3C390.3: More Stable Evidence for Origination of Double-Peaked Broad Balmer Lines from Accretion Disk Near Central Black Hole
aa r X i v : . [ a s t r o - ph . H E ] J u l Mon. Not. R. Astron. Soc. , 1– ?? (2010) Printed 15 November 2018 (MN LaTEX style file v2.2) Xue-Guang Zhang , ⋆ Purple Mountain Observatory, Chinese Academy of Sciences, 2 Beijing XiLu, Nanjing, Jiangsu, 210008, P. R. China Department of Physics and Astronomy, Texas A&M University, College Station, Texas, 77843-4242, U.S.A.
ABSTRACT
In this manuscript, the structure of broad emission line regions (BLRs) of well-mappingdouble-peaked emitter (AGN with broad double-peaked low-ionization emission lines)3C390.3 is studied. Besides the best fitted results for double-peaked broad opticalbalmer lines of 3C390.3 by theoretical disk model, we try to find another way tofurther confirm the origination of double-peaked line from accretion disk. Based onthe long-period observed spectra in optical band around 1995 collected from AGNWATCH project, the theoretical disk parameters of disk-like BLRs supposed by ellip-tical accretion disk model (Eracleous et al. 1995) have been well determined. Throughthe theoretical disk-like BLRs, characters of observed light-curves of broad double-peaked H α of 3C390.3 can be well reproduced based on the reverberation mappingtechnique. Thus the accretion disk model is preferred as one better model for BLRs of3C390.3. Furthermore, we can find that different disk parameters should lead to somedifferent results about size of BLRs of 3C390.3 from the one measured through ob-servational data, which indicates the measured disk parameters are significantly validfor 3C390.3. After that, the precession of theoretical elliptical disk-like BLRs beingconsidered, we can find that the expected line profile in 2000 by theoretical model isconsistent with the observed line profile by HST around 2000. Based on the results,we can further believe that the origination of broad double-peaked balmer emissionlines of 3C390.3 are from accretion disk around central black hole. Key words:
Galaxies:Active – Galaxies:nuclei – Galaxies:Seyfert – quasars:Emissionlines – Galaxies:individual: 3C390.3
The properties of objects with broad double-peaked low-ionization emission lines (hereafter, double-peaked emitters)have been studied for more than two decades, since thedouble-peaked emitters were found in nearby radio galaxies(Stauffer et al. 1983, Oke 1987, Perez et al. 1988, Halpern1990, Chen et al. 1989, Chen & Halpern 1989). Some the-oretical models have been proposed to explain the prop-erties of double-peaked broad emission lines which can beused as one probe of the broad-line regions of active galac-tic nuclei (Eracleous et al. 2009), such as binary black holemodel (Begelman et al. 1980, Gaskell 1983, 1996, Boroson& Lauer 2009, Lauer & Boroson 2009, Zhang et al. 2007),double stream model (Zheng et al. 1990, 1991, Vellieux &Zheng 1991), accretion disk model (Chen et al. 1989, Chen& Halpern 1989, Eracleous et al. 1995, 1997, Bachev 1999, ⋆ [email protected] Hartnoll & Blackman 2000, 2002, Karas et al. 2001, Gezariet al. 2007, Flohic & Eracleous 2008, Lewis et al. 2010, Tran2010, Chornock et al. 2010, Gaskell 2010) etc.. Althoughwhich theoretical model is more preferred for double-peakedemitters is still an open question, the accretion disk modelwhich indicates double-peaked broad emission lines are fromcentral accretion disk is so far the more widely acceptedmodel applied to explain the properties of double-peakedbroad emission lines.Due to the un-obscured emitting region on the recedingjet, the double-stream model can be ruled out for double-peaked emitter 3C390.3 (Livio & Xu 1997). Through thelong-period observational results, binary black hole modelhas also been ruled out due to unreasonable large cen-tral BH masses for some double-peaked emitters, such asArp102B, 3C390.3 (Eracleous et al. 1997). Furthermore,based on the long-period variations of double-peaked broademission lines, accretion disk model is successfully appliedto reproduce the characters of varying observed line profiles c (cid:13) Zhang X.-G. of double-peaked emitters, such as the individual double-peaked emitter NGC1097 (Storchi-Bergmann et al. 1995,1997, 2003), and one sample of double-peaked emitters(Lewis et al. 2010, Gezari et al. 2007). However, we shouldnote that although accretion disk model is so far the widelyaccepted theoretical model for double-peaked emitters, theother theoretical models can be expected to be preferred forsome special double-peaked emitters, such as the x-shapedradio objects which could be candidates for objects with bi-nary black holes in central regions (Merritt & Ekers 2002,Zhang et al. 2007). Thus, only based on the double-peakedappearance of broad emission lines, there is no confirmedway to affirm which theoretical model is more preferred fordouble-peaked emitter.Among the sample of double-peaked emitters (Era-cleous & Halpern 1994, 2003, Eracleous et al. 1995, Strat-eva et al. 2003), 3C390.3 is one well studied double-peakedemitter, also one well-studied mapping AGN (Dietrich et al.1998, O’Brien et al. 1998, Leighly et al. 1997, Shapovalovaet al. 2001, 2010, Sergeev et al. 2002, Peterson et al. 2004,Pronik & Sergeev 2007, Sambruna et al. 2009, Jovanovicet al. 2010). Based on the reverberation mapping technique(Blandford & Mckee 1982) and virialization method (Peter-son et al. 2004, Collin et al. 2006, Peterson & Bentz 2006,Peterson 2010), size of BLRs (distance between central blackhole and broad line emission gas clouds) and central virialBH masses of 3C390.3 have been well determined (Petersonet al. 2004, Onken et al. 2004, Kaspi et al. 2005, Bentz et al.2006, 2009, Brandon & Bechtold 2007). Besides the commonBH masses and size of BLRs, through the theoretical accre-tion disk model applied for observed double-peaked broademission lines, some basic disk parameters of supposed the-oretical disk-like BLRs of 3C390.3 have also been measured(Eracleous & Halpern 1994), such as the inclination angle ofaccretion disk, the inner and outer radius of BLRs in accre-tion disk etc.. However, only due to the best fitted results fordouble-peaked balmer lines by accretion disk model, we cannot firmly confirm that the double-peaked broad emissionlines are exactly coming from disk-like BLRs in accretiondisk around central black hole for 3C390.3.Besides the best fitted results for double-peaked broademission lines by theoretical models, based on the pioneerwork by Blandford & Mckee (1982), geometrical structuresof BLRs can be mathematically structured by so-calledtransfer function in the reverberation mapping techniquethrough some special mathematical methods (such as theMaximum Entropy Method, Narayan & Nityananda, 1986)applied to the properties of long-period observational vary-ing both continuum emission and broad line emission (Pe-terson et al. 1993, 1994, Horne et al. 1991, Goad et al. 1993,Wanders & Horne 1994, Pijpers & Wanders 1994, Krolik1994, Winge et al. 1995, Bentz et al. 2010). However, it isunfortunate that there should be NOT unique solution tothe so-called transfer function used to determine the struc-tures of BLRs of AGN, due to the less complete informa-tion about variations of continuum and broad emission lines(Maoz 1996). Thus, even based on the solution of transferfunction, the supposed theoretical and mathematical geo-metrical structures of BLRs of AGN can NOT still be firmlyconfirmed.In the previous remarkable work about structures ofBLRs of AGN, the main objective is to determine the struc- tures of BLRs through observational properties/characters.However, we think it will be also very interesting to checkwhether the observational properties of long-period vari-ations of broad line emission and/or continuum emissioncould be better reproduced through the reverberation map-ping technique, based on the expected structures of BLRssupposed by theoretical model, which is the main objectiveof our paper.The structures of our paper are as follows. Section 2gives some information about observed spectra of 3C390.3around 1995 and how to find theoretical disk parameters forthe supposed disk-like BLRs through the best fitted resultsfor broad double-peaked balmer lines by theoretical ellipti-cal accretion disk model (Eracleous et al. 1995). Section 3shows the results through the reverberation mapping tech-nique under the disk-like BLRs for 3C390.3. Finally section4 gives some detailed discussions and conclusion. The cos-mological parameters H = 70km · s − Mpc − , Ω Λ = 0 . m = 0 . α rather than double-peaked broad H β , because of the more apparent doublepeaks of broad H α (one peak of double-peaked broad H β is mixed by [OIII] λ , A doublet) and more strongerbroad H α than broad H β . Thus we mainly focus on the66 out of the 133 observed spectra with reliable broad H α within rest wavelength from 6200˚ A to 7300˚ A .There are so far several kinds of accretion disk mod-els which can be applied for double-peaked emitters, cir-cular with/without spiral arms accretion disk model(Chenet al. 1989, Chen & Halpern 1989, Hartnoll & Blackman2002), elliptical accretion disk model (Eracleous et al. 1995),warped accretion disk model (Hartnoll & Blackman 2000),stochastically perturbed accretion disk model (Flohic & Er-acleous 2008) etc.. In this paper, the elliptical accretiondisk model (Eracleous et al. 1995) is preferred, because themodel can explain most of the observational spectral fea-tures of broad double-peaked emission lines (especially fea- c (cid:13) , 1– ?? C390.3: disk-like BLRs near central BH tures for extended asymmetric line wings) with less num-ber of necessary model parameters. Furthermore, the mostpart of flux density of broad double-peaked line emissionis from disk-like BLRs into accretion disk, the existence ofarms (Hartnoll & Blackman 2002) and/or warped structures(Hartnoll & Blackman 2000) and/or bright spots (Flohic &Eracleous 2008) are mainly applied for subtle structures ofdouble-peaked line profiles (such as some cusps around thepeaks etc.), which have few effects on the results based onCross Correlation Function in reverberation mapping tech-nique. The detailed description of the elliptical accretiondisk model with seven model parameters can be found inEracleous et al. (1995). The seven necessary parameters areinner radius r , out radius r , eccentricity of elliptical rings e , local broadening velocity σ , inclination angle of disk-like BLRs i , line emissivity slope ( f r ∝ r − q ) and orienta-tion angle of elliptical rings φ . Through the Levenberg-Marquardt least-squares minimization method applied tofit the double-peaked broad H α by elliptical accretion diskmodel as what we have done for the x-shaped radio sourceSDSS J1130+0058 (Zhang et al. 2007), the seven disk pa-rameters in elliptical accretion disk model can be well de-termined. The procedures to determine the disk parametersfor BLRs of 3C390.3 are as follows.First and foremost, in order to check the results fromreverberation mapping technique under the structures ofBLRs supposed by the accretion disk model, we shouldmeasure reliable theoretical disk parameters for disk-likeBLRs of 3C390.3. Before starting to fit the observed broaddouble-peaked H α , we first check the spectra of 3C390.3by eye, and find that the spectra marked with ’ce’ (cor-responding observatory can be found in Table 1 in Di-etrich et al. 1998) have some unexpected absorption fea-tures around 6500˚ A in rest wavelength. The weird absorp-tion features can not be found in the other spectra ob-served by instruments in other observatories, which shouldbring some larger uncertainties in measured disk param-eters when broad H α is fitted by accretion disk model.Thus the absorption features (rest wavelength from 6507˚ A to 6525˚ A ) in the 24 spectra marked with ’ce’ should be re-jected, when the broad H α are fitted by the elliptical accre-tion disk model for 3C390.3. Besides the weird absorptionfeatures in the 24 spectra marked with ’ce’, in order to re-duce the effects of narrow emission lines ([OI] λ , A ,[NII] λ , A , [SII] λ , A and narrow H α ) in allthe spectra, the parts of narrow emission lines are alsomasked when broad H α are fitted, rest wavelength from6268˚ A to 6326˚ A for [OI] λ A , rest wavelength from 6350˚ A to 6388˚ A for [OI] λ A , rest wavelength from 6533˚ A to6619˚ A for [NII] λ , A and narrow H α , rest wave-length from 6703˚ A to 6743˚ A for [SII] λ , A (the greyshadows shown in Figure 1, Figure 2 and Figure 5). In otherwords, only the double-peaked broad component of H α with-out weird absorption features and without narrow emissionlines are fitted. After the prepared work, the double-peakedbroad H α are fitted two times as follows.Firstly, the 39 spectra with high quality (more than280 reliable data points within rest wavelength range from6160˚ A to 6920˚ A ) and without unexpected absorption fea-tures around 6500˚ A are fitted by the elliptical accretion diskmodel. Then through the measured disk parameters, the twoparameters of eccentricity and inclination angle are firstly determined for the 39 spectra, because eccentricity and in-clination angle should not be changed with passage of time.The mean values of the two parameters for the 39 spectraare accepted as the reliable values for the two parameter.Then all the 66 spectra are fitted again by the accretiondisk model with the accepted constant inclination angle andeccentricity. Figure 1 shows the best fitted results for someselected broad H α by elliptical accretion disk model withMJD from 49770 to 50051. In the figure, two spectra withunexpected absorption features (marked with ’49860ce’ and’49984ce’) are also shown, the shadow areas represent themasked ranges for narrow emission lines. Figure 2 shows thecorresponding residuals ( y obs − y model , observed data minusexpected model data) for the shown examples in Figure 1. Inthe figure, shadow areas represent the narrow emission lines,each double horizontal dashed lines represent the range of[ f − f + 1], where f = 0 , , ...
80 representing the zeropoint for each spectrum are shown as solid horizontal linein the figure. The results shown in Figure 2 and in Figure 1indicate that the elliptical disk model is better for double-peaked broad emission lines of 3C390.3, and further indicatethat the probable existing hot spots and/or warped struc-tures have few effects on the measured flux density of broadH α and few effects on our final results and conclusion, i.e.,the hot spots and/or ward structures are weak for observedspectra of 3C390.3 around 1995, and elliptical accretion diskmodel is efficient and sufficient for 3C390.3 around 1995.Figure 3 shows the distributions of the seven disk pa-rameters, and the distributions of the parameter of log( χ )(the value of the summed squared residuals divided by thedegree of freedom for the returned model parameter val-ues, which is one parameter as the residual to determinewhether the theoretical model is preferred) for the 39 highquality spectra in upper three panels and for all the 66spectra in the other six panels. The final accepted disk pa-rameters are: inner radius r = 216 ± R G , outer radius r = 1263 ± R G , eccentricity e = 0 . ± .
04, inclinationangle i = 29 . ± . ◦ , orientation angle φ = − ± ◦ ,emissivity power slope q = 1 . ± .
26 ( f ( r ) ∝ r − q ) and localbroadening velocity σ = 742 ± / s. Actually, we shouldnote that some of the theoretical disk parameters, r , r , q , φ , σ , should depend on the strength of continuum emis-sion, in other words, the parameters are time dependent.However, there need to be long-term progressive changes inthe ionizing flux to change these variables. Moreover, fromthe results shown in Figure 3, we can find that there aretiny variations for these parameters, which indicates thatthe mean values for the theoretical disk parameters can beused to trace the actual physical disk parameters for 3C390.3around 1995.Before proceeding further, we compare our measureddisk parameters with the previous results reported in theliterature. In the sample of double-peaked emitters from ra-dio galaxies, Eracleous & Halpern (1994) gave the resultsabout disk parameters for BLRs through circular accre-tion disk model (Chen et al. 1989) for double-peaked broadH α observed in 1988 for 3C390.3 ( simple results can alsobe found in Figure 6 and in Section 4.5 in Sambruna etal. 2009), which are some different from our results deter-mined through elliptical accretion disk model (Eracleous etal. 1995). We know that in accretion disk model, full widthat zero intensity (FWZI) of double-peaked broad emission c (cid:13) , 1– ?? Zhang X.-G. lines sensitively depends on inner radius of disk-like BLRs,smaller inner radius leads to broader FWZI. From the fittedresults shown in Figure 4 in Eracluous & Halpern (1994), wecan find that in order to better fit the broad wings of broadH α , the inner radius should be some smaller than 380 R G (the one listed in Eracluous & Halpern 1994). Thus our innerradius r = 216 R G should be reasonable. Peak separationsensitively depends on the outer radius, thus there are simi-lar results about outer radius in Eracluous & Halpern (1994)and in our paper. In order to better fit the cusp featurearound blue peak, the elliptical disk model should be moreefficient than the totally symmetric circular disk model, i.e.,the parameters of eccentricity and orientation angle shouldbe active. The separation between peak intensity and zerointensity of blue (or red) part of H α should depends on theemissivity power slope. The larger distance between our in-ner radius and outer radius indicates that our emissivityslope should be smaller than 3 (the one listed in Eracluous& Halpern 1994). Thus our emissivity slope q = 1 .
65 shouldbe reasonable. Line width of double-peaked broad line sensi-tively depends on inclination angle, thus it is clear there aresimilar value about inclination angle i ∼ ◦ in our paperand in Eracluous & Halpern (1994). Because the ellipticalaccretion disk model is more efficient for 3C390.3 than thecircular accretion disk model, the effects from local broad-ening velocity should be lower. Thus our local broadeningvelocity σ ∼ / s smaller than 1900km / s in Eracluous& Halpern (1994) should be reasonable.Besides the disk parameters, it is interesting to checkthe variations of line profiles of double-peaked broad H α . Asshown in Veilleux & Zheng (1991), there are significant vari-ations of relative flux ratio of the two peaks within the pe-riod from 1974 to 1988. Certainly, the variations can not besuccessfully explained by the elliptical accretion disk model,because the disk precession period of 3C390.3 based on theelliptical accretion disk model is about several hundreds ofyears as we should discuss in the following. However, duringthe period (about 500days) around 1995 included in AGNWATCH project, the variations of flux ratio of the two peaksare tiny as shown in Figure 4. In the figure, two kinds of fluxratios are shown, the one with mean value of 1 . ± .
02 (0.02is standard deviation for the mean value) is the ratio of theblue part to red part of broad H α divided by 6564.61˚ A (thetheoretical center wavelength of H α ), the other one withmean value of 1 . ± .
06 (0.06 is standard deviation) isthe intensity ratio of the blue peak to red peak. Similar re-sults for 3390.3 around 1995 can also be found in Dietrichet al. (1998). The more recent results about the flux ratio ofthe two peaks of 3C390.3 from 1995 to 2007 can be found inShapovalova et al. (2010), there are tiny variations of the fluxratio of the two peaks in the 5years period as shown in Figure13 in Shapovalova et al. (2010). Due to the tiny variations,we believe that there are tiny variations for disk parametersobtained from the observed spectra during 1995, and that isthe reason why we select the spectra observed around 1995.In other words, the structures of BLRs of 3C390.3 are stablearound 1995, which re-confirm that there are tiny variationsof disk parameters shown in Figure 3.Last but not least, we should note the collected 66spectra in optical band for 3C390.3 are the observed spec-tra before the intercaliberation method (Van Groningen &Wanders 1992) applied to consider the effects from differ- ent observational instruments in different configurations asdiscussed in Dietrich et al. (1998). In this paper, we mainlyfocus on the disk parameters, rather than the flux densitiesof broad H α which should be directly collected from AGNWATCH project with contamination being corrected. Themain effect from intercaliberation method on the correctedline profile is the broadening velocity in the method. How-ever, the broadening velocity is only about tens of kilometersper second when intercaliberation method is applied, whichis much smaller than line width of broad H α . Thus, the ef-fects from intercaliberation method on the measured diskparameters through elliptical accretion disk model can betotally ignored.Before to finish the section, we consider the followingquestion whether there are other values for disk parametersin the disk model applied to well fit observed double-peakedbroad H α . In other words, the question is whether the solu-tions to the disk parameters are unique. If the answer is yes,there should be one set of values for the disk parameters inthe following mathematical procedure, and we will try to de-termine whether our mathematical procedure can be appliedto determine the available parameter space. If the answer isno, the following mathematical procedure should be simpleand succinct. To give one precise mathematical solution tothe question is very difficult. We consider the question asfollows. The observed double-peaked broad H α is re-fitted.When procedure starts to fit line profile, one of the diskparameters is fixed to one value much different from the ac-cepted value above (half of the accepted value for the param-eter), and the other disk parameters with the same startingvalues in fitting procedure are free. Then the Levenberg-Marquardt least-squares minimization technique is appliedto find the best fitted results for observed double-peakedbroad H α ∼ craigm/idl/)is used to perform the least-squares fitting and to find thebest solution. In order to clearly compare the fitted resultsfor different disk parameters, the value flux fit − fit is cal-culated, where fit fit flux fit − fit .The apparent and large difference (residual to some extent)between fit fit c (cid:13) , 1– ?? C390.3: disk-like BLRs near central BH In the section above, one kind geometric structure of BLRsof 3C390.3 have been supposed by the theoretical ellipticalaccretion disk model (Eracleous et al. 1995). In this section,we will mainly check whether the supposed disk-like BLRsare valid to reproduce properties of observed continuum andbroad line variability, through reverberation mapping tech-nique.In order to clearly build one physical geometrical struc-ture of disk-like BLRs, the length of one gravitational ra-dius ( R G ) in physical unit should be firstly determined,i.e., it is necessary to determine the masses of central blackhole of 3C390.3. Here the BH masses of 3C390.3, M BH =4 . × M ⊙ , is accepted. For 3C390.3, the two kinds of BHmasses, both virial BH masses (Peterson et al. 2004) andBH masses from M-sigma relation (Tremaine et al. 2002,Ferrarese & Merritt 2001, Gebhardt et al., 2000, G¨ultekinet al. 2009, Woo et al. 2010, Lewis & Eracleous 2006) can befound in literature, which are similar. Thus we do not worryabout the accuracy of BH masses of 3C390.3, and accept R G ∼ . − days based on the BH masses. Throughthe disk parameters above, it is not difficult to build thephysical geometry of the BLRs of 3C390.3 supposed by the-oretical model. Then it is interesting to check the resultsbased on the reverberation mapping technique through thesupposed disk-like BLRs as follows.First and Foremost, we accept the assumptions listedin Peterson (1993) for reverberation mapping technique, 1):the continuum emission is from one central source whichis much smaller than BLRs. The assumption is efficient for3C390.3, although double-peaked broad line of 3C390.3 isassumed from accretion disk. The reported size of BLRsof 3C390.3, the time lag between observed optical balmeremission and observed UV X-ray emission, is about 20 ± R BLRs ∼ − G , through cross correlation func-tion method. Based on the theoretical disk parameters for3C390.3, the flux weighted mean size of BLRs is about567R G (simply calculated by ( r + r ) / (1 . + q ), q ∼ . α . 3): the line emis-sions are in rapid response to ionizing continuum, whichcan be confirmed by the strong correlation between line lu-minosity and continuum luminosity found by Greene & Ho(2005) and by the much shorter recombination time (aboutone hundred seconds for standard BLRs) of balmer emissionlines and much longer dynamic time (about several years forstandard BLRs) than the light travel time across BLRs, asdiscussed in Peterson (1993).Besides, we structure the supposed theoretical struc-tures of BLRs of 3C390.3 as follows. More than 10 tinyclouds (or so-called test particles, if we treat each tiny cloudwith sufficient tiny size) are set in the N elliptical rings (theBLRs), each tiny cloud has its position (radius r and orien- tation angle φ ) and line intensity ( f ). The position in oneelliptical ring for one tiny cloudy is created by, φ ∈ [0 , × π ] r = r ⋆ × (1 + e )1 − e × cos( φ ) (1)where r r ⋆ r and e are the pericenter distance andeccentricity of the disk-like BLRs of 3C390.3, r is the dis-tance from the tiny cloud to the central black hole. Frominner boundary r to outer boundary r , the pericenterdistance for the elliptical rings is evenly separated into Nbins, log( r ) log( r ⋆,i ( i = 1 . . . N )) log( r ) with stepof (log( r ) − log( r )) / ( N − r )) is evenly sep-arated, rather than the parameter of pericenter distance( r ), which provides more areas in inner part of BLRs. Afterthat, the orientation angle φ is evenly separated into M bins,0 φ j ( j = 1 . . . M ) × π with step of 2 × π/ ( M − r ⋆,i and φ j , the supposed theoretical disk-likeBLRs can be separated into ( N − × ( M −
1) tiny ar-eas ( A i,j ( i = 1 . . . N, j = 1 . . . M )). As long as N is largerenough, the ionizing photo propagating time through eachtiny area can be ignored, and each tiny cloud can be sim-ply treated as one point source. The line intensity from eacharea f i,j ( i = 1 . . . N, j = 1 . . . M ) can be directly calculatedby elliptical accretion disk model, and the total line intensity F is the sum of f i,j , f i,j = r ⋆,i +1 Z r ⋆,i φ j +1 Z φ j H ( model ) drdφ ∝ P ( r i , φ j ) X j f i,j = F i ∝ r q ⋆ ⋆,i X i X j f i,j = F (2)where H ( model ) is the integrand function used for accretiondisk model as shown in Eracleous et al. (1995), q ⋆ is differentfrom the emissivity slope in elliptical accretion disk model(however if the radius of each bin is uniformly created, then q ⋆ ∼ . − q as shown in Figure 6), P ( r i , φ j ) is the func-tion depending on radius and orientation angle to calculatethe line intensity of each tiny cloud in the ith elliptical ringwhich can also be found in Figure 6, F i and F mean the lineintensity from the ith elliptical ring and the total line inten-sity from total area. Here, we select N = 60 and M = 400. N = 60 confirms that the light travel time from the i bin to i +1 bin is much less than 1 day (especially for the bins in in-ner part of BLRs), the standard date separation of our inputlight curve of continuum emission. Furthermore, we shouldnote that in our procedure, the listed disk parameters aboveare taken as fixed values, based on the following consider-ations. On the one hand, there are tiny variations of lineprofiles of double-peaked H α observed around 1995. Basedon the observed H α selected rom AGNWATCH, it is verydifficult to find one reliable correlation between line profilevariability and disk parameters (especially orientation angle φ ) through theoretical disk model. In other words, there isno information about the function of φ ( t ) where t is date andtime. On the other hand, the fixed disk parameters through c (cid:13) , 1– ?? Zhang X.-G. tiny varied line profiles around 1995 lead to much simplemathematical procedure.Figure 6 shows the procedures above to build the struc-tures of BLRs of 3C390.3 based on the disk parameters, in-cluding the properties of equation (2). Once the tiny cloudmeet the ionizing photo from central source, the line inten-sity of the tiny cloud is changed immediately as, f i,j ( t ) ∝ f i,j ( t − × ( con i,j ( t ) con i,j ( t −
1) ) α (3)where t is the date with uniform separation of 1 day as dis-cussed below, α is slope of the the corresponding correlationbetween luminosity of H α and continuum luminosity, f i,j and con i,j mean the line intensity from area A ( i, j ) and ar-riving continuum emission for area A ( i, j ). For AGN, α isthe about 1 for QSOs in Greene & Ho (2005), and for lowluminosity AGN in Zhang et al. (2008). However, α ∼ A and luminosity ofbroad H α for the spectra observed around 1995. The val-ues of luminosity of broad H α and continuum luminosityat 5177˚ A are collected from AGN WATCH, the contami-nation has been corrected. The spearman rank correlationcoefficient is about 0.66 with P null ∼ − . Through theLevenberg-Marquardt least-squares minimization technique,the best weighted fitted result for the correlation can be cal-culated, L Hα = 8 . × ( L con (5177 ˚ A ) erg / s ) . ± . erg / s (4)Thus, we accept α ∼ .
26, not ∼
1. Actually, the differentindex of line-continuum luminosity correlation is due to thecontamination of narrow lines around H α . As shown in Di-etrich et al. (1998), the flux density of broad H α includescontributions from narrow lines around H α , and flux den-sities of narrow emission lines are constant for 3C390.3. Ifwe define factor k as flux ratio of pure broad H α to narrowlines, we should find that points with lower luminosity ofH α in Figure 7 have smaller values of k , points with largerluminosity of H α in Figure 7 have larger values of k . If thecontributions of narrow emission lines are corrected, the in-dex for the correlation shown in Figure 7 should be steeperthan 0.26 and near to 1.Figure 8 shows one simple output line curve of broad H α based on one test input light curve of continuum emissiondescribed by one delta function through the disk-like BLRsdetermined elliptical accretion disk model for 3C390.3. Be-cause of the extended BLRs, the delta function is delayedand expanded. Light traveling from the central black hole(we assume that the ionizing photos are from central point)to the innerest boundary of the BLRs is about 5days, fromthe inner boundary ( ∼ R G ) to the point with longestdistance ( ∼ R G , larger than the pericenter distance1263 R G for the out boundary, because the BLRs are ellipti-cal disk-like) from central black hole is about 39 days. Thusin the figure, it is clear that 5 days after the burst of contin-uum, the line intensity starts to vary, and then 39 days afterthe burst of continuum emission, the variation of line inten-sity ends. Because the inner part of BLRs emits most of theline intensity of broad H α , thus the line intensity of totalH α is changed from strong to weak with passage of time asshown in the figure. Furthermore, it should be interesting to check the effects of different geometrical structure on theresponse output broad H α , although we have accepted thereare fixed and stable disk parameters in section above. Weaccepted the disk parameters for 3C390.3 under the stochas-tically perturbed accretion disk model in Flohic & Eracleous(2008, one circular disk part with bright spots), r = 450 R G , r = 1400 R G , σ = 1300km / s, i = 27 o and q = 3, in spite ofthe not well fitted results for line profiles with these param-eters (not good fitted results for broad wings). Under themodel, the output H α is also shown in Figure 8, It is clearthat the response to input continuum described delta func-tion is much different for elliptical disk structure and for cir-cular disk structure. The different response for different geo-metrical structures indicates the different structures of BLRsof AGN should be discriminated through the light curves ofcontinuum emission and broad emission lines emission, espe-cially when there are HOMOGENEOUS and COMPLETEinformation for the light curves. Actually, based on the ob-served light curves of 3C390.3 selected from AGN WATCHproject, there is no way to discriminate different geometricalstructures of BLRs as what we have shown in the followingresults. The results shown in the figure indicate that ourprocedures above DO work, and effects of extended disk-likeBLRs on light curve of emission line can be clearly describedby our procedures.Last but not least, the observed light curve of contin-uum emission at ∼ A collected from AGN WATCH isused as the input light curve of continuum emission. The de-tailed description about the light curve can be found in Di-etrich et al. (1998). There are 70 data points included in thelight curve from MJD2449517 to MJD2450068. We first cre-ate one new light curve of continuum emission with date sep-aration of 1day by linear interpolation method applied to ob-served light curve of continuum. Then we check the expectedoutput light curve of broad H α under the supposed ellipticaldisk-like BLRs. The results are shown in bottom-left panelof Figure 9. It is clear that the expected output light curveof broad H α is consistent with the observed light curve ofbroad H α , the linear correlation coefficient for the correla-tion between output light curve of H α and observed lightcurve of H α is about 0.85 with P null ∼
0. Then through theinput light curve of continuum and the output correspondinglight curve of broad H α , it is interesting to estimate the sizeof BLRs by so-called cross correlation function (CCF). Here,the common interpolated cross-correlation function (ICCF)(Gaskell & Sparke 1986, Gaskell & Peterson 1987, Peterson1993) is applied to quantify time lag between continuumemission and broad lines emission. We do not consider thez-transfer discrete correlation function (ZDCF, Alexander1997, Edelson & Krolik 1988, White & Peterson 1994) anymore, because results from ZDCF are excellent agreementwith the results from ICCF (Peterson et al. 1991, 1992, 2004,Kaspi et al. 2000, Bentz et al. 2010). Furthermore, the cor-responding results based on the disk parameters shown inFlohic & Eracleous (2008) are also calculated, and shown inFigure 9. It is clear that although the example shown in Fig-ure 8 indicates the information from light curves can be usedto confirm which structure should be more preferred, thereis no way to find enough evidence to determine which struc-ture (elliptical disk-like BLRs or circular disk-like BLRs) ispreferred, due to the incomplete and in-homogeneous infor-mation provided from the observed light curves. Thus, we c (cid:13) , 1– ?? C390.3: disk-like BLRs near central BH mainly compare the calculated time lags between continuumemission and broad line emission, under the two structures.Figure 9 shows the CCF results from input light curve ofcontinuum and the output light curve of broad H α , the dis-tribution of the size of BLRs through bootstrap method (acommon Monte-Carlo method to estimate the uncertainty ofparameter, Press et al. 1992, Peterson et al. 1998). Detaileddescriptions about CCF method to estimate size of BLRs(time lag between line emission and continuum emission)and bootstrap method to estimate uncertainties of measuredtime lag can be found in Peterson (1993). From the resultsshown in the figure, we can find that the estimated size ofBLRs through the input light curve of continuum emissionand output light curve of broad H α under elliptical accre-tion disk model is also well consistent with the one esti-mated by the observed light curves of continuum emissionand broad line emission, R BLRs ∼ . ± . − days.We should note that the size of BLRs is the distance frombroad H α emission line region to optical continuum emissionregion, thus the value is some smaller than ∼ − daysestimated by the CCF function from light curve of broadH α and light curve of x-ray/UV emission shown in Diet-rich et al. (1998), Bentz et al. (2009) etc., because thereare probable 5days lag between optical continuum emis-sion and x-ray emission (Dietrich et al. 1998). Certainly,we also calculate the results based on the circular diskmodel shown in Flohic & Eracleous (2008), which shouldbe some different from the results for elliptical accretiondisk R BLRs ∼ . ± . − days. However, there is noenough evidence to against the circular disk-like BLRs for3C390.3, besides the best fitted results for observed line pro-files. If there should homogeneous and complete observedlight curves, the clear final decision should be given.In order to further confirm that the disk-like BLRs de-termined by elliptical accretion disk model is reliable fordouble-peaked emitter 3C390.3, we also check the CCF re-sults for disk-like BLRs with different disk parameters, inspite of the best fitted results for observed double-peakedbroad balmer line. Figure 10 shows the effects of disk pa-rameters on the measured size of BLRs through input con-tinuum emission and output H α emission based on the el-liptical accretion disk model as what we have done above.It is clear that inner radius and emissivity power are thetwo main parameters which have apparent effects on thetheoretically measured size of BLRs of 3C390.3. In the fig-ure, we only show the effects from inner radius, emissivitypower, eccentricity and inclination angle of disk-like BLRs,because there are few effects from the other disk param-eters. Certainly, more reliable evidence to determine andconfirm model parameters should depend on future moredetailed and homogeneous observed light curves of contin-uum emission and broad line emission. The results indicatethat the measured disk parameters for BLRs of 3C390.3 arereliable to some extent, and different geometrical structuresof BLRs based on different disk parameters should lead todifferent theoretically measured size of BLRs from size ofBLRs through observational results.The results above indicate that the elliptical accretiondisk model can be applied to best fit the observed spectra,i.e., the model can provide fine velocity structures for BLRsof 3C390.3. Furthermore, the elliptical accretion disk modelcan provide fine geometrical structures which can be applied to reproduce characters of observed light curve of broad H α .Thus elliptical accretion disk model which can be applied tofit characters of line profiles and variations of broad double-peaked H α is appropriate to double-peaked emitter 3C390.3. As one well-known double-peaked emitter, based on the diskparameters measured above, to check the expected line pro-file of double-peaked broad balmer emission line of 3C390.3in different years/periods is very interesting. Although themore recent observed line profiles of double-peaked broadH α of 3C390.3 in Jan. 2007 can be found in Shapovalova etal. (2010), the observed spectrum in Sep. 2000 by HST STISis collected, because the reduced spectrum in 2000 is publicand conveniently collected from the website of MultimissionArchive at STScI (MAST) (http://archive.stsci.edu/) (HSTProposal 8700, PI: Prof. Andre Martel in Space TelescopeScience Institute). The detailed description about observa-tional technique for the spectrum around 2000 by HST canbe found in Popovic (2003). Here, we mainly check whetherthe observed line profile of broad balmer emission lines in2000 can be reproduced through theoretical elliptical ac-cretion disk model based on the disk parameters measuredfrom spectra observed around 1995 for double-peaked emit-ter 3C390.3.Before proceeding further, the precession period shouldbe determined. Through the obtained disk parameters, therelativistic precession period of the elliptical disk-like BLRsaround central black hole of 3C390.3 can be simply calcu-lated (Weinberg 1972), T pre = 2 × πδ φ ∼ × π π × G × M BH c A (1 − e ) ∼ ∼ e is the ec-centricity. Although, the precession period for outer ellipti-cal rings is very long, the short precession period for innerelliptical rings should lead to some apparent variations ofdouble-peaked broad emission lines from 1995 to 2000.We simply assume that orientation angle is the uniqueparameter to vary from 1995 to 2000 in the elliptical ac-cretion disk model. As what we have done in section 3,the elliptical disk-like BLRs are separated into 60 rings. Itis clear that orientation angle of each ring in 2000 shouldbe some different due to different semi-major axis lengthfor each ring, φ ,i = φ ,i ± × π × T pre,i , where ± means the rotating direction of disk-like BLRs is clock-wise or anticlockwise for observer. After the orientation an-gles of the 60 rings around 2000 are determined, line pro-file expected in 2000 can be re-constructed by the sumof 60 expected double-peaked components from 60 rings,as what we have done in Section 3. Here the theoreticalline profile in 2000 is mainly based on the mean spec-trum around 1995 in AGN WATCH project. The mean ob-served spectrum shown as thin solid line in Figure 11 iscreated by PCA (Principal Components Analysis, so-calledKarhunen-Loeve Transform) method applied for all the 66 c (cid:13) , 1– ?? Zhang X.-G. observed spectra of broad H α around 1995. The conve-nient and public IDL PCA program ’pca solve.pro’ writ-ten by D. Schlegel in Princeton University is used, whichis included in the SDSS software package of IDLSPEC2D(http://spectro.princeton.edu/). Commonly, the first prin-cipal component represents the mean spectrum. From themean spectrum, it is clear that there are similar flux ratio( ∼ .
46) of blue peak to red peak of broad double-peakedH α and similar flux ratio ( ∼
1) of blue part to red part withthose mean values shown in Figure 4.Figure 11 shows the probable observed line profileof broad double-peaked H α of 3C390.3 around 2000, andshows the comparison between the mean observed spectrumaround 1995 and observed spectrum around 2000. Basedon the theoretical accretion disk model, through the resultsshown in top-left panel in Figure 11, we can find that due toprecession period, after about 5 years, the flux ratio of redpeak to blue peak should be changed. In the figure, flux den-sity at blue peaks of all the line profiles have been normalizedto 1. If rotating direction of disk-like BLRs is clockwise toobserver, the expected flux ratio (1.36) of red peak to bluepeak of spectrum around 2000 should be smaller than theone (1.46) of observed spectrum around 1995. If rotating di-rection of disk-like BLRs is anticlockwise to observer, theexpected flux ratio (1.68) in 2000 should be larger than theone (1.46) in 1995. Through the observed spectrum in 2000,the flux ratio of blue peak to red peak is about 1 . ± . α collected from AGN WATCH project.Then based on the disk parameters, the formed geomet-rical structures of BLRs of 3C390.3 are applied to checkthe reverberation mapping results for 3C390.3. The disk-like BLRs supposed by theoretical elliptical accretion diskmodel can well re-produce the observational results aboutreverberation mapping technique. Thus the disk-like BLRsare preferred for 3C390.3. Furthermore, we check the effectsof precession of elliptical disk-like BLRs on the observed lineprofile. After about 5 years, the line profile of broad double-peaked H α observed in 2000 by HST can be well expected bythe theoretical elliptical accretion disk model, based on thedisk parameters measured through spectra observed around1995, which confirms the elliptical accretion disk model isappropriate to double-peaked emitter 3C390.3 . ACKNOWLEDGEMENTS
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Figure 1.
Best fitted results for double-peaked broad H α in rest wavelength by elliptical accretion disk model. Thin solid line representsthe observed spectrum, thick solid line represents the best fitted results for double-peaked broad H α . The vertical dashed line shows theposition for unexpected absorption features around 6500˚ A for two examples marked with ’49860ce’ and ’49984ce’. The observed MJDdate of each spectrum is shown in the right side of the figure. Shadow areas represent the ranges for narrow emission lines.c (cid:13) , 1– ?? C390.3: disk-like BLRs near central BH Figure 2.
The residuals ( y obs − y model , observed data minus expected model data) for the shown examples in Figure 1. Shadowareas represent the ranges for narrow emission lines, each double horizontal dashed lines represent the range of [ f − f + 1], where f = 0 , , ...
80 representing the zero point for each spectrum are shown as solid horizontal lines in the figure.c (cid:13) , 1– ?? Zhang X.-G.
Figure 3.
Distributions of the disk parameters of disk-like BLRs for 3C390.3. The top three subfigures show the distributions ofeccentricity, inclination angle and the parameter of log( χ ) for the 39 spectra with high quality and without unexpected absorptionfeatures around 6500˚ A . Then the other six subfigures show the distributions of the other parameters for all the 66 spectra, inner radius r , outer radius r , emissivity slope q , orientation angle φ , local broadening velocity σ and the parameter of log( χ ). The mean valueof each parameter we accepted is shown in each subfigure. Figure 4.
The variations of the flux ratio of blue peak to red peak (shown as open circles), and the flux ratio of blue part to red partof broad H α (shown as solid circles). The dotted lines represents the mean values of the two kinds of flux ratios.c (cid:13) , 1– ?? C390.3: disk-like BLRs near central BH Figure 5.
Best fitted results for double-peaked broad H α with one fixed parameter with half of accepted value for the disk parameter.In the top panel, thin solid line in histogram mode represents the observed line profile marked with ’49870dr’ in AGN WATCH project,the thick solid line shows the best fitted results with disk parameters having values shown in Figure 3, thin solid line represents the bestfitted results with disk parameter r = 127 . R G , thin dotted line represents the best fitted results with disk parameter r = 670 . R G ,thick dotted line represents the best fitted results with disk parameter sin( i ) = 0 .
25, thin dashed line represents the best fitted resultswith disk parameter q = 0 .
90, thick dashed line represents the best fitted results with disk parameter σ = 364 km/s , thin dot-dashedline represents the best fitted results with disk parameter e = 0 . φ = −
13 in degree. The other seven panels show the corresponding values of flux fit − fit , where fit (cid:13) , 1– ?? Zhang X.-G.
Figure 6.
Top left panel shows the toy structures of the elliptical disk-like BLRs of 3C390.3. The solid line represents the elliptical ringwith pericenter distance r r i r , the innerest one with pericenter distance of r , the outerest one with r . The central black hole islocated at the origin of the coordinates (one focus point of the elliptical ring). Dotted line represents the sphere surface of ionizing photosat one time. Because the BLRs are elliptical disk-like, thus at one time, the ionizing photos arriving in BLRs DO NOT affect all the tinyclouds located in one elliptical ring. Top right panel show the toy showing of the line intensity of broad H α from different bins of radius.Solid line represents the observed H α , dotted line represents the line intensity from ∼ R G (the inner boundary) to ∼ R G , dashedline represents the line intensity from ∼ R G to ∼ R G , dot-dashed line represents the line intensity from ∼ R G to ∼ R G ,double-dot-dashed line represents the line intensity from ∼ R G to 1263 R G (the outer boundary). The vertical dotted line representsthe center wavelength of H α , 6564.61˚A. Bottom left panel shows the correlation between line intensities from different bins ( F i ( r )) andthe corresponding pericenter distances of the bins. Here the bins are created uniformly, thus F ( r ) ∝ r ( ∼ (1 − q )) ∝ r ( − . . Bottom rightpanel shows the properties of line intensities ( f i,j ) of the 23541 data points in sixty elliptical rings with pericenter distances from r to r . The bottom two panels show the properties of Equation (2). c (cid:13) , 1– ?? C390.3: disk-like BLRs near central BH Figure 7.
The correlation between luminosity of broad H α and continuum luminosity at 5177˚ A for 66 observed spectra around 1995.Solid line represents the best fitted result, L Hα ∝ ( L con (5177 ˚ A ) ) . . The dotted line is the one found by Greene & Ho(2005). Figure 8.
The response output broad H α based on the input continuum emission described by one delta function under the ellipticaldisk-like BLRs and circular disk-like BLRs for 3C390.3. The top line shows the continuum emission. The bottom solid line shows thecorresponding response output broad H α under elliptical disk-like BLRs, and dotted line shows the results under circular disk-like BLRs.c (cid:13) , 1– ?? Zhang X.-G.
Figure 9.
Top left panel shows the light curve of continuum, open circles are the observed data points selected from AGN WATCH,solid line represents the input light curve of continuum with separation of 1day. Bottom left panel shows the light curve of broad H α ,open circles are observed values, solid line represents the output light curve under the elliptical disk-like BLRs, dotted line represents theoutput light curve under the circular disk model shown in Flohic & Eracleous (2008). Top right panel shows the CCF function (maximumcoefficient about 0.99) for observed light-curve of continuum emission and output light curve of broad H α . Solid line represents the resultfor elliptical accretion disk model (peak value around 16 days), dotted line shows the result for circular disk model in Flohic & Eracleous(2008) (peak value around 18 days). Bottom right shows the distribution of time lag between observed continuum emission and simulatedbroad H α emission by bootstrap method. Solid line is for elliptical disk model, dotted line is for circular disk model in Flohic & Eracleous(2008). c (cid:13) , 1– ?? C390.3: disk-like BLRs near central BH Figure 10.
The effects of disk parameters on the theoretically measured size of BLRs. Top-left panel shows the effects of inner radius,top-right panel shows the effects of emissivity power, bottom-left panel shows the effects of eccentricity, bottom-right panel shows theeffects of inclination angle.
Figure 11.
To compare the observed line profile by HST in 2000 and mean observed line profile around 1995. Thin dotted line representsthe mean spectrum around 1995 and thick solid line represents the observed line profile by HST in 2000. Two vertical dot-dashedlines mark the positions of red peak and blue peak of double-peaked broad H α . Top left panel shows the theoretical results. Solid linerepresents the mean observed double-peaked line profile around 1995, thick dashed line represents the expected line profile around 2000with clockwise rotating disk-like BLRs, thick dotted line represents the expected line profile around 2000 with anticlockwise rotatingdisk-like BLRs.c (cid:13) , 1–, 1–