:7)(cid:4) (cid:6)(cid:7)(cid:4)
(cid:12)
(cid:19)(cid:9)(cid:10) (cid:6)(cid:7)(cid:5) (cid:6)(cid:7)(cid:5) (cid:6)(cid:7)(cid:5) (cid:6)(cid:7)(cid:5) (cid:6)(cid:7)(cid:5)
(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:12)(cid:1)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:1)(cid:9)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:9)(cid:1)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:9)(cid:1)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:9)(cid:1)(cid:6)(cid:6)(cid:7)(cid:7)(cid:5)(cid:6) (cid:9)
(cid:12)(cid:11)(cid:11)(cid:1)(cid:6)(cid:7)(cid:4) (cid:1)(cid:6)(cid:7)(cid:4) (cid:1)(cid:6)(cid:7)(cid:4) (cid:1)(cid:6)(cid:7)(cid:4) (cid:1)(cid:6)(cid:7)(cid:4)
(cid:10)
(cid:13)(cid:9)(cid:1)(cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:7)(cid:3) (cid:1)(cid:6)(cid:7)(cid:3)
(cid:13)
(cid:12)(cid:1)(cid:6)(cid:7)(cid:2) (cid:1)(cid:6)(cid:7)(cid:2) (cid:1)(cid:6)(cid:7)(cid:2) (cid:1)(cid:6)(cid:7)(cid:2) (cid:1)(cid:6)(cid:7)(cid:2)
(cid:10)(cid:11) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1)(cid:2) (cid:1)(cid:3) (cid:1)(cid:4) (cid:1)(cid:5) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2)
(cid:22)(cid:16)(cid:23)(cid:24)(cid:25)(cid:26)(cid:27)(cid:28)(cid:29)(cid:1)(cid:28)g(cid:30) (cid:22)(cid:16)(cid:23)(cid:24)(cid:5)(cid:5)(cid:27)(cid:28)(cid:29)(cid:1)(cid:28)g(cid:30) (cid:22)(cid:16)(cid:23)(cid:24)(cid:8)(cid:31)(cid:27)(cid:28)(cid:29)(cid:1)(cid:28)g(cid:30) (cid:22)(cid:16)(cid:23)(cid:24)(cid:2)(cid:27)(cid:28)(cid:29)(cid:1)(cid:28)g(cid:30) (cid:22)(cid:16)(cid:23)(cid:24)(cid:31)(cid:27)(cid:28)(cid:29)(cid:1)(cid:28)g(cid:30)
Figure 3.ZDCFbetween Hαand (a) 37, (b) 22, (c)15, (d) 8and(e) 5GHz; ZDCFbetween Hβ and(f) 37, (g) 22, (h)15, (i) 8and
(j)5GHz;ZDCFbetweenHγ and(k)37,(l)22,(m)15,(n)8and(o)5GHz.Thex-axisisinunitsofyrs.
(cid:16) (cid:16)
(cid:6)(cid:9)(cid:1)(cid:11) (cid:6)(cid:9)(cid:10)(cid:4)
(cid:6)(cid:9)(cid:1)(cid:10) (cid:6)(cid:9)(cid:10)(cid:6)
(cid:27)(cid:15)(cid:6)(cid:6)(cid:9)(cid:9)(cid:1)(cid:1)(cid:1)(cid:8) (cid:13)(cid:18)(cid:15) (cid:28) (cid:6)(cid:9)(cid:8)(cid:4) (cid:13)(cid:29)(cid:15) (cid:30)
(cid:24)(cid:25)(cid:16)(cid:13)(cid:26)(cid:21)(cid:6)(cid:6)(cid:6)(cid:9)(cid:9)(cid:9)(cid:6)(cid:6)(cid:1)(cid:7)(cid:2)(cid:6) (cid:6)(cid:6)(cid:16)(cid:9)(cid:9)(cid:1)(cid:8)(cid:4)(cid:6) (cid:16)
(cid:22)(cid:23)(cid:6)(cid:9)(cid:6)(cid:5)
(cid:16)(cid:6)(cid:9)(cid:6)(cid:3) (cid:16) (cid:6)(cid:9)(cid:1)(cid:6) (cid:16)
(cid:6)(cid:9)(cid:6)(cid:7) (cid:6)(cid:9)(cid:6)(cid:2)
(cid:6)(cid:9)(cid:6)(cid:5) (cid:6)(cid:9)(cid:6)(cid:7)
(cid:27)(cid:15)(cid:6)(cid:9)(cid:6)(cid:3) (cid:13)(cid:14)(cid:15) (cid:21) (cid:6)(cid:9)(cid:6)(cid:5) (cid:13)(cid:31)(cid:15)
(cid:21)
(cid:26)(cid:6)(cid:9)(cid:6)(cid:4) (cid:6)(cid:9)(cid:6)(cid:3)
(cid:24)(cid:25)(cid:16)(cid:13)(cid:6)(cid:9)(cid:6)(cid:11) (cid:6)(cid:16)(cid:9)(cid:6)(cid:4) (cid:16)
(cid:22)(cid:23)(cid:6)(cid:9)(cid:6)(cid:10) (cid:6)(cid:9)(cid:6)(cid:11)
(cid:6)(cid:9)(cid:6)(cid:8) (cid:6)(cid:9)(cid:6)(cid:10)
(cid:1)(cid:2)(cid:3)(cid:4) (cid:1)(cid:2)(cid:5)(cid:6) (cid:1)(cid:2)(cid:5)(cid:4) (cid:1)(cid:2)(cid:7)(cid:6) (cid:1)(cid:2)(cid:7)(cid:4) (cid:1)(cid:2)(cid:2)(cid:6) (cid:1)(cid:2)(cid:2)(cid:4) (cid:8)(cid:6)(cid:6)(cid:6) (cid:8)(cid:6)(cid:6)(cid:4) (cid:1)(cid:2)(cid:3)(cid:4) (cid:1)(cid:2)(cid:5)(cid:6) (cid:1)(cid:2)(cid:5)(cid:4) (cid:1)(cid:2)(cid:7)(cid:6) (cid:1)(cid:2)(cid:7)(cid:4) (cid:1)(cid:2)(cid:2)(cid:6) (cid:1)(cid:2)(cid:2)(cid:4) (cid:8)(cid:6)(cid:6)(cid:6) (cid:8)(cid:6)(cid:6)(cid:4)
(cid:16)(cid:17)(cid:18)(cid:16)(cid:19)(cid:20) (cid:17)(cid:16)(cid:18)(cid:19)(cid:20)
(cid:1)(cid:9)(cid:6)
(cid:6)(cid:9)(cid:7)
(cid:6)(cid:9)(cid:3) (cid:13)(cid:20)(cid:15)
(cid:6)(cid:9)(cid:11) (cid:13)"(cid:15)
((cid:19) (cid:6)(cid:9)(cid:8)
(cid:14)’(cid:20)(cid:12)(cid:6)(cid:6)(cid:9)(cid:9)(cid:6)(cid:8) (cid:16) (cid:16)
(cid:20)""’(cid:12)(cid:6)(cid:9)(cid:11)
%(cid:12)(cid:6)(cid:9)(cid:3)
%((cid:16)#(cid:12)(cid:6)(cid:9)(cid:7)(cid:12)(cid:7) (cid:12)(cid:5) (cid:12)(cid:3) (cid:12)(cid:4) (cid:12)(cid:11) (cid:12)(cid:10) (cid:12)(cid:8) (cid:12)(cid:1) (cid:6) (cid:1) (cid:8) (cid:10) (cid:12)(cid:7) (cid:12)(cid:5) (cid:12)(cid:3) (cid:12)(cid:4) (cid:12)(cid:11) (cid:12)(cid:10) (cid:12)(cid:8) (cid:12)(cid:1) (cid:6) (cid:1) (cid:8) (cid:10)
%$$(cid:20)(cid:23)(cid:18)(cid:19)’ (cid:6)(cid:1)(cid:9)(cid:9)(cid:7)(cid:6) (cid:30)(cid:18)!(cid:13)(cid:28)(cid:16)(cid:12) a (cid:15) (cid:30)(cid:18)!(cid:13)(cid:30)(cid:16)(cid:12) a (cid:15)
# (cid:6)(cid:9)(cid:3) (cid:13)!(cid:15) (cid:13))(cid:15)
&&(cid:16) (cid:6)(cid:9)(cid:11)
% (cid:6)(cid:9)(cid:8)
#$ (cid:6)(cid:9)(cid:6) (cid:16) (cid:16)
(cid:12)(cid:6)(cid:9)(cid:8)
(cid:12)(cid:6)(cid:9)(cid:11)
(cid:12)(cid:6)(cid:9)(cid:3)
(cid:12)(cid:6)(cid:9)(cid:7)
(cid:12)(cid:7) (cid:12)(cid:5) (cid:12)(cid:3) (cid:12)(cid:4) (cid:12)(cid:11) (cid:12)(cid:10) (cid:12)(cid:8) (cid:12)(cid:1) (cid:6) (cid:1) (cid:8) (cid:10) (cid:12)(cid:7) (cid:12)(cid:5) (cid:12)(cid:3) (cid:12)(cid:4) (cid:12)(cid:11) (cid:12)(cid:10) (cid:12)(cid:8) (cid:12)(cid:1) (cid:6) (cid:1) (cid:8) (cid:10)
(cid:30)(cid:18)!(cid:13)(cid:21)(cid:12) a (cid:15) (cid:30)(cid:18)!(cid:13) (cid:12) a (cid:15)
Figure 4.Lightcurves ofinfraredemissionin(a)K,(b) L,(c)Jand(d) Hbands.ZDCFbetween Hαand(e)K,(f) L,(g)Jand(h)
Hbands.Thex-axisisinunitsofyrs.
8 H. T. Liu, J. M. Bai and J. M. Wang
Jorstad et al. (2001) concluded that both the radio and γ-
rayeventsareoriginatingfromthesameregionofarelativis-
ticjet.In1990s,itiscommonlythoughtthattheγ-raysare
producedinthejet,butclosertothecentralenginethanthe
radioemission(seee.g.Dermer & Schlickeiser1994).Thusit (cid:10)(cid:2)(cid:5)
isexpectedthatRγ .Rradio.TheconstraintofRγ .Rradio (cid:12)(cid:11)(cid:13)(cid:14)(cid:10)(cid:2)(cid:4)
is allowed by the recent flares of 3C 279 observed by Fermi (cid:10)
and in a multi-wavelength campaign (Abdoet al. 2010d), (cid:1)(cid:2)(cid:7)
(cid:4)(cid:1)
where radio light curves from 5 to 230 GHz fail to show
(cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3) (cid:10)(cid:7)
prominent variations during either the November 2008 or (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:4)(cid:4) (cid:10)(cid:6) θ(cid:11)
theFebruary2009γ-rayflares(oranytimeinbetween).For (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:5)(cid:5)
CaseB,R .0.40–2.62pcforv =0.9–0.995candθ=12◦– (cid:8)(cid:8)(cid:9)(cid:9) (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:6)(cid:6) (cid:10)(cid:5)
γ d (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:7)(cid:7)
21◦. For Case A, the zero-lag position R =4.67–30.81 pc, (cid:10)(cid:4)
γ
which is far away from the BLR. For Case C, R . 9.43–
γ
62.31 pc. Also, R > 4.67–30.81 pc for the positive lags in
γ
Case C. Thus for Case C we have 4.67–30.81 <R .9.43–
γ
62.31 pc for v = 0.9–0.995c and θ = 12◦–21◦. The depen-
d
dence of R and R on v and θ is presented in Fig. 5 (cid:1)(cid:2)(cid:5)
γ radio d
(see three-dimensional plots). R and R increase as v (cid:1)(cid:2)(cid:4)
γ radio d
(cid:13)(cid:11)(cid:14)(cid:15)
increases, but decrease as θ increases. The uncertainties of (cid:1)
v and θ result in thelarger intervals of R and R . For (cid:12)(cid:1)(cid:2)(cid:4)
d γ radio
betterrepresentingintervalsofR ,thesectionsofthethree- (cid:12)(cid:1)(cid:2)(cid:5) (cid:4)(cid:1)
γ
(cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3) (cid:10)(cid:7)
dimensional plots at cosθ = 0.95 are also plotted in Fig. 5 (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:4)(cid:4) (cid:10)(cid:6) θ(cid:11)
(see the bottom panel). For Case B, R . R = 0.44– (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:5)(cid:5)
γ radio
1.28 pc for vd = 0.9–0.995c and cosθ = 0.95. These Rγ (cid:8)(cid:8)(cid:9)(cid:9) (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:6)(cid:6) (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:7)(cid:7) (cid:10)(cid:5)
marginally satisfy R . R . For Case C, we have 5.15– (cid:10)(cid:4)
γ BLR
15.08<R .10.40–30.45 pc.
γ
It is possible that there is a special point D within
segment AG (see Fig. 1a). As the ionizing photons travel
frompointAtoB,thedisturbancestravelfromAtoD,i.e.
Rγ =AD. Thus we haveRγ/vd =RBLR/c, and then (cid:10)(cid:2)(cid:7)
(cid:10)(cid:2)(cid:6)
R
Rγ = BcLRvd. (8) (cid:12)(cid:11)(cid:13)(cid:14)(cid:10)(cid:2)(cid:5)
(cid:10)(cid:2)(cid:4)
Inthiscase,theγ-rayswillleadthelines.Combingequations (cid:10) (cid:4)(cid:1)
(7) and (8), we have (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3) (cid:10)(cid:7)
(cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:4)(cid:4) (cid:10)(cid:6) θ(cid:11)
Rγ =−c1hτ+obzico1sθ. (9) (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:8)(cid:8)(cid:5)(cid:5)(cid:9)(cid:9) (cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:6)(cid:6) (cid:10)(cid:5)
(cid:1)(cid:1)(cid:2)(cid:2)(cid:3)(cid:3)(cid:7)(cid:7)
(cid:10)(cid:4)
In this special case (hereafter Case D), R . R is ex-
γ BLR
pectedfromequation(8).Fromτ− = 2.86years,θ=12◦–
ob −
21◦ and equation (9), we have Rγ .Rradio =0.77–0.81 pc. (cid:9)(cid:10)(cid:11)q(cid:12)(cid:1)(cid:2)(cid:3)(cid:13) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:1)(cid:6)(cid:5)(cid:7)
TheseestimatedR andR =0.83pcsatisfyR .R . (cid:8)(cid:2)(cid:9)(cid:10)(cid:11)
γ BLR γ BLR
This tests the correctness of R . R expected from RRRR
γ BLR (cid:8)(cid:1) gggg
equation (8). This test confirms the reliability of the time
lagsestimatedbytheZDCFmethod.ThoseestimatedR (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:13)(cid:6)(cid:5)(cid:7)(cid:5)
radio (cid:9)(cid:18) gggg
in Case B contain these Rradio estimated in Case D. Thus (cid:15)(cid:14)(cid:16)(cid:17) (cid:14)
CaseDisaspecialCaseB,anditispossibleandreasonable.
Combining equations (7) and (8), one can also obtain (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:12)(cid:6)(cid:5)(cid:7)
(cid:8)(cid:2)(cid:9)(cid:10)(cid:11)
c τ c 1 (cid:8) (cid:1)(cid:2)(cid:3)(cid:1)
RBLR =−1h+obziv cosθ. (10) RRRRgggg
d
aFnrodmeqτu−oabti=on−(120.8),6wyeeahrsa,vevdR= 0.9=–00.9.7975–c0,.9θ0=pc1.2T◦–h2e1s◦e (cid:1)(cid:2)(cid:3)(cid:1) (cid:1)(cid:2)(cid:3)(cid:4) (cid:1)(cid:2)(cid:3)(cid:19)(cid:5)(cid:20)(cid:14)(cid:16)(cid:9)(cid:18) (cid:1)(cid:2)(cid:3)(cid:6) (cid:1)(cid:2)(cid:3)(cid:7) (cid:8)(cid:2)(cid:1)(cid:1)
BLR
estimatedvaluescontainthetypicalsizeofRBLR =0.83pc. Figure 5.Dependence ofdistanceRonvd andθ.Fromthetop
down, the first three panels correspond to Cases A, B and C,
This confirms the reliability of the time lags estimated by
theZDCF method. respectively. The x, y and z-axes are vd inunits of c, θ in units
of degree and logR in units of pc, respectively. The first three
panelsrepresentdependenceofRonvd andθ.Thebottompanel
represents dependence of R on vd in case of cosθ =0.95, where
4 DISCUSSION AND CONCLUSIONS thegriddingarearepresentstheallowedintervalofRγ inCaseC.
ThearrowsrepresenttheupperlimitofRγ inCaseB.
The positions of γ-ray–emitting regions are still an open
and controversial issue in the researches on blazars. Based
Locating positions of γ-ray–emitting regions 9
on the method proposed in section 2, we attempt to locate Bai, Liu & Ma2009).Themethodproposedherecanlocate
the emitting positions of γ-rays within the second bumps R in the jet. The inner emitting regions with R .R
γ γ BLR
in the broad-band SEDs of blazars. In our previous works arelikelythemajorcontributoroftheγ-raysbelow10GeV,
(Liu & Bai2006;Liu, Bai & Ma2008;Bai, Liu & Ma2009), forthattheγ-raysabove10GeVaresubjecttothephoton-
theinternalabsorption for 10 GeV–1 TeV γ-rayswere used photon absorption due to the dense external soft photons
to constrain R , independent of how the γ-rays are pro- at the inner regions (e.g. Liu & Bai 2006; Liu, Bai & Ma
γ
duced. Here, we try to locate R , independent of the ener- 2008;Bai, Liu & Ma2009).Theouteremittingregionswith
γ
gies of γ-rays from the SSCand EC processes. Wefind two R R are likely the major contributor of the γ-rays
γ BLR
≫
emittingregions,theinneroneatsub-pc–pcscalesfromthe above 10 GeV, for that these γ-rays are not subject to the
centralblackholeandtheouteronearoundtensofpcscales. photon-photonabsorptionduetothethinexternalsoftpho-
TheouteronesatisfiesR R (CaseC).Theinnerone tons at the outer regions. For these possible γ-ray emitters
γ BLR
≫
in Case D satisfies R . R . The inner one in Case B at large scales of kpc–Mpc (Bai & Lee 2001; Zhang et al.
γ BLR
mostly satisfies R . R . At the same time, the inner 2009, 2010), ourworks are not applicable.
γ BLR
oneinCaseBpartlysatisfiesRγ >RBLR,i.e.RBLR <Rγ . The most prominent features on VLBI images of
2.62 pc. jets in radio-loud AGNs are the radio core and bright
It was suggested R . R (Ghisellini & Madau knots in the jet (Jorstad et al. 2007). Kovalev et al.
γ BLR
1996). Georganopoulos, Kirk & Mastichiadis (2001) argued (2009) investigated the relation between AGN γ-ray
R .R forpowerfulblazars.Tavecchio & Mazin(2009) emission and pc-scale radio jets. They identified the
γ BLR
assumed R < R for the VHE γ-rays in 3C 279. pc-scale radio core as a likely location for both the γ-ray
γ BLR
Liu, Bai & Ma (2008) and Bai, Liu & Ma (2009) suggested and radio flares. A few hundreds of Schwarzschild radii,
thatR iswithintheBLRfor3C279.Ghisellini et al.(2010) sub-pc-scale, is the preferred jet position where most
γ
modelled theSEDsofbrightFermi blazars,andtheyfound of the dissipation occurs (Ghisellini & Tavecchio 2009;
thatthepositionofthejetdissipationregionR issmaller Ghisellini, Tavecchio & Ghirlanda 2009; Ghisellini et al.
diss
thanR for53out of57FSRQs.However,R >R 2010). Sikora et al. (2009) suggested that the blazar
BLR diss BLR
for BL Lacs. They used R = 1017L1/2 cm to estimate emission zone is located at pc-scale distances from the
BLR d,45
R forBLLacsandFSRQs,whereL isaccretiondisc nucleus.Ghisellini & Madau (1996)suggested thatR isat
BLR d,45 γ
luminosity in units of 1045 erg s−1. It is appropriate to use sub-pc scales. Blandford & Levinson (1995) also suggested
R = 1017L1/2 cm to estimate R for FSRQs, but a sub-pcγ-ray–emitting region from the central black hole.
BLR d,45 BLR
not for BL Lacs because this relation is derived from the These previous findings support R at sub-pc–pc scales.
γ
type1 AGNs.Thus it should bereliable that R <R These R of sub-pc–pc scales are consistent with those
diss BLR γ
for blazars. If the jet dissipation region is equivalent to R obtained in Cases B and D. These sub-pc–pc scale
γ
the γ-ray–emitting region, R < R is equivalent to R obtained in Cases B and D are also consistent with
diss BLR radio
R < R . For 3C 273, R < R (Ghisellini et al. the previous findings of the blazar emission zone and the
γ BLR diss BLR
2010). These previous findings are consistent with our re- dissipation zone. These agreements confirm the reliability
sults of R . R obtained in Cases B and D. It was of our results.
γ BLR
also argued Rγ >RBLR (Lindfors, Valtaoja & Tu¨rler 2005; Itisrecentlyadvancedthatthebulkoftheγ-raysisgen-
Sokolov & Marscher 2005). This is marginally consistent erated in regions of the jet at distances of tens of pc from
with RBLR < Rγ . 2.62 pc obtained in Case B. These the central black hole (e.g. Sikora, Moderski & Madejski
agreements confirm the reliability of the method and as- 2008; Marscher et al. 2010). For Case C, we obtain the
sumptions. outer emitting regions of 4.67–30.81 < R . 9.43–62.31
γ
B¨ottcher (2008) suggested for 3C 279 that R pc and R = 9.43–62.31 pc. These outer emitting re-
γ radio
≫
R for VHE γ-rays. It is recently advanced that the gions are comparable to the γ-ray–emitting regions at dis-
BLR
bulk of the γ-rays is produced in regions of the jet at tances of tens of pc. Tavecchio et al. (2010) found evidence
distances of tens of pc from the central black hole (e.g. of variability on timescales of few hours from the 1.5 years
Sikora, Moderski & Madejski 2008; Marscher et al. 2010). Fermi/LATlightcurvesofFSRQs3C454.3 andPKS1510-
Bai & Lee(2001) predictedtheexistenceof largescale syn- 089. They concluded that significant variability on such
chrotron X-ray jets in radio-loud AGNs, especially, the X- short timescales disfavor the scenario in which the bulk
ray jets are bright on 10 kpc scales in most red blazars of the γ-rays is produced at distances of tens of pc (e.g.
and red blazar-like radio galaxies. According to their pre- Sikora, Moderski & Madejski 2008; Marscher et al. 2010).
dictions,thelargescale synchrotronX-rayjetscan produce Thepreviousresearchesshowthattherearetwopossibleγ-
VHE γ-rays by the SSC process. Zhanget al. (2009, 2010) ray–emittingregions,oneinsideoraroundtheBLRandthe
predicted the hot spots in lobes and the knots in jets to other outside the BLR. This paper gives the same results.
bepossibleGeV–TeVemitters.Fermi/LATmayresolvethe However, the method cannot discriminate between positive
large scale γ-ray emitters than the nuclear emitters. These lags and negative lags on observational grounds alone (at
previous findings support R R as we obtain in least not with the current data), and the application dis-
γ BLR
≫
Case C. Also, R R in Case C is not inconsistent cussed in the paper does not distinguish between the two
γ BLR
≫
with R >R of Lindfors, Valtaoja & Tu¨rler (2005) and proposedscenarios.Weexpectthissituationtochangewith
γ BLR
Sokolov & Marscher(2005).Theseconfirmthereliability of future data, perhaps longer line light curves, such as 10–15
our results. years. The longer line light curves could give stronger con-
Ourpreviousworksareapplicabletotheγ-raysemitted straints on the coupling of the radio light curves with the
from theregions in powerful blazars, whereR is not much line ones.
γ
larger than R (Liu & Bai 2006; Liu, Bai & Ma 2008; For a given line, the relevant time lags generally de-
BLR
10 H. T. Liu, J. M. Bai and J. M. Wang
crease as radio frequency increases from 5 to 37 GHz. The (cid:2)(cid:3)(cid:9)
(cid:2)(cid:3)(cid:10)
trend islikely from theradiativecooling of relativistic elec- (cid:2)(cid:3)(cid:5)
trons. Bai & Lee (2003) deduced the synchrotron time lag (cid:2)(cid:3)(cid:2)
(cid:1)(cid:2)(cid:3)(cid:5)
formula (see equation 9 therein). This formula can be ex- (cid:1)(cid:2)(cid:3)(cid:10)
(cid:1)(cid:2)(cid:3)(cid:9)
pressed as in theobserver’s frame
(cid:1)(cid:2)(cid:3)(cid:8)
(cid:20)(cid:21) (cid:1)(cid:7)(cid:3)(cid:2)
τloabg(yrs)=1492.6√√1δ+(1z+B−D3)/2 (cid:16)νH−1/2−νL−1/2(cid:17), (11) (cid:15)(cid:16)t(cid:11)(cid:17)(cid:18)(cid:19)(cid:12)(cid:13)(cid:14)(cid:1)(cid:1)(cid:1)(cid:1)(cid:7)(cid:7)(cid:7)(cid:7)(cid:3)(cid:3)(cid:3)(cid:3)(cid:8)(cid:9)(cid:10)(cid:5) (cid:11)
(cid:1)(cid:5)(cid:3)(cid:2)
where D is the ”Compton dominance” (see e.g. (cid:1)(cid:5)(cid:3)(cid:5)
(cid:1)(cid:5)(cid:3)(cid:10)
Ghisellini et al. 1998), B is the magnetic field strength
(cid:1)(cid:5)(cid:3)(cid:9)
in units of gauss, δ is the Doppler factor, and ν and (cid:1)(cid:5)(cid:3)(cid:8)
H (cid:1)(cid:2)(cid:3)(cid:4)(cid:2) (cid:1)(cid:2)(cid:3)(cid:5)(cid:6) (cid:1)(cid:2)(cid:3)(cid:5)(cid:2) (cid:1)(cid:2)(cid:3)(cid:7)(cid:6) (cid:1)(cid:2)(cid:3)(cid:7)(cid:2) (cid:1)(cid:2)(cid:3)(cid:2)(cid:6)
νL in units of GHz are high and low frequencies in the n (cid:1)(cid:7)(cid:23)(cid:5)(cid:1)n (cid:1)(cid:7)(cid:23)(cid:5)(cid:11)(cid:17)(cid:25)(cid:22)(cid:26)(cid:1)(cid:7)(cid:23)(cid:5)(cid:21)
observer’s frame, respectively. For 3C 273, Ghisellini et al. (cid:22) (cid:24)
(1998) obtained B = 8.9 G and δ = 6.5. Because the
radio light curves used to calculate the ZDCFs span Figure 6.Relation of time lags τloabg =tνH −tνL and frequency
differencesν−1/2−ν−1/2 between37,22,15,8and5GHz.Solid
more than 20 years and the line light curves span about H L
lineistheexpectation fromtheradiativecooling.
7.5 years, it is better to derive D by using the ratio of
synchrotron to γ-ray average luminosity. D is of the order
of magnitudes of 1 (Tu¨rler et al. 1999). We can obtain (cid:6)(cid:3)(cid:10)
τob(yrs)=12(ν−1/2 ν−1/2)ifD=1isadopted.Thetotal
lag H − L (cid:6)(cid:3)(cid:6)
cooling of both synchrotron and γ-ray emission can lead to
τob(yrs) = 6(ν−1/2 ν−1/2). We calculate the ZDCFs and (cid:1)(cid:6)(cid:3)(cid:10)
lag H − L
timelagsbetweenthelightcurvesof5,8,15,22and37GHz. (cid:1)(cid:7)(cid:3)(cid:6)
The high frequency variations lead the low frequency ones. (cid:19)(cid:20)
Tdihffeeremnecaessurνe−d1/t2ime νla−g1s/2τloaabgreanpdrestehneterdeleinvanFtigf.re6q.ueTnhcye (cid:15)(cid:16)(cid:17)(cid:18)(cid:11)(cid:12)(cid:13)(cid:14)(cid:1)(cid:1)(cid:2)(cid:7)(cid:3)(cid:3)(cid:6)(cid:10)
H − L Dt
observational data are well consistent with the prediction (cid:1)(cid:2)(cid:3)(cid:10)
of τob = 6(ν−1/2 ν−1/2) (see Fig. 6). This agreement
lag H − L (cid:1)(cid:9)(cid:3)(cid:6)
confirms the origin of radiative cooling for the time lags
between the radio light curves used here. Pyatuninaet al. (cid:1)(cid:9)(cid:3)(cid:10)
(cid:1)(cid:2)(cid:3)(cid:4) (cid:1)(cid:2)(cid:3)(cid:5) (cid:1)(cid:2)(cid:3)(cid:6) (cid:1)(cid:7)(cid:3)(cid:8) (cid:1)(cid:7)(cid:3)(cid:2) (cid:1)(cid:6)(cid:3)(cid:4) (cid:1)(cid:6)(cid:3)(cid:5) (cid:6)(cid:3)(cid:6) (cid:6)(cid:3)(cid:5)
(2006, 2007) also found frequency-dependent time delays t (cid:24)(cid:25)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19)(cid:20)
(cid:21)(cid:22)(cid:23)
for strong outbursts in several other blazars. In Fig. 7,
we compare the lags τloabg with the differences of ∆τcent Figure 7. ∆τcent vs τloabg. Circles present Hα, squares Hβ and
between τcent listed in Table 1. The line of ∆τcent = τloabg triangles Hγ. Open symbols present the negative lags and fulled
is consistent with the measured data points (see Fig. 7). symbolsthepositivelagsinTable1.Solidlineis∆τcent=τloabg.
This agreement confirms that the trend, i.e. the lags for a
given line generally decrease as radio frequency increases,
most likely results from the radiative cooling of relativistic uumusedbyPaltani & Tu¨rler(2005).Thisapproachseems
electrons. more direct than based on the lags of the broad lines rela-
In addition, there is another possibility that lower fre- tiveto theradio emission. We calculate the ZDCFbetween
quencies probe larger radii in the jet, as synchrotron self- thelightcurvesoftheUVcontinuumandthe37GHzemis-
absorption is important for increasingly high radius with sion. There is only a little bump closer to the zero-lag for
decreasingradiofrequency.Thesynchrotronself-absorption the ZDCF and the little bump has r = 0.32 0.06. In
max
coefficient α is α ν−(n+4)/2N , where N is the elec- the ZDCFs between the Balmer lines and this ra±dio emis-
ν ν e e
∝
tron density and n is the electron distribution index. For a sion, the bumpsused to calculate τ haver = 0.6–0.7
cent max
homogeneous blob with a radius of r, the synchrotron self- that are much higher than r = 0.32 0.06. This indi-
max
absorption optical depth τ is τ = rα rν−(n+4)/2N cates that the correlation of the UV con±tinuum with this
ν ν ν e
∝ ∝
rν−(n+4)/2/r3 = ν−(n+4)/2/r2. Thus the radio frequency ν radio emission is much weaker than the Balmer lines with
can probe the radius r that scales as r ν−(n+4)/4. Hence, this radio emission. For 22, 15, 8 and 5 GHz, there are the
∝
lowerfrequenciesprobelargerradiiinthejetduetothesyn- samecases asin37GHz.TheUVcontinuumisregarded as
chrotron self-absorption. The higherfrequencies will escape the ionizing continuum that drives the broad lines through
earlierfromtheblobandlatertheloweronesastheblobex- the photoionization process. Thus it is expected that the
pands. Thus the lower frequencies lag the higher ones, and correlationoftheUVcontinuumwiththeradiosynchrotron
the relevant time lags τ are related to frequencies. The emission should be more significant than the broad lines
lag
difference in lags listed in Table 1 could originate from the with the radio emission. However, this expectation is con-
synchrotron self-absorption, and it scales with frequencies trary to the measurements in the paper. This disagreement
as τlag ∝rL−rH∝νL−(1+n/4)−νH−(1+n/4). Thedependence indicatesthattheUVcontinuumislikelynottherealioniz-
ofτ onfrequenciesisdifferentfromthatofequation(11). ingcontinuum.Paltani & Tu¨rler(2005)arguedthattheUV
lag
continuumismuchclosertotheionizingcontinuumthanthe
It seems possible to infer R based on thetime lags optical continuum used by Kaspi et al. (2000). That is, the
radio
oftheradiosynchrotronemissionrelativetotheUVcontin- UVcontinuumisstillnottherealionizingcontinuum.Thus