Resolving the inner accretion flow towards the central supermassive black hole in SDSS J1339+1310
V. N. Shalyapin, L. J. Goicoechea, C. W. Morgan, M. A. Cornachione, A. V. Sergeyev
AAstronomy & Astrophysics manuscript no. LiUSNACo_final © ESO 2021January 5, 2021
Resolving the inner accretion flow towards the centralsupermassive black hole in SDSS J1339+1310 (cid:63)
V. N. Shalyapin , , , L. J. Goicoechea , C. W. Morgan , M. A. Cornachione , and A. V. Sergeyev , Departamento de Física Moderna, Universidad de Cantabria, Avda. de Los Castros s / n, E-39005 Santander, Spaine-mail: [email protected];[email protected] O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12 Acad. Proscury St., UA-61085 Kharkiv, Ukraine Institute of Astronomy of V.N. Karazin Kharkiv National University, Svobody Sq. 4, UA-61022 Kharkiv, Ukrainee-mail: [email protected] Department of Physics, United States Naval Academy, 572C Holloway Rd., Annapolis, MD 21402, USAe-mail: [email protected];[email protected] Institute of Radio Astronomy of the National Academy of Sciences of Ukraine, 4 Mystetstv St., UA-61002 Kharkiv, UkraineJanuary 5, 2021
ABSTRACT
We studied the accretion disc structure in the doubly imaged lensed quasar SDSS J1339 + r -band light curves and UV-visible to near-IR (NIR) spectra from the first 11 observational seasons after its discovery. The 2009 − ff erent timescales, and this microlensing signal permitted us to constrain the half-light radiusof the 1930 Å continuum-emitting region. Assuming an accretion disc with an axis inclined at 60 ◦ to the line of sight, we obtainedlog (cid:0) r / / cm (cid:1) = . + . − . . We also estimated the central black hole mass from spectroscopic data. The width of the C iv , Mg ii , and H β emission lines, and the continuum luminosity at 1350, 3000, and 5100 Å, led to log ( M BH / M (cid:12) ) = . ± .
4. Thus, hot gas responsiblefor the 1930 Å continuum emission is likely orbiting a 4 . × M (cid:12) black hole at an r / of only a few tens of Schwarzschild radii. Key words. accretion, accretion discs – gravitational lensing: micro – gravitational lensing: strong – quasars: individual: SDSSJ1339 +
1. Introduction
Microlensing-induced variability in gravitationally lensedquasars allows astronomers to determine the sizes of compactcontinuum-emission regions in distant active galactic nuclei (e.g.Wambsganss 1998). Hence, this extrinsic variability has becomean extremely powerful tool, as evidenced by results for QSO2237 + z ∼ − (cid:63) Tables 1 and 3 − // cdsweb.u-strasbg.fr / cgi-bin / qcat?J / A + A / vol / page J1339 + z s = z l = ff ecting image B (Shalyapin & Goicoechea2014, henceforth Paper I). Thus, SDSS J1339 + ratio µ B /µ A = ± (cid:15) G , B /(cid:15) G , A = ± ff ected by microlensing (linearextinction; Goicoechea & Shalyapin 2016, henceforth Paper II).In Paper II, we also measured the time delay ∆ t AB = + − d (A isleading), which is a critical quantity for accurately isolating themicrolensing-induced variability from the source quasar’s intrin-sic variability. The macrolens magnification is usually denoted by M , but we use µ instead to avoid any confusion with massesArticle number, page 1 of 11 a r X i v : . [ a s t r o - ph . GA ] J a n & A proofs: manuscript no. LiUSNACo_final
Fig. 1.
Light curves of SDSS J1339 + r -band brightness records of the two quasar images are based onobservations from four di ff erent facilities that are labelled as LT, MT, ST, and PS1 (see main text). Magnitudes of a field star are o ff set by + In this paper, we mainly focus on the structure of the in-ner accretion flow in SDSS J1339 + r -bandlight curves and UV-visible to near-IR (NIR) spectra spanning 11years (2009 − r –band microlensing vari-ability and the size of the corresponding continuum source arediscussed in Sect. 5. Our conclusions appear in Sect. 6. Through-out the paper, we use a flat cosmology with H =
70 km s − Mpc − , Ω M = Ω Λ =
2. Observational data
Within the framework of the Gravitational LENses and DArkMAtter (GLENDAMA) project , whose objective is to performand analyse observations of a sample of ten gravitationallylensed quasars (Gil-Merino et al. 2018), we are conducting an r -band monitoring of SDSS J1339 + − − − https://gravlens.unican.es The updated light curves of SDSS J1339 + r filterwith a central wavelength (CWL) of 6247 Å during 68 epochs,and the IO:O CCD camera (Sloan r filter with CWL = (cid:48)(cid:48) .
40. The first part of the Panoramic Survey Telescopeand Rapid Response System project (PS1; Chambers et al. 2019)also imaged the double quasar in the r band with CWL = (Flewelling et al. 2020) includedwarp frames at six epochs over the 2011 − (cid:48)(cid:48) . − and good seeing conditions (median FWHM of 1 (cid:48)(cid:48) . R filter (CWL = (cid:48)(cid:48) .
266 pixel − scale, andseveral 180 or 300 s exposures were obtained at each of thesix epochs. Basic pre-processing tasks were then applied to MTframes: bias subtraction, trimming, flat fielding, and World Co-ordinate System mapping. The median FWHM was 1 (cid:48)(cid:48) .
15. Inaddition, the science archive of the National Optical Astron- http://panstarrs.stsci.edu Article number, page 2 of 11. N. Shalyapin et al.: Resolving the inner accretion flow towards the central supermassive black hole in SDSS J1339 + Table 2.
Spectroscopic observations in the 2009 − Date Instrumentation a Wavelength range (Å) Res. Power Main emission lines Ref2012-Mar-16 SDSS-BOSS 3600 − α , C iv , C iii ], Mg ii − α , C iv , C iii ], Mg ii − iv , C iii ], Mg ii − iv , C iii ], Mg ii − α , C iv , C iii ] 32016-Feb-18 HST-WFC3-UVIS 2000 − α , C iv − α , C iv , C iii ], Mg ii , H β , [O iii ] 52018-Feb-23 VLT-XSHOOTER 3050 − α , C iv , C iii ], Mg ii , H β , [O iii ] 52019-Mar-15 TNG-NICS-HK 13500 − α − α , C iv Notes. ( a ) SDSS-BOSS ≡ Baryon Oscillation Spectroscopic Survey (BOSS) spectrograph for the SDSS, GTC-OSIRIS-R500x ≡ OSIRISinstrument (R500x grism) on the 10.4 m Gran Telescopio Canarias (GTC), HST-WFC3-UVIS ≡ UVIS channel of the WFC3 instrument on the
Hubble
Space Telescope (HST), VLT-XSHOOTER ≡ XSHOOTER spectrograph (UVB, VIS, and NIR arms) on the 8.2 m Very Large Telescope(VLT), TNG-NICS-HK ≡ NICS instrument (HK grism) on the 3.6 m Telescopio Nazionale Galileo (TNG), and NOT-ALFOSC-G18 ≡ ALFOSCinstrument (grism
References. (1) Dawson et al. (2013); (2) Paper I; (3) Paper II; (4) Lusso et al. (2018); (5) VLT-XSHOOTER programme 099.A-0018 (PI: M.Fumagalli); (6) This paper. omy Observatory provides public access to frames of SDSSJ1339 + R -band exposures (CWL = − (cid:48)(cid:48) .
37 pixel − scale, andthree 300 s exposures are available for each observation night.These ST frames were conveniently pre-processed before start-ing photometry. The median FWHM for the 16 observing epochswas 1 (cid:48)(cid:48) . r -band magnitude of a reference starwas used for calibrating quasar magnitudes, and typical errorsof new LT data were estimated from root-mean-square devia-tions between magnitudes on consecutive nights (see Paper II).MT errors were derived from standard deviations of magnitudeson each observation night, while we adopted the typical errorsin LT records as the PS1 and ST photometric uncertainties. The11-year light curves are available in Table 1 at the CDS: Column1 lists the observing date (MJD −
50 000), Cols. 2 − − r bands (in 219 out of 241 epochs), there are data at slightly redderwavelengths in 22 epochs. This results in an e ff ective, weightedaverage wavelength of 6237 Å, which translates to a UV contin-uum emission at 1930 Å. We also note that the LT data are inreasonably good agreement with those from PS1 and ST.The light curves over the full observing period 2009 − http://archive.noao.edu monitoring period and show that the adopted error bar is veryconservative. Spectroscopic observations of SDSS J1339 + . However, the BOSS spectrograph collectedlight into a 2 (cid:48)(cid:48) -diameter optical fibre (Dawson et al. 2013), whichwas centred on image A in the first epoch and on image B in thesecond. Hence, the two-epoch observations do not provide cleanspectra of A or B. For instance, in the first epoch, although thespectral energy distribution mainly corresponds to A, a signifi-cant contribution of B and the lensing galaxy is also expected.We also conducted long-slit spectroscopy with the GTC, theTNG, and the NOT as part of the GLENDAMA project. TheGTC-OSIRIS observations allowed us to resolve A, B, and G,and accurately extract their individual spectra (Paper I; Paper II).Using the R500R grism, the C iv emission line in quasar spectraappears close to its blue edge, whereas the Mg ii emission lineis located on its red edge. The C iv emission of the quasar is,however, seen in the central part of the R500B grism wavelengthrange. Additionally, our spectroscopic follow-up of both quasarimages with NOT-ALFOSC and TNG-NICS, provided relativelynoisy shapes for the C iv emission line and the first detection ofH α emission. These recent spectra will be presented in a futurepaper and not further considered here.The HST Data Archive also contains slitless spectroscopyof SDSS J1339 + + + and B + ) agrees with that of − − http://archive.stsci.edu/hst Article number, page 3 of 11 & A proofs: manuscript no. LiUSNACo_final
Fig. 2.
HST-WFC3-UVIS spectra of SDSS J1339 + + and B + ( + − and B − ( − r -band frames on 14February 2016 are also shown for comparison purposes. Fig. 3.
VLT-XSHOOTER spectra of SDSS J1339 + and B − ). However, the throughput of the G280 grism is higherfor the + + and B + as our final data. These HST-WFC3-UVIS spectra are available in tabular format at the CDS: Table3a includes wavelengths in Å (Col. 1), and fluxes and flux errorsof A in 10 − erg cm − s − Å − (Cols. 2 and 3), while Table 3bincludes wavelengths in Å (Col. 1), and fluxes and flux errors ofB in 10 − erg cm − s − Å − (Cols. 2 and 3). The spectral energydistributions show the C iv emission line around 5000 Å ( ∼ , and details on the observing programme are given in http://archive.eso.org/cms.html Table 2. For each of the two epochs, we used the 2700 (3 × ff at profiles in the spatial directionfor each wavelength bin. Telluric absorption in the VIS and NIRarms was also corrected via the Molecfit software (Smette et al.2015; Kausch et al. 2015). Final calibrated spectra of A, B, andG on 6 April 2017 are available at the CDS: Table 4 containswavelengths in Å (Col. 1), fluxes and flux errors of A (Cols. 2and 3), fluxes and flux errors of B (Cols. 4 and 5), and fluxes andflux errors of G (Cols. 6 and 7). The wavelength coverage rangesfrom 3050 − − erg cm − s − Å − .These VLT-XSHOOTER spectra are also shown in Fig. 3. In ad-dition to C iv emission of the quasar in the UVB arm spectra(top panel), Mg ii and H β emissions are also seen around 9000 Å( ∼ ∼
3. Extinction and lens models
The position on the sky of SDSS J1339 + / IPAC Extragalactic Database provided Milky Waytransmission factors ( (cid:15) MW ) of 0.93 at 4362 Å, 0.98 at 9693 Å,and 0.99 at 16478 Å. These wavelengths correspond to 1350,3000, and 5100 Å in the quasar rest-frame (see Sect. 4). Whilethe Galaxy produces equal extinction in both quasar images,the lensing galaxy gives rise to a di ff erential extinction betweenimages. According to Paper II, emission lines in GTC-OSIRISspectra and a linear extinction law in G (e.g. Prévot et al. 1984)lead to a dust extinction ratio (ratio between the transmission ofB and that of A) of 1.33 ± ii absorption at the lens redshift is much strongerin A than in B. Therefore, it is reasonable to assume that thelens galaxy’s dust essentially a ff ects image A, which translatesto transmission factors ( (cid:15) G , A ) of 0.56 ± ± ± (cid:15) G , B = ff ective radius, ellipticity, andposition angle in the fifth column of Table 1 of Paper I as con-straints. The image fluxes were also considered to derive lensmodels. These fluxes are consistent with the macrolens magni-fication ratio measured in Paper II (see Sect. 1). The overall setof constraints allowed us to fit 11 free parameters with d.o.f. =
0, where ’d.o.f.’ denotes the degrees of freedom. We usedthe GRAVLENS / LENSMODEL software (Keeton 2001), adopt-ing a gravitational lens scenario that consists of three compo-nents. De Vaucouleurs (DV) and Navarro-Frenk-White (NFW;e.g. Navarro et al. 1996, 1997) mass profiles describe the stellar(light traces mass) and dark components of the main deflectorG, whereas an external shear (ES) accounts for additional de-flectors. https://ned.ipac.caltech.edu Article number, page 4 of 11. N. Shalyapin et al.: Resolving the inner accretion flow towards the central supermassive black hole in SDSS J1339 + Table 5. DV + NFW + ES lens models. f ∗ κ κ ∗ /κ γ µ ∆ t AB (d)A B A B A B A B0.1 0.67 0.90 0.02 0.05 0.30 0.35 52.1 9.1 22.70.2 0.62 0.86 0.05 0.11 0.34 0.45 31.7 5.5 27.70.3 0.73 0.84 0.07 0.17 0.23 0.40 42.7 7.5 21.50.4 0.65 0.79 0.10 0.24 0.29 0.52 25.1 4.4 28.10.5 0.57 0.73 0.14 0.32 0.36 0.65 16.3 2.9 34.60.6 0.48 0.68 0.20 0.42 0.42 0.77 11.5 2.0 41.10.7 0.40 0.63 0.28 0.52 0.49 0.90 8.5 1.5 47.60.8 0.32 0.58 0.40 0.65 0.56 1.02 6.6 1.2 54.20.9 0.24 0.52 0.60 0.81 0.62 1.15 5.2 0.9 60.71.0 0.16 0.47 1.00 1.00 0.69 1.27 4.3 0.7 67.2 Notes.
The ten lens models fit the observational constraints with χ ∼ =
0; see main text). The parameter f ∗ represents the luminous massof G relative to that for the model without dark matter halo ( f ∗ = κ ), stellar to total convergence ratio ( κ ∗ /κ ), shear( γ ), and macrolens magnification ( µ ) for each model and image position. The last column shows the predicted time delay between images for eachmodel. The sequence of DV + NFW + ES models started by assumingthat all mass of G is traced by light, namely constant mass-to-light ratio model. The free parameters of such a model were theposition, mass scale, e ff ective radius, ellipticity, and position an-gle of the DV profile, the strength and direction of the ES, andthe position and flux of the source quasar. By progressively de-creasing the luminous component of G and adding a concentricdark matter halo, we completed a sequence of ten realistic lensmodels with f ∗ ranging between 1.0 and 0.1, where f ∗ is the massof G in stars (DV profile) relative to its maximum value in theabsence of a dark matter halo (we note that f ∗ was called f M / L in several previous papers; e.g. Morgan et al. 2018; Cornachioneet al. 2020). For the f ∗ < ff ective radius of the DVprofile, the mass scale of the NFW profile, the strength and di-rection of the ES, and the position and flux of the source quasar.Some local parameters (at image positions) of theDV + NFW + ES models are shown in Table 5. The last threecolumns of Table 5 give the magnification factor of A and Bfor each time delay, so we took the measured delay ( ∆ t AB = + − d; Paper II, and discussion in Appendix A) as an additional con-straint to estimate reliable intervals for µ A and µ B . First, resultsfor the models in the range 0.6 ≤ f ∗ ≤ y = µ A (or µ B ) and x = ∆ t AB , we derived laws y ∝ x − α ,where the power-law index is α ≈
2. Second, these x - y relation-ships and the extreme values of the measured delay interval ( x =
41 and 52 d) led to µ A = ± µ B = ±
4. Black hole mass
For a given broad emission line, it is thought that the line-emitting gas is distributed within the gravitational potential ofthe central SMBH, so there is a relationship between its motion,the size of the region, and the SMBH mass ( M BH ; e.g. Vester-gaard & Peterson 2006, and references therein). The gas motionis responsible for the emission-line width, while the radius ofthe line-emitting region scales roughly as the square root of thecontinuum luminosity (e.g. Koratkar & Gaskell 1991; Bentz etal. 2009). Hence, we aimed to use the single-epoch spectra ofSDSS J1339 + ff ected by microlensing. Thus, we only considered image A when estimating M BH . We were pri-marily interested in the width of the C iv , Mg ii , and H β emissionlines, as well as the continuum flux for emissions at 1350, 3000,and 5100 Å (e.g. Vestergaard & Peterson 2006; Vestergaard &Osmer 2009). After the de-redshifting of the observed spectra ofA to the quasar rest-frame, λ rest = λ obs / (1 + z s ), if the continuumflux F cont , A ( λ rest ) is in 10 − erg cm − s − Å − and the corre-sponding luminosity L cont ( λ rest ) is in erg s − , then both quantitiesare related through the equation L cont ( λ rest ) = . × λ rest F cont , A ( λ rest ) (cid:15) MW ( λ rest ) (cid:15) G , A ( λ rest ) µ A . (1)All factors in the denominator of Eq. (1) are discussed in Sect. 3.The C iv emission line is well resolved in the GTC-OSIRIS-R500B spectrum of image A. In Fig. 4 of Paper II, we presenteda multi-component decomposition of its profile in both images.For clarity, the carbon line profile in A is also depicted in thetop panel of Figure 4. After subtracting the local continuum, theresidual signal is modelled as a sum of three Gaussian contribu-tions. We focused on the C iv total (broad + narrow) emissionline and calculated the square root of its second moment ( σ line ;Peterson et al. 2004). The line width was then estimated from thespectral resolution-corrected line dispersion σ l = ( σ − σ ) / = − . Moreover, the continuum flux at λ rest = × − erg cm − s − Å − , thatis F cont , A (1350Å) = iv line (see the bottom panel of Figure 4). Thus, we obtainedan independent line width σ l = − based on HST data.Despite the fact that both spectra (GTC and HST) yield simi-lar values of σ l , the F cont , A (1350Å) values in the two observingepochs were very di ff erent. The continuum flux in February 2016was F cont , A (1350Å) = r -band fluxbetween May 2014 (minimum level) and February 2016 (maxi-mum level) is also seen in Figure 1. From Eq. (1), accounting foruncertainties in the dust extinction and macrolens magnificationof image A, we found log[ L cont (1350Å)] = ± ± iv line width and L cont (1350Å), and we used their Eq. (8) to ob-tain C iv -based masses. The spectral observations in May 2014(GTC) and February 2016 (HST) led to log [ M BH (C iv ) / M (cid:12) ] = Article number, page 5 of 11 & A proofs: manuscript no. LiUSNACo_final
Fig. 4.
Multi-component decomposition of the C iv line profile in SDSSJ1339 + iv broad + C iv narrow + He ii complex. The grey rectangleshighlight the two spectral regions that we used to remove a linear con-tinuum under the emission line, and the vertical dotted lines correspondto the centres of the Gaussians. The top panel displays GTC-OSIRIS-R500B data in May 2014, while the bottom panel incorporates HST-WFC3-UVIS data in February 2016. ± ± σ l and L cont (1350Å)since the uncertainty in log [ M BH (C iv ) / M (cid:12) ] is dominated by anintrinsic scatter of ± − in σ l propagates to ± M BH (C iv ) / M (cid:12) ], whereas the uncertainties in L cont (1350Å)propagate to ± iv -based masses are consistent within er-rors, and this would permit us to ’confidently’ calculate the av-erage, we carefully analysed the Mg ii and H β emission lines inthe VLT-XSHOOTER spectrum of A in April 2017. These VLTobservations were made at an epoch for which the r -band fluxreached an intermediate level (see Figure 1), and therefore theymay help to decide whether one of the two C iv -based estimatesis relatively biased or not. In Figure 5, we show multi-componentdecompositions of the Mg ii and H β profiles (see the caption fordetails). First, we measured FWHM(Mg ii ) = − and Fig. 5.
Multi-component decomposition of the Mg ii and H β line pro-files in SDSS J1339 + top panel , after subtractinga power-law continuum, the residual signal is modelled as a sum of twocontributions, i.e. Mg ii broad emission (Gaussian curve around the ver-tical dotted line) and Fe ii pseudo-continuum. There is no evidence of aMg ii narrow line or an additional very broad component. The contin-uum windows at 2195 − − ii pseudo-continuum is created from the Fe ii template of Tsuzuki et al. (2006) convolved with a Gaussian functionto account for the Doppler broadening of Fe ii lines. The bottom panel displays the decomposition in the spectral region around the H β emis-sion. The grey rectangle highlights one of the two windows that we usedto remove a power-law continuum under emission lines (3790 − − β broad + H β narrow + [O iii ] doublet, plus the Fe ii contribution from two individual lines inthe spectral range 4750 − F cont , A (3000Å) = L cont (3000Å)] = ± λ rest = (cid:2) M BH (Mg ii ) / M (cid:12) (cid:3) values ranging between 8.58 and 8.70, in good agreement with Article number, page 6 of 11. N. Shalyapin et al.: Resolving the inner accretion flow towards the central supermassive black hole in SDSS J1339 + SDSS J1339+1310
HJD - 2450000 (days) m A ( t ) − m B ( t + d a y s ) Year
Fig. 6.
Image B r -band light curve from the LT shifted by the 47-d time delay and subtracted from the contemporaneous magnitude of image A,i.e. m A ( t ) − m B ( t +
47 d) (equivalent to a ratio in flux units), leaving only variability that is not intrinsic to the source itself. Plotted in black are fivegood fits to the microlensing variability from our Monte Carlo routine. those from the C iv line width and L cont (1350Å) in the GTC spec-trum taken in May 2014.From the decomposition in the bottom panel of Figure 5and Eq. (1), we also derived FWHM(H β ) = − , F cont , A (5100Å) = L cont (5100Å)] = ± β emission to deter-mine FWHM(H β ). The FWHM(H β ) and log[ L cont (5100Å)] val-ues yielded log (cid:2) M BH (H β ) / M (cid:12) (cid:3) = ± M BH (C iv ) / M (cid:12) ] from GTCdata. We finally adopted log ( M BH / M (cid:12) ) = ±
5. Accretion disc size from microlensing variability
We analysed the r -band light curves using the Monte Carlo anal-ysis technique in Kochanek (2004). The method is fully de-scribed in that paper, but we provide a brief summary here. Us-ing the convergence κ , convergence due to stars κ ∗ , shear γ , andshear position angle θ γ from each of the models in our sequence(see Table 5), we generated a set of 40 magnification patterns permacro model to represent the microlensing conditions at the lo-cation of each lensed image. Our model sequence has 10 macromodels in the range 0 . ≤ f ∗ ≤ . dN ( M ) / dM ∝ M − . . The square magnification patterns repre-sent a region 40 r E on a side, where r E is the source-plane pro-jection of the Einstein radius of a 1M (cid:12) star. With dimensions of8192 × . × (cid:104) M ∗ / M (cid:12) (cid:105) / cm on the source plane, where (cid:104) M ∗ (cid:105) isthe mean mass of a lens galaxy star.We convolved the magnification patterns with a simpleShakura & Sunyaev (1973) thin disc model for the surfacebrightness profile of the accretion disc at a range of source sizes14 . ≤ log(ˆ r s / (cid:104) M ∗ / M (cid:12) (cid:105) / cm) ≤ .
0. The quantity ˆ r s is a thindisc scale radius where the hat indicates that the distance is be-ing reported in ’Einstein units’ in which quantities are scaled bya factor of the mean mass of a star in the lens galaxy. For exam-ple, converting a scale radius or velocity in Einstein units intoa physical unit is accomplished using r s = ˆ r s (cid:104) M ∗ / M (cid:12) (cid:105) / and v e = ˆ v e (cid:104) M ∗ / M (cid:12) (cid:105) / , respectively.In essence our technique is an attempt to reproduce the ob-served microlensing variability using a realistic model for condi-tions in the lens galaxy. We run our model magnification patternsby a range of model source sizes on a range of trajectories in anattempt to fit the observed data. According to Bayes’ theorem,the likelihood of the set of physical ξ p and trajectory ξ t parame-ters given the data D is P ( ξ p , ξ t | D ) ∝ P ( D | ξ p , ξ t ) P ( ξ p ) P ( ξ t ) , (2)where P ( ξ t ) and P ( ξ p ) are the prior probabilities for the trajectoryand physical variables, respectively. In a given trial, we chosethe velocity randomly from the uniform logarithmic prior 1 . ≤ log[ˆ v e / ( (cid:104) M ∗ / M (cid:12) (cid:105) / km s − )] ≤ .
0. We evaluated the goodness-of-fit with the chi-square statistic in real time during each trial,and for computational e ffi ciency we aborted and discarded anyfit with χ / d.o.f. ≥ Monte Carlo fits perset of magnification patterns for a grand total of 4 × trials.Of those trials, ∼ met our χ threshold, and the remainder ofour analysis was performed on those solutions. In Figure 6, wedisplay examples of five good fits to the observed microlensingvariability.We generated a statistical prior for the e ff ective veloc-ity between source, lens and observer using four components. Article number, page 7 of 11 & A proofs: manuscript no. LiUSNACo_final Source Plane ˆ v e ¡ › M ∗ /M fl fi / km s − ¢ d P ( v ) / d l og ( v ) P ( v e ) (model) P (ˆ v e ) › M ∗ /M fl fi d P ( › M ∗ fi ) / d l og ( › M ∗ fi ) Fig. 7.
Distributions for the e ff ective source velocity and mean microlens mass. Left panel : Probability density for the e ff ective velocity ˆ v e (inEinstein units (cid:104) M ∗ / M (cid:12) (cid:105) / km s − ) across the source plane from the ensemble of Monte Carlo fits to the observed light curves (heavy black curve).The lighter black curve is our prior on the true e ff ective velocity of source (in physical units km s − ) generated from a model of the e ff ective velocityof source, lens, observer and the velocity dispersion of lens galaxy stars. Right panel : Probability density for the mean mass of a lens galaxy star (cid:104) M ∗ (cid:105) derived by convolving the probability density for the e ff ective velocity ˆ v e with our model for the true e ff ective velocity (see left panel). Since (cid:104) M ∗ / M (cid:12) (cid:105) = ( v e / ˆ v e ) , the distribution is broad. The expectation value for (cid:104) M ∗ (cid:105) = . + . − . M (cid:12) is lower than the predictions of standard IMFmodels, but our results for the accretion disc size are consistent when we assume a more physical uniform prior 0 . ≤ (cid:104) M ∗ / M (cid:12) (cid:105) ≤ . ˆ r s ¡ › M ∗ /M fl fi / cm ¢ d P ( ˆ r s ) / d l og ( ˆ r s ) r / (cm) d P ( r / ) / d l og ( r / ) SDSS J1339+1310 λ rest =1930 Å T disk =7 . K S c h w a r z c h il d R a d i u s f o r . × M fl I S C O f o r . × M fl No Mass Prior . < › M ∗ /M fl fi < . Scaled to λ =2500 Å Fig. 8.
Accretion disc structure in SDSS J1339 + Left panel : Probabilty density for the source size in Einstein units ( (cid:104) M ∗ / M (cid:12) (cid:105) / cm). Thedistribution levels o ff at ∼ × cm since the pixel scale in our magnification patterns is 1 . × cm. All solutions become equally likely belowthat size scale. Right panel : Probability density for the half light radius of the continuum-emission region in SDSS J1339 + λ rest = i = .
5. The solid black curve was derived by convolving our probability density for (cid:104) M ∗ (cid:105) (right panel of Fig. 7)with that of ˆ r s (see left panel). The dashed black curve assumed a uniform prior on the mean mass of a lens galaxy star 0 . ≤ (cid:104) M ∗ (cid:105) ≤ .
0. The solidgreen curve shows the result without the mass prior scaled to 2500 Å for comparison to other models. The Schwarzschild radius r Sch = GM BH / c and ISCO at 3 r Sch are plotted for reference.
We found the transverse velocity of the observer by calculat-ing the northern ( v O , n = − . − ) and eastern ( v O , e = − . − ) components of the CMB dipole across the line ofsight to the target. Following Bolton et al. (2008), we estimatedthe velocity dispersion σ ∗ =
379 km s − in the lens galaxy usingthe monopole term of its gravitational potential. We estimatedthe peculiar velocity of source and lens using their redshifts, fol-lowing the prescription of Mosquera & Kochanek (2011). Usingthe technique presented in Kochanek (2004), we combined thevelocities to generate a probability density for the e ff ective ve-locity (see the left panel of Figure 7). Also shown in the left panel of Figure 7 is the probability density for the e ff ective ve-locity in Einstein units ˆ v e yielded by marginalising over the othervariables in the set of successful solutions from the Monte Carlorun P (ˆ v e | D ) ∝ (cid:90) P ( D | p , ˆ v e ) P ( p ) P (ˆ v e ) d p , (3)where P ( D | p , ˆ v e ) is the probability of fitting the data in a partic-ular trial, P ( p ) sets the priors on the microlensing variables ξ p & ξ t , and P (ˆ v e ) is the (uniform) prior on the e ff ective velocity. Thetotal probability is then normalised so that (cid:82) P (ˆ v e | D ) d ˆ v e =
1. We
Article number, page 8 of 11. N. Shalyapin et al.: Resolving the inner accretion flow towards the central supermassive black hole in SDSS J1339 + carried out an analogous Bayesian integral to find the probabil-ity density for the source size in Einstein units, dP (ˆ r s ) / d log(ˆ r s ),which we display in the left panel of Figure 8.Now, to convert our result from Einstein units to true phys-ical units, we developed a probability density for the mean mi-crolens mass (cid:104) M ∗ (cid:105) (see the right panel of Figure 7) by convolv-ing the prior on v e with the probability density on ˆ v e from thesimulation since ˆ v e = v e (cid:104) M ∗ / M (cid:12) (cid:105) − / . To find the probabilitydensity for the source size in physical units, dP ( r s ) / d log r s , weconvolved the probability density for (cid:104) M ∗ (cid:105) with that of ˆ r s . As-suming an inclination angle of 60 ◦ , we display the resulting dis-tribution for the half-light radius ( r / ) in the right panel of Fig-ure 8. In Fig. 8, we also show the probability density for r / using an assumed uniform prior on the mean microlens mass0 . ≤ (cid:104) M ∗ / M (cid:12) (cid:105) ≤ .
0. While the two results are fully consistent,we promote the measurement without the uniform mass prior,the expectation value for which is log { ( r / / cm)[cos i / . / } = . + . − . . This measurement is the half-light radius of the quasarcontinuum source at the rest-frame e ff ective wavelength λ rest = σ bounds of the time delay, 41 and 52 d. We found sizemeasurements of log { ( r / / cm)[cos i / . / } = . + . − . andlog { ( r / / cm)[cos i / . / } = . + . − . , respectively. These arefully consistent with the size measurement for the 47-d delay,demonstrating that time delay uncertainty has a small impact onthe size.
6. Conclusions
We measured the virial mass of the SMBH at the centre of SDSSJ1339 + M BH / M (cid:12) ) = ± ff ects (e.g. extinction in the quasar hostgalaxy and microlens magnification) are expected to play a sec-ondary role or even o ff set each other. While it is di ffi cult to ac-curately quantify these e ff ects, when correction factors rangingfrom 2 / / < ∼ ff orts to obtain virial black holemasses from samples of lensed quasars (e.g. Peng et al. 2006;Greene et al. 2010; Assef et al. 2011). The sixth and eighthcolumns of Table 5 in Assef et al. (2011) show black hole massestimates based on Balmer lines for a sample of twelve objects.A quarter of the 12 lensed quasars harbour SMBHs with a typi-cal mass ≤ . × M (cid:12) , and SDSS J1339 + M BH = . × M (cid:12) , the gravi-tational radius is r g = GM BH / c = . × cm. This blackhole mass also determines the ISCO radius of the gas in aSchwarzschild geometry, which amounts to r ISCO = . × cm. In addition, the observed microlensing variability in the r band allowed us to constrain the half-light radius of the re-gion where the UV continuum at 1930 Å is emitted. We foundlog { ( r / / cm)[cos i / . / } = . + . − . , leading to a radial size ofabout 2 . × cm ∼ r ISCO for i = ◦ . Therefore, althoughUV observations are required to resolve the ISCO around theSMBH powering SDSS J1339 + M BH and r / ) yielded an Eddington factor log ( L /η L E ) = ± i = ◦ . Despite the large uncertainty, the central value ofthis factor is consistent with a reasonable radiative e ffi ciency η ≈ .
16 ( L / L E ).In Figure 8, we also display the probability density for thehalf-light radius of the accretion disc in SDSS J1339 + λ rest = { ( r / / cm)[cos i / . / } = . + . − . is at 21 − r g for an inclination of 60 ◦ . This 1 σ inter-val is barely consistent with the prediction of the accretion discsize - black hole mass relation (Morgan et al. 2010) as updatedby Morgan et al. (2018)log[ r / / cm] = (16 . ± . + (0 . ± .
15) log( M BH / M (cid:12) ) , (4)which predicts an accretion disc half-light radius at 2500 Åof 106 ≤ r / / r g ≤
243 for a black hole of mass M BH = . × M (cid:12) . The minor discrepancy could easily be explained bythe scatter in the SDSS J1339 + ◦ assumption, the inclinationcorrection would also bring the measurement into closer agree-ment with the Morgan et al. (2018) scaling relation. However, itis important to realise that very high inclinations are unlikely inthe presence of a dusty torus surrounding the gas disc (Antonucci1993). Acknowledgements.
This paper is based on observations made with the Liver-pool Telescope (LT) and the AZT-22 Telescope at the Maidanak Observatory.The LT is operated on the island of La Palma by Liverpool John Moores Uni-versity in the Spanish Observatorio del Roque de los Muchachos (ORM) of theInstituto de Astrofisica de Canarias (IAC) with financial support from the UKScience and Technology Facilities Council. We thank the sta ff of the LT for akind interaction before, during and after the observations. The Maidanak Ob-servatory is a facility of the Ulugh Beg Astronomical Institute (UBAI) of theUzbekistan Academy of Sciences, which is operated in the framework of scien-tific agreements between UBAI and Russian, Ukrainian, US, German, French,Italian, Japanese, Korean, Taiwan, Swiss and other countries astronomical insti-tutions. We also present observations with the Nordic Optical Telescope (NOT)and the Italian TNG, operated on the island of La Palma by the NOT Scien-tific Association and the Fundación Galileo Galilei of the Istituto Nazionale diAstrofisica, respectively, in the Spanish ORM of the IAC. We also used datataken from several archives: National Optical Astronomy Observatory ScienceArchive, Pan-STARRS1 Data Archive, Sloan Digital Sky Survey Data Releases,HST Data Archive, and ESO Science Archive Facility, and we are grateful to themany individuals and institutions who helped to create and maintain these pub-lic databases. This research has been supported by the MINECO / AEI / FEDER-UE grant AYA2017-89815-P and University of Cantabria funds to L.J.G. andV.N.S. This work was also supported by NSF award AST-1614018 to C.W.M.and M.A.C.
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The light curves of the two images of SDSS J1339 + − ∆ t AB , we considered a magnitude o ff set ∆ m AB for each of the nine seasons in 2009 and 2012 − ff sets account for long-timescale extrinsic (microlensing)variability. Our technique is fully described in Sect. 5.1 of PaperII, and it relies on a comparison between the curve A and thetime-shifted and binned curve B. The time-shifted magnitudesof B are binned around the dates of A, and the semisize of binsis denoted by α .For α =
20 d, in Table A.1, we compare the best solutionin Paper II and the new best solution through the updated lightcurves. The combined light curve for this new solution is alsoshown in the nine panels of Fig. A.1. As expected, there is a goodagreement between the global trends of both images. Althougha reasonably good agreement is also seen within some particularseason (e.g. 2009, 2015 and 2018), short-timescale microlens-ing variability is present (e.g. intra-seasonal events / gradients in2013 − α =
20 d, wealso found a 47-d solution that is practically as good as the onein the third column of Table A.1. Additionally, using 1000 pairsof synthetic curves (see Paper II), we derived best solutions for α =
15, 20, and 25 d. The distribution of 3000 delays resultingfrom simulated light curves and a reasonable range of α values,permited us to estimate uncertainties. Only delays within the in-terval from 46 to 50 d have an individual probability greater than10%, leading to an overall probability of 85%, and hence a con-servative 1 σ measurement ∆ t AB = ± σ measurement from the seasonalmicrolensing model in Paper II ( ∆ t AB = + − d).In Paper II, we also tried to account for all extrinsic vari-ability using cubic splines and the PyCS software (Tewes et al.2013; Bonvin et al. 2016). However, such a method did not pro-duce very robust results because it was not originally designedto model extrinsic variations that are as fast as or faster than in-trinsic ones (Tewes et al. 2013). Despite this fact, we obtaineda 1 σ confidence interval ∆ t AB = + − d using simulated lightcurves and a weak prior on the true time delay (i.e. it cannotbe shorter than 30 d or longer than 60 d). Hence, the spline-like microlensing model led to a significantly enlarged error bar,which is adopted in this paper. We think this 1 σ interval is ex-aggeratedly large, and thus very conservative. First, consideringonly long-timescale extrinsic variability, a decade of monitoringobservations with the LT and other telescopes strongly supportsan error bar covering the delay range of 46 −
50 d (see above).This model exclusively has one non-linear parameter (time de-lay) and is appropriate. It accounts for extrinsic variations thatdistort the apparent long-term intrinsic signal, while the short-term extrinsic signal is assumed to be an extra-noise. Second,when all extrinsic variability is modelled, one deals with a com-plex non-linear optimisation, which may yield local minima, de-generacies, and so on. We have not yet found a fair way to si-multaneously fit the delay and all microlensing activity. Despite
Table A.1.
Best solutions for α =
20 d.
Paper II This paper ∆ t AB (d) 47 48 ∆ m AB (2009) 0.349 0.348 ∆ m AB (2012) 0.419 0.417 ∆ m AB (2013) 0.133 0.139 ∆ m AB (2014) 0.118 0.116 ∆ m AB (2015) 0.304 0.302 ∆ m AB (2016) — 0.189 ∆ m AB (2017) — 0.159 ∆ m AB (2018) — 0.261 ∆ m AB (2019) — 0.136 Notes.
The time-dependent magnitude o ff set ∆ m AB ( t ) = m A ( t ) − m B ( t +∆ t AB ) is assumed to be constant within each season. All seasonal o ff setsare positive because we use the opposite sign to that in Paper II. Fig. A.1.
Combined light curve in the r band from the best solution inthe third column of Table A.1. The A curve (red circles) is comparedto the magnitude- and time-shifted B curve (blue squares). Open cir-cles and squares are associated with the full brightness records, whilefilled circles and squares correspond to periods of overlap between bothrecords. In the overlap periods, magnitudes of B are binned around datesof A using α =
20 d (filled squares; see main text). these drawbacks, we are working on PyCS-based codes to ac-count for the full microlensing signal in SDSS J1339 +1310-likesystems. These codes could produce robust results in a near fu-ture.