Estimation of the size and structure of the broad line region using Bayesian approach
Amit Kumar Mandal, Suvendu Rakshit, C. S. Stalin, R. G. Petrov, Blesson Mathew, Ram Sagar
MMNRAS , 1–19 (2020) Preprint 5 January 2021 Compiled using MNRAS L A TEX style file v3.0
Estimation of the size and structure of the broad line region usingBayesian approach
Amit Kumar Mandal , (cid:63) , Suvendu Rakshit , , C. S. Stalin ,R. G. Petrov , Blesson Mathew , Ram Sagar Department of Physics, CHRIST (Deemed to be University), Hosur Road, Bangalore 560 029, India Indian Institute of Astrophysics, Block II, Koramangala, Bangalore, 560 034, India Aryabhatta Research Institute of Observational Sciences, Manora Peak, Nainital 263002, India Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Quantum, Vesilinnantie 5, 20014 University of Turku, Finland Observatoire de la C ˆ o te d’Azur, CNRS, Laboratoire Lagrange, Universit ´ e C ˆ o te d’Azur, Parc Valrose, B ˆ a t. H. Fizeau, F-06108 Nice, France Accepted 2020 December 30. Received 2020 December 28; in original form 2019 November 20
ABSTRACT
Understanding the geometry and kinematics of the broad line region (BLR) of activegalactic nuclei (AGN) is important to estimate black hole masses in AGN and studythe accretion process. The technique of reverberation mapping (RM) has providedestimates of BLR size for more than 100 AGN now, however, the structure of the BLRhas been studied for only a handful number of objects. Towards this, we investigatedthe geometry of the BLR for a large sample of 57 AGN using archival RM data. Weperformed systematic modeling of the continuum and emission line light curves usinga Markov Chain Monte Carlo method based on Bayesian statistics implemented inPBMAP (Parallel Bayesian code for reverberation − MAPping data) code to constrainBLR geometrical parameters and recover velocity integrated transfer function. Wefound that the recovered transfer functions have various shapes such as single-peaked,double-peaked and top-hat suggesting that AGN have very different BLR geometries.Our model lags are in general consistent with that estimated using the conventionalcross-correlation methods. The BLR sizes obtained from our modeling approach isrelated to the luminosity with a slope of 0 . ± .
026 and 0 . ± .
084 based onH β and H α lines, respectively. We found a non-linear response of emission line fluxesto the ionizing optical continuum for 93% objects. The estimated virial factors forthe AGN studied in this work range from 0.79 to 4.94 having a mean at 1 . ± . Key words: galaxies: active − galaxies: Seyfert − (galaxies:) model: Bayesian Active Galactic Nuclei (AGN) are believed to be poweredby the accretion of matter on to super massive black hole(SMBH; 10 − M (cid:12) ) located at the center of galaxies(Lynden-Bell 1969; Salpeter 1964). This extreme physicalprocess is responsible for the radiation we receive from AGNover a wide range of energies predominantly emitted in X-ray, UV and optical wavelengths. The SMBH is surroundedby the accretion disk and the optical/UV emission seen inthe spectral energy distribution of an AGN is attributedto the thermal emission from the accretion disk. Farther (cid:63) E-mail: [email protected] from the accretion disk on scales of about ∼ © a r X i v : . [ a s t r o - ph . GA ] J a n Mandal et al. ity of 10 − erg s − , the inner extent of the torus isaround 0 . − . −
100 light-days (Suganuma et al.2006). Thus, the central region of AGN is highly compact,and difficult to probe using any current imaging techniques.However, recently, from interferometric observations carriedout in IR using the GRAVITY instrument on the EuropeanVery Large Telescope (VLT), Gravity Collaboration et al.(2018) were able to resolve the central region in 3C 273 onscales of about 0.12 parsec. On much larger scales in AGNare the clouds in the narrow line region that are responsiblefor the narrow emission lines we see in the spectrum of AGNwith widths of few hundreds of km/sec.One of the defining characteristics of AGN is that theyshow flux variations (Wagner & Witzel 1995; Ulrich et al.1997). This is known since their discovery, though, the causesof flux variations are not yet understood. In spite of that,the flux variability characteristic of AGN provides a veryuseful way to probe the spatially unresolved inner regionsin them. A technique that uses the variability of AGN toprobe their central regions is known as reverberation map-ping (RM; Blandford & McKee 1982; Peterson 1993). Thismethod is based on the variation of the line-fluxes from theBLR in response to the the continuum UV-optical flux vari-ations from the accretion disk. The time delay ( τ ) measuredusing the traditional cross-correlation techniques (Edelson &Krolik 1988; Peterson 1993) between the continuum flux andline flux variations is the average light travel time from theaccretion disk to the BLR, which in principle gives the aver-age radius of the BLR. Having the BLR size ( R BLR = τ /c ,where c is the velocity of light) and the width of the broademission line (∆ V ), measurable from the spectrum, the massof the black hole (M BH ) in an AGN can be estimated usingthe virial relation, M BH = f BLR (cid:18) ∆ V R BLR G (cid:19) (1)where G represents the gravitational constant and f BLR isthe virial factor that depends on the geometry and kine-matics of BLR. The method of RM has been used to mea-sure M BH in more than 100 AGN with most of the mea-surements coming from the compilation of Bentz & Katz(2015), the Sloan Digital Sky Survey Reveberation Mea-surement project; SDSS − RM (Grier et al. 2017b) and theSuper-Eddington Accretion in Massive Black Holes project(Du et al. 2014, 2016, 2018; Wang et al. 2014). The f BLR in Equation 1 is calibrated considering both AGN and lo-cal quiescent galaxies follow the same M − σ ∗ relation (e.g.,Onken et al. 2004; Woo et al. 2015), where σ ∗ is the stel-lar velocity dispersion. However, it is not clear whether aconstant f BLR can be used to estimate M BH for all AGNconsidering the complex geometry and kinematics of indi-vidual AGN. Ho & Kim (2014) performed a recalibration ofthe virial factor and found that it depends on the bulge typeof the host galaxy, the f BLR for classical bulges and ellip-tical bulge objects are twice larger than pseudo bulge ob-jects. Pancoast et al. (2014) performed dynamical modelingof BLR and found that f BLR correlates with the inclinationof the objects and has different values for different objects. Inaddition to getting M BH values, RM observations involving optical and IR photometric observatios as well as IR spectro-scopic monitoring observations can be used to constrain theinner edge of the dusty torus in AGN(Suganuma et al. 2006;Koshida et al. 2014; Pozo Nu˜nez et al. 2014; Mandal et al.2018; Landt et al. 2019; Mandal et al. 2020). Recently, fromhigh resolution radio observations using the Very Large Ar-ray, Carilli et al. (2019) have imaged the torus in Cygnus A.GRAVITY Collaboration et al. (2019) partially resolved thesize and structure of hot dust using VLTI/GRAVITY andreported the increase of the physical radius with bolometricluminosity in 8 Type 1 AGN.Most of the RM studies available in literature aremainly focused on estimating BLR sizes and M BH whichare solely driven by the quality of the available RM databoth in terms of time resolution and signal-to-noise ratio(SNR). This approach makes the geometry and kinematicsof the central engine of BLR remain unknown. However, forsources with densely sampled and good SNR spectra, it isin principle possible to calculate time delays as a functionof velocity across the emission line profile and better con-strain the geometry and kinematics of the gas in the BLR(e.g., Ulrich & Horne 1996; Bentz et al. 2010; Grier et al.2013; Xiao et al. 2018). Also, modeling of RM data usingBayesian approach has led to constrain the geometry anddynamics of the BLR, estimate AGN parameters, as well as, f BLR for individual objects (Pancoast et al. 2011; Breweret al. 2011; Pancoast et al. 2012, 2014; Li et al. 2018). A geo-metrical modeling code, PBMAP (Parallel Bayesian code forreverberation − MAPping data) developed by Li et al. (2013)in addition to providing several parameters, e.g., BLR size,inclination angle ( θ inc ), opening angle ( θ opn ), also includesnon-linear response of the line emission to the continuumand allow for detrending the light curves (Welsh 1999; Den-ney et al. 2010; Li et al. 2013, 2019). This technique wasapplied to a sample of 40 objects using archival H β line andcontinuum light curves by Li et al. (2013) and they were ableto recover velocity integrated transfer function. They foundthat the BLR structure for H β line is mainly disk-like. Sucha flattened disk like BLR is also seen in the high resolutionobservations of 3C 273 with the VLT (Gravity Collabora-tion et al. 2018). Also, in Li et al. (2013) the observed linefluxes were better reproduced using the non-linear responseof the line to the continuum that has not been consideredin previous RM studies. It is therefore important to extendthis approach to a large number of AGN to examine differ-ences if any in the geometry of the BLR between differentAGN. Towards this, we carried out a systematic modelingof the RM data available in the literature to investigate thegeometry of the BLR. For this we used the PBMAP codeto model the emission line and continuum light curves byconstraining several BLR parameters such as (a) the BLRsize, (b) θ inc , (c) θ opn and the non-linear response index. Wealso calculated f BLR for a number of sources by constrain-ing the geometry of the BLR. The paper is structured asfollows. In Section 2, we describe the sample selection. Wepresent our analysis in Section 3. Our results are given inSection 4 followed by the summary in Section 5. For the cos-mological parameters we assumed H = 73 km s − Mpc − , Ω m = 0 .
27 and Ω Λ = 0 . MNRAS000
27 and Ω Λ = 0 . MNRAS000 , 1–19 (2020)
LR Modeling The objective of this work is to constrain the geometry ofthe BLR as well as other characteristic properties of AGNby modeling the continuum and line light curves. This re-quires spectrophotometric monitoring observations of AGN.We therefore, collected data for all objects that are in theblack hole mass database by Bentz & Katz (2015) and theSDSS-RM program (Shen et al. 2016; Grier et al. 2017b)from the literature with the following two additional con-straints (i) the objects must have continuum and line lightcurves. The line light curves can be either of Mg II, H β or H α and (ii) BLR structure of the objects was not investigatedpreviously. With the above constraints we arrived at a sam-ple of 57 objects. Of the 57 objects, 22 have data for bothH β and H α lines, 3 have data for both H β and MgII lines, 25have only H β , 4 have only H α and 3 have data for only MgIIline with a total of 82 independent measurements. The datafor these objects were from Shen et al. (2016), Grier et al.(2017b), Wang et al. (2014), Grier et al. (2012), Bentz et al.(2014), Peterson et al. (2014), Rafter et al. (2013), Du et al.(2014) and Shapovalova et al. (2013). For the objects takenfrom Shen et al. (2016), the continuum light curves pertainto the measurements at 5100 ˚A, while for the objects takenfrom Grier et al. (2017b), the continuum light curves belongto the photometric monitoring observations done in g and i bands. The details of the objects selected for this study aregiven in Table 1.For this work, we directly downloaded the continuumand line light curves from the literature in their original formi.e. magnitude or flux versus time, without any further spe-cial treatment. Note that different authors followed differentmethods for their data analysis. In some cases the presenceof constant flux component in the continuum light curvesfrom the host-galaxy were removed by the respective au-thors (Bentz et al. 2014; Wang et al. 2014; Shen et al. 2016)by difference imaging analysis of the images. However, insome cases the removal of the host galaxy was not done e.g.,the f light curves from Grier et al. (2012); Rafter et al.(2013); Du et al. (2014); Grier et al. (2017b) are not hostgalaxy subtracted. We note that host galaxies contribute aconstant flux to the continuum light curves, however, thiscan vary depending on the seeing variations between differ-ent epochs of observations (Peterson 2001). Though this canhave some effect on the deduced amplitude of variations (Pe-terson 2001), it does not affect the estimation of the modelparameters and the main conclusions of the paper. Simi-larly, as our sample comes from different sources, not allbroad emission line light curves have their narrow compo-nent subtracted. For example, Shen et al. (2016); Grier et al.(2017b) subtracted the narrow component while Du et al.(2014) used the total H β profile to generate the H β lightcurves. We characterized the line and continuum variability of oursample of sources using the F var parameter (Vaughan et al. 2003) and it is defined as F var = (cid:115) ( σ − ¯ (cid:15) err )¯ x (2)where ¯ x is the average flux in the light curve. The samplevariance σ and the mean error ¯ (cid:15) err are given as σ = 1 N − N (cid:88) i =1 ( x i − ¯ x ) (3)¯ (cid:15) err = 1 N N (cid:88) i =1 (cid:15) i (4)where (cid:15) i is the uncertainty in each flux measurement. Theuncertainty in F var is calculated as (Rani et al. 2017) err ( F var ) = (cid:118)(cid:117)(cid:117)(cid:116)(cid:32)(cid:114) N ¯ (cid:15) err ¯ x F var (cid:33) + (cid:32)(cid:114) ¯ (cid:15) err N x (cid:33) (5)The results of our variability analysis are given in Table 2where we also mention the values of R , which is the ratio be-tween the maximum and minimum fluxes in the light curves. We used the PBMAP code developed by Li et al. (2013)to perform the light curve modeling. A detailed descriptionof this code can be found in Li et al. (2013). However, wedescribe briefly the methodology here. The data that areneeded for the code are the observed continuum and linelight curves. Using the irregularly sampled continuum lightcurve, the code reconstructs the continuum light curve usingthe damped random walk model (DRW; Kelly et al. 2009)following a Bayesian approach. Many investigations in theliterature suggest that the optical flux variations in AGNcan be well explained by DRW (e.g., Koz(cid:32)lowski et al. 2010;MacLeod et al. 2010; Zu et al. 2011).The AGN continuum variability is modeled as a randomprocess in which the co-variance matrix S of the signal canbe expressed as S ( t i − t j ) = σ d exp (cid:20) − (cid:18) | t i − t j | τ d (cid:19) α (cid:21) (6)Here, t i and t j are the two epochs and the co-variance func-tion depends on the time difference t i − t j , τ d is the dampingtimescale, σ d is the standard deviation of variation and α isthe smoothening parameter which is fixed to unity in themodel calculation as it is shown to be sufficient for variabil-ity (Kelly et al. 2009). Then using a model of BLR and thereconstructed continuum light curve, the code reconstructsthe line light curve. In the code (a) the BLR is modeled asan axisymmetric disk consisting of a large number of point-like, discrete clouds of equal density, which re-radiate theUV/optical continuum as emission lines, (b) the BLR cloudssubtend a solid angle denoted by the opening angle ( θ opn ),and the BLR is viewed at an inclination angle ( θ inc ) and(c) the central source that ionizes the BLR is point like,thereby emitting isotropically. The model regenerates thevelocity integrated line light curve represented as below f l ( t ) = A (cid:90) Ψ( τ ) f (1+ γ ) c ( t − τ ) dτ (7) MNRAS , 1–19 (2020)
Mandal et al.
Table 1.
Details of the objects used in this study. Here τ cent is in days, FWHM and σ are in km s − and log L is in erg s − .No. α δ Type z line τ cent FWHM σ log L Reference1 00:10:31.01 +10:58:29.5 Sy1 0.090 H β . +3 . − . ±
145 3321 ±
107 44 . ± .
050 D2 02:30:05.52 -08:59:53.2 Sy1 0.016 H β . +7 . − . - - 42 . ± .
050 C3 06:52:12.32 +74:25:37.2 Sy1 0.019 H β . +1 . − . ± ±
68 43 . ± .
060 D4 11:39:13.92 +33:55:51.1 Sy1 0.033 H β . +0 . − . , 23 . +7 . − . - - 42 . ± .
090 G, C5 12:42:10.61 +33:17:02.7 Sy1 0.044 H β . +2 . − . - - 43 . ± .
040 H6 13:42:08.39 +35:39:15.3 Sy1 0.003 H β . +1 . − . ±
330 1544 ±
98 41 . ± .
144 EH α . +1 . − . - - 41 . ± .
144 E7 14:05:18.02 +53:15:30.0 QSO 0.467 H β . +14 . − . ±
44 1232 ±
16 44 . ± .
001 BH α - - - 44 . ± .
001 B8 14:05:51.99 +53:38:52.1 QSO 0.455 H α . +8 . − . ±
84 1590 ±
24 43 . ± .
002 B9 14:07:59.07 +53:47:59.8 Sy1 0.173 H β . +4 . − . ±
59 1790 ±
10 43 . ± .
001 A10 14:08:12.09 +53:53:03.3 Sy1 0.116 H β . +1 . − . ±
36 1409 ±
11 43 . ± .
001 BH α . +4 . − . ±
15 1185 ± . ± .
001 B11 14:09:04.43 +54:03:44.2 QSO 0.658 H β . +8 . − . ±
455 5284 ±
54 44 . ± .
003 B12 14:09:15.70 +53:27:21.8 Sy1 0.258 H α . +2 . − . ±
20 3232 ±
40 43 . ± .
002 B13 14:10:04.27 +52:31:41.0 QSO 0.527 H β . +4 . − . ±
85 2126 ±
35 44 . ± .
001 BH α - - - 44 . ± .
001 B14 14:10:18.04 +53:29:37.5 QSO 0.470 Mg II 32 . +12 . − . - - AH β . +2 . − . ±
288 1781 ±
38 43 . ± .
003 BH α . +7 . − . ±
365 1738 ±
31 43 . ± .
003 B15 14:10:31.33 +52:15:33.8 Sy2 0.608 H β . +1 . − . ±
112 1619 ±
38 43 . ± .
002 B16 14:10:41.25 +53:18:49.0 QSO 0.359 H β . +4 . − . ±
51 1909 ±
12 43 . ± .
001 BH α . +1 . − . ±
26 1318 ±
11 43 . ± .
001 B17 14:11:12.72 +53:45:07.1 QSO 0.587 H β . +7 . − . ±
77 1221 ±
36 44 . ± .
002 A18 14:11:15.19 +51:52:09.0 QSO 0.572 H β . +11 . − . ±
164 1423 ±
32 44 . ± .
001 BH α - - - 44 . ± .
001 B19 14:11:23.42 +52:13:31.7 Sy1 0.472 H β . +1 . − . ±
40 1443 ±
11 44 . ± .
001 BH α . +0 . − . ±
44 1346 ±
13 44 . ± .
001 B20 14:11:35.89 +51:50:04.5 QSO 0.650 H β . +8 . − . ±
491 1527 ±
22 44 . ± .
003 B21 14:12:14.20 +53:25:46.7 QSO 0.458 Mg II 36 . +10 . − . - - A22 14:12:53.92 +54:00:14.4 Sy1 0.187 H β . +5 . − . ±
130 1758 ±
22 42 . ± .
003 A23 14:13:14.97 +53:01:39.4 QSO 1.026 H β . +4 . − . ± ±
34 44 . ± .
038 B24 14:13:18.96 +54:32:02.4 QSO 0.362 H β . +1 . − . ±
137 1353 ±
23 43 . ± .
001 B25 14:13:24.28 +53:05:27.0 QSO 0.456 H β . +10 . − . ±
77 6101 ±
48 43 . ± .
002 BH α . +7 . − . ±
31 4569 ±
51 43 . ± .
002 B26 14:14:17.13 +51:57:22.6 QSO 0.604 Mg II 29 . +3 . − . - - AH β . +3 . − . ±
221 2788 ±
48 43 . ± .
012 B27 14:15:32.36 +52:49:05.9 Sy1 0.715 H β . +9 . − . ±
243 857 ±
32 44 . ± .
003 B28 14:16:25.71 +53:54:38.5 Sy1 0.263 H β . +7 . − . ±
93 1636 ±
11 43 . ± .
018 AH α . +15 . − . ±
28 1298 ± . ± .
018 ”29 14:16:44.17 +53:25:56.1 QSO 0.425 Mg II 17 . +2 . − . - - A30 14:16:45.15 +54:25:40.8 QSO 0.244 H β . +20 . − . ±
97 1902 ±
20 43 . ± .
002 AH α . +2 . − . ±
19 3927 ±
30 43 . ± .
002 B31 14:16:45.58 +53:44:46.8 Sy1 0.442 H β . +2 . − . ±
70 990 ±
19 43 . ± .
008 AH α . +4 . − . ±
60 796 ±
23 43 . ± .
008 B32 14:16:50.93 +53:51:57.0 QSO 0.527 Mg II 25 . +2 . − . - - A33 14:17:06.68 +51:43:40.1 Sy1 0.532 H β . +12 . − . ±
104 743 ±
24 44 . ± .
001 A34 14:17:12.30 +51:56:45.5 Sy1 0.554 H β . +1 . − . ±
153 9475 ±
33 43 . ± .
012 BH α - - - 43 . ± .
012 B35 14:17:24.59 +52:30:24.9 Sy1 0.482 H β . +12 . − . ±
163 2036 ±
39 43 . ± .
002 BH α - - - 43 . ± .
002 B36 14:17:29.27 +53:18:26.5 QSO 0.237 H β . +5 . − . ±
367 6318 ±
38 43 . ± .
002 BH α . +23 . − . ±
66 5157 ±
40 43 . ± .
002 B37 14:17:51.14 +52:23:11.1 QSO 0.281 H α . +2 . − . ±
66 3384 ±
71 42 . ± .
007 B38 14:18:56.19 +53:58:45.0 QSO 0.976 H β . +6 . − . ±
61 7568 ±
70 45 . ± .
002 B39 14:19:23.37 +54:22:01.7 Sy1 0.152 H β . +0 . − . ±
55 1205 ± . ± .
001 BH α . +4 . − . ±
23 1018 ± . ± .
001 B40 14:19:41.11 +53:36:49.6 QSO 0.646 H β . +3 . − . ±
136 1232 ±
30 44 . ± .
017 B41 14:19:52.23 +53:13:40.9 QSO 0.884 H β . +5 . − . ± ±
64 44 . ± .
006 BMNRAS000
006 BMNRAS000 , 1–19 (2020)
LR Modeling Table 1 – continued No. α δ Type z line τ cent FWHM σ L
Reference42 14:19:55.62 +53:40:07.2 QSO 0.418 H β . +5 . − . ±
226 2291 ±
33 43 . ± .
003 BH α - - - 43 . ± .
003 B43 14:20:10.25 +52:40:29.6 QSO 0.548 H β . +5 . − . ±
114 6259 ±
23 44 . ± .
001 BH α . +7 . − . * - - 44 . ± .
001 B44 14:20:23.88 +53:16:05.1 QSO 0.734 H β . +3 . − . ±
109 7165 ±
36 44 . ± .
005 B45 14:20:38.52 +53:24:16.5 QSO 0.265 H β . +2 . − . ±
64 1362 ±
33 43 . ± .
001 AH α . +10 . − . ±
41 1320 ±
17 43 . ± .
001 B46 14:20:39.80 +52:03:59.7 QSO 0.474 H β . +6 . − . , 20 . +0 . − . ±
55 1360 ±
20 44 . ± .
001 A, BH α . +10 . − . ±
80 1352 ±
24 44 . ± .
001 B47 14:20:43.53 +52:36:11.4 QSO 0.337 H α . +0 . − . ±
114 1372 ±
40 43 . ± .
002 B48 14:20:49.28 +52:10:53.3 QSO 0.751 Mg II 34 . +6 . − . - - AH β . +9 . − . ±
136 5013 ±
49 44 . ± .
002 B49 14:20:52.44 +52:56:22.4 QSO 0.676 H β . +1 . − . ±
141 7195 ±
40 45 . ± .
001 B50 14:21:03.53 +51:58:19.5 Sy1 0.263 H β . +3 . − . ±
82 1089 ±
22 43 . ± .
018 BH α - - - 43 . ± .
018 B51 14:21:12.29 +52:41:47.3 QSO 0.843 H β . +3 . − . ±
153 3658 ±
56 44 . ± .
008 B52 14:21:35.90 +52:31:38.9 Sy1 0.249 H β . +0 . − . ±
35 1026 ±
14 43 . ± .
001 BH α . +1 . − . ±
11 907 ± . ± .
001 B53 14:24:17.22 +53:02:08.9 QSO 0.890 H β . +4 . − . ±
90 1252 ±
11 44 . ± .
060 B54 15:36:38.40 +54:33:33.2 Sy1 0.039 H β . +8 . − . - - 43 . ± .
030 C55 15:59:09.62 +35:01:47.6 Sy1 0.031 H β . +3 . − . - - 43 . ± .
060 C56 17:19:14.49 +48:58:49.4 Sy1 0.024 H β . +54 . − . - - 42 . ± .
140 I57 23:03:15.67 +08:52:25.3 Sy1 0.016 H β . +3 . − . - - 43 . ± .
030 FA:Shen et al. (2016), B:Grier et al. (2017b), C:Wang et al. (2014), D:Grier et al. (2012), E:Bentz et al. (2014), F:Peterson et al. (2014),G:Rafter et al. (2013), H:Du et al. (2014), I: Shapovalova et al. (2013). *lag derived from ICCF analysis (see Appendix A).Note: Col. (1): Number. Col. (2): RA. Col. (3): Dec. Col. (4): Type of the object. Col. (5): Redshift. Col. (6): Emission line. Col. (7):Centroid lag obtained from CCF analysis retrieved from literature. Col. (8): FWHM. Col. (9): Line dispersion. Col. (10): Opticalhost-galaxy corrected luminosity at 5100 ˚A. Col. (11): Reference. with the transfer function ψ ( τ ) = (cid:88) i δ ( τ − τ i ) w i (cid:18) I i R i (cid:19) γ (8)where τ i represents the time lag from the i th cloud ata distance R i to the central source, A denotes the responsecoefficient, w i is the weight of the cloud to the responseof the continuum, I i depicts any possible anisotropic ef-fects and deviations from the continuum, and γ presentsthe non-linearity of the response. The weight w i is fixedto unity and I i is neglected in all calculations. A value of γ =0 points to the linear response of BLR to the continuumvariations. The reduced χ value ( χ /dof ) which is definedin Li et al. (2013) is used to determine the quality of thegenerated light curves. When the value of χ /dof was large( > χ /dof is slightly larger after detrending, we obtainedbetter estimates of BLR size with smaller uncertainty. Thefinal fitting results are given in Table 3 for H β and in Table4 for H α and MgII. AGN have been extensively studied for their variability andit has been found that optical variability of AGN correlateswith many of their physical properties. Most of these stud-ies concentrate on photometric monitoring, however, in suchstudies, broad emission lines too can fall in the photometricpass band. The best way to study line and continuum vari-ability separately is through spectroscopic monitoring obser-vations, however, it is time consuming. A data set suitablefor such a study is the one accumulated for RM studies.Though, the line and continuum light curves accumulatedfrom RM observations and used in this work are primar-ily used to understand the BLR, they are also a good dataset to investigate the variability of AGN. As we have bothcontinuum and line light curves, we characterized the lineand continuum variability of our sample using F var (Edelsonet al. 2002; Vaughan et al. 2003). The light curves for someobjects analyzed here, were corrected for the constant hostgalaxy contamination to the continuum and the narrow-linecontamination to the line fluxes. For few sources the hostgalaxy and the narrow line contribution to the continuumand line fluxes were not removed. This will have some ef-fect on the derived F var values reported here as the fluxcontribution from host galaxy could lead to low values ofF var (Peterson 2001). However, this will not lead to biaseson the comparative analysis of the F var values between dif-ferent emission lines and the continuum. The distribution
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Mandal et al.
Table 2.
Result of the analysis of variability. The median SNR of the light curves are mentioned. α δ F var R span (∆ t )(days) δt mean (days) SNR SNRNo continuum line continuum line continuum line continuum line continuum line1 00:10:31.01 +10:58:29.5 0.109 0.102 1.482 1.442 137.79 127.28 0.67 1.61 64 362 02:30:05.52 -08:59:53.2 0.062 0.042 1.438 1.283 116.75 116.75 1.54 1.54 169 2663 06:52:12.32 +74:25:37.2 0.130 0.097 1.667 1.399 138.85 117.86 0.68 1.25 128 654 11:39:13.92 +33:55:51.1 0.085 0.093 1.510 1.500 146.79 146.79 4.45 4.45 68 725 12:42:10.61 +33:17:02.7 0.058 0.048 1.260 1.284 146.71 146.71 2.93 2.93 131 986 13:42:08.39 +35:39:15.3 0.071 0.171 1.337 1.841 47.01 47.01 1.62 1.62 164 2907 0.164 1.909 47.01 47.01 1.62 1.62 164 9838 14:05:18.02 +53:15:30.0 0.021 0.059 1.171 1.586 206.74 176.98 0.64 5.71 139 179 0.049 1.490 206.74 173.00 0.64 5.77 139 1810 14:05:51.99 +53:38:52.1 0.024 0.046 1.421 1.449 206.75 173.00 0.66 5.77 53 2111 14:07:59.07 +53:47:59.8 0.049 0.126 1.217 1.713 176.98 176.98 5.71 5.71 987 7012 14:08:12.09 +53:53:03.3 0.026 0.103 1.359 1.639 195.03 176.98 0.94 5.71 158 2813 0.022 0.056 1.144 1.363 206.75 173.00 0.79 5.77 90 2214 14:09:04.43 +54:03:44.2 0.114 0.130 1.696 2.135 206.74 176.98 0.92 5.71 37 1515 14:09:15.70 +53:27:21.8 0.030 0.059 1.180 1.337 206.75 173.00 0.50 5.77 148 2616 14:10:04.27 +52:31:41.0 0.012 0.032 1.142 1.197 206.74 176.98 0.63 5.71 143 3517 0.012 0.019 1.142 1.313 206.74 173.00 0.63 5.77 143 2018 14:10:18.04 +53:29:37.5 0.064 0.170 1.482 2.097 176.98 176.98 5.71 5.71 211 2119 0.023 0.039 1.222 1.384 206.75 176.98 0.42 5.71 63 1520 0.023 0.037 1.222 1.381 206.75 173.00 0.42 5.77 63 1921 14:10:31.33 +52:15:33.8 0.037 0.164 1.391 2.449 206.74 176.98 0.90 5.71 57 1622 14:10:41.25 +53:18:49.0 0.070 0.121 2.014 1.645 195.02 176.98 0.77 5.71 23 5123 0.070 0.050 2.014 1.241 195.02 173.00 0.77 5.77 23 7524 14:11:12.72 +53:45:07.1 0.030 0.044 1.128 1.261 176.98 176.98 6.32 6.32 386 6025 14:11:15.19 +51:52:09.0 0.035 0.046 1.434 1.226 195.01 176.98 0.77 5.71 31 4326 0.030 0.079 1.253 4.246 206.74 173.00 0.63 5.77 49 727 14:11:23.42 +52:13:31.7 0.072 0.125 1.356 1.561 195.01 176.98 0.95 5.71 40 3328 0.071 0.065 1.515 1.286 206.79 173.00 0.66 5.77 41 4929 14:11:35.89 +51:50:04.5 0.055 0.067 2.003 3.174 195.07 176.98 0.51 5.71 14 630 14:12:14.20 +53:25:46.7 0.028 0.112 1.130 1.753 176.98 176.98 5.71 5.71 852 6931 14:12:53.92 +54:00:14.4 0.055 0.136 1.232 1.912 176.98 176.98 5.90 5.90 446 2232 14:13:14.97 +53:01:39.4 0.045 0.149 4.060 2.769 195.06 176.98 0.59 5.71 6 733 14:13:18.96 +54:32:02.4 0.048 0.041 1.408 1.294 191.86 176.98 0.66 5.71 64 2934 14:13:24.28 +53:05:27.0 0.029 0.055 1.250 1.298 195.06 176.98 0.79 5.71 60 2935 0.029 0.098 1.203 1.440 206.75 173.00 0.69 5.77 134 3836 14:14:17.13 +51:57:22.6 0.094 0.120 1.414 1.553 176.98 176.98 6.10 6.10 79 2537 0.032 0.406 3.880 8.170 195.07 176.98 0.82 5.71 8 438 14:15:32.36 +52:49:05.9 0.114 0.091 3.890 1.769 195.06 176.98 0.71 5.71 13 2039 14:16:25.71 +53:54:38.5 0.068 0.037 1.270 1.173 176.98 176.98 5.90 5.90 792 15240 0.053 0.010 1.290 1.104 206.75 173.00 1.02 5.77 84 5441 14:16:44.17 +53:25:56.1 0.044 0.095 1.165 1.550 176.98 176.98 5.90 5.90 301 3042 14:16:45.15 +54:25:40.8 0.072 0.282 1.308 3.842 176.98 176.98 5.71 5.71 440 2143 0.041 0.138 1.281 1.751 206.82 173.00 0.54 5.77 93 1644 14:16:45.58 +53:44:46.8 0.076 0.141 1.628 1.944 176.98 176.98 5.71 5.71 270 2145 0.025 0.031 1.198 1.434 206.82 173.00 0.53 5.77 76 1546 14:16:50.93 +53:51:57.0 0.037 0.106 1.160 1.566 176.98 176.98 5.90 5.90 181 3747 14:17:06.68 +51:43:40.1 0.038 0.045 1.142 1.217 176.98 176.98 5.71 5.71 473 5748 14:17:12.30 +51:56:45.5 0.115 0.348 12.431 5.887 206.78 176.98 0.42 5.90 9 449 0.115 0.602 12.431 9.087 206.78 173.00 0.42 5.97 9 350 14:17:24.59 +52:30:24.9 0.064 0.044 1.359 1.305 206.78 176.98 0.48 5.71 65 4051 0.064 0.018 1.359 1.287 206.78 173.00 0.48 5.77 65 2952 14:17:29.27 +53:18:26.5 0.014 0.050 1.147 1.426 195.06 176.98 0.67 5.71 118 3353 0.015 0.022 1.077 1.197 206.75 173.00 0.63 5.77 294 2954 14:17:51.14 +52:23:11.1 0.029 0.043 1.399 1.188 195.09 173.00 0.44 5.77 33 3655 14:18:56.19 +53:58:45.0 0.014 0.058 1.644 1.435 206.78 176.98 0.69 5.71 112 3556 14:19:23.37 +54:22:01.7 0.062 0.109 1.308 1.479 206.78 176.98 0.69 5.71 87 2657 0.062 0.061 1.308 1.305 206.78 173.00 0.69 5.77 87 2458 14:19:41.11 +53:36:49.6 0.056 0.041 3.212 1.443 195.11 176.98 0.56 5.71 32 2059 14:19:52.23 +53:13:40.9 0.088 0.035 1.859 1.516 206.78 176.98 0.67 5.71 24 1260 14:19:55.62 +53:40:07.2 0.047 0.131 1.253 2.014 206.78 153.02 0.84 5.67 50 11MNRAS000
Result of the analysis of variability. The median SNR of the light curves are mentioned. α δ F var R span (∆ t )(days) δt mean (days) SNR SNRNo continuum line continuum line continuum line continuum line continuum line1 00:10:31.01 +10:58:29.5 0.109 0.102 1.482 1.442 137.79 127.28 0.67 1.61 64 362 02:30:05.52 -08:59:53.2 0.062 0.042 1.438 1.283 116.75 116.75 1.54 1.54 169 2663 06:52:12.32 +74:25:37.2 0.130 0.097 1.667 1.399 138.85 117.86 0.68 1.25 128 654 11:39:13.92 +33:55:51.1 0.085 0.093 1.510 1.500 146.79 146.79 4.45 4.45 68 725 12:42:10.61 +33:17:02.7 0.058 0.048 1.260 1.284 146.71 146.71 2.93 2.93 131 986 13:42:08.39 +35:39:15.3 0.071 0.171 1.337 1.841 47.01 47.01 1.62 1.62 164 2907 0.164 1.909 47.01 47.01 1.62 1.62 164 9838 14:05:18.02 +53:15:30.0 0.021 0.059 1.171 1.586 206.74 176.98 0.64 5.71 139 179 0.049 1.490 206.74 173.00 0.64 5.77 139 1810 14:05:51.99 +53:38:52.1 0.024 0.046 1.421 1.449 206.75 173.00 0.66 5.77 53 2111 14:07:59.07 +53:47:59.8 0.049 0.126 1.217 1.713 176.98 176.98 5.71 5.71 987 7012 14:08:12.09 +53:53:03.3 0.026 0.103 1.359 1.639 195.03 176.98 0.94 5.71 158 2813 0.022 0.056 1.144 1.363 206.75 173.00 0.79 5.77 90 2214 14:09:04.43 +54:03:44.2 0.114 0.130 1.696 2.135 206.74 176.98 0.92 5.71 37 1515 14:09:15.70 +53:27:21.8 0.030 0.059 1.180 1.337 206.75 173.00 0.50 5.77 148 2616 14:10:04.27 +52:31:41.0 0.012 0.032 1.142 1.197 206.74 176.98 0.63 5.71 143 3517 0.012 0.019 1.142 1.313 206.74 173.00 0.63 5.77 143 2018 14:10:18.04 +53:29:37.5 0.064 0.170 1.482 2.097 176.98 176.98 5.71 5.71 211 2119 0.023 0.039 1.222 1.384 206.75 176.98 0.42 5.71 63 1520 0.023 0.037 1.222 1.381 206.75 173.00 0.42 5.77 63 1921 14:10:31.33 +52:15:33.8 0.037 0.164 1.391 2.449 206.74 176.98 0.90 5.71 57 1622 14:10:41.25 +53:18:49.0 0.070 0.121 2.014 1.645 195.02 176.98 0.77 5.71 23 5123 0.070 0.050 2.014 1.241 195.02 173.00 0.77 5.77 23 7524 14:11:12.72 +53:45:07.1 0.030 0.044 1.128 1.261 176.98 176.98 6.32 6.32 386 6025 14:11:15.19 +51:52:09.0 0.035 0.046 1.434 1.226 195.01 176.98 0.77 5.71 31 4326 0.030 0.079 1.253 4.246 206.74 173.00 0.63 5.77 49 727 14:11:23.42 +52:13:31.7 0.072 0.125 1.356 1.561 195.01 176.98 0.95 5.71 40 3328 0.071 0.065 1.515 1.286 206.79 173.00 0.66 5.77 41 4929 14:11:35.89 +51:50:04.5 0.055 0.067 2.003 3.174 195.07 176.98 0.51 5.71 14 630 14:12:14.20 +53:25:46.7 0.028 0.112 1.130 1.753 176.98 176.98 5.71 5.71 852 6931 14:12:53.92 +54:00:14.4 0.055 0.136 1.232 1.912 176.98 176.98 5.90 5.90 446 2232 14:13:14.97 +53:01:39.4 0.045 0.149 4.060 2.769 195.06 176.98 0.59 5.71 6 733 14:13:18.96 +54:32:02.4 0.048 0.041 1.408 1.294 191.86 176.98 0.66 5.71 64 2934 14:13:24.28 +53:05:27.0 0.029 0.055 1.250 1.298 195.06 176.98 0.79 5.71 60 2935 0.029 0.098 1.203 1.440 206.75 173.00 0.69 5.77 134 3836 14:14:17.13 +51:57:22.6 0.094 0.120 1.414 1.553 176.98 176.98 6.10 6.10 79 2537 0.032 0.406 3.880 8.170 195.07 176.98 0.82 5.71 8 438 14:15:32.36 +52:49:05.9 0.114 0.091 3.890 1.769 195.06 176.98 0.71 5.71 13 2039 14:16:25.71 +53:54:38.5 0.068 0.037 1.270 1.173 176.98 176.98 5.90 5.90 792 15240 0.053 0.010 1.290 1.104 206.75 173.00 1.02 5.77 84 5441 14:16:44.17 +53:25:56.1 0.044 0.095 1.165 1.550 176.98 176.98 5.90 5.90 301 3042 14:16:45.15 +54:25:40.8 0.072 0.282 1.308 3.842 176.98 176.98 5.71 5.71 440 2143 0.041 0.138 1.281 1.751 206.82 173.00 0.54 5.77 93 1644 14:16:45.58 +53:44:46.8 0.076 0.141 1.628 1.944 176.98 176.98 5.71 5.71 270 2145 0.025 0.031 1.198 1.434 206.82 173.00 0.53 5.77 76 1546 14:16:50.93 +53:51:57.0 0.037 0.106 1.160 1.566 176.98 176.98 5.90 5.90 181 3747 14:17:06.68 +51:43:40.1 0.038 0.045 1.142 1.217 176.98 176.98 5.71 5.71 473 5748 14:17:12.30 +51:56:45.5 0.115 0.348 12.431 5.887 206.78 176.98 0.42 5.90 9 449 0.115 0.602 12.431 9.087 206.78 173.00 0.42 5.97 9 350 14:17:24.59 +52:30:24.9 0.064 0.044 1.359 1.305 206.78 176.98 0.48 5.71 65 4051 0.064 0.018 1.359 1.287 206.78 173.00 0.48 5.77 65 2952 14:17:29.27 +53:18:26.5 0.014 0.050 1.147 1.426 195.06 176.98 0.67 5.71 118 3353 0.015 0.022 1.077 1.197 206.75 173.00 0.63 5.77 294 2954 14:17:51.14 +52:23:11.1 0.029 0.043 1.399 1.188 195.09 173.00 0.44 5.77 33 3655 14:18:56.19 +53:58:45.0 0.014 0.058 1.644 1.435 206.78 176.98 0.69 5.71 112 3556 14:19:23.37 +54:22:01.7 0.062 0.109 1.308 1.479 206.78 176.98 0.69 5.71 87 2657 0.062 0.061 1.308 1.305 206.78 173.00 0.69 5.77 87 2458 14:19:41.11 +53:36:49.6 0.056 0.041 3.212 1.443 195.11 176.98 0.56 5.71 32 2059 14:19:52.23 +53:13:40.9 0.088 0.035 1.859 1.516 206.78 176.98 0.67 5.71 24 1260 14:19:55.62 +53:40:07.2 0.047 0.131 1.253 2.014 206.78 153.02 0.84 5.67 50 11MNRAS000 , 1–19 (2020) LR Modeling Table 2 – continued α δ F var R span (∆ t ) (days) δt mean (days) SNR SNRNo. continuum line continuum line continuum line continuum line continuum line61 14:19:55.62 +53:40:07.2 0.047 0.038 1.253 1.617 206.78 148.05 0.84 5.92 50 1462 14:20:10.25 +52:40:29.6 0.109 0.201 2.217 2.753 195.10 176.98 0.55 5.71 25 2663 0.106 0.107 1.758 1.738 206.78 143.98 0.53 5.76 40 1464 14:20:23.88 +53:16:05.1 0.116 0.088 1.850 1.914 206.78 176.98 0.68 5.71 23 1065 14:20:38.52 +53:24:16.5 0.057 0.085 1.302 1.426 176.98 176.98 5.71 5.71 516 4966 0.022 0.029 1.368 1.218 206.79 173.00 0.46 5.77 84 2667 14:20:39.80 +52:03:59.7 0.070 0.105 1.245 1.601 176.98 176.98 5.90 5.90 415 5768 0.075 0.045 1.440 1.272 206.77 173.00 0.80 5.77 55 4569 14:20:43.53 +52:36:11.4 0.013 0.049 1.161 1.268 195.10 173.00 0.41 5.77 68 3270 14:20:49.28 +52:10:53.3 0.074 0.116 1.326 1.532 176.98 176.98 6.10 6.10 249 4471 0.113 0.148 1.684 2.295 195.09 176.98 0.70 5.71 24 1472 14:20:52.44 +52:56:22.4 0.018 0.029 1.128 1.142 206.78 176.98 0.68 5.71 71 7273 14:21:03.53 +51:58:19.5 0.010 0.069 1.160 1.699 206.77 176.98 0.80 5.71 149 3474 0.010 0.024 1.160 1.187 206.77 173.00 0.80 5.77 149 4475 14:21:12.29 +52:41:47.3 0.037 0.110 1.375 2.033 195.10 176.98 0.54 5.90 33 876 14:21:35.90 +52:31:38.9 0.021 0.293 1.184 3.738 206.77 176.98 0.66 5.71 89 1277 0.021 0.123 1.184 1.604 206.77 173.00 0.66 5.77 89 3378 14:24:17.22 +53:02:08.9 0.148 0.710 2.665 1.017 206.78 176.98 1.04 5.90 15 579 15:36:38.40 +54:33:33.2 0.045 0.047 1.184 1.249 109.65 109.65 2.49 2.49 185 28480 15:59:09.62 +35:01:47.6 0.053 0.035 1.284 1.147 55.86 55.86 2.15 2.15 124 12881 17:19:14.49 +48:58:49.4 0.309 0.099 3.964 1.731 8138.42 8392.42 71.39 71.73 11 3382 23:03:15.67 +08:52:25.3 0.035 0.062 1.204 1.381 137.80 108.86 0.50 1.51 140 51Note: Col. (1): Number. Col. (2): RA. Col. (3): Dec. Col. (4): Excess variance for continuum. Col. (5): Excess variance for line. Col. (6):Maximum to minimum flux ratio for continuum. Col. (7): Maximum to minimum flux ratio for line. Col. (8): Total duration ofobservation for continuum. Col. (9): Total duration of observation for line. Col. (10): Mean cadence of observation for continuum. Col.(11): Mean cadence of observation for line. Col. (12): Median signal to noise ratio for continuum. Col. (13): Median signal to noise ratiofor line. log F var N u m b e r continuumline Figure 1.
Distribution of excess variance, F var , of the objects stud-ied here. of the amplitude of variability, F var for both the continuumand line (that includes MgII, H β and H α ) are given in Fig.1. A two sample Kolmogorov-Smirnov (KS) test indicates that the two distributions are indeed different with a statis-tic of 0.317 and a p value of 4.0 × − . We found meanF var values of 0 . ± .
001 and 0 . ± .
012 for continuumand line, respectively. We have a total of 50 measurementsfor H β , 26 for H α and 6 for MgII line. Separating the sam-ple based on different lines, for H β sample, we found meanF var values of 0 . ± .
002 and 0 . ± .
012 for continuumand line, respectively. For H α sample, the mean F var valuesfor continuum and line are 0 . ± .
001 and 0 . ± . var of 0 . ± . . ± .
002 for continuum and line, respectively. TheF var in line is thus found to exceed than that of the con-tinuum. Such increased variations in emission lines relativeto the continuum support the deviation of BLR from thelinear response to the ionizing continuum (Rashed et al.2015; Li et al. 2013). Though photoionization models predictthat MgII line should be less responsive to the continuumthan Balmer lines (Korista & Goad 2000, 2004), Woo (2008)found F var in Mg II line higher than the continuum too, sim-ilar to what is found in this work. For intermediate-redshiftquasars the MgII line may originate almost in the same re-gion as H β , as can be seen in the cases of NGC 3783 andNGC 4151, for which similar time lags were obtained usingH β and MgII lines (Reichert et al. 1994; Peterson et al. 2004;Metzroth et al. 2006; Woo 2008). Therefore, it is possible todetect a similar kind of line variability in both the H β andMgII lines in these objects. MNRAS , 1–19 (2020)
Mandal et al.
Table 3.
Results of BLR modeling. The line light curves are from H β . For objects with *, detrending was done, while for others detrendingwas not done. For the objects with • the BLR model fits are shown in Fig. 2 and Fig. B1. α δ continuum log( τ d )(days) τ model (days) θ inc (degree) θ opn ( degree ) γ f BLR χ /dof . ± .
88 11 . ± . . ± .
43 46 . ± . − . ± .
10 — 1.1302:30:05.52 -08:59:53.2 — 0 . ± .
58 50 . ± .
30 67 . ± .
52 36 . ± .
93 0 . ± .
08 0 . ± .
36 1.2002:30:05.52 -08:59:53.2* — — 54 . ± .
54 75 . ± .
54 28 . ± .
49 — — 1.2006:52:12.32 +74:25:37.2 — — 43 . ± .
49 44 . ± .
61 44 . ± .
18 — — 1.4706:52:12.32 +74:25:37.2* — 2 . ± .
32 11 . ± .
54 32 . ± .
22 38 . ± . − . ± .
09 1 . ± .
19 1.6211:39:13.92 +33:55:51.1 — 0 . ± .
80 10 . ± . . ± .
59 47 . ± .
90 0 . ± .
15 — 0.9011:39:13.92 +33:55:51.1 — 0 . ± .
20 5 . ± .
66 56 . ± .
31 47 . ± .
27 0 . ± .
19 — 0.8511:39:13.92 +33:55:51.1* — — 5 . ± .
96 54 . ± .
86 47 . ± .
31 — — 0.9012:42:10.61 +33:17:02.7 — — 52 . ± .
74 73 . ± .
91 35 . ± .
71 — — 0.8912:42:10.61 +33:17:02.7* — 1 . ± .
32 51 . ± .
43 77 . ± .
85 25 . ± . − . ± .
12 0 . ± .
25 1.6013:42:08.39 +35:39:15.3 — 0 . ± .
10 2 . ± .
76 51 . ± .
92 48 . ± .
82 1 . ± .
28 — 1.0814:05:18.02 +53:15:30.0 g 1 . ± .
26 23 . ± .
46 47 . ± .
79 48 . ± . . ± .
82 — 1.0614:05:18.02 +53:15:30.0 i — 24 . ± .
90 45 . ± .
24 47 . ± .
98 — — 1.0814:07:59.07 +53:47:59.8 • — 0 . ± .
08 18 . ± .
50 65 . ± .
13 36 . ± .
54 1 . ± .
29 0 . ± .
38 1.2414:08:12.09 +53:53:03.3 g — 11 . ± .
50 39 . ± .
34 43 . ± .
13 — — 1.5114:08:12.09 +53:53:03.3 i 2 . ± .
82 11 . ± .
86 40 . ± .
47 44 . ± .
76 2 . ± .
18 — 1.1714:09:04.43 +54:03:44.2 g 2 . ± .
82 15 . ± .
40 44 . ± .
21 46 . ± .
96 0 . ± .
14 — 1.0114:09:04.43 +54:03:44.2 i — 19 . ± .
29 49 . ± .
77 48 . ± .
84 — — 0.8614:10:04.27 +52:31:41.0 g 0 . ± .
36 44 . ± .
03 51 . ± .
39 50 . ± .
49 2 . ± .
47 — 1.1314:10:18.04 +53:29:37.5 g 1 . ± .
62 15 . ± .
00 48 . ± .
93 47 . ± .
78 2 . ± .
41 — 0.8914:10:31.33 +52:15:33.8* g 1 . ± .
46 30 . ± .
52 29 . ± .
58 34 . ± .
56 2 . ± .
53 1 . ± .
62 2.9814:10:41.25 +53:18:49.0 i 2 . ± .
58 27 . ± .
66 32 . ± .
51 41 . ± .
78 0 . ± .
19 — 1.0214:11:12.72 +53:45:07.1 • — 0 . ± .
84 21 . ± .
60 26 . ± .
59 32 . ± .
17 0 . ± .
29 2 . ± .
05 0.9714:11:15.19 +51:52:09.0 i 1 . ± .
20 42 . ± .
86 62 . ± .
28 45 . ± .
42 0 . ± .
26 — 0.9814:11:23.42 +52:13:31.7 i 2 . ± .
64 15 . ± .
53 38 . ± .
10 45 . ± .
90 1 . ± .
15 — 0.7514:11:35.89 +51:50:04.5 g — 17 . ± .
72 45 . ± .
66 45 . ± .
90 — — 1.1514:11:35.89 +51:50:04.5 i 1 . ± .
26 17 . ± .
39 45 . ± .
68 45 . ± .
04 1 . ± .
73 — 1.0614:12:53.92 +54:00:14.4 — 0 . ± .
66 24 . ± .
14 42 . ± .
23 44 . ± . . ± .
39 — 1.0114:13:14.97 +53:01:39.4 g — 33 . ± .
13 49 . ± .
67 35 . ± .
01 — — 1.6514:13:14.97 +53:01:39.4 i 1 . ± .
90 33 . ± .
30 52 . ± .
20 42 . ± .
84 1 . ± .
71 — 1.4214:13:18.96 +54:32:02.4 g 1 . ± .
06 20 . ± .
32 30 . ± .
58 31 . ± .
12 1 . ± .
48 1 . ± .
00 1.3214:13:18.96 +54:32:02.4 i — 19 . ± .
08 47 . ± .
97 44 . ± .
80 — — 1.5314:13:24.28 +53:05:27.0 g — 29 . ± .
51 53 . ± .
36 45 . ± .
19 — — 1.0214:13:24.28 +53:05:27.0 i 1 . ± .
62 21 . ± .
83 53 . ± .
75 47 . ± .
18 0 . ± .
24 — 0.8614:14:17.13 +51:57:22.6 i 2 . ± .
84 11 . ± .
14 41 . ± .
69 43 . ± .
08 1 . ± .
66 — 2.0014:14:17.13 +51:57:22.6* i — 11 . ± .
66 43 . ± .
71 44 . ± .
01 — 1.9714:15:32.36 +52:49:05.9 i − . ± .
14 7 . ± .
64 44 . ± .
95 44 . ± .
17 0 . ± .
27 — 1.1814:16:25.71 +53:54:38.5 — — 37 . ± .
28 41 . ± .
29 52 . ± .
13 — — 1.0214:16:25.71 +53:54:38.5* — 1 . ± .
12 26 . ± . . ± .
79 39 . ± .
38 0 . ± .
11 0 . ± .
30 1.6114:16:45.15 +54:25:40.8 — — 22 . ± .
89 58 . ± .
50 46 . ± .
53 — — 1.7514:16:45.15 +54:25:40.8* — 0 . ± .
90 19 . ± .
34 53 . ± .
09 49 . ± .
75 2 . ± .
21 — 1.6514:16:45.58 +53:44:46.8 — 0 . ± .
74 17 . ± .
87 41 . ± .
84 48 . ± .
78 2 . ± .
38 — 1.1014:17:06.68 +51:43:40.1 — — 25 . ± .
29 50 . ± . . ± .
50 — — 2.3614:17:06.68 +51:43:40.1* • — 1 . ± .
32 22 . ± .
95 57 . ± .
62 51 . ± .
78 1 . ± .
41 — 1.5014:17:12.30 +51:56:45.5 g 2 . ± .
56 17 . ± .
55 42 . ± .
37 44 . ± . . ± .
40 — 1.2414:17:24.59 +52:30:24.9 g 2 . ± .
42 19 . ± .
28 39 . ± .
99 43 . ± .
19 0 . ± .
46 — 1.3914:17:29.27 +53:18:26.5 g — 13 . ± .
96 48 . ± .
21 46 . ± .
17 — — 1.4314:17:29.27 +53:18:26.5 i 1 . ± .
30 13 . ± .
38 45 . ± .
07 45 . ± .
06 1 . ± .
53 — 1.3414:18:56.19 +53:58:45.0 g — 34 . ± .
56 39 . ± .
28 44 . ± .
30 — — 2.2914:18:56.19 +53:58:45.0* g 0 . ± .
74 17 . ± .
89 40 . ± .
97 43 . ± .
66 2 . ± .
53 — 2.3214:19:23.37 +54:22:01.7 g 2 . ± .
58 15 . ± .
93 48 . ± .
69 46 . ± .
82 0 . ± .
20 — 1.3514:19:41.11 +53:36:49.6 g — 26 . ± .
56 45 . ± .
78 45 . ± .
06 — — 1.5114:19:41.11 +53:36:49.6 i 2 . ± .
50 33 . ± .
66 40 . ± .
57 43 . ± .
54 0 . ± .
54 — 1.3314:19:52.23 +53:13:40.9 g 2 . ± .
58 21 . ± .
70 36 . ± .
47 42 . ± .
07 0 . ± .
81 — 1.7314:19:55.62 +53:40:07.2 g 2 . ± .
54 8 . ± .
76 42 . ± .
21 43 . ± .
02 2 . ± .
24 — 1.4314:20:10.25 +52:40:29.6* i 1 . ± .
66 5 . ± .
96 61 . ± .
02 39 . ± .
76 2 . ± .
04 0 . ± .
39 7.0914:20:23.88 +53:16:05.1 g 2 . ± .
42 11 . ± .
60 53 . ± .
47 45 . ± .
72 0 . ± .
63 — 1.4714:20:23.88 +53:16:05.1 i — 14 . ± .
43 52 . ± .
91 44 . ± .
07 — — 1.3714:20:38.52 +53:24:16.5 — 1 . ± .
14 25 . ± .
33 50 . ± .
85 51 . ± .
20 0 . ± .
22 — 1.0514:20:39.80 +52:03:59.7 — — 29 . ± .
07 22 . ± .
81 27 . ± .
85 — — 1.5614:20:39.80 +52:03:59.7* — 0 . ± .
00 27 . ± .
51 27 . ± .
09 33 . ± .
82 1 . ± .
36 1 . ± .
92 1.0214:20:49.28 +52:10:53.3 g — 47 . ± .
19 14 . ± .
98 19 . ± .
13 — — 2.0114:20:49.28 +52:10:53.3 i 2 . ± .
60 46 . ± .
44 17 . ± .
38 25 . ± . − . ± .
12 3 . ± .
33 1.8514:20:49.28 +52:10:53.3* i — 42 . ± .
59 26 . ± .
62 34 . ± .
34 — — 1.2114:20:52.44 +52:56:22.4 g 0 . ± .
94 16 . ± .
07 49 . ± .
60 48 . ± .
68 0 . ± .
24 — 0.7114:21:03.53 +51:58:19.5 g 1 . ± .
20 20 . ± .
99 37 . ± .
62 38 . ± .
71 2 . ± .
32 1 . ± .
07 2.8314:21:12.29 +52:41:47.3 g — 18 . ± .
35 41 . ± .
47 44 . ± .
07 — — 1.1314:21:12.29 +52:41:47.3 i 1 . ± .
34 15 . ± .
25 42 . ± .
63 45 . ± .
13 2 . ± .
59 — 1.1514:21:35.90 +52:31:38.9 g — 7 . ± .
79 15 . ± .
91 20 . ± .
85 — — 8.0614:21:35.90 +52:31:38.9* • g 2 . ± .
42 6 . ± .
14 15 . ± .
49 21 . ± .
72 2 . ± .
04 4 . ± .
20 8.1414:24:17.22 +53:02:08.9 g 2 . ± .
80 19 . ± .
46 47 . ± .
15 46 . ± .
20 2 . ± .
45 — 2.38
MNRAS000
MNRAS000 , 1–19 (2020)
LR Modeling Table 3 – continued α δ continuum log( τ d ) (days) τ model (days) θ inc (degree) θ opn (degree) γ f BLR χ /dof . ± .
22 26 . ± .
92 63 . ± .
38 47 . ± .
73 0 . ± .
15 — 1.2915:59:09.62 +35:01:47.6 — 1 . ± .
16 13 . ± .
46 57 . ± .
92 49 . ± .
99 0 . ± .
16 — 1.4217:19:14.49 +48:58:49.4 — 1 . ± .
54 65 . ± .
93 64 . ± .
44 45 . ± . − . ± .
03 — 1.1217:19:14.49 +48:58:49.4* — — 65 . ± .
10 58 . ± .
23 49 . ± .
21 — — 1.2123:03:15.67 +08:52:25.3 — — 52 . ± .
86 54 . ± .
46 10 . ± . . ± .
22 7 . ± .
41 42 . ± .
72 44 . ± .
45 0 . ± .
08 — 2.16
Table 4.
Results for H α and Mg II lines. For objects with *, detrending was done, while for others detrending was not done. For theobjects with • the BLR model fits are shown in Fig. 2 and Fig. B1 . α δ continuum log( τ d ) (days) τ model (days) θ inc (degree) θ opn (degree) γ χ /dof . ± .
02 2 . ± .
24 42 . ± .
05 42 . ± .
29 1 . ± .
28 1.5614:05:18.02 +53:15:30.0 g 1 . ± .
09 20 . ± .
03 43 . ± .
63 45 . ± .
51 0 . ± .
06 1.6314:05:51.99 +53:38:52.1 g 1 . ± .
60 41 . ± .
92 40 . ± .
22 45 . ± .
43 0 . ± .
75 1.3614:08:12.09 +53:53:03.3 g 2 . ± .
21 11 . ± .
54 40 . ± .
48 44 . ± .
00 1 . ± .
37 1.0814:09:15.70 +53:27:21.8 g 1 . ± .
52 46 . ± .
90 32 . ± .
35 38 . ± .
43 2 . ± .
46 0.9214:10:04.27 +52:31:41.0 g 1 . ± .
14 7 . ± .
72 47 . ± .
67 45 . ± .
02 0 . ± .
04 1.6014:10:18.04 +53:29:37.5 g 1 . ± .
51 23 . ± .
05 39 . ± .
69 45 . ± .
30 1 . ± .
72 1.0314:10:41.25 +53:18:49.0 g — 26 . ± .
19 32 . ± .
69 39 . ± .
91 — 1.1414:10:41.25 +53:18:49.0 i 2 . ± .
41 21 . ± .
21 37 . ± .
96 43 . ± . − . ± .
08 0.9414:11:15.19 +51:52:09.0 g 0 . ± .
10 1 . ± .
05 45 . ± .
93 45 . ± .
99 0 . ± .
93 1.3914:11:23.42 +52:13:31.7 g 2 . ± .
35 39 . ± .
60 46 . ± .
38 48 . ± .
25 0 . ± .
10 0.9414:13:24.28 +53:05:27.0 g 2 . ± .
26 47 . ± .
86 35 . ± .
00 43 . ± . − . ± .
32 0.5814:16:25.71 +53:54:38.5 g 2 . ± .
24 38 . ± .
20 38 . ± .
54 45 . ± . − . ± .
19 0.9514:16:45.15 +54:25:40.8 g 2 . ± .
51 17 . ± .
40 51 . ± .
10 49 . ± .
71 2 . ± .
32 1.1614:16:45.58 +53:44:46.8 g 1 . ± .
14 18 . ± .
47 44 . ± .
35 45 . ± .
07 1 . ± .
84 1.3214:17:12.30 +51:56:45.5 • g 2 . ± .
35 3 . ± .
12 43 . ± .
21 44 . ± . − . ± .
48 1.5114:17:24.59 +52:30:24.9 g 2 . ± .
21 6 . ± .
55 43 . ± .
72 44 . ± . − . ± .
27 1.3414:17:29.27 +53:18:26.5 g 1 . ± .
27 3 . ± .
92 45 . ± .
83 45 . ± .
93 0 . ± .
77 1.6714:17:51.14 +52:23:11.1 g — 17 . ± .
44 48 . ± .
32 46 . ± .
07 — 0.9414:17:51.14 +52:23:11.1 i 1 . ± .
17 13 . ± .
68 47 . ± .
29 45 . ± .
99 0 . ± .
26 0.8614:19:23.37 +54:22:01.7 g 2 . ± .
50 62 . ± .
74 40 . ± .
54 42 . ± .
31 0 . ± .
24 1.2114:19:55.62 +53:40:07.2 g 2 . ± .
39 3 . ± .
67 46 . ± .
89 45 . ± .
41 0 . ± .
66 1.1714:20:10.25 +52:40:29.6 g 2 . ± .
37 46 . ± . . ± .
53 44 . ± .
25 0 . ± .
39 1.7314:20:38.52 +53:24:16.5 g 1 . ± .
14 24 . ± .
53 49 . ± .
44 46 . ± .
83 0 . ± .
34 0.9414:20:39.80 +52:03:59.7 g 2 . ± .
57 35 . ± .
38 37 . ± .
81 42 . ± . − . ± .
09 1.2614:20:43.53 +52:36:11.4 i 1 . ± .
73 3 . ± .
65 44 . ± .
20 43 . ± .
30 2 . ± .
35 1.5214:21:03.53 +51:58:19.5 g 1 . ± .
12 5 . ± .
29 45 . ± .
76 44 . ± .
91 0 . ± .
58 1.2314:21:35.90 +52:31:38.9 g — 14 . ± .
46 29 . ± .
67 37 . ± .
13 — 2.3014:21:35.90 +52:31:38.9* g 2 . ± .
24 13 . ± .
27 30 . ± . . ± .
54 2 . ± .
06 2.1414:10:18.04 +53:29:37.5 — 0 . ± .
61 32 . ± .
74 44 . ± .
21 43 . ± .
54 2 . ± .
26 1.3014:12:14.20 +53:25:46.7* • — 0 . ± .
86 38 . ± .
95 4 . ± .
79 6 . ± .
97 2 . ± .
03 4.9114:14:17.13 +51:57:22.6 — 0 . ± .
49 28 . ± .
42 46 . ± .
77 46 . ± .
84 0 . ± .
24 0.9214:16:44.17 +53:25:56.1 — − . ± .
10 19 . ± .
90 32 . ± .
46 36 . ± .
58 1 . ± .
36 1.1314:16:50.93 +53:51:57.0 — 0 . ± .
04 17 . ± .
67 45 . ± .
06 44 . ± .
23 2 . ± .
39 1.0714:20:49.28 +52:10:53.3 — 1 . ± .
20 34 . ± .
24 62 . ± .
69 47 . ± .
15 1 . ± .
26 1.23
Modeling of the BLR using a Bayesian approach was devel-oped by Pancoast et al. (2011) and subsequently applied toArp 151 (Brewer et al. 2011) and Mrk 50 (Pancoast et al.2012). In addition to Mrk 50 and Arp 151, more AGN weresubjected to BLR modeling (Pancoast et al. 2014; Grier et al.2017a; Williams et al. 2018; Li et al. 2013). The BLR mod-eling used in this work is based on Li et al. (2013), whichis an independent implementation of the approach of Pan-coast et al. (2011), however, with the additional inclusion of(a) non-linear response of emission lines to the continuum variations and (b) option to carry out a detrending of thelight curves. Here, we analysed the data for 57 objects with82 independent measurements for H β , H α and MgII lines,which is twice the number of AGN studied earlier (Li et al.2013) for uncovering the characteristics of BLR. We show inFig. 2 few examples to illustrate our BLR model fits to theirobserved continuum and line reverberation data. The modelreproduces the observed light curves for all the objects. Inthese plots the data points with error bars are the observedlight curves and the thick solid lines are the reconstructedlight curves by the model. For the object J1412+534, few MNRAS , 1–19 (2020) Mandal et al. points of the observed line light curve deviate from the re-constructed light curve. These points are also found to de-viate from the general trend of the observed line light curvethat results of larger χ /dof value of 4.91 pointing to poorfitting to the light curve. For the object J1421+525, there isa discrepancy between the observed and modeled line lightcurve. The χ /dof of 8.14 obtained here could be due topoor sampling and/or SNR of the emission line measure-ments. The corresponding transfer functions for those fourobjects are given in the right hand panel of Fig. 2. We foundthe transfer functions to have different shapes. For exam-ple in J1412+534 (top panel; α = 14:12:14.20, δ =53:25:46.7), the transfer function is single peaked at τ = τ lag . For this object the BLR modeling gives θ inc = 4.0 ± θ opn = 6.0 ± α = 14:07:59.07, δ = 53:47:59.8) isdouble peaked, for which we obtain θ inc = 65.0 ± θ opn = 37.0 ± α = 14:17:06.68, δ = 51:43:40.1), the transfer func-tion has a top hat structure with derived θ inc and θ opn of57.9 ± ± θ inc tends to produce a double-peaked transfer function, asseen in the case of object J1407+537 (third panel of Fig.2 from the top) with θ inc = 65.0 ± θ inc in-creases, the object appears more edge on and the radiationcoming both from the front and back surfaces makes a dou-ble peak transfer function where the stronger peak appearscloser to the center. b) a larger opening angle θ opn tendsto broaden the transfer functions toward top-hat as seen incase of J1417+517 (bottom panel of Fig. 2) which has a θ opn of 51.8 ± θ opn increases the BLR tends to aspherical geometry and the virial motion of the clouds con-tributes to the transfer function making the transfer functionbroaden towards a top-hat structure.We show in Fig. 3 the distribution of χ /dof ob-tained for the best fit model returned by PBMAP. Thefits are indeed bad (with χ /dof >
4) for a few sources,namely J141214.20+532546.7, J141941.11+533649.6 andJ142135.90+523138.9. These sources have poor quality (lessnumber of points and sparsely sampled) data and is the likelycause for large χ /dof. Though the overall distribution of χ /dof seems skewed to values larger than 1.0, in majorityof the sources, we obtained a low χ /dof close to 1.0. Forabout 60% of the light curves we obtained χ /dof ≤ χ /dof in some objects is due to them having contin-uum and line light curves with SNR <
50. Also, systematicerrors due to calibration which are usually not included inthe reported uncertainties of the original data could affectthe χ value. Overall, the continuum and emission line lightcurves generated by the model are in good agreement withthe observed data.Fig. 4 shows the distribution of the non-linearity pa-rameter γ obtained from modeling, we found < γ MgII > = 1 . ± . < γ Hβ > = 1 . ± .
03 and < γ Hα > = 0 . ± . β and H α , respectively. This clearly indicates anon-linear response of emission-lines from BLR to the ioniz-ing optical continuum. Such non-linear response of line fluxto the ionizing continuum can be due to the anisotropic andnon axis-symmetric emission coming from different spectralregions in AGN (Korista & Goad 2000, 2004; Gaskell et al.2019). Note that the shorter wavelength UV continuum usu-ally vary larger compared to the longer wavelength opticalcontinuum, therefore, depending on the continuum, the re-sponse of a given emission line could be different (O’Brienet al. 1995; Zhu et al. 2017). ˚A for H β line fitting Kelly et al. (2009) modeled the light curves of 100 quasarsusing DRW and found the time scale of variability to cor-relate with luminosity. Recently, Lu et al. (2019) performedDRW modeling of 73 AGN including high-accreting sources,which are also studied here. They found that the dampingtime scale is strongly correlated with luminosity with a slopeof 0 . ± .
09. However, MacLeod et al. (2010) using SDSSstripe 82 data, did not find any strong correlation with lu-minosity. In our fitting, emission line and continuum modelparameters are fitted simultaneously allowing us to studythis relation.We show in Fig. 5 the dependence of the derived restframe damping time scale on the observed host-galaxy cor-rected continuum luminosity at 5100 ˚A. We found that thedamping time scale τ d is positively correlated with the lu-minosity at 5100 ˚A. From linear least squares fitting to thedata we foundlog (cid:18) τ d ( Hβ ) (cid:19) = β + α log( λL λ )(5100˚A) (9)with α = 0 . ± .
06 and β = − . ± .
67. The slopeof the correlation is similar to the value of α = 0 . ± . β lags. We note that the scatter in the relationis much higher than Lu et al. (2019), mainly because theymodeled continuum light curves with only two main parame-ters while we fitted both continuum and BLR model parame-ters simultaneously. Moreover, their sample does not includeSDSS RM sample, which has relatively less time samplingand variability. A carefully analysis suggests that the moredeviant points have lower variability and hence the modelparameters are not well constrained.To check the correlation between the damping timescale and luminosity at 5100 ˚A, we estimated the Spear-man rank correlation coefficient (r s ) using Monte Carlo sim-ulation where each point in the τ d − λ L λ plane is modifiedby a random Gaussian deviate consistent with the mea-sured uncertainty. From the distribution obtained for 10000Monte Carlo iterations, the median value of r s is found tobe 0 . +0 . − . with a probability ( p ) of no correlation of0 . +0 . − . . The upper and lower errors are the values atthe 15.9 and 84.1 percentile of the distributions of those10000 iterations. Koz(cid:32)lowski (2017a,b) suggested that deriv-ing damping time from short duration light curves leads to MNRAS000
67. The slopeof the correlation is similar to the value of α = 0 . ± . β lags. We note that the scatter in the relationis much higher than Lu et al. (2019), mainly because theymodeled continuum light curves with only two main parame-ters while we fitted both continuum and BLR model parame-ters simultaneously. Moreover, their sample does not includeSDSS RM sample, which has relatively less time samplingand variability. A carefully analysis suggests that the moredeviant points have lower variability and hence the modelparameters are not well constrained.To check the correlation between the damping timescale and luminosity at 5100 ˚A, we estimated the Spear-man rank correlation coefficient (r s ) using Monte Carlo sim-ulation where each point in the τ d − λ L λ plane is modifiedby a random Gaussian deviate consistent with the mea-sured uncertainty. From the distribution obtained for 10000Monte Carlo iterations, the median value of r s is found tobe 0 . +0 . − . with a probability ( p ) of no correlation of0 . +0 . − . . The upper and lower errors are the values atthe 15.9 and 84.1 percentile of the distributions of those10000 iterations. Koz(cid:32)lowski (2017a,b) suggested that deriv-ing damping time from short duration light curves leads to MNRAS000 , 1–19 (2020)
LR Modeling F continuumSNR=851.9156650 56675 56700 56725 56750 56775 56800 56825 56850 MJD F M g II lineSNR=69.19 0 20 40 60 80 1000.000.010.020.030.040.050.060.07 T r a n s f e r F un c t i o n /dof=4.91100110120 F gb a n d continuumSNR=88.686650 6700 6750 6800 6850 MJD 50000 F H lineSNR=12.27 0 5 10 15 200.0000.0250.0500.0750.1000.1250.1500.1750.200 T r a n s f e r F un c t i o n /dof=8.14131415 F continuumSNR=987.3656650 56675 56700 56725 56750 56775 56800 56825 56850 MJD F H lineSNR=70.42 0 20 40 60 80 1000.0000.0050.0100.0150.0200.0250.0300.035 T r a n s f e r F un c t i o n /dof=1.243.23.43.6 F continuumSNR=472.5156650 56675 56700 56725 56750 56775 56800 56825 56850 MJD F H lineSNR=57.32 0 20 40 60 80 1000.0000.0050.0100.0150.020 T r a n s f e r F un c t i o n /dof=1.5 Figure 2.
Examples of BLR model fits to four objects J1412+534,J1421++525, J1407+537 and J1417+517 from top to bottom,respectively. In the left hand panels, the data points with errorbars are the observed light curves. The thick solid lines are thereconstructed light curve. The grey shaded areas represent theuncertainties in the reconstructed light curves. The correspondingtransfer function for each objects are shown on the right handpanels. biased results and the time length of the light curve mustbe 10 times the true damping time scale. We note that re-verberation light curves are usually shorter in length com-pared to the long-term survey light curves such as thosefrom the Sloan Digital Sky Survey and the Catalina RealTime Transient Survey. In fact, the median ratio of the to-tal span (∆t) of the light curves to the damping time scale τ d is 4.84 and 4.35 for continuum and line light curves, respec-tively. Considering objects with light curve length > × τ d ,which includes a total 20 objects from our sample and 21 / dof N u m b e r Figure 3.
Distribution of χ /dof returned by the models for theobjects analysed in this work. N u m b e r MgIIHH
Figure 4.
Distribution of non-linearity parameter γ for differentemission lines. objects from Li et al. (2013), the Spearman rank correla-tion coefficient is found to be 0 . +0 . − . with p -value of0 . +0 . − . (10000 iterations) for the τ d − λ L λ relation. Theleast-square fit using Equation 9 provides α = 0 . ± .
08 and β = − . ± .
50. The correlation thus obtained between τ d and λ L λ is significant at greater than 90% level. This resultis consistent with Lu et al. (2019), who studied the opticalvariability characteristic of reverberation mapped AGN andfound α = 0 . ± .
09 and β = − . ± .
06 in the τ d − λ L λ relation, for sources with light curve lengths greater than 10times τ d . R modBLR and R CCFBLR
In Fig. 6 we show a comparison of the size of the BLR derivedby the modeling approach ( R modBLR ) with that obtained usingthe conventional cross-correlation function (CCF) analysis MNRAS , 1–19 (2020) Mandal et al. L (5100Å) d ( d a y s )( H ) This WorkLi et al. (2013)
Figure 5.
Relation between the damping time scale ( τ d ) and themonochromatic continuum luminosity at 5100 ˚A. Here, the filledgreen circles are the objects studied in this work, while filledblack circles represent the objects taken from Li et al. (2013).The dashed red line is the best fit to the data points includingmeasurements from this work and Li et al. (2013). ( R CCFBLR ). The model BLR size is in general consistent withthat obtained from CCF, however, with a large scatter. Themedian of the ratio between BLR size estimated by modelingand CCF is 1 .
09 with standard deviation of 1 . R BLR larger than thatobtained by CCF analysis, a few others have model R BLR smaller than that of CCF. The median of the ratio of R BLR model to R BLR
CCF (see lower panel of Fig. 6) is found tobe 1 . ± .
24, where 3 objects are found to deviate fromthe unit ratio by a factor larger than 3. The objects thatshow larger deviation from the R mod BLR = R CCF
BLR line also havelarge χ /dof ( > R BLR . Reverberation mapping observation over the years have ledto a power law relation ( R BLR ∝ L α ) between the size of theBLR and the optical luminosity of the AGN. The R BLR − L relation is very important as it enables the determination ofM BH from single epoch spectroscopic observations. Also the R BLR − L relation can provide a means to consider AGN asstandard candles (Loli Mart´ınez-Aldama et al. 2019). There-fore, it is important to check if the derived R BLR from fit-ting shows the power law dependence with luminosity thatwe know from observation. As we have sources over a var-
BLR size using CCF method (days) B L R s i z e u s i n g m o d e l ( d a y s ) H lags H lags MgII lags R BLR ( model ) / R BLR ( CCF ) N u m b e r Figure 6. (Top) Comparison of the BLR size obtained in this workfrom the model and that from CCF analysis taken from literature.Red colored circles correspond to H β lags, whereas green and bluecircles correspond to H α and Mg II lags, respectively. The blackdashed line shows y=x, while the blue dashed lines are y = x ± σ ,where σ = 15 .
59 days is the standard deviation of the BLR sizesobtained from CCF analysis. (bottom) Distribution of the ratio ofthe BLR size using model ( R BLR ( model ) ) to that obtained fromCCF ( R BLR ( CCF ) ). ied range of redshift, R BLR from model fitting has beenfound using lines of H β , H α and Mg II. The relation be-tween R BLR and luminosity for H β is shown in Fig. 7. Notethat we adopted host-corrected luminosities from the origi- MNRAS000
59 days is the standard deviation of the BLR sizesobtained from CCF analysis. (bottom) Distribution of the ratio ofthe BLR size using model ( R BLR ( model ) ) to that obtained fromCCF ( R BLR ( CCF ) ). ied range of redshift, R BLR from model fitting has beenfound using lines of H β , H α and Mg II. The relation be-tween R BLR and luminosity for H β is shown in Fig. 7. Notethat we adopted host-corrected luminosities from the origi- MNRAS000 , 1–19 (2020)
LR Modeling nal literature . Details on host-subtraction can be found inthe original literature.Using weighted linear least squares fit we obtained thefollowing relationlog (cid:18) R BLR( Hβ ) (cid:19) = β + α log( λL λ )(5100˚A) (10)with α = 0.58 ± β = − ± α = 0 . +0 . − . and β = − . +2 . − . obtained by Bentz et al. (2009) with R BLR obtained byCCF analysis of the observed continuum and line lightcurves. Bentz et al. (2013) found a slope of α = 0 . +0 . − . and β = 1 . +0 . − . considering lag-luminosity relation oflog (cid:16) R BLR(H β ) (cid:17) = β + α log( λ L λ / erg s − ) (5100˚A). Ourvalues closely match with those obtained by Bentz et al.(2013) considering the uncertainties. Li et al. (2013) usingthe approach adopted in this work for 40 quasars with Hβ measurements found a value of α = 0.55 ± β line.Similarly, the relation between R BLR and L for ob-jects with H α measurements is shown in Fig. 8. We usedonly measurements with fractional error less than 1. Usingweighted linear least squares fit to the data we foundlog (cid:18) R BLR( Hα ) (cid:19) = β + α log( λL λ )(5100˚A) (11)with α = 0 . ± .
12 and β = − . ± .
16 as shown by thedashed blue line. Using unweighted linear least squares fitto the data as shown by dashed red line, we foundlog (cid:18) R BLR( Hα ) (cid:19) = β + α log( λL λ )(5100˚A) (12)with α = 0 . ± .
08 and β = − . ± .
67 which closelymatches with α =0.5 based on simple photoionization argu-ments. We note that the unweighted fit is driven by a sin-gle data point at low luminosity. This point corresponds tothe object J1342+356 (NGC 5273), which has a luminos-ity of log L AGN = 41 . ± .
144 erg s − and a BLR size of2 . +1 . − . days based on H α line obtained from traditionalCCF analysis by Bentz et al. (2014). The BLR size obtainedfrom our modeling approach is 2 . ± .
24 days which isconsistent with that obtained by Bentz et al. (2014).We have six objects with Mg II line light curves. Forthose objects the relation between R
BLR and L is givenin Fig. 9. We plotted the data with the formlog (cid:18) R BLR(
MgII ) (cid:19) = β + α log( λL λ )(5100˚A) (13)and we found α = 0 . ± .
08 and β = − . ± .
58. The re-lation between R BLR and luminosity of Mg II deviates fromthe value expected from photoionization argument. This isonly due to the poor quality of measurement available onsmall number of sources. We note that the R BLR − L re-lation of H α line has a luminosity range of 10 . to 10 . erg s − and majority of them are above 10 erg s − , whereasfor Mg II line the luminosity ranges only between 10 . to10 . erg s − . R BLR measurements on large number of ob-jects spanning over a wide range of luminosities are needed In Fig. 7, we excluded one measurement for which the host-corrected luminosity is not available in the literature L (5100Å) R B L R ( H ) ( m o d e l )( d a y s ) This WorkLi et al. (2013)
Figure 7.
Relation between the radius of the BLR obtained fromthe model for sources with H β light curves and their continuumluminosity at 5100 ˚A. Here, filled green circles are the objectsstudied in this work, while the filled black circles are the objectsfrom Li et al. (2013). The dashed red line is the best fit to thedata points including measurements from this work and Li et al.(2013). to firmly establish the relationship between R BLR and lumi-nosity based on H α and Mg II emission lines and therefore,the coefficients of Equations 12 and 13, should be taken withcaution. f BLR
The virial factor f BLR given in Equation 1 depends on fac-tors such as the kinematics, geometry and inclination of theBLR. One of the many factors provided by the Bayesianbased modeling approach carried out here is the capabilityto estimate f BLR . For a disk like BLR, (see Collin et al. 2006;Li et al. 2013; Rakshit et al. 2015) f BLR can be written as f BLR ≈ (sin θ opn + sin θ inc ) − (14)where θ inc is the inclination angle and θ opn is the open-ing angle of the disk. Following Li et al. (2013) we calculated f BLR for only those objects with θ opn < ◦ . Our calculatedvalues of f BLR range from 0.79 to 4.94, with a mean valueof 1 . ± .
77. A distribution of f BLR is shown in Fig. 10.Collin et al. (2006) found a value of < log( f BLR ) > = 0.18.Our average value of < log( f BLR ) > = 0.17 closely matcheswith that found by Collin et al. (2006). The large error barsin our f BLR values are due to large uncertainties in both θ inc and θ opn .It is also possible to get an estimate of f BLR for sourcesthat have stellar velocity dispersion measurements. For lo-cal inactive galaxies a tight correlation is known to exist be-tween M BH and bulge or spheroid stellar velocity dispersion( σ ∗ ). This correlation (Ferrarese & Merritt 2000; Gebhardt MNRAS , 1–19 (2020) Mandal et al. L (5100Å) R B L R ( H ) ( m o d e l )( d a y s ) Unweighted best linear fitWeighted best linear fit
Figure 8. R BLR v/s luminosity relation for sources with H α lightcurves. The dashed blue and red lines are the weighted and un-weighted linear least squares fit, respectively, to the data points. L (5100Å) R B L R ( M g II ) ( m o d e l )( d a y s ) Figure 9.
Relation between the radius of the BLR and the con-tinuum luminosity for objects with MgII line light curves. Thedashed red line is the weighted linear least squares fit to the datapoints. et al. 2000) is given aslog (cid:18) M BH M (cid:12) (cid:19) = α + β log (cid:16) σ ∗
200 kms − (cid:17) (15)with α = 8 . ± .
06 and β = 4 . ± .
32 (Tremaine et al.2002). Assuming AGN too follow the above equation, onecan estimate M BH . Comparing this M BH with the virialproduct VP = (cid:16) ∆ V R BLR G (cid:17) obtained by reverberation map- f BLR ( model ) N u m b e r < f BLR ( model ) > = 1.78 ± 1.77 Figure 10.
Distribution of the virial factor f BLR obtained for theobjects analysed in this work ping, we can get an estimate of f BLR as f BLR = M σ ∗ BH VP . (16)For a total of seven sources in our sample, we could ob-tain both the f BLR measurements, one based on the Bayesianbased BLR modeling approach and the other obtained fromthe ratio of M BH based on Equation 15 to the virial productobtained from RM. We found a good correlation between thetwo virial factors (see Fig. 11). Considering the dispersionof ∼ . M BH − σ ∗ relation our 1D modeling ap-proach is able to provide f BLR consistent with that obtainedfrom RM method and M BH and σ ∗ relation. From linear leastsquares fit to the data points in Fig. 11, we found a Spear-man rank correlation coefficient of 0 . +0 . − . and a p-value of0 . +0 . − . . Removing the data point with f BLR >
10, also theone with very large uncertainty, linear least squares fit gavea linear correlation coefficient of 0.14 +0 . − . and a p value of0 . +0 . − . . Though, the points are scattered around the dot-ted line in Fig. 11, the derived f BLR(model) have large errorbars and this could be the reason for no tight correlation be-tween the scale factors obtained by both the methods. Mostof the values of f
BLR(model) are found to be lesser than 3,which points to a BLR with a thick geometry and viewed atan inclination angle. Given the fact that f BLR has a largerange, the M BH values obtained from single epoch measure-ments adopting a single f BLR are bound to have large un-certainties. Mej´ıa-Restrepo et al. (2018) by comparing M BH obtained by accretion disk model fitting and virial methodsfound that f BLR is correlated with the width of the broademission lines as f BLR ∝ FWHM − .Also, the ratio of FWHM to the line dispersion of broadH β line is suggested to be correlated with the inclination an-gle (Collin et al. 2006; Goad et al. 2012). However, Pancoastet al. (2014) could not find any correlation using a smallsample of 5 objects having good quality measurements. Weused the available FWHM and line dispersion measurementsfrom the RMS spectra of broad H β line collected from theliterature. We plot the inclination angle from the model as a MNRAS000
BLR(model) are found to be lesser than 3,which points to a BLR with a thick geometry and viewed atan inclination angle. Given the fact that f BLR has a largerange, the M BH values obtained from single epoch measure-ments adopting a single f BLR are bound to have large un-certainties. Mej´ıa-Restrepo et al. (2018) by comparing M BH obtained by accretion disk model fitting and virial methodsfound that f BLR is correlated with the width of the broademission lines as f BLR ∝ FWHM − .Also, the ratio of FWHM to the line dispersion of broadH β line is suggested to be correlated with the inclination an-gle (Collin et al. 2006; Goad et al. 2012). However, Pancoastet al. (2014) could not find any correlation using a smallsample of 5 objects having good quality measurements. Weused the available FWHM and line dispersion measurementsfrom the RMS spectra of broad H β line collected from theliterature. We plot the inclination angle from the model as a MNRAS000 , 1–19 (2020)
LR Modeling f BLR f B L R ( m o d e l ) Figure 11.
Relation between f BLR( model ) obtained from model fitsand f BLR calculated from the ratio of M BH from stellar velocitydispersion ( σ ∗ ) to the virial product (VP). The dashed red linerepresents the y=x line. log (FWHM/ ) i n c i n d e g r ee s Figure 12.
Inclination angle from model as a function of the ratioof the FWHM to the line dispersion σ of the H β line. function of the ratio of the FWHM to the line dispersion inFig. 12. We do not find any strong correlation. Though ourmeasurements have large error bars, the results agree withthe finding of Pancoast et al. (2014). M BH and accretion rates Black hole masses are calculated using Equation 1, wherewe adopted f BLR and R BLR of the H β line obtained fromthe model. The velocity width ∆ V can be measured eitherfrom the full width at half maximum (FWHM) or from theline dispersion σ H β . We estimated the black hole masses for × × σ ∗ (km s − ) × × × l og [ M B H ( m o d e l ) / M (cid:12) ] M − σ ∗ relationM BH (FWHM)M BH ( σ H β ) Figure 13.
Comparison of black hole masses obtained from modelwith the M − σ ∗ relation. The dashed black line represents theM − σ ∗ relation. Only the objects having stellar velocity disper-sion ( σ ∗ ) are included in the plot. those 11 objects which have f BLR (model) measurements us-ing both FWHM and line dispersion σ H β separately as σ H β gives less biased M BH measurement than using the FWHM(Peterson 2011; Grier et al. 2012). In Fig. 13, we comparedthe M BH(model) values with the M − σ ∗ relation as given inEquation 15. We found that most of the M BH(model) mea-surements using FWHM lie above M − σ ∗ relation, whereas,most of the M BH(model) values obtained using σ H β lie be-low the M − σ ∗ line. But considering the uncertainties allM BH(model) measurements are found to be consistent withthe M − σ ∗ relation.We also calculated the dimensionless accretion rate asgiven by Du et al. (2018)˙ M = 20 . (cid:18) L cos i (cid:19) / m − (17)where m = M BH / M (cid:12) , L = L / ergs − and i is the inclination angle. Our obtained values for those 11objects as mentioned in Table 5 indicate low to moderatelyaccreting black holes with ˙ M ranging from 0.002 to 2.266. Modeling of the continuum and line light curves to estimatevarious BLR parameters depends on the SNR of the lightcurves. Collier et al. (2001) and Horne et al. (2004) suggestedthat BLR parameters can be well recovered (a) with contin-uum light curves of SNR ∼
100 and (b) line light curves ofSNR ∼
30. But it is often difficult to find RM data satisfyingthe above mentioned qualities.The distribution of the SNR of the continuum and linelight curves used in this work is shown in Fig. 14 (top left).
MNRAS , 1–19 (2020) Mandal et al.
Table 5. M BH and accretion rate ˙ M measurements. α δ log( M BH )(FWHM) log( M BH )( σ H β ) ˙ M . ± .
70 7 . ± .
70 0.01806:52:12.32 +74:25:37.2 8 . ± .
85 7 . ± .
54 0.01114:07:59.07 +53:47:59.8 7 . ± .
38 6 . ± .
37 0.23214:10:31.33 +52:15:33.8 7 . ± .
63 7 . ± .
62 0.51014:11:12.72 +53:45:07.1 7 . ± .
62 7 . ± .
61 2.26614:13:18.96 +54:32:02.4 7 . ± .
66 7 . ± .
63 0.56314:16:25.71 +53:54:38.5 7 . ± .
35 7 . ± .
33 2.18814:20:39.80 +52:03:59.7 8 . ± .
60 7 . ± .
60 0.18714:20:49.28 +52:10:53.3 9 . ± .
59 8 . ± .
58 0.00214:21:03.53 +51:58:19.5 7 . ± .
65 6 . ± .
65 0.21114:21:35.90 +52:31:38.9 7 . ± .
86 6 . ± .
85 0.420
SNR N u m b e r continuumline SNR (continuum) l o g ( d ) / l o g ( d ) SNR (continuum) R B L R ( m o d e l ) / R B L R ( m o d e l ) SNR (continuum) i n c / i n c SNR (continuum) o p n / o p n SNR (continuum) / Figure 14.
From top left to bottom right: SNR distribution of all the objects in continuum and line and comparison of the recoveredmodel parameters τ (cid:48) d , R (cid:48) BLR(model) , θ (cid:48) inc , θ (cid:48) opn and γ (cid:48) from the SNR degraded simulated light curves to those obtained from the originallight curves. Measurements from each object are shown by an unique colour. The sample median is also shown by a star marker. Thedashed black lines represent the y=1 lines, whereas the dashed blue lines represent the best polynomial fit to the sample median valuesin each panel. The vertical green and red lines correspond to the SNR values where the comparisons deviate from the unit ratio by 10%and 30%, respectively. They span a wide range from as low as 5 to as high as 1000.The median SNR of the continuum and line light curves usedin this work is about 84 and 30, respectively. To access theeffects of SNR on the derived BLR parameters, we carriedout simulations. We firstly selected objects with continuumlight curves with SNR greater than 300. We arrived at a totalof 10 objects. We then degraded the SNR of the continuumand line light curves of those 10 objects by multiplying afactor of 2, 3, 4, 5, 8, 10 and 15 to the original flux errors and adding a Gaussian random deviate of zero mean andstandard deviation given by the new flux errors. We thenapplied the PBMAP code on the simulated light curves andextracted the BLR parameters. Here, the ratio of the recov-ered to the original BLR parameters are plotted against thecontinuum SNR. It is evident from Fig. 14, that this ratiois close to unity for most of the BLR parameters, except forthe radius of the BLR, where it is found to deviate by 10%and 30%, when the SNR of the continuum are 130 and 100,
MNRAS000
MNRAS000 , 1–19 (2020)
LR Modeling as shown by the vertical green and red lines, respectively.Similarly, for the line light curves too, we found that the ra-tio of the recovered to the original BLR parameters are closeto unity except for the BLR size, which deviates by 10% and30%, when the SNR of the line are 25 and 15, respectively.This is also in agreement with the continuum SNR cut-offof 100 suggested by Collier et al. (2001) and Horne et al.(2004) to extract BLR parameters from RM data and lineSNR cut-off of 15, considering an accuracy of 70% to theoriginal recovered parameters.For the 57 objects studied in this work, we have a totalof 82 different measurements of H β , H α and MgII lines, outof which ∼
42% of objects have continuum and line SNRgreater than 100 and 15, respectively. Also, for all the objectsthe BLR sizes obtained from model fits are consistent withthose obtained from conventional CCF analysis within theerrors. However, as the SNR is found to have a major effecton the derived sizes of the BLR from the simulations, we notethat the values of the size of the BLR obtained for sourceswith continuum and line light curves with SNR lesser than100 and 15, respectively, needs to be used with caution. Wealso carried out an analysis of the correlation of τ d and theBLR sizes obtained from model to the luminosity to onlythose sources that have the continuum and line light curvesSNR greater than 100 and 15, respectively. Though the trendof the correlation is similar to that of the full sample, thesignificance of the correlation is not strong due to the lownumber of sources.We show in Appendix B (see Fig. B1), sample lightcurves and the recovered transfer functions for two sources.One belongs to J1411+537 that has good quality light curveswith continuum and line SNR of about 386 and 60, respec-tively. The other light curves belong to J1417+519, thathas SNR of about 9 and 3 for the continuum and line lightcurves, respectively. From these light curves it is clear thatBLR parameters are well constrained only for sources withgood SNR data. We analysed RM data collected from the literature for atotal of 57 AGN that includes 51 AGN with H β data, 26AGN with H α data and 6 AGN with MgII line data. Themain motivation is to constrain the structure and dynamicsof the BLR that emits MgII, H β and H α . We summarize ourresults below(i) The estimated BLR sizes using our approach are ingeneral consistent with that calculated from conventionalCCF analysis.(ii) The best-fitted model H β BLR size is correlated with L having a slope of 0 . ± .
03. This is similar to whatis known in literature from CCF analysis. We also examinedthe correlation of R
BLR (H α ) with the continuum luminos-ity at 5100 ˚A and found a slope of 0 . ± .
08 similar towhat is expected from photo-ionization calculations. How-ever more H α measurements are needed to better constrainthis correlation.(iii) We estimated virial factor using geometrical param-eters and obtained a mean of 1.78 ± BH from M − σ ∗ relation to the virial product (VP) obtained from RM. Using line light curves only it is not pos-sible to constrain the virial factor f BLR (Li et al. 2013). Forthat reason our measured f BLR have large uncertainties be-cause of large errors present in both θ inc and θ opn obtainedfrom the model fitting.(iv) We found a close correspondence between the BLRsize found from model and that estimated from CCF anal-ysis, however, some objects do show large deviation. Theobjects that show large deviation from the R BLR (model) =R
BLR (CCF) line have poor quality light curves.(v) The mean value of the non linearity parameter γ isfound to be non zero for different lines indicating devia-tion from linear response of the line emission to the opticalionizing continuum. This may be due to a) the anomalousbehaviour of the BLR region because of the poor correlationbetween optical continuum variability and the ionizing con-tinuum variability (Edelson et al. 1996; Maoz et al. 2002;Gaskell et al. 2019) and b) anisotropic line emission fromthe partially optically thick BLR. This anisotropic effect isnot considered in the model used here.(vi) Variability analysis of the sample indicates that linevaries more than the continuum. The damping time scaleobtained from modeling is found to be positively correlatedwith the continuum luminosity at 5100 ˚A.(vii) From the analysis of the simulated light curves, weconclude that reliable estimation of BLR size as well as otherparameters via the modeling approach requires continuumand line light curves with SNR greater than 100 and 15,respectively.This work has considerably increased the number of ob-jects investigated through geometrical modeling of the BLR.Despite that, we were able to estimate f BLR for only abouta dozen objects. Analysis of high quality data sets for morenumber of AGN are needed to find precise estimates of f BLR which can then be used with the conventional RM techniquesto estimate more accurate M BH values. ACKNOWLEDGEMENTS
We thank the referee for valuable comments and suggestionsthat helped to improve the quality of the manuscript. Weare thankful to Yan-Rong Li (IHEP, CAS) for making thecode PBMAP available and providing instruction to run thecode. AKM and RS acknowledge support from the NationalAcademy of Sciences, India.
DATA AVAILABILITY
The data used in this article are taken from the literature,the references of which are given in Table 1.
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LR Modeling
50 0 50 100 lag (days) CC F Figure A1.
The red solid line represents the average ICCF betweeng-band and H α line while the histogram shows the centroid lagdistribution for object J1420+526 having a τ cent = 49 . +11 . − . days in observed frame of the object. APPENDIX A: BLR LAG MEASUREMENT OFJ1420+526 FOR H α LINE USING ICCF
Grier et al. (2017b) did not perform CCF analysis to mea-sure the H α lag for the object J1420+526. We estimated theH α lag for this object using Interpolated Cross-correlationFunction (ICCF) analysis method as shown in Fig. A1. Thelag and its uncertainty are estimated using a Monte Carlosimulation based on the flux randomization (FR) and ran-dom subset selection (RSS) described in Peterson et al.(1998), Wandel et al. (1999) and Peterson et al. (2004). Themedian of the centroid distribution is considered as finallag while uncertainties were estimated within a 68% confi-dence interval around the median value. We obtained therest frame H α lag of 32 . +7 . − . days from ICCF method.The lag estimated based on modeling is 46 . ± . APPENDIX B: EXAMPLES OF MODEL FIT LIGHTCURVES AND TRANSFER FUNCTIONS
We show in Figure B1 light curves for two objects, namelyJ1411+537 having high SNR in the continuum and line, andJ1411+537 having poor SNR in both the light curves. Fromthe figure it is evident that the geometrical model parame-ters ( θ inc and θ opn ) are well-constrained for J1411+537 butnot constrained for J1411+537. This is due to the low SNRof the continuum and line light curves in J1411+537. This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS , 1–19 (2020) Mandal et al. F continuumSNR=385.7456650 56675 56700 56725 56750 56775 56800 56825 56850 MJD F H lineSNR=60.37 0 20 40 60 80 1000.0000.0050.0100.0150.0200.0250.030 T r a n s f e r F un c t i o n /dof=0.97 010 F gb a n d continuumSNR=8.626650 6700 6750 6800 6850 MJD 50000 F H lineSNR=3.31 0 20 40 60 80 1000.000.020.040.060.080.100.12 T r a n s f e r F un c t i o n /dof=1.51 (days) P r o b d e n s i t y (median) =20.28±9.64days 1 0 1 2 3 log d (days) P r o b d e n s i t y log d(median) =0.66±0.42days 0 20 40 60 80 inc (deg) P r o b d e n s i t y inc(median) =19.22±22.18deg 0 20 40 60 80 opn (deg) P r o b d e n s i t y opn(median) =26.93±23.41deg0.0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.81.01.2 P r o b d e n s i t y (median) =0.45±0.29 0.0 0.2 0.4 0.6 0.8 1.0 F P r o b d e n s i t y F (median) =0.58±0.26 0.0 0.5 1.0 1.5 2.0 2.50.00.20.40.60.81.01.21.4 P r o b d e n s i t y (median) =0.86±0.310 20 40 60 (days) P r o b d e n s i t y (median) =4.92±24.13days 1.0 1.5 2.0 2.5 log d (days) P r o b d e n s i t y log d(median) =2.37±0.35days 0 20 40 60 80 inc (deg) P r o b d e n s i t y inc(median) =42.67±26.12deg 0 20 40 60 80 opn (deg) P r o b d e n s i t y opn(median) =44.53±25.97deg0.0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.81.0 P r o b d e n s i t y (median) =0.49±0.29 0.0 0.2 0.4 0.6 0.8 1.0 F P r o b d e n s i t y F (median) =0.53±0.29 1 0 1 20.00.51.01.52.02.5 P r o b d e n s i t y (median) = 0.77±0.37 Figure B1. (Top) Model fits for the source (J1411+537) with high SNR light curves (left) and the source (J1417+519) with low SNRlight curve (right). In the left-hand panels the data points with error bars are the observed light curves and the thick solid lines arethe reconstructed light curves. The gray shaded areas represent the uncertainties in the reconstructed light curves. The correspondingtransfer function for each object is shown on the right hand panels. The SNR of the light curve is mentioned at each panel. Posteriorprobability distributions of different model parameters are also shown for J1411+537 (middle) and J1417+519 (bottom).MNRAS000