X-ray monitoring of gravitationally lensed radio-loud quasars with Chandra
Mustafa Burak Dogruel, Xinyu Dai, Eduardo Guerras, Matthew Cornachione, Christopher W. Morgan
DDraft version September 17, 2019
Typeset using L A TEX preprint style in AASTeX62
X-RAY MONITORING OF GRAVITATIONALLY LENSED RADIO-LOUD QUASARS WITH
CHANDRA
Mustafa Burak Dogruel, Xinyu Dai, Eduardo Guerras, Matthew Cornachione, andChristopher W. Morgan Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, 440 W. Brooks St. Norman,OK 73019, USA Department of Physics, United States Naval Academy, 572C Holloway Road, Annapolis, MD 21402, USA (Received September 17, 2019)
Submitted to ApJABSTRACTIn this work, we calculated the sizes of unresolved X-ray emission regions in three grav-itationally lensed radio-loud quasars, B 1422+231, MG J0414+0534 and Q 0957+561,using a combination of imaging and spectral analysis on the X-ray data taken fromthe
Chandra X-Ray Observatory . We tentatively detected FeK α emission lines inMG J0414+0534 and Q 0957+561 with over 95% significance, whereas, we did notsignificantly detect FeK α emission in B 1422+231. We constructed differential mi-crolensing light curves from absorption corrected count rates. We subsequently per-formed a microlensing analysis on the X-ray microlensing light curves to measurethe X-ray source sizes in soft (0.83–3.6 keV), hard (3.6–21.8 keV), and full (0.83–21.8 keV) bands, based on either Bayesian or maximum likelihood probabilities. ForB 1422+231, sizes from the two methods are consistent with each other, e.g. R hardX /R G =6 . ± .
48 (Bayesian), 11 . ± .
75 (maximum likelihood), where R G = GM BH /c ).However, for MG J0414+0534 and Q 0957+561, the two methods yield completely dif-ferent results suggesting that more frequently sampled data with better signal-to-noiseratio are needed to measure the source size for these two objects. Comparing the ac-quired size values with the radio-quiet sample in the literature we found that our resultsare consistent with X-ray source size scaling approximately as R X ∝ M BH with the massof the central supermassive black hole. Our results also indicate that radio-loud quasarstend to have larger unresolved X-ray emission sizes compared to the radio-quiet ones. Keywords: quasars: individual (MG J0414+0534, Q 0957+561, B 1422+231) – quasars:emission lines – gravitational lensing: strong – gravitational lensing: micro– accretion disks
Corresponding author: Mustafa Burak [email protected] a r X i v : . [ a s t r o - ph . C O ] S e p Dogruel et al. INTRODUCTIONUnification schemes of active galactic nuclei (AGNs) have indicated that AGNs are separated intotwo physically distinct classes, radio-loud and radio-quiet (Wilson & Colbert 1995; Urry & Padovani1995), where the radio-loudness is caused by the presence of relativistic jets. Depending on redshiftand luminosity, radio-loud AGNs constitute roughly ∼ −
25% of AGN population (Kellermannet al. 1989; Jiang et al. 2007). The relativistic radio jets of these radio-loud AGNs have also beenobserved in X-rays, which was a surprising discovery of
Chandra based on early jet models, e.g.,PKS 0637–752 (Schwartz et al. 2000; Chartas et al. 2000). The fact that many of these jets can alsobe easily detected in X-rays means that the X-ray emission from radio-loud quasars emanates notonly close to the accretion disc, as the radio-quiet counterparts, but also from the jets. The resolvedX-ray emission from radio-loud quasars is associated with kpc-scale jets (e.g. Chartas et al. 2000;Marshall et al. 2018), whereas the unresolved X-ray emission from radio-loud quasars is still notclear. This elusiveness creates a major challenge in interpreting the properties of quasar continuumin X-rays for radio-loud quasars. The unresolved component of X-ray emission is thought to bea combination of corona emission, resembling the case of radio-quiet AGNs, and the contributionfrom the unresolved jet. Measuring the spatial extent of the unresolved X-ray emission in radio-loudquasars and comparing that with the measurements of radio-quiet quasars will provide an additionalconstraint on separating the jet and corona contributions. For this purpose, quasar microlensingphenomenon provides one of the strongest methods.AGNs have a critical role in cosmic evolution. For instance, observations of z > σ ) of the stellar bulge/spheroid, (e.g. Kormendy & Richstone 1995;Ferrarese & Merritt 2000; McConnell & Ma 2013) shows that these black holes regulate galaxyevolution and vice versa. Powered by the central super massive black hole, AGN feedback is anindispensable component in modeling galaxy evolution (Somerville et al. 2008). Despite these crucialaspects, the structure of AGNs is not yet fully understood. For radio-quiet quasars, the thin discmodel does not predict X-ray emission for massive AGNs, and the emission is expected from a corona(Blaes 2007). One of the biggest problems in testing accretion disc models is that the central engine ofAGNs cannot be resolved even with space telescopes (Mosquera et al. 2013). For instance, accordingto some rough estimates, the angular size of the central engine is of the order of nano-arcseconds(Dai et al. 2010).Quasar microlensing is induced by the joint lensing of an ensemble of stellar mass objects in aforeground galaxy between the observer and the quasar. The technique has been proven to be anefficient way of probing the innermost regions of AGNs (e.g. Dai et al. 2010; Mosquera et al. 2013;Blackburne et al. 2014). Since the quasar, the lens galaxy and the stars within it, and the observerhave relative motion transverse to the line of sight (Wambsganss 2006), the angular location of thequasar relative to the lens galaxy changes with time. Thus, the magnification of each image of thequasar varies due to microlensing, which leads to uncorrelated flux variations between the lensedimages. The microlensing magnifications also depend on the relative sizes of the emission region(here the accretion disc of the quasar) and also on the Einstein radius of the star, which can beapproximated for a cosmological lens as R E = (cid:114) GMc D os D ls D ol ∼ × cm (cid:115) MM (cid:12) (cid:115) D os c/H D ls D ol (1)where M is the mass of the deflector, D os , D ls , D ol are the angular diameter distances between theobserver, lens and the source respectively, and c/H is the Hubble radius. This dependence impliesthat the smaller the source size, the greater the microlensing amplitude, which means that theamplitude of the microlensing variations can be used to measure the source size.The largest microlensing amplitudes are observed in X-rays (Chartas et al. 2002; Dai et al. 2003;Mosquera et al. 2013). The UV photons emitted from the inner regions of accretion disc undergoinverse Compton scattering by the relativistic electrons in the corona to produce X-ray continuumwhich can be characterised by a power law. Since electron scattering is isotropic, some of thesephotons are scattered back to the disc, forming the reflection component which can also includeemission features such as the FeK α fluorescent line (the strongest of those emission lines) at 6.4keV in the rest frame (George & Fabian 1991; Fabian et al. 1995; Gou et al. 2011). Studying thegravitational microlensing of X-rays from quasars provides us with an opportunity to estimate thesize of the X-ray emitting region of the accretion disc. Even though gravitationally lensed quasarsare quite few in numbers, they provide a powerful and effective tool to probe the inner structure ofquasars which cannot be resolved spatially by telescopes. Another benefit of microlensing analysis isthat it can be used to measure the innermost stable circular orbit of the central supermassive blackholes which makes it possible to constrain the spin of the black holes (Dai et al. 2019). Furthermore,microlensing analysis can constrain the discrete lens population including extragalactic planets (Dai& Guerras 2018).In this study, we present the X-ray spectra and light curves for three gravitationally lensed radio–loud quasars MG J0414+0534, Q 0957+561, and B 1422+231. We extract the full (0.83 – 21.8 keVrest frame), soft (0.83 – 3.6 keV), and hard (3.6 – 21.8 keV) X-ray band light curves and comparethem with image flux ratio predictions without microlensing to measure the microlensing signals.We model the microlensing variability and then generate a probability density function (PDF) toconstrain the size of the unresolved X-ray emitting region of the aforementioned three radio-loudquasars. Finally, we discuss the results in Section 5. Throughout the paper, we assume a flat ΛCDMcosmology with H = 70 km s − Mpc − , Ω m = 0 . Λ = 0 . OBSERVATIONS AND DATA ANALYSISObservations were performed with the Advanced CCD Imaging Spectrometer on the
Chandra X-RayObservatory which has an on-axis point spread function (PSF) of 0 . (cid:48)(cid:48)
5. We selected three radio-loudquasars that have multi epoch observations in the
Chandra
Data Archive and yielded three lenseswith their properties listed in Table 1. Stacked Chandra images of the three targets are shown inFigure 1. All data were reprocessed using CIAO 4.7 software tools.2.1. Imaging Analysis http://cda.harvard.edu/chaser/ http://cxc.harvard.edu/ciao/ Dogruel et al.
Figure 1.
Stacked
Chandra images of MG J0414+0534, Q 0957+561 and B 1422+231.
Table 1.
Lens Data For Selected Radio-Loud QuasarsObject z s z l R E t E t R G ∆ t obs M BH R G (light days) (years) (years) (years) ( × M (cid:12) ) (light days)MG J0414+0534 2.64 0.96 8.054 19.39 3.08 11.75 1.82 (C IV) 0.104Q 0957+561 1.41 0.36 12.788 12.39 1.11 10.19 2.01 (C IV) 0.114B 1422+231 3.62 0.34 12.305 23.94 4.29 11.48 4.79 (C IV) 0.273Source and lens redshifts ( z s and z l ) are taken from CASTLES.Einstein radius crossing time ( t E ) and the mass of the supermassive black hole ( M BH ) are taken from Mosquera &Kochanek (2011). t R G is 10 R G crossing time. R E is calculated assuming a mean stellar mass of (cid:104) M ∗ (cid:105) = 0 . M (cid:12) in lens galaxies.Time span of the observations are given under ∆ t obs .Gravitational radius R G = GM BH /c , which is half of the Schwarzschild radius R S , is given in the last column. We later separated the events into soft and hard bands where the energy boundary was selectedto be 3.6 keV in the observed frame to acquire comparable count rates (as given in Tables 2–4)between the two energy bands. For all three systems, we subtracted the background emission fromimage count rates using concentric circular regions with inner and outer radii of ∼ (cid:48)(cid:48) and ∼ (cid:48)(cid:48) respectively. Apart from Q 0957+561, the first gravitationally lensed quasar detected (Walsh et al.1979) with well separated images, the angular separation of lensed components of B 1422+231 andMG J0414+0534 can be as small as 0 . (cid:48)(cid:48) . (cid:48)(cid:48)
5, respectively. Therefore, it is evidently not suitable toperform aperture photometry since it will be contaminated by the flux of nearby sources in the image.Consequently, to accurately measure the image count rates, we used PSF fitting method with therelative positions of the lensed components which were taken from the CASTLES database. Afterthe acquisition of background subtracted count rates, they were further corrected for both Galacticabsorption and absorption by the lens galaxy measured from the spectral analysis.2.2. Spectral Analysis
We first extracted the spectra of individual images with CIAO, using circles of radii ∼ . (cid:48)(cid:48) XSPEC (Arnaud 1996) to analyse the spectra. We modelled the spectra usinga power law modified by Galactic absorption and lens galaxy absorption. We also added Gaussianemission lines to the models. During the spectral fitting which was performed within the energy rangeof 0.4–8 keV, we allowed the power law index (Γ) to vary, assumed the same Galactic absorption forall images fixed at the value calculated by Dickey & Lockman (1990), and set the N H of the lensgalaxy free so that the absorption from the lens galaxy could vary independently. After fitting allthe spectra, we calculated the absorbed to unabsorbed flux ratio ( f abs /f unabs ) for each image whichwe used for acquiring the absorption corrected count rates. We give these absorption corrected countrates in Tables 2, 3 and 4. The results of the spectral fit are presented in Figures 2, 3, and 4 while Dogruel et al. the resulting parameters are listed in Tables 5, 6, and 7. Finally, we obtained the flux variationswhich are free from Galactic and lens galaxy absorptions.
Table 2.
Absorption corrected count rates for Q 0957+561.Obs ID Date Exp A full A soft A hard B full B soft B hard
362 16 Apr 2000 47.662 240 . +13 . − . . +8 . − . . +5 . − . . +9 . − . . +6 . − . . +3 . − . . +13 . − . . +7 . − . . +12 . − . . +8 . − . . +5 . − . . +7 . − . . +9 . − . . +4 . − . . +5 . − . . +13 . − . . +6 . − . . +7 . − . . +8 . − . . +5 . − . . +5 . − . . +9 . − . . +6 . − . . +6 . − . . +18 . − . . +5 . − . . +5 . − . . +10 . − . . +5 . − . . +6 . − . . +10 . − . . +5 . − . . +5 . − . . +9 . − . . +5 . − . . +6 . − . . +9 . − . . +6 . − . . +5 . − . . +6 . − . . +4 . − . . +4 . − . . +7 . − . . +4 . − . . +5 . − . . +6 . − . . +4 . − . . +4 . − . . +7 . − . . +5 . − . . +4 . − . . +7 . − . . +4 . − . . +4 . − . . +6 . − . . +17 . − . . +4 . − . . +11 . − . . +11 . − . . +8 . − . . +8 . − . . +5 . − . . +5 . − . . +12 . − . . +7 . − . . +9 . − . . +8 . − . . +5 . − . . +6 . − . . +11 . − . . +6 . − . . +7 . − . . +19 . − . . +5 . − . . +6 . − . . +10 . − . . +6 . − . . +9 . − . Note —Count rates are in units of 10 − s − . Exposure time is given under “Exp” in units of 10 s . Emission Lines
We tentatively detected FeK α fluorescence line in image A of MG J0414+0534, confirming theearlier detection by Chartas et al. (2002), and in both images of Q 0957+561, but not in B 1422+231.As can be seen from Tables 5 and 7, the rest frame energies of the detected FeK α lines are consistentwith the neutral FeK α emission at 6.4 keV. Shifts in the line energy are seen in both Q 0957+561 Aand B. We also found that adding two lines instead of one in image B of Q 0957+561 significantlyimproved the fit. In this case, we measure a redshifted line at 6.23 keV and a blueshifted line at 6.88keV. Such FeK α line shifts have previously been detected in a sample of radio-quiet lensed quasars(Chen et al. 2012; Chartas et al. 2017).To calculate the statistical significance of the detected emission features, we used a Monte Carlosimulation approach proposed by Protassov et al. (2002). From this, we determined the distributionof the F -statistic between the null model (absorbed power law) with no emission lines and thealternative model (absorbed power law including one or more Gaussian emission lines) for 5000spectra simulated from the null model with XSPEC. Each simulated spectrum was binned the sameas the actual spectrum, and fitted with the null model, then fitted again with the alternative model.After these fits for two different models, F -test was performed for each simulation, and finally, thestatistical significance value was calculated by comparing the F -test values from simulations and theones from real data ( F obs ). Additionally, analytical significance was obtained from the probabilitycorresponding to F obs , i.e. result of F -test applied to the data. The results of the simulations areshown in Figures 5, 6, and 7. The significance values are given in Table 8. −4 −3 R a t e ( c oun t s s − k e V − ) FeK α MGJ0414+0534 A10.5 2 5−2−101 ∆ χ Energy (keV) −3 R a t e ( c oun t s s − k e V − ) MGJ0414+0534 B10.5 2 5−202 ∆ χ Energy (keV) −4 −3 R a t e ( c oun t s s − k e V − ) MGJ0414+0534 C10.5 2 5−4−202 ∆ χ Energy (keV) −4 −3 R a t e ( c oun t s s − k e V − ) MGJ0414+0534 D10.5 2 5−2−1012 ∆ χ Energy (keV)
Figure 2.
Stacked spectra of MG J0414+0534 and spectral fits. The sub-panels show the statistical residualsin units of 1 σ standard deviations. Dogruel et al. −4 −3 R a t e ( c oun t s s − k e V − ) B1422+231 A10.5 2 5−2024 ∆ χ Energy (keV) −4 −3 R a t e ( c oun t s s − k e V − ) B1422+231 B10.5 2 5−2024 ∆ χ Energy (keV) −4 −3 R a t e ( c oun t s s − k e V − ) B1422+231 C10.5 2 5−1012 ∆ χ Energy (keV) −4 −3 R a t e ( c oun t s s − k e V − ) B1422+231 D10.5 2 5−2024 ∆ χ Energy (keV)
Figure 3.
Stacked spectra of B 1422+231 and spectral fits. The sub-panels show the statistical residuals. −4 −3 R a t e ( c oun t s s − k e V − ) FeK α Q0957+561 A1 100.5 2 5−202 ∆ χ Energy (keV) −3 R a t e ( c oun t s s − k e V − ) FeK α Q0957+561 B1 100.5 2 5−2−1012 ∆ χ Energy (keV)
Figure 4.
Stacked spectra of Q 0957+561 and spectral fits. The sub-panels show the statistical residuals. P r o b a b i l i t y F obs = 2.18 6.52 keV lineSignificance = 0.986 MG J0414+0534
Figure 5. F -statistic distribution derived from Monte Carlo simulations for image A of MG J0414+0534. Dogruel et al. T a b l e . A b s o r p t i o n c o rr ec t e d c o un t r a t e s f o r M G J + . O b s I DD a t e E x p A f u ll A s o f t A h a r d B f u ll B s o f t B h a r d C f u ll C s o f t C h a r d D f u ll D s o f t D h a r d J a n . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . A p r . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . A u g20007 . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . N o v . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . F e b . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . N o v . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . J a n . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . O c t . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . N o t e — C o un t r a t e s a r e i nun i t s o f − s − . E x p o s u r e t i m e i s g i v e nund e r “ E x p ” i nun i t s o f s . T a b l e . A b s o r p t i o n c o rr ec t e d c o un t r a t e s f o r B + . O b s I DD a t e E x p A f u ll A s o f t A h a r d B f u ll B s o f t B h a r d C f u ll C s o f t C h a r d D f u ll D s o f t D h a r d J un . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . M a y . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . D ec . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . N o v . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . N o t e — C o un t r a t e s a r e i nun i t s o f − s − . E x p o s u r e t i m e i s g i v e nund e r “ E x p ” i nun i t s o f s . Table 5.
Spectral Fit Results For MG J0414+0534.Image Γ N H E line (keV) σ line (keV) EW (keV) Flux χ ν P ( χ ν )( × cm − ) ( × − erg cm − s − )A 1 . +0 . − . . +0 . − . . +0 . − . . ∗ . +0 . − . . +0 . − . . +0 . − . . +0 . − . . . . . . . . . . . +0 . − . . +0 . − . . +0 . − . . . . . . . . . . . +0 . − . . +0 . − . . +0 . − . . . . . . . . . . . +0 . − . Notes:
Reduced χ is defined by χ ν = χ /ν where ν is the degree of freedom. Errors are derived at 68% confidence level. Thelast column gives the probability of exceeding χ for ν degrees of freedom. Parameters marked with an asterisk are unconstrained. Table 6.
Spectral Fit Results For B 1422+231Image Γ N H Flux χ ν P ( χ ν )( × cm − ) ( × − erg cm − s − )A 1 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . Table 7.
Spectral Fit Results For Q 0957+561
Image Γ N H E line1 σ line1 EW Line1 E line2 (keV) σ line2 EW Line2 Flux χ ν P ( χ ν )( × cm − ) (keV) (keV) (keV) (keV) (keV) (keV) ( × − erg cm − s − )A 1 . +0 . − . . +0 . − . . +0 . − . . ∗ . +0 . − . . . . . . . . . . . +0 . − . . +0 . − . . +0 . − . . +0 . − . < .
14 0 . +0 . − . . +0 . − . . ∗ . +0 . − . . +0 . − . Table 8.
Significance of the Detected LinesLens Image E line (keV) Monte Carlo AnalyticalSignificance SignificanceMG J0414+0534 A 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . MICROLENSING LIGHT CURVESIn this work, the microlensing light curves were measured based on the absorption corrected countrates given in Tables 2 – 4. Our aim was to analyse the differential microlensing light curves, thedeparture of the measured microlensed flux ratios from the intrinsic flux ratios (Guerras et al. 2017).As for time-delay effects, as shown by Schechter et al. (2014), the amplitude of source variabilityfor luminous quasars in X-rays is small compared to both observational errors and microlensingamplitudes. This makes the source variability unlikely to contribute significantly to microlensing2
Dogruel et al. P r o b a b ili t y F obs = 2.527.02 keV lineSignificance = 0.962 Q0957+561A
Figure 6. F -statistic distribution derived from Monte Carlo simulations for image A of Q 0957+561. P r o b a b ili t y F obs = 5.16.88 keV lineSignificance = 0.999 Q0957+561B P r o b a b ili t y F obs = 2.86.23 keV lineSignificance = 0.98 Q0957+561B
Figure 7. F -statistic distributions derived from Monte Carlo simulations for image B of Q 0957+561. signal. We will explore this effect further by including quasar variability models in the microlensinganalysis for long time-delay lenses (Cornachione et al. in preparation). We calculated the baseline fluxratios from the macrolensing models using the expression for magnification µ = 1 / | (1 − κ ) − γ | where κ is the convergence (the dimensionless surface mass density of the lens galaxy) and γ is the shearparameter which is responsible for the distortion of images. The κ and γ values for MG J0414+0534and B 1422+231 were taken from Schechter et al. (2014), whereas the values for Q 0957+561 weretaken from Mediavilla et al. (2009). Baseline ratios are calculated with, for example between theA-B image pair, − . µ B /µ A ). The microlensing light curves are shown in Figures 8-10. Since3 -1.5-1.0-0.50.00.51.00.00.51.01.5 m - m ( A ) Figure 8.
Microlensing light curves of MG J0414+0534 in magnitude scale. the microlensing light curve depends only on flux ratios, the change of
Chandra effective area overtime does not affect our microlensing light curves.Continuing the notion from Guerras et al. (2017) and Guerras et al. (2018), we also examine theroot mean square (rms) of microlensing variability for our targets. Here, microlensing amplitudes( ϕ ) are the departures from the baseline ratio, and they can be calculated between images, e.g. Aand B, at time t j from ϕ AB ( t j ) = ε Bj ε Aj = f Bj f Aj µ A µ B (2)where f is the measured flux, µ is the macrolensing magnification, and ε is the microlensing mag-nification. For each image pair, we calculate the mean microlensing amplitude ( ϕ ) and its rms.Finally, we give the relation between these two parameters in Figure 11 in units of magnitudes where∆ m = − . ϕ and (∆ m ) rms = − . ϕ rms . The linear relation is compatible with the results ofGuerras et al. (2017). MICROLENSING ANALYSIS AND CONSTRAINTS ON THE SIZE OF X-RAY EMISSIONREGIONAs we can see from Table 1, the time spans of the observations (∆ t obs ) for our selected targetsare sufficiently long, especially when compared to 10 R G (typical X-ray source size for radio-quietquasars) crossing times ( t R G ), thus the microlensing light curves span a sufficiently long period tosee the typical magnification patterns produced by stars.Our aim was to obtain probability distributions of the source size for each target individually, byfitting the differential microlensing light curves following Kochanek (2004). During this process, weused all images for a target. Here, we first generated magnification maps for each image of each4 Dogruel et al.
Figure 9.
Microlensing light curves of Q 0957+561 in magnitude scale. -0.8-0.6-0.4-0.20.00.20.4-1.0-0.50.00.51.0 m - m ( A ) Figure 10.
Microlensing light curves of B 1422+231 in magnitude scale. −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2Δm−2−1012345 ( Δ m ) R M S Q0957-B/AMG0414-B/AMG0414-C/AMG0414-D/A B1422-B/AB1422-C/AB1422-D/A GuerrasΔetΔal.2017−2 −1 0 1 2 3 4Δm−2−10123456 ( Δ m ) R M S This studyRadio-Quiet from Guerras et al.2017Fit from Guerras et al.2017
Figure 11.
Upper panel:
RMS of microlensing variability in hard X-rays for different image pairs in oursample of radio-loud quasars.
Lower panel:
Comparison with the radio-quiet sample from Guerras et al.(2017). Dogruel et al. target using the three parameters, the dimensionless surface mass density κ , shear γ , and fractionof surface density in stars κ ∗ /κ . Since we previously acquired κ and γ from macrolens models, thelast parameter required for generating maps is κ ∗ . We calculated this parameter from the calibratedrelations of Oguri et al. (2014) and then we used these values in generating magnification maps withInverse Polygon Mapping algorithm (Mediavilla et al. 2006). The lensing parameters are listed inTable 9 including R/R eff (where R eff is the effective radius within which half of the luminosity isemitted), κ ∗ , κ and γ values. Table 9.
Macrolens Model Parameters of TargetsQuasar Image
R/R eff κ ∗ /κ κ γ Map dimensionsPixels R E R G MG J0414+0534 A 1.617 0.288 0.489 0.454 4000 × . × . × × . × . × × ×
33 1500 × We took a constant deflector mass of (cid:104) M ∗ (cid:105) = 0 . M (cid:12) and generated 4000 × R G × R G in the sourceplane. Due to sparsity of caustics for Q 0957+561, we generated maps with larger pixel sizes butkeeping the number of pixels the same, spanning 4005 R G × R G for this target. Consideringthe values of Einstein radius ( R E ) of a 0 . M (cid:12) star for each target, the maps span, in the sourceplane, 155 ×
155 light-days (19 . × . R E ) for MG J0414+0534, 409 ×
409 light-days (33 × R E )for B 1422+231, and 458 ×
458 light-days (13 . × . R E ) for Q 0957+561. We convolved thesemaps with a Gaussian kernel representing a source model, using the disc surface brightness profile, I ( R ) ∝ e − r /R X where R X is the X-ray source size. Following the work of Guerras et al. (2017),we used a logarithmic grid where R X /R G = e . n with n = 0 , , , . . . ,
40. For each value of n , weproduced a large number (up to N = 300000) of simulated light curves choosing randomly orientedtracks on the convolved maps, with lengths equalling the time spans of the observations. An exampleof these random tracks is shown in Figure 12. We compared the simulated light curves to the datausing χ statistics, where χ for each epoch t i is χ ( t i ) = (cid:88) j (cid:88) k The track which yields the best fit light curves for MG J0414+0534 shown on the map of imageA. Small circles show the epochs of the actual observations. Darker colours represent smaller magnification. calculated, e.g. for images A and B of a 4-image lensed quasar, using the expression1 σ AB,i = σ C,i σ D,i ( σ A,i σ B,i σ C,i ) + ( σ A,i σ B,i σ D,i ) + ( σ A,i σ C,i σ D,i ) + ( σ B,i σ C,i σ D,i ) (4)from Kochanek (2004), where σ j,i are the uncertainties in magnitude units of each image j at eachepoch t i . Lastly, σ ( µ jk ) is the uncertainty of the baseline ratio between images j and k .For each trial m with a random track on the map, we calculated the likelihood of the source size R X for each epoch t i with L m ( t i , R X ) = e − χ m ( t i ) / , and we acquired the total likelihood for each epochby adding the likelihoods of all trials, L ( t i , R X ) = N (cid:88) m =1 e − χ m ( t i ) / . (5)We then obtained the probability of the differential microlensing amplitude ∆ m jk for a particularsource size R X by multiplying the likelihoods of all epochs, p (∆ m jk | R X ) = (cid:89) t i L ( t i , R X ) (6)After obtaining the probabilities p (∆ m jk | R X ) for each source size, we normalised them by their sumand plotted against the source size. Finally, we acquired the size estimates by fitting each probabilitydistribution with a Gaussian. Probability distributions are shown in Figure 13–15 whereas the sizeestimates, assuming a “face-on disc” in which the inclination angle of the disc is i = 0 ◦ , are given intable 10. If the disc is not viewed face-on, these estimates will scale as (cos i ) − / (Dai et al. 2010).8 Dogruel et al. Table 10. X-ray Source Size Estimates With Bayesian ProbabilitiesQuasar log( R softX /cm ) log( R hardX /cm ) log( R fullX /cm ) R softX /R G R hardX /R G R fullX /R G MG J0414+0534 16 . ± . 17 16 . ± . 14 16 . ± . 16 45 . ± . 75 82 . ± . 73 61 . ± . 87Q 0957+561 16 . ± . 14 16 . ± . 14 16 . ± . 14 125 . ± . 15 132 . ± . 95 132 . ± . 82B 1422+231 15 . ± . 37 15 . ± . 39 15 . ± . 05 2 . ± . 97 6 . ± . 48 11 . ± . Finally, in Figures 17 and 18, we present a sample of best-fit light curves taking into account theobtained R X values.We also calculated the source size for Q 0957+561 in full band considering different macro models,which are described by the fraction of mass in the de Vaucouleurs component ( f ∗ ). We took modelswith 0 . ≤ f ∗ ≤ κ and γ corresponding to these f ∗ values, andcalculated the probability distribution of source size from simulated light curves. Here, we obtainedthe probability for a particular source size R X by summing the probabilities from all f ∗ values.Accordingly, source size was calculated to be log R fullX /cm = 16 . ± . 10, which is in accordancewith the value log R fullX /cm = 16 . ± . 14 given in Table 10. The probability distribution obtained byconsidering all macro models, and the one obtained by taking the macro parameters from Mediavillaet al. (2009) are given in Figure 19. Finally, for the hard band, we calculated the source sizes whichhave the maximum likelihood, i.e., which correspond to the best fit light curves with the lowest χ .We give the resulting source sizes in Table 11, and best fit light curves corresponding to those sizesin Figures 17 and 18. Table 11. Source Sizes With Maximum LikelihoodQuasar R softX /R G R hardX /R G R fullX /R G MG J0414+0534 21 . +26 . − . . +1 . − . . +38 . − . Q 0957+561 2 . ± . 60 2 . ± . 60 2 . ± . 47B 1422+231 10 . ± . 05 11 . ± . 75 21 . ± . To compare our results with the sizes of other lensed quasars in UV and X-ray bands, we usedthe data given in Morgan et al. (2010) and plotted the accretion disc sizes against black hole mass(Figure 16). As seen in Figure 16, our size estimates are in agreement with the apparent relationbetween the X-ray source size and the black hole mass, roughly as R X ∝ M BH . These results alsoimply that the radio-loud quasars tend to have larger X-ray emission regions compared to radio-quiet quasars. In an effort to understand the origin of this difference, we also examine the rms ofmicrolensing variability. From Figure 11, we could see that radio-quiet quasars HE 0435-1223 andQJ 0158-4325 have very similar microlensing amplitudes to the ones in our sample. However, theirhard X-ray region sizes are log R X /cm = 14 . X (cm)0.000.050.100.150.200.250.300.35 P r o b a b ili t y HardSoftFull X /R G Figure 13. Probability distribution of source size for B 1422+231 X (cm)0.000.050.100.150.20 P r o b a b ili t y HardSoftFull 10 20 50 100R X /R G Figure 14. Probability distribution of source size for MG J0414+0534 Dogruel et al. X (cm)0.000.050.100.150.20 P r o b a b ili t y HardSoftFull 50 100 200 300 400R X /R G Figure 15. Probability distribution of source size for Q 0957+561 microlensing amplitudes as mentioned above, X-ray sizes are much smaller than their Einstein radii.This fact that the resulting source sizes are very different despite the similar microlensing amplitudes,raises even more questions. As seen in Figures 17 and 18, model light curves do not fit the smallfluctuations, which possibly provides an explanation for why the data yield large values of rms ofmicrolensing variability despite the large source size. Besides, as expected for large source size,when rms is calculated from the model, they are much smaller than the ones calculated from theobservations. Lastly, as seen from Figures 20 – 22, even though there are light curve solutions fromsmall source sizes with lower χ values, these are very few in numbers. However, large source sizesdominantly contribute to probability with slightly bigger χ values, which explains the large sourcesizes being much more probable even though their light curves do not fit the small fluctuationswell. Obviously, the fact that smaller χ values are achieved with smaller R X also explains whythe maximum likelihood source sizes are extremely small (apart from B 1422+231) compared to theresults from Bayesian analysis. DISCUSSION AND CONCLUSIONIn this paper, we present the X-ray monitoring results of three lensed radio-loud quasarsMG J0414+0534, Q 0957+561 and B 1422+231. We performed both spectroscopic and photometricanalysis of Chandra archival data. In our spectroscopic analysis, we found that a power law modelmodified by absorption with additional Gaussian emission lines provide good fits to spectral data.1 BH /M ⊙ l o g R ( c m ) MG0414Q0957 B1422 OpticalHard X-raysSoft X-raysR Optical ∝ M BH R X ∝ M BH (Quiet+Loud)R X ) M BH (Quiet) Figure 16. Accretion disc sizes plotted against black hole mass As a result of these fits, we tentatively detected the characteristic FeK α line in MG J0414+0534 andQ 0957+561 with over 95% significance.FeK α line shifts detected in our spectral analysis might be caused by a caustic passing through theinner accretion disc as discussed by Chartas et al. (2012). The two lines in image B of Q 0957+561can be new examples of the distortions of a single FeK α line due to special relativistic Doppler andgeneral relativistic effects, then magnified by microlensing. For radio-quiet quasars, as concludedby Chartas et al. (2017), these shifts in FeK α line energy is formed by reflection from the materialnear the black hole horizon because of the small X-ray corona size. Here, our Bayesian microlensingX-ray size for Q 0957+561 is much larger. Assuming little general relativistic effects, Doppler shiftedFeK α line energy calculated with the source size given in Table 10 can reach 7 . ± . 26 keV whenmagnified by a microlensing caustic, which is in fact compatible with the observed line energies inboth images.We also obtained microlensing light curves from flux ratios measured from PSF fitting of theabsorption corrected data. As seen in Figures 8–10, there is no significant difference in flux ratiosbetween soft and hard X-ray bands, i.e. an energy dependent microlensing, apart from the C imageof MG J0414+0534 at modified Julian date around 52000, which needs to be further confirmed withmore observations.From the size estimates given in table 10, we calculated the size ratios of soft and hard aslog( R hardX /R softX ) = 0 . ± . , . ± . 19, 0 . ± . 53 for MG J0414+0534, Q 0957+561 andB 1422+231 respectively. These values do not support the intuitive idea of the hard componentbeing more compact than the soft one, towards which also Mosquera et al. (2013) could not find astrong evidence.Our X-ray microlensing analysis results for Q 0957+561 suggest a much smaller X-ray source sizecompared to the X-ray/UV and optical reverberation mapping results from Gil-Merino et al. (2012)2 Dogruel et al. −0.4−0.20.00.2 B-A −1.0−0.50.0 C-B−1.0−0.50.0 Δ m C-A −1.5−1.0−0.5 D-B52000 53000 54000 55000 56000−1.5−1.0−0.5 D-A 52000 53000 54000 55000 56000−0.6−0.4−0.2 C-D B 1422Δ231 MJD−1.5−1.0−0.50.00.5 B-A −0.50.0 C-B−1.0−0.50.0 Δ m C-A −1.0−0.50.0 D-B52000 53000 54000 55000 56000−1.5−1.0−0.50.0 D-A 52000 53000 54000 55000 56000−101 C-D MG J0414Δ0534 MJD Figure 17. Observed light curves along with the five best fitting models for B 1422+231 (top) andMG J0414+0534 (bottom) taking into account the calculated source sizes. Curves shown in brown rep-resent the minimum χ , i.e., source size with maximum likelihood. Δ m Q 0957Δ561 Figure 18. Observed light curves along with the five best fitting models for Q 0957+561 taking into accountthe calculated source sizes. The curve shown in brown represents the minimum χ , i.e., source size withmaximum likelihood. X (cm)0.00.10.20.30.40.5 P r o b a b ili t y From all macrolens modelsκ and γ from Mediavilla et al. 20091 10 20 50 100R X /R G Figure 19. Probability distributions of source size in full band for Q 0957+561. Dogruel et al. F r e q u e n c y MG J0414+0534 R X / R G = 1.68 R X / R G = 21.52 R X / R G = 45.57 Figure 20. χ distribution for 10 trials on maps of MG J0414+0534 for χ < F r e q u e n c y Q 0957+561 R X / R G = 2.12 R X / R G = 121.66 R X / R G = 221.68 Figure 21. χ distribution for 10 trials on maps of Q 0957+561 for χ < F r e q u e n c y B 1422+231 R X / R G = 1.68 R X / R G = 11.81 R X / R G = 29.05 Figure 22. χ distribution for 10 trials on maps of B 1422+231 for χ < in which they found R X ∼ R S ∼ . 05 pc (with M BH = 2 . × M (cid:12) ), whereas our result is R X ∼ R S ∼ . Facilities: Chandra X-Ray Satellite Software: XSPEC (Arnaud 1996)6 Dogruel et al. REFERENCES Arnaud, K. A. 1996, in Astronomical Society ofthe Pacific Conference Series, Vol. 101,Astronomical Data Analysis Software andSystems V, ed. G. H. Jacoby & J. Barnes, 17Blackburne, J. A., Kochanek, C. S., Chen, B.,Dai, X., & Chartas, G. 2014, ApJ, 789, 125,doi: 10.1088/0004-637X/789/2/125Blaes, O. 2007, in Astronomical Society of thePacific Conference Series, Vol. 373, The CentralEngine of Active Galactic Nuclei, ed. L. C. Ho& J.-W. Wang, 75Chartas, G., Agol, E., Eracleous, M., et al. 2002,ApJ, 568, 509, doi: 10.1086/339162Chartas, G., Kochanek, C. S., Dai, X., et al. 2012,ApJ, 757, 137,doi: 10.1088/0004-637X/757/2/137Chartas, G., Krawczynski, H., Zalesky, L., et al.2017, ApJ, 837, 26,doi: 10.3847/1538-4357/aa5d50Chartas, G., Worrall, D. M., Birkinshaw, M.,et al. 2000, ApJ, 542, 655, doi: 10.1086/317049Chen, B., Dai, X., Kochanek, C. S., et al. 2012,ApJ, 755, 24, doi: 10.1088/0004-637X/755/1/24Dai, X., Chartas, G., Agol, E., Bautz, M. W., &Garmire, G. P. 2003, ApJ, 589, 100,doi: 10.1086/374548Dai, X., & Guerras, E. 2018, ApJ Letters, 853,L27, doi: 10.3847/2041-8213/aaa5fbDai, X., Kochanek, C. S., Chartas, G., et al. 2010,ApJ, 709, 278,doi: 10.1088/0004-637X/709/1/278Dai, X., Steele, S., Guerras, E., Morgan, C. W., &Chen, B. 2019, arXiv e-prints, arXiv:1901.06007.https://arxiv.org/abs/1901.06007Dickey, J. M., & Lockman, F. J. 1990, ARA&A,28, 215,doi: 10.1146/annurev.aa.28.090190.001243Fabian, A. C., Nandra, K., Reynolds, C. S., et al.1995, MNRAS, 277, L11,doi: 10.1093/mnras/277.1.L11Ferrarese, L., & Merritt, D. 2000, ApJL, 539, L9,doi: 10.1086/312838George, I. M., & Fabian, A. C. 1991, MNRAS,249, 352, doi: 10.1093/mnras/249.2.352Gil-Merino, R., Goicoechea, L. J., Shalyapin,V. N., & Braga, V. F. 2012, ApJ, 744, 47,doi: 10.1088/0004-637X/744/1/47 Gou, L., McClintock, J. E., Reid, M. J., et al.2011, ApJ, 742, 85,doi: 10.1088/0004-637X/742/2/85Guerras, E., Dai, X., & Mediavilla, E. 2018, arXive-prints, arXiv:1805.11498.https://arxiv.org/abs/1805.11498Guerras, E., Dai, X., Steele, S., et al. 2017, ApJ,836, 206, doi: 10.3847/1538-4357/aa5728Jiang, L., Fan, X., Ivezi´c, ˇZ., et al. 2007, ApJ, 656,680, doi: 10.1086/510831Kellermann, K. I., Sramek, R., Schmidt, M.,Shaffer, D. B., & Green, R. 1989, AJ, 98, 1195,doi: 10.1086/115207Kochanek, C. S. 2004, ApJ, 605, 58,doi: 10.1086/382180Kormendy, J., & Richstone, D. 1995, ARA&A, 33,581, doi: 10.1146/annurev.aa.33.090195.003053Marshall, H. L., Gelbord, J. M., Worrall, D. M.,et al. 2018, ApJ, 856, 66,doi: 10.3847/1538-4357/aaaf66McConnell, N. J., & Ma, C.-P. 2013, ApJ, 764,184, doi: 10.1088/0004-637X/764/2/184Mediavilla, E., Mu˜noz, J. A., Lopez, P., et al.2006, ApJ, 653, 942, doi: 10.1086/508796Mediavilla, E., Mu˜noz, J. A., Falco, E., et al.2009, ApJ, 706, 1451,doi: 10.1088/0004-637X/706/2/1451Morgan, C. W., Kochanek, C. S., Morgan, N. D.,& Falco, E. E. 2010, ApJ, 712, 1129,doi: 10.1088/0004-637X/712/2/1129Morgan, C. W., Hainline, L. J., Chen, B., et al.2012, ApJ, 756, 52,doi: 10.1088/0004-637X/756/1/52Mosquera, A. M., & Kochanek, C. S. 2011, ApJ,738, 96, doi: 10.1088/0004-637X/738/1/96Mosquera, A. M., Kochanek, C. S., Chen, B.,et al. 2013, ApJ, 769, 53,doi: 10.1088/0004-637X/769/1/53Oguri, M., Rusu, C. E., & Falco, E. E. 2014,MNRAS, 439, 2494, doi: 10.1093/mnras/stu106Protassov, R., van Dyk, D. A., Connors, A.,Kashyap, V. L., & Siemiginowska, A. 2002,ApJ, 571, 545, doi: 10.1086/339856Schechter, P. L., Pooley, D., Blackburne, J. A., &Wambsganss, J. 2014, ApJ, 793, 96,doi: 10.1088/0004-637X/793/2/96Schwartz, D. A., Marshall, H. L., Lovell, J. E. J.,et al. 2000, ApJL, 540, 69, doi: 10.1086/3128757