Hints of correlation between broad-line and radio variations for 3C 120
aa r X i v : . [ a s t r o - ph . H E ] N ov Hints of correlation between broad-line and radio variations for3C 120
H. T. Liu , , J. M. Bai , , J. M. Wang , and S. K. Li , [email protected] ABSTRACT
In the paper, we investigate correlation between broad-line and radio variations for broad-lineradio galaxy 3C 120. By the z-transformed discrete correlation function method and the model-independent flux randomization/random subset selection (FR/RSS) Monte Carlo method, wefind that the broad H β line variations lead the 15 GHz variations. The FR/RSS method showsthat the H β line variations lead the radio variations by a factor of τ ob = 0 . ± .
01 yr. Thistime lag can be used to locate the position of emitting region of radio outbursts in jet, on theorder of ∼ Subject headings: galaxies: active – galaxies: individual (3C 120) – galaxies: jets – quasars: emissionlines – radio continuum: galaxies
1. INTRODUCTION
According to the reverberation mapping model(e.g. Blandford & McKee 1982), the broad emis-sion line variations follow the ionizing contin-uum variations through the photoionization pro-cess. The variation correlations between broad-lines and continua were observed with time lagsin type 1 active galactic nuclei (AGNs, seee.g. Kaspi & Netzer 1999; Kaspi et al. 2000;Peterson et al. 2005). The disturbances from thecentral engine in AGNs are transported with ioniz-ing continua to broad-lines. Theoretical researchesshow that the jets can be ejected from inner accre-tion disk in the vicinity of the central black hole(e.g. Penrose 1969; Blandford & Znajek 1977; Yunnan Observatories, Chinese Academy of Sciences,Kunming, Yunnan 650011, China Key Laboratory for the Structure and Evolution of Ce-lestial Objects, Chinese Academy of Sciences, Kunming,Yunnan 650011, China Key Laboratory for Particle Astrophysics, Institute ofHigh Energy Physics, Chinese Academy of Sciences, 19BYuquan Road, Beijing 100049, China Theoretical Physics Center for Science Facilities, Chi-nese Academy of Sciences, Beijing 100049, China
Blandford & Payne 1982; Meier et al. 2001).Rawlings & Saunders (1991) indicated a disk-jet symbiosis with comparable power channelledthrough the disk and the jet. Correlations be-tween radio powers and broad-line luminositiesare found for AGNs and are regarded as evidencefor the disk-jet symbiosis (see e.g. Celotti et al.1997; Cao & Jiang 1999, 2001; Wang et al. 2003;Liu & Bai 2010). These previous results indicatethat the disturbances in the central engine arelikely propagated outwards along the jets. Obser-vations show that dips in the X-ray emission, gen-erated in the central engine, are followed by ejec-tions of bright superluminal radio knots in the jetsof AGNs and microquasars (e.g. Marscher et al.2002; Arshakian et al. 2010). The dips in theX-ray emission are well correlated with the ejec-tions of bright superluminal knots in the radiojets of 3C 120 (Chatterjee et al. 2009) and 3C111 (Chatterjee et al. 2011). The outbursts arephysically linked to the ejections of superlumi-nal knots (e.g. T¨urler et al. 2000). Then theseoutbursts of broad-line and jet emission might re-spond to the stronger disturbances in the centralengine. It is expected that there might be correla-1ions with time lags between variations of broad-line and jet emission. A method was proposed toconnect the time lags, the size of broad-line region(BLR), and the location of jet emission for blazar3C 273 (Liu et al. 2011a, hereafter Paper I).The BLRs are important to gamma-ray emis-sion in blazars. The gamma rays from blazarsare generally believed to be from a relativistic jetwith a small viewing angle (Blandford & Rees1978). The diffuse radiation field of BLR couldhave a strong impact on the expected externalCompton (EC) spectrum of the most powerfulblazars (see e.g. Sikora et al. 1994; Wang 2000;Liu & Bai 2006; Reimer 2007; Liu et al. 2008;Sitarek & Bednarek 2008; Tavecchio & Ghisellini2008; Bai et al. 2009; Tavecchio & Mazin 2009).This strong impact rises from two factors. Oneof them is the seed photons from the BLR inthe inverse Compton scattering, and the seedphotons significantly influence the EC spectrum.The other is photon-photon absorption betweenthe seed photons and the gamma-ray photons ofthe EC spectrum. There is a underlying phys-ical factor that constrains how much the abovetwo factors influence on the gamma-ray spectrum.The underlying factor is the location of gamma-ray–emitting region relative to the BLR. If thegamma-ray–emitting region is inside the BLR, thegamma-ray spectrum will shift to higher energiesand the gamma-ray luminosity will become largerdue to the relativistic effects. At the same time,the photon-photon absorption becomes more sig-nificant as the emitting region goes deeper intothe BLR (see Liu & Bai 2006; Liu et al. 2008;Bai et al. 2009). As the emitting region is out-side the BLR, the gamma-ray spectrum will shiftto lower energies and the gamma-ray luminositywill become lower due to the relativistic effects.At the same time, the photon-photon absorptionbecomes insignificant as the emitting region keepsaway from the BLR. Thus it is valuable to connectthe BLR size with the location of jet emission. Itwill be an important step for this connection toconfirm correlation between variations of broad-lines and radio emission of jet and to estimate therelevant time lags. In the paper, we study thisissue in the broad-line radio galaxy 3C 120.The structure of this paper is as follows. Sec-tion 2 presents method. Section 3 presents appli-cation to 3C 120. Section 3 contains three subsec- tions: subsection 3.1 presents constraint on timelag, subsection 3.2 data of 3C 120, and subsec-tion 3.3 analysis of time lag. Section 4 is fordiscussion and conclusions. In this work, we as-sume the standard ΛCDM cosmology with H =70 km s − Mpc − , Ω M = 0.27, and Ω Λ = 0.73.
2. METHOD
According to equation (7) in Paper I, we havea relation between R BLR , R radio , and τ ob R BLR = R radio (cid:18) cv d − cos θ (cid:19) − c h τ ob i z , (1)where R BLR is the size of the BLR, R radio is theradio-emitting location of the jet, c is the speedof light, v d is the travelling speed of disturbancesdown the jet, equivalent to the bulk velocity ofjet v j , θ is the viewing angle of the jet axis tothe line of sight, and h τ ob i ≡ τ ob is the mea-sured time lag of the radio emission relative tothe broad lines. From the velocity β = v j /c and the viewing angle θ , we have the apparentspeed β a = β sin θ/ (1 − β cos θ ), which gives β = β a / ( β a cos θ + sin θ ). Substituting this expressionof β for the velocity term in equation (1), we have R BLR = R radio sin θβ a − c h τ ob i z . (2)From equation (2), we have an expression to esti-mate h τ ob ih τ ob i = (cid:18) R radio sin θβ a − R BLR (cid:19) zc . (3)
3. APPLICATION TO 3C 120
3C 120, at redshfit z = 0 . M ⊙ (Peterson et al.1998a, 2004). The Very Long Baseline Array (VLBA) imag-ing observations revealed a very complex radiojet in 3C 120, such as superluminal components,stationary components, and trailing componentsin inner jet (G´omez et al. 2001; Jorstad et al.2005; Chatterjee et al. 2009; Le´on-Tavares et al.2010). There are two stationary features in theradio jet, D and S1 (Le´on-Tavares et al. 2010).The feature D is located at the base of the jet,and could be the core of the jet. The feature S1 ismost likely a standing shock formed in the jet. Asthe moving knots pass through the stationary fea-ture S1, these knots will produce outbursts. Theprocess was tested in the optical light curves of3C 120 with peaks corresponding to the movingcomponent passages through S1. It is not possibleto verify whether the radio flux density reacted tothe passage of moving features in the same fashionas the optical continuum. The prominent superlu-minal feature o reaches it maximum flux densityaround 0.5 mas from the radio core (G´omez et al.2001). The stationary feature S1 was identified at ∼ ∼ ∼ θ = 20 . ± . ◦ (Jorstad et al.2005). These global parameters are widely ac-cepted by other researches. The 15 GHz com-ponents may correspond to the strongest eventsin the central engine (Le´on-Tavares et al. 2010).Due to the optical depth, the 15 GHz outburstmay follow the 43 GHz outburst. The emittinglocation of the 15 GHz outburst is estimated asthe sum of the distance of 0.5 pc from the coronato the VLBA core and the de-projected distanceof 0.0–0.7 mas from the VLBA core. Under thestandard ΛCDM cosmology we considered, an an-gular separation of 1 mas in the sky correspondsto a projected linear distance of 0.66 pc. Thede-projected distance of 0.7 mas from the ra-dio core is equal to 0.7 × θ =0.7 × . ◦ =1.32 pc. The distance of 15 GHz out-burst emitting region from the central engine is R radio ∼ β line has a BLR size of R BLR = 43 . +27 . − . light-days, i.e. R BLR =0 . +0 . − . ly (Peterson et al. 1998a). The appar-ent speeds of the moving components with well-determined motions are all within a range of β a =4 . ± . R BLR = 0 .
12 ly, β a = 4 . θ = 20 . ◦ and R radio =1.63–5.93 ly, we derive τ ob >
0. This posi-tive time lag means that the broad-line variationslead the radio variations.
We make use of the 15 GHz light curve with ahigher sampling rate of 59 times per year. Thisradio light curve is published in Richards et al.(2011). For the H β line, Nu˜nez et al (2012)presents a light curve with a very dense sam-pling of 20 times per month, and also Grier et al.(2012) presents a light curve of sampling 20 timesper month in the reverberation mapping observa-tions. These light curves are presented in Figure1, and are used to analyze the cross-correlationbetween them. The z-transformed discrete correlation function(ZDCF; Alexander 1997) is used to analyze timelags characterized by the centroid of the ZDCF.The ZDCF method is straightforward to deter-mine whether there is a time lag between differentlight curves, and firstly it is applied to analyzethe time lags. The centroid time lag τ cent is com-puted by all the points with correlation coefficientsnot less than 0.8 times the maximum of correla-tion coefficients in the ZDCF bumps closer to thezero-lag. The uncertainties of each point in theZDCFs only take into account the uncertaintiesfrom the measurements by Monte Carlo simula-tion, and the uncertainties of time lags are under-estimated (see Liu et al. 2011b, hereafter PaperII). Thus we use the model-independent flux ran-domization/random subset selection (FR/RSS)Monte Carlo method (Peterson et al. 1998b) tore-estimate the time lags and their uncertain-ties in the cross-correlation results. The FR/RSSmethod is based on the discrete correlation func-tion (DCF) method (Edelson & Krolik 1988) forthe sparsely sampled light curves, and on the inter-polated cross-correlation function (ICCF) methodfor the densely sampled light curves.3
008 2009 2010 2011 20121.52.02.53.03.54.04.5 1.52.02.53.03.54.04.5 F l u x ( - e r g c m - s - ) (a)15 GHz F l u x ( Jy ) Date (yr) H b H b +0.32 yr(b) 15 GHz F l u x ( - e r g c m - s - ) F l u x ( Jy ) Date (yr)
Fig. 1.— Light curves of H β and 15 GHz emission.Black open triangles denote the H β light curve ofNu˜nez et al (2012). Black open circles denote theH β light curve of Grier et al. (2012). Black solidcircles denote the 15 GHz light curves in units ofJy. The H β line is in units of 10 − erg cm − s − .Gray solid circles denote the H β light curve movedalong the x - and y -axes. The H β line light curves with a very dense sam-pling are published in 2012 (Grier et al. 2012;Nu˜nez et al 2012). 3C 120 is densely observedfrom 2008.0 to 2012.5 in the 15 GHz radio mon-itoring program with the 40 m telescope at theOwens Valley Radio Observatory (Richards et al.2011). Firstly, it is obvious that the H β line lightcurve in Grier et al. (2012) can be well matchedwith the outburst in the 15 GHz light curve from2011.0 to 2011.3 as the line light curve is movedright by 0.32 yr (see Figure 1b). The ZDCFmethod and the FR/RSS method are performed toinvestigate the correlation between these H β linelight curves and the 15 GHz light curve, and esti-mate the time lags from the correlation. As thesetwo line light curves are combined into one lightcurve, the calculated ZDCF is presented in Figure2a. The horizontal and vertical error bars in Fig-ure 2a represent the 68.3 per cent confidence inter-vals in the time lags and the relevant correlationcoefficients, respectively. There are positive andnegative correlations (see Figure 2a). The posi-tive correlation has a time lag around 0.3 yr. TheH β line variations lead the 15 GHz variations bya factor of ∼ τ cent = 0 . +0 . − . yr. The FR/RSS method gives τ cent = 0 . +0 . − . yr with a mean of peak corre-lation coefficients r = 0 . ± .
07 in Monte Carlosimulations of 10,000 runs (see Figure 2b). Thistime lag is well consistent with that lag derivedfrom the ZDCF method.The 15 GHz light curve shows a simple base-line superimposed with some outbursts and flares(see Figure 3a). This baseline should influence thecross-correlation function between this radio lightcurve and the H β line light curve. Thus we sub-tract this baseline assumed as a simple gaussianprofile from the 15 GHz light curve. It is obviousthat the simple gaussian profile can well accountfor the underlying baseline in the 15 GHz lightcurve (see Figure 3a). The cross-correlation func-tion between the residual radio light curve and theH β line light curve is calculated with the ZDCFmethod and the FR/RSS method. The calculatedZDCF is presented in Figure 3b. The positivecross-correlation around 0.3 yr is re-confirmed,and the significance of cross-correlation is signif-4 t cent =0.305 -0.002+0.011 (yr)(a) C r o ss C o rr e l a t i on C oe ff i c i en t Lag (15GHz-H b ) (yr) (b) t cent =0.336 -0.010+0.012 (yr) F r equen cy t cent (yr) Fig. 2.— (a) ZDCF between the H β and 15 GHzlight curves. (b) Distribution of τ cent obtainedwith the FR/RSS method. The vertical dashedline is the median of distribution, and the dottedlines show the 68.3 per cent confidence interval of τ cent . icantly improved with this residual light curve.The ZDCF method gives τ cent = 0 . +0 . − . yr.The FR/RSS method gives τ cent = 0 . ± . r = 0 . ± .
02 in Monte Carlo simulations of10,000 runs (see Figure 3c). This time lag is inexcellent agreement with that lag derived from theZDCF method. The broad H β line variations leadthe 15 GHz variations. Hereafter, τ cent is equiva-lent to τ ob .
4. DISCUSSION AND CONCLUSIONS
We simplify the ionizing continuum region to bea point. This simplification indicates that the dis-turbances will simultaneously be transported out-wards with the ionizing continuum and the rela-tivistic jet, i.e. it makes equations (1)–(3) to bevalid. This simplification will influence the timelag τ ob . The disturbances in the accretion diskwill take a certain time to travel between their lo-cation of origin and the event horizon of the cen-tral black hole. Then the disturbances will takesome time to pass through the ionizing continuumregion to the event horizon. For 3C 120, the UVionizing continuum region is located at ∼ r g fromthe black hole, where r g = GM BH /c is the gravi-tational radius of the black hole (Chatterjee et al.2009). The black hole mass is on the order of10 M ⊙ (Peterson et al. 1998a, 2004), and the sizeof ∼ r g is on the order of 10 − ly. If the dis-turbances are a thermal fluctuation propagatinginward, it should have an effective speed . . c (Chatterjee et al. 2009), to cause a time delay of & .
001 yr for the distance of ∼ r g . This timedelay should be negligible compared with the timelag τ ob = 0 .
34 yr. In estimation of the magni-tude of τ ob in section 3.1, we use the distance of ∼ τ ob . The coronal radius is ∼ r g (Chatterjee et al. 2009). The jet velocity near thecentral engine will be ∼ ∼ r g will cause a time delay onthe order of 10 − yr. The time delay is negligible.From equation (2), we have an expression toestimate R radio from β a , θ , R BLR and τ ob R radio = β a sin θ (cid:18) R BLR + c h τ ob i z (cid:19) . (4)5 (a) H b +0.32 yr H b +0.32 yr F l u x ( - e r g c m - s - ) F l u x ( Jy ) Date (yr) -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0 t cent =0.328 -0.004+0.014 (yr) (b) C r o ss C o rr e l a t i on C oe ff i c i en t Lag (15GHz-H b ) (yr) t cent =0.34 -0.01+0.01 (yr)(c) F r equen cy t cent (yr) Fig. 3.— (a) Comparison between the 15 GHz andH β light curves. Black right triangles are the 15GHz light curve subtracted by a assumed simplebaseline denoted with the black solid line. Graysymbols are the H β light curve moved along the x -and y -axes. Other symbols are same as in Figure1. (b) ZDCF between the modified 15 GHz lightcurve and the H β light curve in black color. (c)Distribution of τ cent obtained with the FR/RSSmethod. The vertical dashed and dotted lines aresame as in Figure 2b. For β a = 4 . ± . θ = 20 . ± . ◦ , R BLR =0 . +0 . − . ly, and τ ob = 0 . ± .
01 yr, we have R radio = 5 . ± .
16 ly from Monte Carlo sim-ulations based on equation (4). Thus we have R BLR ≪ R radio for 3C 120. Fermi -Large AreaTelescope (LAT) detected gamma rays from 3C120 (Kataoka et al. 2011), and it was suggestedthat the GeV emission of broad-line radio galax-ies is most likely dominated by the beamed ra-diation of relativistic jets observed at intermedi-ate viewing angles. The radio and gamma-rayemitting regions are closely connected with eachother, and there is R γ . R radio between the radio-emitting position R radio and the gamma-ray–emitting location R γ (e.g., Dermer & Schlickeiser1994; Jorstad et al. 2001; Kovalev et al. 2009;Sikora et al. 2009; Abdo et al. 2010). It is un-clear for 3C 120 that R γ . R BLR or R γ > R BLR ,which will significantly influence the gamma-rayspectrum produced in the EC processes. Thelocations of gamma-ray–emitting regions rela-tive to the BLRs are still an open and con-troversial issue in the researches on blazars.There are three options for the issue. The firstoption is that R γ . R BLR for the powerfulblazars (e.g. Ghisellini & Madau 1996; Liu et al.2008; Bai et al. 2009; Tavecchio & Mazin 2009;Ghisellini et al. 2010). The second one is that R γ > R BLR (e.g. Bai & Lee 2001; Lindfors et al.2005; Sokolov & Marscher 2005; Sikora et al.2008; Marscher et al. 2010; Zhang et al. 2009,2010). The third option is that the same sourcecan display both behaviors. That is, most of thetime the dissipation region is inside the BLR, butthere could be some epochs when the gamma-ray–emitting region drift outside the BLR. The veryfirst idea was advanced in Foschini et al. (2011),and a very clear case with multi-wavelength cover-age was recently found by Ghisellini et al. (2013).The gamma-ray light curves and the correspond-ing broad-line light curves should shed light onthis issue.The chosen parameters are average for thejet, and do not correspond to any of the com-ponents identified in Jorstad et al. (2005) andChatterjee et al. (2009). The jet components willhave different orientations and different velocities.This seems to be an issue for the choice of jetparameters in equations (1)–(4). The reverbera-tion mapping model assumes the linear response6f broad emission lines to ionizing continuum. Infact, the line response is not linear. It is mostlikely that the line and radio emission respondnonlinearly to the events in the central engine.Thus some weaker events in the central enginemight not produce the correlative responses in theradio and broad-line variations. Both radio andbroad-line emission may have good responses tothe strongest events in the central engine, andtheir relevant outbursts should have good match-ing. There is a matching between these outburstsin the H β line and 15 GHz light curves sampleddensely. However, the overall complexity of thelight curves and the jet structure at radio bandsmay lead to difficulties of cross-identifying individ-ual events in different bands. Thus it is difficultto identify the radio knots and radio outburstscorresponding to the broad-line outbursts. Weinvestigated the correlation and time lag betweenthe radio and broad-line light curves by comparingtheir profiles and cross-correlating them.The 15 GHz light curve is observed with the40 m telescope at the Owens Valley Radio Obser-vatory. The 40 m telescope can not resolve theinner jet on the pc scales. Then the 15 GHz fluxescontain all the emission from the inner jet. It isdifficult to identify the component responsible forthe 15 GHz outburst. It is not possible to de-termine the relevant velocities of this componentalong the jet from the central engine to the emit-ting site of outburst. Thus the average velocity ofprimary components rather than trailing featureswill be a good proxy of the global velocity of com-ponent emitting outburst. The viewing angle isthe same case as the velocity. The similar choiceis accepted for the jet parameters for 3C 273 (seePaper I). There are positive and negative time lagsbetween radio variations and those of broad-linesH α , H β , and H γ due to the relative short cover-age of these line light curves in 3C 273. The longerultraviolet line light curves show that these broad-line variations lag the radio variations (see PaperII). Thus the broad-line variations lag the radiovariations. A constraint of R γ . Fermi -LAT set alimit of R γ < R γ . β line variations. We derive τ ob =0 . ± .
01 yr from the FR/RSS method. Thistime lag is consistent with that estimated fromthe ZDCF method. Monte Carlo simulations givethe radio-emitting location R radio = 5 . ± . R γ . R γ < F ermi -LAT observations of gamma-rayflares in 3C 273. The underlying baseline of 15GHz light curve significantly influences the corre-lation between broad H β line and 15 GHz varia-tions. The subtraction of this baseline from the 15GHz light curve can well improve the correlation.The longer H β line light curve well sampled maytest the correlation. The existence of this corre-lation is a key to connect the BLR size with theemitting location of jet, and it is important to thegamma-ray emission of AGNs.We are grateful to Dr. L. Foschini for construc-tive comments and suggestions. HTL thanks theNational Natural Science Foundation of China(NSFC; Grant 11273052) for financial support.JMB acknowledges the support of the NSFC(Grant 11133006). HTL thanks the financial sup-port of the Youth Innovation Promotion Associ-ation, CAS and the project of the Training Pro-gramme for the Talents of West Light Foundation,CAS. REFERENCES
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