New two-colour light curves of Q0957+561: time delays and the origin of intrinsic variations
V. N. Shalyapin, L. J. Goicoechea, E. Koptelova, A. Ullan, R. Gil-Merino
aa r X i v : . [ a s t r o - ph ] O c t Astronomy&Astrophysicsmanuscript no. astroph c (cid:13)
ESO 2018October 8, 2018
New two-colour light curves of Q0957+561:time delays and the origin of intrinsic variations
V. N. Shalyapin , L. J. Goicoechea , E. Koptelova , , A. Ull´an and R. Gil-Merino Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12 Proskura St., Kharkov 61085, Ukrainee-mail: [email protected] Departamento de F´ısica Moderna, Universidad de Cantabria, Avda. de Los Castros s / n, 39005 Santander, Spaine-mail: [email protected] Sternberg Astronomical Institute, Universitetski pr. 13, 119992 Moscow, Russiae-mail: [email protected] Graduate Institute of Astronomy, Jhongli City, Taoyuan County 320, Taiwane-mail: [email protected] Robotic Telescopes Group, Centro de Astrobiolog´ıa (CSIC-INTA), associated to the NASA Astrobiology Institute, Ctra de Ajalvir,km 4, 28850 Torrej´on de Ardoz, Madrid, Spaine-mail: [email protected] Instituto de F´ısica de Cantabria (CSIC-UC), Avda. de Los Castros s / n, 39005 Santander, Spaine-mail: [email protected] Preprint online version: October 8, 2018
ABSTRACT
Aims.
We extend the gr -band time coverage of the gravitationally lensed double quasar Q0957 + gr light curves permit usto detect significant intrinsic fluctuations, to determine new time delays, and thus to gain perspective on the mechanism of intrinsicvariability in Q0957 + Methods.
We use new optical frames of Q0957 +
561 in the g and r passbands from January 2005 to July 2007. These frames are part ofan ongoing long-term monitoring with the Liverpool robotic telescope. We also introduce two photometric pipelines that are appliedto the new gr frames of Q0957 + Results.
The gr light curves of Q0957 +
561 show several prominent events and gradients, and some of them (in the g band) leadto a time delay between components ∆ t BA = ± σ ). We do not find evidence of extrinsic variability in the light curves ofQ0957 + g band and the corresponding event in the r band.The gr cross-correlation reveals a time lag ∆ t rg = ± σ ; the g -band event is leading) that confirms a previous claim of theexistence of a delay between the g and r band in this lensed quasar. Conclusions.
The time delays (between quasar components and between optical bands) from the new records and previous ones insimilar bands indicate that most observed variations in Q0957 +
561 (amplitudes of ∼
100 mmag and timescales of ∼
100 d) are veryprobably due to reverberation within the gas disc around the supermassive black hole.
Key words. techniques: photometric – gravitational lensing – black hole physics – quasars: individual: Q0957 +
1. Introduction
Studies of optical continuum variability in gravitationally lensed quasars (GLQs) have a main advantage: one is usually able todisentangle intrinsic from extrinsic signal in GLQs (e.g., Kundi´c et al. 1997; Paraficz et al. 2006; Goicoechea et al. 2008, PaperI). Following the original idea by Refsdal (1964), intrinsic variations in brightness records of GLQs have mainly been used toestimate global time delays between components, and to discuss the structure of galaxy mass halos and the expansion rate of theUniverse (e.g., Kochanek et al. 2004, and references therein). Less e ff ort has been devoted to investigating the nature of intrinsicfluctuations, which are generated by mechanisms of variability in lensed quasars. This can be done by measuring time delaysbetween components and between optical bands, using prominent events in segments of long-term light curves. Time delays betweentwo given components of a GLQ (determined from di ff erent pairs of twin features) arise from gravitational lensing of flares in thevariable source. While the flaring of a well-defined emission region (e.g., a ring of the accretion disc) produces a set of similardelays, the existence of flares in some widely separated zones can lead to important time delay di ff erences (Yonehara 1999). Foreither of the two components, time delays between optical bands (or interband time delays) refer to time lags arising from physicalphenomena within the quasar.The gravitationally lensed double quasar Q0957 +
561 at z = ff erent optical bands with di ff erent telescopes. To derive a global time delay between quasar components, some previous studiesused large data sets incorporating all kinds of fluctuations, i.e., noisy or poorly sampled features as well as noticeable gradients andevents on several timescales. These large data sets are based on frames that were taken in the 1980s and 90s, and they lead to a global Shalyapin et al.: New two-colour light curves of Q0957 + delay of about 423 −
425 d (Oscoz et al. 2001; Ovaldsen et al. 2003a). The Apache Point Observatory (APO) experiment permittedinvestigators to follow-up the variability in the g and r bands during the 1995 and 1996 seasons, i.e., covering 1.5 years (Kundi´c et al.1997). This monitoring programme with the APO 3.5 m telescope produced accurate light curves of both components Q0957 + + S / N ≥ g band (a prominent event in A and the replica event in B; S / N ∼ + − d (95% confidence interval). Complementary to this result, Collier (2001) found that the r -band main twinevents lag with respect to the ones in the g -band by 3.4 + . − . d (68% confidence interval), and this interband delay was interpreted asclear evidence for reprocessing in the accretion disc of the quasar.Goicoechea (2002) reanalysed the APO g -band data set to obtain two di ff erent gravitational lens time delays of 417.0 ± ± S / N ∼
3) and it clearly disagrees with the 417-day value. The APO mainand secondary twin events in the g band are associated with a main flare and a secondary flare in the variable source, respectively.From the time delay di ff erence of 15 ± Ω =
Λ = gr -band time coverage of Q0957 + gr light curvesto detect prominent intrinsic events similar to the APO ones. These new features should allow us to determine new time delays andto improve our understanding of the mechanism causing the intrinsic variability. The paper is organised as follows: in Section 2, wepresent new data of Q0957 +
561 based on recent observations with the Liverpool 2 m telescope (LT) in the g and r bands, spanning2.5 years. We describe the observations, the pre-processing, and the photometric procedure for determining calibrated and correctedmagnitudes of field stars and quasar components. This last reduction procedure consists of two new pipelines specially designed forthe LT. In Section 3 we study the time delays between the two components of Q0957 +
561 as well as the possible delays betweenthe g and r band in the new data set. In Section 4 we summarize our results. From the APO and LT delays of Q0957 + ∼
100 mmag and lasting ∼
100 d.
2. Data acquisition and reduction
Liverpool Quasar Lens Monitoring (LQLM) I is the first phase of an optical follow-up of lensed quasars, undertaken using theRATCam optical CCD camera on the Liverpool robotic telescope (Steele et al. 2004) between January 2005 and July 2007. Thefirst scientific output of LQLM I was reported in Paper I, and we concentrate here on the observations of Q0957 +
561 in the g and r filters. The field of view and the pixel scale (binning 2 ×
2) were ∼ . ′ × . ′ . ′′ −
200 s ( g band) and 120 s ( r band). We obtained 286 frames in the g band and 264 frames in the r band. The LT observed for atotal science time of ∼ + . This performs three basic instrumental reductions: bias subtraction,trimming of the overscan regions, and flat fielding. We also apply a bad-pixel mask (made available by the Angstrom project;Kerins et al. 2006), and correct bad pixels on the CCD. The next step is the pre-selection of frames, based on individual inspection,to assure that exposures verify some elemental conditions (e.g., that the telescope pointing was accurate enough so that the lenssystem was included in the field of view, that there is no strongly degraded signal, etc), and that seeing ( FWHM ) and sky level(background) values do not exceed reasonable bounds. We only consider frames with
FWHM < ′′ due to the separation betweenthe two quasar components (A and B) of ∼ ′′ . The pre-selected database contains 199 frames in the g band and 210 frames in the r band. This means that ∼
75% of the original LT frames were initially useful.
In a first step, we take a reference frame, i.e., a high-quality frame with small
FWHM and large signal-to-noise ratio (
S NR ). Wethen measure the positions (with respect to the left bottom corner of the reference frame) of seven reference stars and both quasarimages. We select the 7 brightest stars in the Sloan Digital Sky Survey (SDSS) catalog (e.g., Adelman-McCarthy et al. 2007).These stars, having g (SDSS) and r (SDSS) magnitudes below 18 and 17, respectively, were labeled as X, G, F, H, D, E, and R stars See the Web site http: // telescope.livjm.ac.uk / Info / TelInst / Inst / RATCam / index.php. See the DR6 Catalogue Archive Server site http: // cas.sdss.org / astrodr6 / en / . Funding for the SDSS has been provided by the Alfred P. SloanFoundation, the Participating Institutions, the NASA, the NSF, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max PlanckSociety. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutionsare The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, LosAlamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New MexicoState University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington.halyapin et al.: New two-colour light curves of Q0957 +
561 3
Fig. 1.
Observations of Q0957 +
561 with the Liverpool robotic telescope in the g band. We display system subframes (left panels),model subframes (middle panels), and residual subframes (right panels) for five frames taken during the 2.5-year monitoring period(see main text).in Figure 1 and Table 1 of Ovaldsen et al. (2003a). Several Image Reduction and Analysis Facility (IRAF) tasks are also used toidentify the available reference objects (in general, less than 7 stars) and the quasar components in the rest of the frames.In a second step, our photometric pipeline performs aperture photometry of bright field stars and quasar images. This IRAFprocedure is used to estimate initial instrumental fluxes (sources and their associated backgrounds) and to improve the initial sourcepositions on each frame. The pipeline also cuts the original frames in order to produce square subframes with 64 pixels per side:the system subframe (around the centre of the lens system) and subframes of stars (around the bright stars), and makes a PSFsubframe containing the clean 2D profile of the H star (removing the local background). This last empirical PSF is required whenperforming PSF fitting. The point-like sources (quasar components and stars) are modelled by means of the empirical PSF, whereasthe extended source (lensing elliptical galaxy) is modelled by a de Vaucouleurs profile convolved with the empirical PSF. Afterobtaining all subframes for a given frame, PSF photometry on the stellar and system (crowed field) subframes is performed withIMFITFITS software (McLeod et al. 1998). The pipeline is written in the Python programming language , and incorporates thecapabilities of IRAF (through the PyRAF interface) and IMFITFITS, as well as additional numerical and graphical tools.To determine accurate quasar fluxes, one needs to use a set of constraints. For Q0957 + ff ective radius,ellipticity, and position angle (a de Vaucouleurs profile was fitted to HST images). Due to the relatively low brightness of the lensinggalaxy in the frames and the proximity of the B component to the galaxy, we determine the galaxy-to-H star ratio ( GAL / H ) in the gr bands from the best LT frames, in terms of FWHM and
S NR values. The H star is relatively bright and it is present in all frames.We then apply the pipeline to all frames (whatever their qualities) in each optical filter, by setting the galaxy fluxes to those derivedfrom the
GAL / H ratio and H star fluxes, and allowing the remaining free parameters to vary.The photometry pipeline output includes the system subframes, their model subframes (best fits) and the associated residualsubframes (system subframes after subtracting model subframes). In Fig. 1 we show system subframes (left panels), model sub-frames (middle panels), and residual subframes (right panels) corresponding to five frames in the g band. From top to bottom:March 16, 2005 ( FWHM = . ′′ S NR = χ = FWHM = . ′′ S NR = χ = IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research inAstronomy (AURA) under cooperative agreement with the National Science Foundation. See the Web site http: // / . Shalyapin et al.: New two-colour light curves of Q0957 + Fig. 2.
Colour coe ffi cient in the g band. The values are distributed around the central discontinuous line (average coe ffi cient), andmost of them are placed between the top and bottom discontinuous lines (filled circles). Only seven extreme values (triangles andopen circles) exceed these limits.26, 2006 ( FWHM = . ′′ S NR = χ = FWHM = . ′′ S NR = χ = FWHM = . ′′ S NR = χ = S NR values are inferred from the A images (having fluxes similar tothose of B images) and the χ values quantitatively describe the quality of the fits (i.e., these represent the standard reduced χ forthe best fits). All subframes in Fig. 1 have been expanded by a factor of 2. The visual comparison between left and middle panelsas well as the inspection of patterns of residual brightness (right panels) indicate that the photometric method works well. Thepipeline also produces a basic data release file containing values of all relevant instrumental fluxes (stars and quasar images) andrelative instrumental magnitudes of both quasar components, e.g., g ∗ A − g ∗ E and g ∗ B − g ∗ E in the g band. To check the reliability of ourPSF fitting procedure, we applied a deconvolution technique (Koptelova et al. 2005) to two sets of frames in October-December2005 ( gr bands). The relative instrumental magnitudes from the deconvolution method agreed with the records from the PSF fittingtechnique (see Fig. 3 of Goicoechea et al. 2007). We use a transformation pipeline (in the Python programming language) to obtain SDSS magnitudes from instrumental magnitudesthat are corrected for systematic e ff ects. The whole calibration-correction process is outlined in Appendix A. Only frames with S NR ≥
100 over Q0957 + g band, this selection leads to 170 frames.In the r band, besides the S NR based selection, the surviving frames from the first season (January-June 2005) are also removed.Several of these ∼ r -band frames with S NR above 100 (first season) are characterized by an anomalous image formation. Thus,the high-quality data set in the r band includes 167 frames.The transformation pipeline fits the deviations between instrumental and standard g magnitudes of the 7 reference stars to thetransformation model that incorporates a zero-point term ( α g ), a colour coe ffi cient ( β g ), and inhomogeneity coe ffi cients ( γ g , nm ). Eq.(A.11) shows the relationship between the observed magnitude deviation and the model to describe it. The zero-point term and thecolour coe ffi cient are allowed to vary over time because the atmospheric and instrumental conditions significantly evolve duringthe 2.5 years of monitoring. The last ingredient of the model is a linear-quadratic inhomogeneity term, which is related to the 2Dposition on the CCD and tries to correct the possible inhomogeneous response over the camera area (e.g., Manfroid et al. 2001;Magnier & Cuillandre 2004). Each source occupies di ff erent positions on the CCD area during the robotic monitoring period, sothis could complicate the collecting of accurate brightness records.With respect to the least squares fit, in Fig. 2 we plot the solution of β g . The β g values are distributed around an average colourcoe ffi cient h β g i = − .
097 (central discontinuous line in Fig. 2), which is close to the typical coe ffi cient (see comments in AppendixA). The scatter is σ ( β g ) = h β g i ± . σ ( β g ) limits also appear in Fig. 2 (top and bottom discontinuous lines). Inrelation to the average coe ffi cient, there are seven extreme values representing changes from 100%, i.e., values around either − β g are a consequence of atmospheric-instrumental perturbations during the hard winter in January-February 2006. From thebest solutions of γ g , nm , the pipeline also produces the 2D inhomogeneity pattern, i.e., P < n + m ≤ γ g , nm x n y m . This is depicted in Fig. 3.In the transformation procedure, we set the origin of coordinates at the centre of the 1024 × ∼
80 mmag, which is consistent with results from otheroptical telescopes (e.g., Manfroid et al. 2001; Magnier & Cuillandre 2004). It is evident that the inhomogeneity pattern in Fig. 3plays a role in achieving 1 −
2% photometric accuracy. halyapin et al.: New two-colour light curves of Q0957 +
561 5
Fig. 3.
Inhomogeneity map in the g band. The zero inhomogeneity level is described by means of a continuous line that crosses thecentre of the 1024 × − − − − − −
60, and −
70 mmag.
Fig. 4.
Final magnitudes of Q0957 + + g band of the SDSS photometricsystem. These g -SDSS light curves include noticeable fluctuations covering a 2.5-year monitoring period from January 2005 toJune 2007.After the g -band fit, the pipeline computes the calibrated and corrected records of the reference stars and both quasar imagesfrom Eq. (A.13). The 14 − − ∼ ff erent times, the standard intranight deviations of the stellar curves do nottrace their scatters (see however Paper I). This is not surprising because the intranight variations exclusively correspond to severalnights in the second season, which covers a small fraction of the total monitoring period. Thus, after some preliminary test usingthe stellar records, we find a non-biased estimator of uncertainties (typical errors): stellar scatters are well traced by the standarddeviations between adjacent magnitudes that are separated by ≤ g -SDSS magnitudes of Q0957 + Shalyapin et al.: New two-colour light curves of Q0957 + Fig. 5.
Final magnitudes of Q0957 + + r band of the SDSS photometricsystem. The r -SDSS records from October 2005 to June 2007 (two whole seasons) incorporate di ff erent prominent features that arealso seen in the g -SDSS curves (see Fig. 4), with the g -SDSS features having a larger amplitude.A final refinement (selection) is taken into account. Our last selection criterion is colour based: frames with extreme colourcoe ffi cients (see the triangles and open circles in Fig. 2) are also removed from the data set. This leads to 163 surviving frames.We obtain uncertainties (see above) of about 16 mmag in both ∼ − − + + g -SDSS light curves include important gradients and prominentevents, which resemble those reported by Kundi´c et al. (1997) using APO observations in the g band. The whole monitoring periodconsists of three observational seasons: January-June 2005 (first season), October 2005-June 2006 (second season), and October2006-June 2007 (third season). Besides the three observational seasons, there are two important gaps in the LT monitoring as aconsequence of the annual occultation of the lens system.The whole procedure in the g band is repeated in the r band. All frames with extreme colour coe ffi cients are not consideredin building the final light curves, so we use a data set incorporating 142 frames. With respect to the quasar brightness records,we achieve ∼
1% photometry (errors of about 12 mmag). The final (grouped) magnitudes are presented in Fig. 5, where the topand bottom panels display the records of Q0957 + + r -SDSS light curves trace promi-nent fluctuations that are weaker than the corresponding fluctuations in g -SDSS (see Fig. 4 and subsection 3.2). A similar resultwas claimed by the APO team (Kundi´c et al. 1995, 1997), and some evidence for chromatic variability was also suggested byUll´an et al. (2003) (see also the BVRI variations in Serra-Ricart et al. 1999). The LT records in the red region of the optical spec-trum are less noisy than previous curves at red wavelengths (e.g., Kundi´c et al. 1997; Serra-Ricart et al. 1999), which is due to acombination of an absence of relatively short variations and strict selection procedures.
3. Time delays of Q0957+561
The g -band light curve of A in the second season (October 2005-June 2006) shows significant fluctuations that are repeated in the g -band light curve of B during the third season (October 2006-June 2007). Taking into account the expected delay range of 415 − g -SDSS magnitudes of A and B in the second and third seasons, respectively,to accurately measure the time delay(s) between both components of Q0957 + The gr records are available at http: // grupos.unican.es / glendama / .halyapin et al.: New two-colour light curves of Q0957 +
561 7
Fig. 6.
Comparison between the g -band light curve of A in the second season (shifted by 420 d; see main text) and the g -band lightcurve of B in the third season. The A record (filled circles) shows two di ff erent features separated by a gap of about 50 d: while thefirst feature contains an event AE1 g and the beginning of another consecutive event AE2 g , the second feature describes the (noisy)decline in flux of AE2 g . A vertical line is drawn to distinguish between the two events AE1 g and AE2 g . Replica events BE1 g andBE2 g are clearly seen in the B record (open circles). Table 1.
Magnitude o ff set and time delay measurements in the g band. Brightness records Method O ff set a (mag) Delay b (d)A(season 2)-B(season 3) χ − ± ± D − ± ± χ − ± ± δ - 417 ± a Magnitude o ff set between the A and B components, where the sign ” − ” means that A is fainter (see Fig. 6). From δ we do not measure theshift in magnitude, since δ is a technique based on autocorrelation and cross-correlation functions. All measurements are 1 σ intervals. b Delay of the replica variation in B with respect to the variation in A (the A component is leading). All measurements are 1 σ intervals. About one half of the frames with 80 < S NR <
100 correspond to the second season, and thus, they could help to trace thevariability of A and to minimize uncertainties in time delay estimates. Their photometric outputs (magnitudes of A) are consistentwith results from
S NR ≥
100 frames at adjacent epochs, so we recover them and expand the g -band record of A in the second season.In Fig. 6, the A light curve, shifted by 420 d (filled circles), and the unchanged B light curve (open circles) are plotted. A referencevalue of 420 d is used to shift in time one component and to compare it with the other (see above and Introduction). The A recordshows two di ff erent features separated by a gap of about 50 d (caused by atmospheric-instrumental problems in January-February2006; see subsection 2.3). The first feature in the A curve consists of an event AE1 g and the beginning of another consecutive eventAE2 g , whereas the second feature is a noisy trend associated with the decline in flux of AE2 g . These two consecutive events havean amplitude of about 100 mmag and a duration of 50 −
150 d, and similar fluctuations BE1 g and BE2 g are evident in the B record.Firstly, we analyse the twin events AE1 g -BE1 g and AE2 g -BE2 g . The S / N values for them (the ratios between their semi-amplitudes and their mean photometric errors) are ( S / N ) AE g ∼ S / N ) BE g ∼ ( S / N ) BE g ∼ g is a prominent event, it is poorly traced as a consequence of the 50-day gap and the noisy right wing. Thus, we are not able todetermine a reliable value of ( S / N ) AE g , and the e ff ective signal-to-noise ratio for AE2 g could be significantly less than 3 −
4. Thedi ffi culties in inferring a time delay from the AE2 g -BE2 g twin events confirm our suspicions. Unfortunately, it is not possible tomeasure two independent delays, one from AE1 g -BE1 g and the other from AE2 g -BE2 g . The only options are the estimation of adelay related to the two flares in the source of intrinsic variability, i.e., using all events in Fig. 6, or a delay corresponding to the firstflare, i.e., from AE1 g -BE1 g .Secondly, to calculate the two-flare time delay and magnitude o ff set (i.e., a constant magnitude shift between the light curves ofthe two quasar components), we use two techniques: χ minimization (e.g., Kundi´c et al. 1997; Ull´an et al. 2006) and the minimumdispersion ( D ) method (Pelt et al. 1994, 1996), characterized by a bin semisize ( α ) and a decorrelation length ( δ ). The choice of α = δ = χ minimization ( α = ff set: ∆ t BA =
417 d and ∆ m BA = − χ ∼ − ” in the ∆ m BA value means that the A component is fainter. The D minimization ( δ = ∆ t BA =
416 d and ∆ m BA = − ff set and time delay are inferred from 1000 repetitions of the experiment(synthetic light curves based on the observed records). The 1 σ intervals appear in Table 1. Table 1 indicates that the error in time Shalyapin et al.: New two-colour light curves of Q0957 + Fig. 7.
Overlapping periods and di ff erence light curves in the g band. We show the overlap between the A (filled circles) and B(open circles) whole records, when the A magnitudes are shifted by the best solutions of the time delay and the magnitude o ff set(left panels). We also draw the di ff erence light curve (right panels). The three overlap periods cover ∼
20 d (top panels), ∼
90 d(middle panels), and ∼
60 d (bottom panels).delay from the χ minimization is substantially less than the error from the minimum dispersion method. Both measurements of thetwo-flare time delay are consistent with the APO main delay in the g band (see Introduction).Thirdly, we exclusively use the AE1 g -BE1 g twin events. The idea is to accurately measure the gravitational lens delay associatedwith only one flare produced in the source of variability. This time we focus on the δ method (see, e.g., Paper I) and the χ minimization, which produces a delay error smaller than the delay uncertainty from the minimum dispersion technique (see Table 1).The δ technique obtains the optimal match between the time-shifted discrete autocorrelation function ( DAF ) and the discrete cross-correlation function (
DCF ; Edelson & Krolik 1988). From the χ minimization ( α = ff set are 417 d and − χ ∼ δ method and 1000 synthetic light curves, the delaymeasurement (1 σ interval) is identical to that derived from the χ technique (see Table 1). Therefore, the LT first twin events areuseful to determine a robust time delay ∆ t BA = ± σ ). This is fully consistent with the APO main delay (Kundi´c et al.1997; Goicoechea 2002). The δ analysis also indicates that ∆ t BA ≤
424 d (99% confidence interval), so the AE1 g -BE1 g delay isinconsistent (at about the 3 σ level) with the APO secondary delay (Goicoechea 2002). The r -band curves of AE1-BE1 are not usedto determine a time delay because S / N < ff erence light curve between theA and B components, since no extrinsic variability should result in a flat di ff erence light curve. To obtain the di ff erence light curve,the magnitude- and time-shifted light curve of image A is subtracted from the light curve of image B (e.g., Schmidt & Wambsganss1998; Gil-Merino et al. 2001). In Fig. 7 (left panels), we show the overlap between the A (filled circles) and B (open circles) wholerecords, when the A magnitudes are shifted by the best solutions of the time delay and the magnitude o ff set. The di ff erence lightcurve is also plotted in the right panels of Fig. 7. The overlap between A-first season and B-second season covers a very short periodof about 20 d (see the top panels of Fig. 7). For this overlap period, the di ff erence curve contains two consecutive deviations fromthe zero level, which are not significative (e.g., Gil-Merino et al. 2001). The overlap between A-second season and B-third season halyapin et al.: New two-colour light curves of Q0957 +
561 9
Fig. 8.
Comparison between the
DCF (filled circles) and the h DAF i (open circles). While the DCF is the gr cross-correlationfunction, the h DAF i is the average of the gg and rr autocorrelation functions. We use the AE3 g -AE3 r events (see main text) andthree bin semisizes: α =
20 (top panel), 25 (middle panel), and 30 (bottom panel) d.is much more important than the first overlap (in the top panels). In the middle panels of Fig. 7, we display the situation before the50-day gap (see above and Fig. 6), where the di ff erence curve has a noisy trend that is consistent with zero. In the bottom panels,the behaviour after the 50-day gap is shown. In this last period, the di ff erence curve is also mainly noise. However, a clear eventappears at the beginning of the overlapping period, i.e., six consecutive points are placed above the zero level. Although this naivelycould be interpreted as the wing of a microlensing event (i.e., extrinsic variability), the A data were obtained at the end of a hardwinter in which the colour coe ffi cient strongly deviated (40 − ffi cients are not considered in the analysis (see the triangles and the open circle around day 3770 in Fig. 2), additional adjacentframes are also unsuitable for fine variability studies. Therefore, bad weather and anomalous behaviour of the LT devices are themost reasonable explanations for the anomalous variation in A that is simultaneously observed in both components. In summary,we do not find evidence of extrinsic variability in the light curves of Q0957 + The time delay between optical-UV continuum flux variations at two di ff erent wavelengths can be used to test the variabilitysecenario (e.g., Collier et al. 1999). It might be produced by reprocessing of high energy radiation in an accretion disc around asupermassive black hole. The reprocessing hypothesis assumes that the optical-UV variations are the response of the gas in thedisc to higher-energy fluctuations in the vecinity of the disc axis. Moreover, the existence of a radiative coupling between thevariations is also assumed, i.e., the time delay represents a light-travel time between two disc annuli (see details in Collier et al.1999). Collier et al. (1999) measured two time lags between fluctuations at two optical wavelengths and the corresponding UVfluctuations (UV variability leading optical variations) in the records of NGC 7469 at z = ∼ − + + Fig. 9.
Normalised δ function from the AE3 g -AE3 r events. We use bin semisizes α =
20 (dotted line), 25 (dashed line), and 30(solid line) d. In Fig. 8, we can observe the presence of time shifts between the
DCF and h DAF i , which translate into interbanddelay peaks centered on 3 − g leading AE3 r ). Table 2.
Time lag measurements from the AE3 g -AE3 r events. α a (d) Time lag b (d) Probability of lags ≤ ± ± ± ± ± a We use the δ technique (see main text) and five values of the bin semisize α . b All measurements are 1 σ intervals, and positive lags mean that the r -band event is delayed in relation to the arrival of the associated g -bandevent. of about 3.4 d between the r -band and g -band APO main events ( g -band events leading those in the r band), which translates intoa rest-frame lag of about 1.4 d, in excellent agreement with predictions of the disc reprocessing scenario. This first delay betweenoptical bands for a GLQ requires an independent confirmation as well as new e ff orts with other GLQs (e.g., Koptelova et al. 2006),and here we try to reach the first goal.For such a task, we focus on the LT events with highest S / N . The AE1-BE1 twin events are ruled out because ( S / N ) < r band. However, there are two very prominent variations around day 4150 in the top panels of Figs. 4 − g and AE3 r variations last ∼
250 d (the whole light curves of A in the third season are considered as large events) andhave signal-to-noise ratios above 6. We use fluxes in arbitrary units f = × − . m to compare AE3 g and AE3 r . The use offluxes (instead of magnitudes m ) permits a fair cross-correlation between two records that, apart from a possible delay, di ff er in amultiplicative constant and an additive constant. On average, the light curves were sampled two times per week. However, there are20-day gaps around day 4180. Unfortunately, due to a combination of the kind of variability (time asymmetric events consisting ofslow rises and rapid declines) and these short gaps close to the maxima, it is not possible to infer a reliable DCF with good timeresolution, i.e., α ≤
10 d (see above). For α <
20 d, 20-day artifacts at lags of ±
50 d appear in the
DCF . This unphysical signalat ±
50 d is only avoided using longer bins with α ≥
20 d, so we are forced to take relatively long bins. This is not a problemat all, but the measurement would be more accurate (but not more reliable) with better time resolution. Some
DCF (filled circles)and h DAF i (open circles) trends are shown in Fig. 8. The top, middle, and bottom panels of Fig. 8 contain the results for α = h DAF i is the average of the gg and rr autocorrelation functions, whereas DCF represents the gr cross-correlation function.In Fig. 8, there are no important distortions in the features of the DCF compared to the features in the h DAF i , but the existenceof a delay of several days is evident. In other words, to get an optimal match, the h DAF i should be shifted by several days. Possiblevalues of this time shift ( θ ) versus the associated δ ( θ ) values normalised by its minimum value δ ( θ ) are plotted in Fig. 9. The δ ( θ ) function was defined in Eq. (7) of Serra-Ricart et al. (1999) (see also above), and we use α =
20 (dotted line), 25 (dashedline), and 30 (solid line) d in Fig. 9. This figure displays relatively narrow peaks centered on 3 − g leading AE3 r ). Uncertainties are again computed by applying the δ minimization to 1000 synthetic data sets. Throughthe distributions of delays ( α = −
40 d), five 1 σ measurements are presented in Table 2. The δ results in Table 2 agree with theprevious time lag determination from APO light curves, and we adopt ∆ t rg = ± α = ∆ t rg ≤ σ measurement. halyapin et al.: New two-colour light curves of Q0957 +
561 11
4. Summary and conclusions
Liverpool Quasar Lens Monitoring is a long-term project to follow the optical ( gri bands) variability of 10 −
20 GLQs with theLiverpool robotic telescope (Steele et al. 2004). The first phase of this project (LQLM I) was conducted between January 2005 andJuly 2007. While in Paper I we mainly studied the intrinsic variability of Q0909 +
532 in the r band, in this paper we present themonitoring programme of Q0957 +
561 in the gr bands. A main goal of our project (LQLM) is to considerably increase the publicdatabase of GLQs. Thus, all LQLM I pre-processed frames of Q0909 +
532 and Q0957 +
561 are publicly available on the Lens ImageArchive of the German Astrophysical Virtual Observatory .We have fully developed two photometric pipelines through the 3 years of observations and analyses. The transformationpipeline incorporates zero-point, colour, and inhomogeneity corrections in the instrumental fluxes, so photometry to the 1 − + + ∼
80 mmag (from maximum to minimum) and is consistent with studies in other optical telescopes (e.g., Manfroid et al.2001; Magnier & Cuillandre 2004). Moreover, the colour coe ffi cient is allowed to vary through time, because the atmospheric-instrumental conditions signicantly evolve through 2.5 years of monitoring. Due to atmospheric-instrumental problems at someepochs, the colour coe ffi cient reaches anomalous values, i.e., we obtain dramatic deviations with respect to the average coe ffi cient.Thus, the frames corresponding to an anomalous coe ffi cient are removed or not considered.The LT gr light curves of Q0957 +
561 show several prominent events and gradients, and some of them (in the g band) are used toinfer a time delay between components ∆ t BA = ± σ ). This gravitational lens delay from new g -band events is in agreementwith the delay from the previous APO g -band main events (Kundi´c et al. 1997), so the associated UV flares in the variable source(APO and LT events) probably originate in the same emission region (Yonehara 1999). Taking into account that the previous APO gr -band main events are plausibly due to reverberation within an irradiated accretion disc (Collier 2001), the new gr -band eventsare likely related to flares in the central accretion disc. In addition, the delay between the two new LT large events in the g and r bands: ∆ t rg = ± σ ; the g -band event is leading), coincides with the estimation by Collier (2001) and agrees with flaresgenerated during reprocessing in the accretion disc. Therefore, most APO-LT variations in the g and r bands are very probablyassociated with the gas disc around the supermassive black hole (only the APO secondary events have been associated with flaresthat were produced far away from the accretion disc; see Introduction). The detection of the same interband delay (between the g and r band) in the two monitoring campaigns (APO and LT) also suggests that the accretion disc reprocessing in Q0957 +
561 is ausual occurance at di ff erent times for di ff erent prominent flares. Hence, very likely, most observed variations in the g and r bands(APO and LT fluctuations with an amplitude of ∼
100 mmag and lasting ∼
100 d) are associated with reverberation within the gasdisc around the supermassive black hole.We add 2.5 years of time coverage to the previous 1.5-year gr -band records of Q0957 + ff erence lightcurves are consistent with zero. Thus, there is no evidence of extrinsic variations in both APO and LT independent experimentsseparated by ∼
10 years. These results disagree with the claim by Schild (2005) that microlenses in the lensing galaxy a ff ectthe observed variability. Therefore, the complex quasar structure suggested by this author is not supported by the gr -band lightcurves of Q0957 + +
561 (together with other monitorings done between both experiments) is a promising tool for studying the quasar structureand the composition of the lensing halo (e.g., Schmidt & Wambsganss 1998; Kochanek 2004).
Acknowledgements.
We thank an anonymous referee for several comments that improved the presentation of our results. We also thank C. Moss for guidance inthe preparation of the robotic monitoring project with the Liverpool telescope. The Liverpool Telescope is operated on the island of La Palma by Liverpool JohnMoores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Scienceand Technology Facilities Council. We thank B. McLeod for providing the IMFITFITS software to us. We use information taken from the Sloan Digital Sky Survey(SDSS) Web site, and we are grateful to the SDSS team for doing that public database. This research has been supported by the Spanish Department of Educationand Science grants AYA2004-08243-C03-02 and AYA2007-67342-C03-02, University of Cantabria funds, grant for young scientists of the President of the RussianFederation (number MK-2637.2006.2), Deutscher Akademischer Austausch Dienst (DAAD) grant number A / / References
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The initial transformation equations for a given reference star are g ∗ ( t j ) = g + A g ( t j ) + C g ( t j )( g − r ) , (A.1) r ∗ ( t k ) = r + A r ( t k ) + C r ( t k )( r − i ) , (A.2)where g ∗ and r ∗ are the instrumental magnitudes of the star, g , r , and i are its standard magnitudes, A g and A r are the zero-pointterms (including instrumental and atmospheric corrections), and C g and C r are the colour coe ffi cients. The zero-point terms andthe colour coe ffi cients are expected to significantly change during the 2.5-year monitoring period, so we explicitly consider theirtime evolution. Here, t j and t k denote observation times in the g and r bands, respectively. As we are initially interested in the usualsystematic corrections, Eqs. (A.1 −
2) do not include other possible terms (see here below). Instead of the LT photometric system( ugriz ≡ u ′ g ′ r ′ i ′ z ′ ), we want to use the SDSS ”natural” system, since accurate standard magnitudes are available in this SDSS 2.5msystem (e.g., Smith et al. 2002; Stoughton et al. 2002). SDSS magnitudes are also suitable for comparing our results with futuredata of Q0957 +
561 using di ff erent facilities and / or SDSS quasar studies / databases (e.g., Vanden Berk et al. 2004; Schneider et al.2007). From equations for transforming LT magnitudes to magnitudes in the SDSS system : g = g S DS S + B g ( g − r ) + K g , (A.3) r = r S DS S + B r ( r − i ) + K r , (A.4)and equations that relate LT and SDSS colours: g − r = a gr ( g − r ) S DS S + b gr , (A.5) r − i = a ri ( r − i ) S DS S + b ri , (A.6)it is possible to rewrite Eqs. (A.1 −
2) as g ∗ ( t j ) = g S DS S + α g ( t j ) + β g ( t j )( g − r ) S DS S , (A.7) r ∗ ( t k ) = r S DS S + α r ( t k ) + β r ( t k )( r − i ) S DS S . (A.8)The α g term and the β g coe ffi cient are given by (it is trivial to write expressions for α r and β r ) α g ( t j ) = A g ( t j ) + K g + b gr [ B g + C g ( t j )] , (A.9) β g ( t j ) = a gr [ B g + C g ( t j )] . (A.10) See the Web site http: // / dr6 / algorithms / .halyapin et al.: New two-colour light curves of Q0957 +
561 13
Table A.1.
Adopted standard magnitudes of the reference stars.
Star g SDSS r SDSS i SDSS
X 14.213 13.849 13.750G 14.461 14.157 14.060F 14.513 14.186 14.089H 15.116 14.422 14.174D 15.485 14.951 a a The SDSS catalogue seems to contain a wrong value of the r -SDSS magnitude of the D star ( r SDSS = r -SDSS magnitude is inferred through the r SDSS vs. VR relationship: r SDSS = V − . V − R ) + .
39. This law is based onthe r -SDSS magnitudes of the rest of stars and the corresponding VR magnitudes in Tables 1-2 of Ovaldsen et al. (2003b). Taking into account typical values of C g ( ∼ − . C r ( ∼ . B g ( ∼ − . B r ( ∼ − . a gr ∼ a ri ∼
1, we expecttypical colour coe ffi cients β g ∼ − .
089 and β r ∼ − . .In order to achieve 1 −
2% photometric accuracy with the RATCam camera (on the LT), one additional detail must be takeninto account in the transformation equations (A.7 − ∼
50 mmag (e.g., Manfroid et al. 2001; Magnier & Cuillandre2004). For example, this kind of error could be related to twilight flats. During twilight exposures, some scattered light (within thedome) would reach the camera, and thus, the illumination would not be homogeneous. This e ff ect invalidates the basic hypothesisof homogeneous illumination. Here, we assume a second order 2D polynomial to account for the inhomogeneity term, so the finaltransformation equations are g ∗ ( t j ) = g S DS S + α g ( t j ) + β g ( t j )( g − r ) S DS S + X < n + m ≤ γ g , nm x n ( t j ) y m ( t j ) , (A.11) r ∗ ( t k ) = r S DS S + α r ( t k ) + β r ( t k )( r − i ) S DS S + X < n + m ≤ γ r , nm x n ( t k ) y m ( t k ) , (A.12)where ( x , y ) is the 2D position of the star on the CCD. To find the relevant parameters in the g band, i.e., α g ( t j ), β g ( t j ), and γ g , nm ,we may fit the observed magnitude deviations (instrumental − standard) of the seven reference stars to the model incorporating thethree systematic terms: zero-point, colour, and inhomogeneity. Once the fit has been made, the g -SDSS magnitude of any point-likesource (star or quasar) is derived in a straightforward way: g ( S DS S ) = g S DS S + δ = g ∗ ( t j ) − α g ( t j ) − β g ( t j )( g − r ) S DS S − X < n + m ≤ γ g , nm x n ( t j ) y m ( t j ) . (A.13)In Eq. (A.13), δ represents the deviation caused by random noise (e.g., photon noise) and unkown (but presumibly small) systematiccorrections. For a non-variable star (e.g., a reference star), variations in g ( S DS S ) are generated by noise ( δ ). However, for variablestars or quasars, there are two kinds of variability. While true variability is due to time evolution of g S DS S , noise is an additionalsource of fluctuations. The ( g − r ) S DS S colour of Q0957 +
561 might also evolve over time. Thus, the use of an average colour h ( g − r ) S DS S i in the colour correction introduces a systematic noise δ col = β g ( t j ) δ ( g − r ) S DS S associated with the colour variation.Fortunately, for moderate fluctuations with amplitude of ∼
25 mmag (e.g., Kundi´c et al. 1995), the amplitude of the colour noise isonly ∼ r -SDSS magnitude of a source is given by an expression similar to Eq. (A.13). List of Objects ‘Q0957 + + + + + + + + + + + + + + ‘Q0957 + + + + + + + + + + + + + + + + + + ++