Correlated Multi-Waveband Variability in the Blazar 3C~279 from 1996 to 2007
R. Chatterjee, S. G. Jorstad, A. P. Marscher, H. Oh, I. M. McHardy, M. F. Aller, H. D. Aller, T. J. Balonek, H. R. Miller, W. T. Ryle, G. Tosti, O. Kurtanidze, M. Nikolashvili, V. M. Larionov, V. A. Hagen-Thorn
aa r X i v : . [ a s t r o - ph ] A ug Correlated Multi-Waveband Variability in the Blazar 3C 279 from1996 to 2007
Ritaban Chatterjee , Svetlana G. Jorstad , , Alan P. Marscher , Haruki Oh , , Ian M.McHardy , Margo F. Aller , Hugh D. Aller , Thomas J. Balonek , H. Richard Miller ,Wesley T. Ryle , Gino Tosti , Omar Kurtanidze , Maria Nikolashvili , Valeri M. Larionov ,and Vladimir A. Hagen-Thorn ABSTRACT
We present the results of extensive multi-waveband monitoring of the blazar3C 279 between 1996 and 2007 at X-ray energies (2-10 keV), optical R band,and 14.5 GHz, as well as imaging with the Very Long Baseline Array (VLBA)at 43 GHz. In all bands the power spectral density corresponds to “red noise”that can be fit by a single power law over the sampled time scales. Variations influx at all three wavebands are significantly correlated. The time delay betweenhigh and low frequency bands changes substantially on time scales of years. Amajor multi-frequency flare in 2001 coincided with a swing of the jet toward amore southerly direction, and in general the X-ray flux is modulated by changesin the position angle of the jet near the core. The flux density in the core at 43GHz—increases in which indicate the appearance of new superluminal knots—issignificantly correlated with the X-ray flux. Institute for Astrophysical Research, Boston University, 725 Commonwealth Avenue, Boston, MA 02215 Astronomical Institute of St. Petersburg State University, Universitetskij Pr. 28, Petrodvorets, 198504St. Petersburg, Russia Current address: Department of Physics, University of California, Berkeley, CA 94720-7300 Department of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UnitedKingdom Astronomy Department, University of Michigan, 830 Dennison, 501 East University Street, Ann Arbor,Michigan 48109-1090 Department of Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, NY 13346 Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30303 Department of Physics, University of Perugia, Via A. Pascoli, 06123 Perugia, Italy Abastumani Astrophysical Observatory, Mt. Kanobili, Abastumani, Georgia
Subject headings: galaxies: quasars: general — galaxies: quasars: individual(3C 279) — physical data and processes—X-rays: observations — radio contin-uum: galaxies
1. Introduction
Blazars form a subclass of active galactic nuclei (AGN) characterized by violent variabil-ity on time scales from hours to years across the electromagnetic spectrum. It is commonlythought that at radio, infrared, and optical frequencies the variable emission of blazarsoriginates in relativistic jets and is synchrotron in nature (Impey & Neugenbauer 1988;Marscher 1998). The X-ray emission is consistent with inverse Compton (IC) scattering ofthese synchrotron photons, although seed photons from outside the jet cannot be excluded(Mause et al. 1996; Romanova & Lovelace 1997; Coppi & Aharonian 1999; B la˙zejowski et al.2000; Sikora et al. 2001; Chiang & B¨ottcher 2002; Arbeiter et al. 2005). The models maybe distinguished by measuring time lags between the seed-photon and Compton-scatteredflux variations. Comparison of the amplitudes and times of peak flux of flares at differentwavebands is another important diagnostic. For this reason, long-term multi-frequency mon-itoring programs are crucially important for establishing a detailed model of blazar activityand for constraining the physics of relativistic jets. Here we report on such a program thathas followed the variations in emission of the blazar 3C 279 with closely-spaced observationsover a time span of ∼
10 years.The quasar 3C 279 (redshift=0.538; Burbidge & Rosenburg 1965) is one of the mostprominent blazars owing to its high optical polarization and variability of flux across theelectromagnetic spectrum. Very long baseline interferometry (VLBI) reveals a one-sidedradio jet featuring bright knots (components) that are “ejected” from a bright, presumablystationary “core” (Jorstad et al. 2005). The measured apparent speeds of the knots observed 3 –in the past range from 4 c to 16 c (Jorstad et al. 2004), superluminal motion that results fromrelativistic bulk velocities and a small angle between the jet axis and line of sight. RelativisticDoppler boosting of the radiation increases the apparent luminosity to ∼ times the valuein the rest frame of the emitting plasma.Characterization of the light curves of 3C 279 includes the power spectral density (PSD)of the variability at all different wavebands.The PSD corresponds to the power in the vari-ability of emission as a function of time scale. Lawrence et al. (1987) and McHardy & Czerny(1987) have found that the PSDs of many Seyfert galaxies, in which the continuum emissioncomes mainly from the central engine, are simple “red noise” power laws, with slopes be-tween − −
2. More recent studies indicate that some Seyfert galaxies have X-ray PSDsthat are fit better by a broken power law, with a steeper slope above the break frequency(Uttley et al. 2002; McHardy et al. 2004; Markowitz et al. 2003; Edelson & Nandra 1999;Pounds et al. 2001). This property of Seyferts is similar to that of Galactic black hole X-raybinaries (BHXRB), whose X-ray PSDs contain one or more breaks (Belloni & Hasinger 1990;Nowak et al. 1999). However, in blazars most of the X-rays are likely produced in the jetsrather than near the central engine as in BHXRBs and Seyferts. It is unclear a priori whatthe shape of the PSD of nonthermal emission from the jet should be, a question that weanswer with the dataset presented here.The raw PSD calculated from a light curve combines two aspects of the dataset: (1) theintrinsic variation of the object and (2) the effects of the temporal sampling pattern of theobservations. In order to remove the latter, we apply a Monte-Carlo type algorithm basedon the “Power Spectrum Response Method” (PSRESP) of Uttley et al. (2002) to determinethe intrinsic PSD (and its associated uncertainties) of the light curve of 3C 279 at each ofthree wavebands. Similar complications affect the determination of correlations and timelags of variable emission at different wavebands. Uneven sampling, as invariably occurs,can cause the correlation coefficients to be artificially low. In addition, the time lags canvary across the years owing to physical changes in the source. In light of these issues, weuse simulated light curves, based on the underlying PSD, to estimate the significance of thederived correlation coefficients.In § § § §
2. Observations and Data Analysis2.1. Monitoring of the X-ray, Optical, and Radio Flux Density
Table 1 summarizes the intervals of monitoring at different frequencies for each of thethree wavebands in our program. We term the entire light curve “monitor data”; shortersegments of more intense monitoring are described below.The X-ray light curves are based on observations of 3C 279 with the Rossi X-ray TimingExplorer (RXTE) from 1996 to 2007. We observed 3C 279 in 1222 separate pointings with theRXTE, with a typical spacing of 2-3 days. The exposure time varied, with longer on-sourcetimes—typically 1-2 ks—after 1999 as the number of fully functional detectors decreased,and shorter times at earlier epochs. For each exposure, we used routines from the X-raydata analysis software FTOOLS and XSPEC to calculate and subtract an X-ray backgroundmodel from the data and to model the source spectrum from 2.4 to 10 keV as a power lawwith low-energy photoelectric absorption by intervening gas in our Galaxy. For the latter,we used a hydrogen column density of 8 × atoms cm − . There is a ∼ α x ,defined by f x ∝ ν α x , where f x is the X-ray flux density and ν is the frequency, has anaverage value of − . ∼
10 years of observation,and remained negative throughout.We monitored 3C 279 in the optical R band over the same time span as the X-rayobservations. The majority of the measurements between 1996 and 2002 are from the 0.3m telescope of the Foggy Bottom Observatory, Colgate University, in Hamilton, New York.Between 2004 and 2007, the data are from the 2 m Liverpool Telescope (LT) at La Palma,Canary Islands, Spain, supplemented by observations at the 1.8 m Perkins Telescope ofLowell Observatory, Flagstaff, Arizona, 0.4 m telescope of the University of Perugia Obser-vatory, Italy, 0.7 m telescope at the Crimean Astrophysical Observatory, Ukraine, the 0.6m SMARTS consortium telescope at the Cerro Tololo Inter-American Observatory, Chile,and the 0.7 m Meniscus Telescope of Abastumani Astrophysical Observatory in Abastumani,Republic of Georgia. We checked the data for consistency using overlapping measurementsfrom different telescopes, and applied corrections, if necessary, to adjust to the LT system. 5 –We processed the data from the LT, Perkins Telescope, Crimean Astrophysical Observatory,and Abastumani Astrophysical Observatory in the same manner, using comparison stars 2,7, and 9 from Gonzalez-Perez et al. (2001) to determine the magnitudes in R band. Thefrequency of optical measurements over the ∼ ∼
100 points over 200 days between 2004 January and July. Figure 2displays these segments along with the entire 10-year light curve. A small part of the opticaldata is given in Table 3. The whole dataset will be available in the electronic version of ApJ.We have compiled a 14.5 GHz light curve (Fig. 3) with data from the 26 m antennaof the University of Michigan Radio Astronomy Observatory. Details of the calibration andanalysis techniques are described in Aller et al. (1985). The flux scale is set by observationsof Cassiopeia A (Baars et al. 1977). The sampling frequency was usually of order once perweek. An exception is a span of about 190 days between 2005 March and September whenwe obtained 60 measurements, averaging one observation every ∼ Starting in 2001 May, we observed 3C 279 with the Very Long Baseline Array (VLBA)at roughly monthly intervals, with some gaps of 2-4 months. The sequence of images fromthese data (Fig. 4 to Fig. 9) provides a dynamic view of the jet at an angular resolution ∼ . θ jet with respect to the core as that ofthe brightest component within 0.1-0.3 mas of the core. As seen in Figure 11, θ jet changes 6 –significantly ( ∼ ◦ ) over the 11 years of VLBA monitoring. Figure 12 displays a samplingof the VLBA images at epochs corresponding to the circled points in the lower panel ofFigure 11.We determine the apparent speed β app of the moving components using the same pro-cedure as defined in Jorstad et al. (2005). The ejection time T is the extrapolated epochof coincidence of a moving knot with the position of the (presumed stationary) core in theVLBA images. In order to obtain the most accurate values of T , given that non-ballisticmotions may occur (Jorstad et al. 2004, 2005), we use only those epochs when a componentis within 1 mas of the core, inside of which we assume its motion to be ballistic. θ jet , T , and β app between 1996 and 2007 are shown in Table 5. As part of the modeling of the images,we have measured the flux density of the unresolved core in all the images, and display theresulting light curve in Figure 13.
3. Power Spectral Analysis and Results
For all three wavebands, we used the monitor, medium, and longlook data to calculatethe PSD at the low, intermediate, and high frequencies of variation, respectively. Since wedo not have any longlook data at 14.5 GHz, we determine the radio PSD up to the highestvariational frequency that can be achieved with the medium data.
We follow Uttley et al. (2002) to calculate the PSD of a discretely sampled light curve f ( t i ) of length N points using the formula | F N ( ν ) | = " N X i =1 f ( t i ) cos(2 πνt i ) + " N X i =1 f ( t i ) sin(2 πνt i ) . (1)This is the square of the modulus of the discrete Fourier transform of the (mean subtracted)light curve, calculated for evenly spaced frequencies between ν min and ν max , i.e., ν min , 2 ν min , .. ., ν max . Here, ν min =1/ T ( T is the total duration of the light curve, t N − t ) and ν max = N /2 T equals the Nyquist frequency ν Nyq . We use the following normalization to calculate the finalPSD: P ( ν ) = 2 Tµ N | F N ( ν ) | , (2)where µ is the average flux density over the light curve. 7 –We bin the data in time intervals ∆ T ranging from 0.5 to 25 days, as listed in Table 6,averaging all data points within each bin to calculate the flux. For short gaps in the timecoverage, we fill empty bins through linear interpolation of the adjacent bins in order toavoid gaps that would distort the PSD. We account for the effects of longer gaps, such assun-avoidance intervals and the absence of X-ray data in 2000, by inserting in each of thesimulated light curves the same long gaps as occur in the actual data. We use a variant of PSRESP (Uttley et al. 2002) to determine the intrinsic PSD of eachlight curve. The method is described in the Appendix. PSRESP gives both the best-fit PSDmodel and a “success fraction” that indicates the goodness of fit of the model.The PSDs of the blazar 3C 279 at X-ray, optical, and radio frequencies show red noisebehavior, i.e., there is higher amplitude variability on longer than on shorter timescales. TheX-ray PSD is best fit with a simple power law of slope − . ± .
3, for which the successfraction is 45%. The slope of the optical PSD is − . ± . − . ± . − . − to 10 − Hz and − . − .
5, respectively) while calculating thesuccess fractions (McHardy et al. (2006)). Although this gives lower success fractions thanthe simple power-law model for the whole paramater space, a break at a frequency . − Hz with a high frequency slope as steep as − .
4. Cross-correlation Analysis and Results
We employ the discrete cross-correlation function (DCCF; Edelson & Krolik 1988) methodto find the correlation between variations at pairs of wavebands. We bin the light curves ofall three wavebands in 1-day intervals before performing the cross-correlation. In order to 8 –determine the significance of the correlation, we perform the following steps :1. Simulation of M (we use M =100) artificial light curves generated with a Monte-Carloalgorithm based on the shape and slope of the PSD as determined using PSRESP for bothwavebands (total of 2 M light curves).2. Resampling of the light curves with the observed sampling function.3. Correlation of random pairs of simulated light curves (one at each waveband).4. Identification of the peak in each of the M random correlations.5. Comparison of the peak values from step 4 with the peak value of the real correlationbetween the observed light curves. For example, if 10 out of 100 random peak values aregreater than the maximum of the real correlation, we conclude that there is a 10% chanceof finding the observed correlation by chance. Therefore, if this percentage is low, then theobserved correlation is significant even if the correlation coefficient is substantially lowerthan unity.As determined by the DCCF (Figure 16), the X-ray variations are correlated with thoseat both optical and radio wavelengths in 3C 279. The peak X-ray vs. optical DCCF is 0.66,which corresponds to a 98% significance level. The peak X-ray vs. radio DCCF is relativelymodest (0.42), with a significance level of 79%. The radio-optical DCCF has a similar peakvalue (0.45) at a 62% significance level. The cross-correlation also indicates that the opticalvariations lead the X-ray by 20 ±
15 and the radio by 260 +60 − days, while X-rays lead theradio by 240 +50 − days. The uncertainties in the time delays are the FWHM of the peaks inthe correlation function. The X-ray and the optical light curves are correlated at a very high significance level.However, the uncertainty in the X-ray-optical time delay is comparable to the delay itself. Tocharacterize the variation of the X-ray/optical time lag over the years, we divide both lightcurves into overlapping two-year intervals, and repeat the DCCF analysis on each segment.The result indicates that the correlation function varies significantly with time (Fig. 17) overthe 11 years of observation. Of special note are the following trends:1. During the first four years of our program (96-97, 97-98, 98-99) the X-ray variations leadthe optical (negative time lag).2. There is a short interval of weak correlation in 1999-2000.3. In 2000-01, the time delay shifts such that the optical leads the X-ray variations (positivetime lag). This continues into the next interval (2001-02).4. In 2002-03, there is another short interval of weak correlation (not shown in the figure). 9 –5. In the next interval (2003-04), the delay shifts again to almost zero.6. Over the next 3 years the correlation is relatively weak and the peak is very broad,centered at a slightly negative value.This change of time lag over the years is the main reason why the peak value of the overallDCCF is significantly lower than unity. We discuss the physical cause of the shifts in cross-frequency time delay in § We find a significant correlation (maximum DCCF=0.6) between the PA of the jet andthe X-ray flux (see Figure 18). The changes in the position angle lead those in the X-ray fluxby 80 ±
150 days. The large uncertainty in the time delay results from the broad, nearly flatpeak in the DCCF. This implies that the jet direction modulates rather gradual changes inthe X-ray flux instead of causing specific flares. This is as expected if the main consequenceof a swing in jet direction is an increase or decrease in the Doppler beaming factor on a timescale of one or more years.
We follow Valtaoja et al. (1999) by decomposing the X-ray and optical light curvesinto individual flares, each with exponential rise and decay. Our goal is to compare theproperties of the major long-term flares present in the X-ray and optical lightcurves. Beforethe decomposition, we smooth the light curve using a Gaussian function with a 10-dayFWHM smoothing time. We proceed by first fitting the highest peak in the smoothed lightcurve to an exponential rise and fall, and then subtracting the flare thus fit from the lightcurve. We do the same to the “reduced” light curve, i.e., we fit the next highest peak.This reduces confusion created by a flare already rising before the decay of the previousflare is complete. We fit the entire light curve in this manner with a number of individual(sometimes overlapping) flares, leaving a residual flux much lower than the original flux atall epochs. We have determined the minimum number of flares required to adequately modelthe lightcurve to be 19 (X-ray) and 20 (optical), i.e., using more than 19 flares to model theX-ray light curve does not change the residual flux significantly.Figure 19 compares the smoothed light curves with the summed flux (sum of contribu-tions from all the model flares at all epochs). We identify 13 X-ray/optical flare pairs inwhich the flux at both wavebands peaks at the same time within ±
50 days. Since both light 10 –curves are longer than 4200 days and there are only about 20 significant flares during thistime, it is highly probable that each of these X-ray/optical flare pairs corresponds to thesame physical event. There are some X-ray and optical flares with no significant counterpartat the other waveband. We note that this does not imply complete absence of flaring activityat the other wavelength, rather that the corresponding increase of flux was not large enoughto be detected in our decomposition of the smoothed light curve.We calculate the area under the curve for each flare to represent the total energy outputof the outburst. In doing so, we multiply the R-band flux density by the central frequency(4 . × Hz) to estimate the integrated optical flux. For each of the flares, we determinethe time of the peak, width (defined as the mean of the rise and decay times), and areaunder the curve from the best fit model. Table 7 lists the parameters of each flare pair,along with the ratio ζ XO of X-ray to optical energy output. The time delays of the flarepairs can be divided into three different classes: X-ray significantly leading the optical peak(XO, 6 out of 13), optical leading the X-ray (OX, 3 out of 13), and nearly coincident (by <
10 days, the smoothing length) X-ray and optical maxima (C, 4 out of 13). The numberof events of each delay classification is consistent with the correlation analysis (Figure 17).XO flares dominate during the first and last segments of our program, but OX flares occurin the middle. In both the DCCF and flare analysis, there are some cases just before andafter the transition in 2001 when variations in the two wavebands are almost coincident (Cflares).The value of ζ XO ≈ ζ XO = 1 .
4. In all the othercases it is less than unity by a factor of a few. In all the C flares ζ XO ≈
1, while in the 3 OXcases the ratio ≪
1. In the C pairs, the width of the X-ray flare profile ∼ The core region on VLBI images becomes brighter as a new superluminal knot passesthrough it (Savolainen et al. 2002); hence, maxima in the 43 GHz light curve of the coreindicate the times of ejection of knots. We find that the core (Figure 13) and X-ray lightcurves are well correlated (correlation coefficient of 0.6), with changes in the X-ray fluxleading those in the radio core by 130 +70 − days (see Figure 20). The broad peak in the cross-correlation function suggests that the flare-ejection time delay varies over a rather broadrange. This result is consistent with the finding of Lindfors et al. (2006) that high-energyflares generally occur during the rising portion of the 37 GHz light curve of 3C 279. 11 –Since some flares can be missed owing to overlapping declines and rises of successiveevents, we can determine the times of superluminal ejections more robustly from the VLBAdata. Table 5 lists the ejection times and apparent speeds of the knots identified by our pro-cedure. We cannot, however, associate an X-ray flare with a particular superluminal ejectionwithout further information, since flux peaks and ejection times are disparate quantities. Wepursue this in a separate paper that uses light curves at five frequencies between 14.5 and350 GHz to analyze the relationship between superluminal knots and flares in 3C 279.
5. Discussion5.1. Red Noise Behavior and Absence of a Break in the PSD
The PSDs at all three wavebands are best fit with a simple power law which correspondsto red noise. The red noise nature—greater amplitudes on shorter time scales—of the fluxvariations at all three wavebands revealed by the PSD analysis is also evident from visualinspection of the light curves of 3C 279 (Figures 1, 2, and 3).The PSD break frequency in BHXRBs and Seyferts scales with the mass of the black hole(Uttley et al. 2002; McHardy et al. 2004, 2006; Markowitz et al. 2003; Edelson & Nandra1999). Using the best-fit values and uncertainties in the relation between break timescale,black-hole mass, and accretion rate obtained by McHardy et al. (2006), we estimate theexpected value of the break frequency in the X-ray PSD of 3C 279 to be 10 − . ± . Hz, whichis just within our derived lower limit of 10 − . Hz. Here we use a black-hole mass of 10 M ⊙ (Woo & Urry 2002; Liu, Jiang & Gu 2006) for 3C 279 and a bolometric luminosity of thebig blue bump of 4 × ergs/s (Hartman et al. 1996). If we follow McHardy et al. (2006)and set the low-frequency slope of the X-ray PSD at − . − .
4, a break at a frequency . − Hz cannot be rejected at the 95%confidence level. An even longer light curve is needed to place more stringent limits on thethe presence of a break at the expected frequency.
The cross-frequency time delays uncovered by our DCCF analysis relate to the relativelocations of the emission regions at the different wavebands, which in turn depend on thephysics of the jet and the high-energy radiation mechanism(s). If the X-rays are synchrotronself-Compton (SSC) in nature, their variations may lag the optical flux changes owing to thetravel time of the seed photons before they are up-scattered. As discussed in Sokolov et al. 12 –(2004), this is an important effect provided that the angle ( θ obs ) between the jet axis andthe line of sight in the observer’s frame is sufficiently small, . . ◦ ± . ◦ , in the caseof 3C 279, where we have adopted the bulk Lorentz factor (Γ = 15 . ± .
5) obtained byJorstad et al. (2005). According to Sokolov et al. (2004), if the emission region is thicker(thickness ∼ radius), the allowed angle increases to 2 ◦ ± . ◦ . X-rays produced by inverseCompton scattering of seed photons from outside the jet (external Compton, or EC, process)may lag the low frequency emission for any value of θ obs between 0 ◦ and 90 ◦ . However, inthis case we expect to see a positive X-ray spectral index over a significant portion of aflare if θ obs is small, and the flares should be asymmetric, with much slower decay than rise(Sokolov & Marscher 2005). This is because the electrons that up-scatter external photons(radiation from a dusty torus, broad emission-line clouds, or accretion disk) to X-rays haverelatively low energies, and therefore have long radiative cooling times. Expansion coolingquenches such flares quite slowly, since the EC flux depends on the total number of radiatingelectrons (rather than on the number density), which is relatively weakly dependent on thesize of the emitting region.Time delays may also be produced by frequency stratification in the jet. This occurswhen the electrons are energized along a surface (e.g., a shock front) and then move away ata speed close to c as they lose energy via synchrotron and IC processes (Marscher & Gear1985). This causes the optical emission to be radiated from the region immediately behindthe surface, with the IR emission arising from a somewhat thicker region and the radiofrom an even more extended volume. An optical to radio synchrotron flare then beginssimultaneously (if opacity effects are negligible), but the higher-frequency peaks occur earlier.On the other hand, SSC (and EC) X-rays are produced by electrons having a range ofenergies that are mostly lower than those required to produce optical synchrotron emission(McHardy et al. 1999). Hence, X-rays are produced in a larger region than is the case forthe optical emission, so that optical flares are quenched faster and peak earlier. Flatter PSDin the optical waveband is consistent with this picture.In each of the above cases, the optical variations lead those at X-ray energies. Butin majority of the observed flares, the reverse is true. This may be explained by anotherscenario, mentioned by B¨ottcher et al. (2007), in which the acceleration time scale of thehighest-energy electrons is significantly longer than that of the lower-energy electrons, andalso longer than the travel time of the seed photons and/or time lags due to frequencystratification. In this case, X-ray flares can start earlier than the corresponding opticalevents.We thus have a working hypothesis that XO (X-ray leading) flares are governed bygradual particle acceleration. OX events can result from either (1) light-travel delays, since 13 –the value of θ obs determined by Jorstad et al. (2005) (2 . ◦ ± . ◦ ) is close to the requiredrange and could have been smaller in 2001-03 when OX flares were prevalent, or (2) frequencystratification. One way to test this further would be to add light curves at γ -ray energies,as will be possible with the upcoming Gamma Ray Large Area Space Telescope (GLAST).If the X and γ rays are produced by the same mechanism and the X-ray/optical time lag isdue to light travel time, we expect the γ -ray/optical time lag to be similar. If, on the otherhand, the latter delay is caused by frequency stratification, then it will be shorter, since IC γ rays and optical synchrotron radiation are produced by electrons of similarly high energies.If the synchrotron flare and the resultant SSC flare are produced by a temporary increasein the Doppler factor of the jet (due to a change in the direction, Lorentz factor, or both),then the variations in flux should be simultaneous at all optically thin wavebands. It ispossible for the C flare pairs to be produced in this way. Alternatively, the C events couldoccur in locations where the size or geometry are such that the time delays from light traveland frequency stratification are very short compared to the durations of the flares.As is discussed in § ∼ c in 2000 to ∼ − c in 2001-2003. This coincided with the onset of a swing toward a moresoutherly direction of the trajectories of new superluminal radio knots. We hypothesizethat the change in direction also reduced the angle between the jet and the line of sight, sothat the Doppler factor δ of the jet increased significantly, causing the elevated flux levelsand setting up the conditions for major flares to occur at all wavebands. The pronouncedvariations in flux during the 2001-2002 outburst cannot be explained solely by fluctuationsin δ , however, since the time delay switched to OX rather than C. Instead, a longer-termswitch to a smaller viewing angle would have allowed the SSC light-travel delay to becomeimportant, causing the switch from XO to OX flares. 14 – The relative amplitude of synchrotron and IC flares depends on which physical param-eters of the jet control the flares. The synchrotron flux is determined by the magnetic field B , the total number of emitting electrons N e , and the Doppler factor of the flow δ . The ICemission depends on the density of seed photons, number of electrons available for scattering N e , and δ . An increase solely in N e would enhance the synchrotron and EC flux by the samefactor, while the corresponding SSC flare would have a higher relative amplitude owing tothe increase in both the density of seed photons and number of scattering electrons. If thesynchrotron flare were due solely to an increase in B , the SSC flare would have a relativeamplitude similar to that of the synchrotron flare, since B affects the SSC output only byincreasing the density of seed photons. In this case, there would be no EC flare at all. Fi-nally, if the synchrotron flare were caused solely by an increase in δ , the synchrotron andSSC flux would rise by a similar factor, while the EC flare would be more pronounced, sincethe density and energy of the incoming photons in the plasma frame would both increase bya factor δ. Table 8 summarizes these considerations.The location of the emission region should also have an effect on the multi-wavebandnature of the flares. The magnetic field and electron energy density parameter N both de-crease with distance r from the base of the jet: B ∼ r − b and N ∼ r − n ; we adopt n = 2 and b = 1 and assume a conical geometry. The cross-sectional radius R of the jet expands with r , R ∝ r . We have performed a theoretical calculation of the energy output of flares thatincludes the dependence on the location of the emission region. We use a computer codethat calculates the synchrotron and SSC radiation from a source with a power-law energydistribution of electrons N ( γ ) = N γ − s within a range γ min to γ max , where γ is the energyin units of the electron rest mass. We introduce time variability of the radiation with anexponential rise and decay in B and/or N with time. In addition, we increase γ max withtime in some computations in order to simulate the gradual acceleration of the electrons.The synchrotron emission coefficient is given by j ν ( ν ) = νN k ′ Z γ max γ min γ − s (1 − γkt ) s − dγ Z + ∞ νk ′ γ K ( ξ ) dξ, (3)where K is the modified Bessel function of the second kind of order . We adopt s = 2 . ν c = k ′ γ , while the synchrotron energyloss rate is given by dE/dt = − kγ . Both k and k ′ are functions of B and are given by k = 1 . × − B and k ′ = 4 . × B . The inverse-Compton (SSC in this case) emissioncoefficient is given by 15 – j Cν = Z ν Z γ ν f ν i j ν ( ν i ) Rσ ( ǫ i , ǫ f , γ ) N ( γ ) dγdν i , (4)where we approximate that the emission/scattering region is uniform (i.e., we ignore fre-quency stratification) and spherical with radius R . The Compton cross-section σ is a functionof γ as well as the incident ( ν i ) and scattered ( ν f ) frequencies of the photons: σ ( ν i , ν f , γ ) = 332 σ T ν i γ [8 + 2 x − x + 4 x ln( x , (5)where x ≡ ν f / ( ν i γ ) and σ T is the Thompson cross-section.In Figure 21, the top left panel shows the synchrotron and SSC flares at a given distance r from the base of the jet, where r is a constant times a factor a fac ( a fac =1). The right panelshows the same at a farther distance ( a fac = 5). The flares are created by an exponentialrise and decay in the B field, while the value of γ max is held constant. The total time of theflares is fixed at 10 seconds (120 days). We can see from Figure 21 that at larger distances(right panel) the SSC flare has a lower amplitude than the synchrotron flare even thoughat smaller values of r (left panel) they are comparable. The bottom panels of Figure 21are the same as above except that the value of γ max increases with time, as inferred fromthe forward time delay that occurs in some events. We see the same effect as in the toppanels. In Figure 22, the top and bottom panels show similar results, but in these cases theflares are created by an exponential rise and fall in the value of N . Again, the results aresimilar. Figure 23 shows segments of the actual X-ray and optical light curves, which arequalitatively similar to the simulated ones. The energy output of both synchrotron and SSCflares decreases with increasing r , but more rapidly in the latter. As a result, the ratio ofSSC to synchrotron energy output ζ XO decreases with r . The case ζ XO ≪ B and N .From Table 7, we can see that in 7 out of 13 of the flare pairs ζ XO ≪
1. In one pair, ζ XO >
1, and in all other pairs, ζ XO ≈
1. Our theoretical calculation suggests that thepairs where the ratio is less than 1 are produced at a larger distance from the base of thejet than those where the ratio &
1. The size of the emission region should be related to thecross-frequency time delay, since for all three explanations of the lag a larger physical size ofthe emission region should lead to a longer delay. We can then predict that the X-ray/opticaltime delay of the latter flares should be smaller than for the pairs with ratio <
1. Indeed,inspection of Table 7 shows that, for most of the pairs, shorter time delays correspond tolarger ζ XO , as expected. The smaller relative width of the optical C flares supports theconclusion that these occur closer to the base of the jet than the other flare pairs. 16 –
6. Conclusions
This paper presents well-sampled, decade-long light curves of 3C 279 between 1996and 2007 at X-ray, optical, and radio wavebands, as well as monthly images obtained withthe VLBA at 43 GHz. We have applied an algorithm based on a method by Uttley et al.(2002) to obtain the broadband PSD of nonthermal radiation from the jet of 3C 279. Cross-correlation of the light curves allows us to infer the relationship of the emission across differentwavebands, and we have determined the significance of the correlations with simulated lightcurves based on the PSDs. Analysis of the VLBA data yields the times of superluminalejections and reveals time variations in the position angle of the jet near the core. We haveidentified 13 associated pairs of X-ray and optical flares by decomposing the light curves intoindividual flares. Comparison of the observed radiative energy output of contemporaneous X-ray and optical flares with theoretical expectations has provided a quantitative evaluation ofsynchrotron and SSC models. We have discussed the results by focusing on the implicationsregarding the location of the nonthermal radiation at different frequencies, physical processesin the jet, and the development of disturbances that cause outbursts of flux density in blazars.Our main conclusions are as follows:(1) The X-ray, optical, and radio PSDs of 3C 279 are of red noise nature, i.e., there is higheramplitude variability at longer time scales than at shorter time scales. The PSDs can bedescribed as power laws with no significant break, although a break in the X-ray PSD at avariational frequency . − Hz cannot be excluded at a 95% confidence level.(2) X-ray variations correlate with those at optical and radio wavebands, as expected ifnearly all of the X-rays are produced in the jet. The X-ray flux correlates with the projectedjet direction, as expected if Doppler beaming modulates the mean X-ray flux level.(3) X-ray flares are associated with superluminal knots, with the times of the latter indicatedby increases in the flux of the core region in the 43 GHz VLBA images. The correlation hasa broad peak at a time lag of 130 +70 − days, with X-ray variations leading.(4) Analysis of the X-ray and optical light curves and their interconnection indicates thatthe X-ray flares are produced by SSC scattering and the optical flares by the synchrotronprocess. Cases of X-ray leading the optical peaks can be explained by an increase in the timerequired to accelerate electrons to the high energies needed for optical synchrotron emission.Time lags in the opposite sense can result from either light-travel delays of the SSC seedphotons or gradients in maximum electron energy behind the shock fronts.(5) The switch to optical-leading flares during the major multi-frequency outburst of 2001coincided with a decrease in the apparent speeds of knots from 16-17 c to 4-7 c and a swingtoward the south of the projected direction of the jet near the core. This behavior, as wellas the high amplitude of the outburst, can be explained if the redirection of the jet (only a1 ◦ -2 ◦ change is needed) caused it to point closer to the line of sight than was the case before 17 –and after the 2001-02 outburst.(6) Contemporaneous X-ray and optical flares with similar radiative energy output originatecloser to the base of the jet, where the cross-section of the jet is smaller, than do flares inwhich the optical energy output dominates. This is supported by the longer time delay inthe latter case. This effect is caused by the lower electron density and magnetic field andlarger cross-section of the jet as the distance from the base increases.Further progress in our understanding of the physical structures and processes in com-pact relativistic jets can be made by increasing the number of wavebands subject to intensemonitoring. Expansion of such monitoring to a wide range of γ -ray energies will soon bepossible when GLAST scans the entire sky several times each day. When combined withsimilar data at lower frequencies as well as VLBI imaging, more stringent tests on modelsfor the nonthermal emission from blazars will be possible.We thank P. Uttley for many useful discussions. The research at Boston Universitywas funded in part by the National Science Foundation (NSF) through grant AST-0406865and by NASA through several RXTE Guest Investigator Program grants, most recentlyNNX06AG86G, and Astrophysical Data Analysis Program grant NNX08AJ64G. The Uni-versity of Michigan Radio Astronomy Observatory was supported by funds from the NSF,NASA, and the University of Michigan. The VLBA is an instrument of the National RadioAstronomy Observatory, a facility of the National Science Foundation operated under coop-erative agreement by Associated Universities, Inc. The Liverpool Telescope is operated onthe island of La Palma by Liverpool John Moores University in the Spanish Observatorio delRoque de los Muchachos of the Instituto de Astrofisica de Canarias, with financial supportfrom the UK Science and Technology Facilities Council. Facilities:
VLBA, RXTE, Liverpool:2m, Perkins
A. Power Spectrum Response Method (PSRESP)
In this study, we determine the shape and slope of the PSD of the light curves of 3C 279using the PSRESP method (Uttley et al. 2002). This involves the following steps:1. Calculation of the PSD of the observed light curve (PSD obs ) with formulas (1) and (2).2. Simulation of M artificial light curves of red noise nature with a trial shape (simple powerlaw, broken power law, bending power law, etc.) and slope. We use M = 100.3. Resampling of the simulated light curves with the observed sampling function.4. Calculation of the PSD of each of the resampled simulated light curves (PSD sim , i , i=1, M ). The resampling with the observed sampling function (which is irregular) adds the same 18 –distortions to the simulated PSDs that are present in the real PSD (PSD obs ).5. Calculation of two functions similar to χ : χ = ν max X ν = ν min ( P SD obs − PSD sim ) (∆ P SD sim ) (A1)and χ , i = ν (max X ν = ν min ( P SD sim , i − PSD sim ) (∆ P SD sim ) , (A2)where PSD sim is the average of (PSD sim , i ) and ∆PSD sim is the standard deviation of (PSD sim , i ),with i=1, M .6. Comparison of χ with the χ distribution. Let m be the number of χ , i for which χ is smaller than χ , i . Then m / M is the success fraction of that trial shape and slope,a measure of its success at representing the shape and slope of the intrinsic PSD.7. Repetition of the entire procedure (steps 2 to 6) for a set of trial shapes and slopes ofthe initial simulated PSD to determine the shape and slope that gives the highest successfraction. We scan a range of trial slopes from − . − . . sim , i that are present in PSD obs .On the other hand, if a light curve is not continuously sampled, power from frequencieshigher than the Nyquist frequency ( ν Nyq ) is shifted or “aliased” to frequencies below ν Nyq .The observed PSD in that case will be distorted by the aliased power, which is added tothe observed light curve from timescales as small as the exposure time ( T exp ) of the obser-vation (about 1000 seconds for the X-ray light curve). Ideally, we should account for thisby simulating light curves with a time-resolution as small as 1000 seconds so that the sameamount of aliasing occurs in the simulated data. This involves excessive computing time fordecade-long light curves. To avoid this, we follow Uttley et al. (2002) by simulating lightcurves with a resolution 10 T exp . To calculate the aliasing power from timescales from T exp
19 –to 10 T exp , we use an analytic approximation of the level of power added to all frequencies bythe aliasing, given by P C = 1 ν Nyq − ν min Z (2 T exp ) − ν Nyq P ( ν ) dν. (A3)We use PSRESP to account for aliasing at frequencies lower than (10 T exp ) − .We also add Poisson noise to the simulated light curves: P noise = P Ni =1 ( σ ( i )) N ( ν Nyq − ν min ) , (A4)where σ ( i ) are observational uncertainties. For details of the noise processes, readers shouldrefer to Uttley et al. (2002)The goal of adding the noise and resampling with the observed sampling function isto simulate a dataset that has the same properties, including the imperfections, as theobserved one. This provides a physically meaningful comparison of the observed PSD withthe distribution of the simulated PSDs. REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
22 –Table 1: Start and end times of observations presented in this study.X-ray Optical RadioDataset Start End Start End Start EndLonglook Dec 96 Jan 97 Mar 05 Jun 05Medium Nov 03 Sep 04 Jan 04 Jul 04 Mar 05 Sep 05Monitor Jan 96 Jun 07 Jan 96 Jun 07 Jan 96 Sep 07 23 –Table 2. X-ray (2-10 keV) light curve data from RXTE (first 5 rows).MJD Exp. (s) Flux Error α Err count rate Err105.1275 688 1.314e-11 1.818e-12 0.466 0.226 2.766e+00 1.722e-01106.2820 720 1.343e-11 1.648e-12 0.489 0.206 2.810e+00 1.602e-01107.2621 672 1.150e-11 1.829e-12 0.425 0.246 2.393e+00 1.625e-01108.2144 672 1.299e-11 1.568e-12 0.544 0.221 2.747e+00 1.670e-01109.2619 624 1.173e-11 1.440e-12 0.597 0.245 2.474e+00 1.688e-01... ... ... ... ... ... ... ... MJD = Julian date minus 2450000 Units: erg cm − s − “Energy” spectral index Photon counts s − per PCU detectorTable 3. Optical (R Band) light curve data (first 5 rows).MJD mag err Flux Density err46.9514 14.383 0.007 5.837 0.03871.7330 15.170 0.032 2.827 0.08286.6356 15.386 0.032 2.317 0.06791.6813 14.740 0.032 4.201 0.122100.6226 14.878 0.032 3.700 0.107... ... ... ... ... MJD = Julian date minus 2450000 Units: mJy 24 –Table 4. Radio (14.5 GHz) light curve data (first 5 rows).MJD Flux Density (Jy) error97.00 17.51 0.2098.00 17.74 0.19101.00 18.62 0.15103.00 17.54 0.44104.00 18.28 0.22... ... ... MJD = Julian date minus2450000 25 –Table 5: Ejection times, apparent speeds, and position angle of superluminal knots.Knot T T (MJD ) β app θ (deg) C8 1996.09 ± ±
36 5.4 ± − ± ± ±
44 12.9 ± − ± ± ±
58 9.9 ± − ± ± ±
40 10.1 ± − ± ± ±
33 16.9 ± − ± ± ±
26 16.4 ± − ± ± ±
33 18.2 ± − ± ± ±
18 17.2 ± − ± ± ±
18 16.9 ± − ± ± ±
44 6.2 ± − ± ± ±
58 4.4 ± − ± ± ±
44 6.6 ± − ± ± ±
44 6.0 ± − ± ± ±
18 16.7 ± − ± ± ±
22 12.4 ± − ± ± ±
55 16.5 ± − ± MJD = Julian date minus 2450000 Average position angle of knot within 1 mas of the core.
26 –Table 6: Parameters of the light curves for calculation of PSD.Dataset T (days) ∆T (days) log( f min ) log( f max ) N points Longlook 55.0 0.5 -6.67 -4.93 111X-ray Medium 301.0 5.0 -7.40 -5.93 127Monitor 4150.0 25.0 -8.55 -6.63 1213Longlook 86.0 1.0 -6.86 -5.23 94Optical Medium 185.0 5.0 -7.17 -5.92 77Monitor 4225.0 25.0 -8.55 -6.63 995Radio Medium 189.0 4.0 -7.18 -5.83 59Monitor 3984.0 25.0 -8.53 -6.63 609 27 –Table 7: Total energy output (area) and widths of flare pairs.ID X-ray Optical ∆ T TDC ζ XO Time Area Width Time Area Width (days)1 119 (1996.10) 33.2 6.0 134 (1996.14) 76.3 12.0 -15 XO 0.442 717 (1997.74) 371.8 90.0 744 (1997.81) 929.5 97.5 -27 XO 0.403 920 (1998.30) 172.8 50.0 944 (1998.36) 278.2 35.0 -24 XO 0.624 1050 (1998.65) 338.7 70.0 1099 (1998.79) 502.8 57.5 -49 XO 0.675 1263 (1999.24) 160.7 77.5 1266 (1999.24) 168.9 42.5 -3 C 0.956 1509 (1999.91) 699.8 202.5 1517 (1999.93) 715.4 90.0 -8 C 0.987 2045 (2001.38) 103.7 60.0 2029 (2001.33) 568.3 65.0 16 OX 0.188 2151 (2001.67) 453.6 62.5 2126 (2001.60) 1188.3 57.5 25 OX 0.389 2419 (2002.40) 193.5 80.0 2422 (2002.41) 222.6 40.0 -3 C 0.8710 3185 (2004.50) 191.8 92.5 3191 (2004.52) 218.6 55.0 -6 C 0.8811 3416 (2005.13) 217.7 70.0 3444 (2005.21) 198.7 50.0 -28 XO 1.0912 3792 (2006.16) 525.3 120.0 3814 (2006.22) 375.6 67.5 -22 XO 1.4013 4035 (2006.83) 324.2 105.0 4008 (2006.76) 1068.4 75.0 27 OX 0.30 Units: MJD (yr) Units: 10 − erg cm − Units: days Ratio of X-ray to optical energy output integrated over flare
Table 8: Ratio of synchrotron to SSC or EC flare amplitude expected when a physicalparameter varies. Parameter varied SSC/Synch EC/Synch δ ≈ > N e > ≈ ≈ < F l u x ( - e r g c m - s - ) Monitor 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2003.8 2004 2004.2 2004.4 2004.6 F l u x ( - e r g c m - s - ) Medium 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1996.94 1996.98 1997.02 1997.06 1997.1 F l u x ( - e r g c m - s - ) YEAR Longlook
Fig. 1.— X-ray (2-10 keV) data on different time-scales. In the upper panel, the arrowsshow the times of superluminal ejections and the line segments perpendicular to the arrowsshow the uncertainties in the times of ejection. 29 – F l u x D en s i t y ( m Jy ) Monitor 0 2 4 6 8 10 2004 2004.1 2004.2 2004.3 2004.4 2004.5 2004.6 F l u x D en s i t y ( m Jy ) Medium 0 2 4 6 8 10 2005.2 2005.24 2005.28 2005.32 2005.36 2005.4 2005.44 2005.48 F l u x D en s i t y ( m Jy ) YEAR Longlook
Fig. 2.— Optical (R-band) data on different time-scales. 30 –
10 15 20 25 30 35 1996 1998 2000 2002 2004 2006 2008 F l u x D en s i t y ( Jy ) Monitor 14 15 16 17 18 2005.2 2005.3 2005.4 2005.5 2005.6 2005.7 2005.8 F l u x D en s i t y ( Jy ) YEAR Medium
Fig. 3.— Radio (14.5 GHz) data on different time-scales. 31 –Fig. 4.— Sequence of VLBA images at 7 mm during 2001. The images are convolved withthe beam of the size 0.38 × − ◦ . The global peak over all maps is 17.24Jy/Beam. The contour levels are 0.25, 0.354, 0.5, 0.707, ..., 90.51 % of the global peak. Theangular scale given at the bottom is in milliarcseconds (mas). 32 –Fig. 5.— Sequence of VLBA images at 7 mm during 2002. For details see caption of Figure4. 33 –Fig. 6.— Sequence of VLBA images at 7 mm during 2003. For details see caption of Figure4. 34 –Fig. 7.— Sequence of VLBA images at 7 mm during 2004. For details see caption of Figure4. 35 –Fig. 8.— Sequence of VLBA images at 7 mm during 2005. For details see caption of Figure4. 36 –Fig. 9.— Sequence of VLBA images at 7 mm during 2006. For details see caption of Figure4. 37 –Fig. 10.— Angular separation from the core vs. epoch of all knots brighter than 100 mJywithin 2.0 mas of the core. The black lines indicate the motion of each knot (denoted by agiven color of data points) listed in Table 2. A knot is identified through continuity of thetrajectory from one epoch to the next. The diameter of each symbol is proportional to thelogarithm of the flux density of the knot, as determined by model fitting of the VLBA data. 38 – F l u x ( - e r g c m - s - ) X-ray, Monitor 0 5 10 15 20 25 30 35 F l u x D en s i t y ( m Jy ) Optical, Monitor 10 15 20 25 30 35 F l u x D en s i t y ( Jy ) P o s i t i on A ng l e ( D eg r ee ) YEAR
Fig. 11.— Variation of X-ray flux, optical flux, radio flux and position angle of the jet from1996 to 2008. The circled data points in the bottom panel are the epochs shown in Fig. 12. 39 –Fig. 12.— VLBA images at one epoch during each year of 11-year monitoring. The imagesare convolved with the beam of the size 0.38 × − ◦ . The map peak is17.0 Jy/Beam. The contour levels are 0.15, 0.3, 0.6, ...,76.8 % of the peak. The angularscale given at the bottom is in milliarcseconds (mas). The circled points in Fig. 11 (bottompanel) correspond to these images. 40 – C o r e F l u x D en s i t y ( Jy bea m - ) YEAR
Fig. 13.— Light curve of the VLBA core region at 43 GHz. The jagged line through thedata points is drawn solely to aid the eye to follow the variability. Statistical and systematicuncertainty in each measurement is difficult to determine accurately, but is typically 10-20%. 41 – l og PS D (r m s H z - ) X-ray: Slope = -2.3 0 2 4 6 8 l og PS D (r m s H z - ) Optical: Slope = -1.7 0 2 4 6 8 -8.5 -8 -7.5 -7 -6.5 -6 -5.5 -5 l og PS D (r m s H z - ) log [Frequency (Hz)]Radio: Slope = -2.3 Fig. 14.— Result of application of the PSRESP method to the light curves. PSD of theobserved data at high, medium and low frequency range are given by the solid, dashedand dotted jagged lines respectively while the underlying power-law model is given by thedotted straight line. Points with error bars (open squares, solid circles and asterisks forhigh, medium and low frequency range respectively) correspond to the mean value of thePSD simulated from the underlying power-law model (see text). The errorbars are thestandard deviation of the distribution of simulated PSDs. The broadband PSD in all threewavelengths can be described by a simple power law. 42 – S u cc e ss F r a c t i on X-ray 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -2.4-2.2-2-1.8-1.6-1.4-1.2-1 S u cc e ss F r a c t i on Optical 0 0.2 0.4 0.6 0.8 1 -2.4-2.2-2-1.8-1.6-1.4-1.2-1 S u cc e ss F r a c t i on Power-law SlopeRadio
Fig. 15.— Success fraction vs. slope for all three PSDs. The success fractions indicate thegoodness of fit obtained from the PSRESP method (see text). 43 – -0.6-0.4-0.2 0 0.2 0.4 0.6 0.8
DCC F Xray-Optical-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5
DCC F Xray-Radio-0.4-0.2 0 0.2 0.4 0.6 0.8 -600 -400 -200 0 200 400 600
DCC F Time Delay (Days) Optical-Radio
Fig. 16.— Discrete cross-correlation function (DCCF) of the optical, X-ray, and radio mon-itor data. The time delay is defined as positive if the variations at the higher frequencywaveband lag those at the lower frequency. 44 – -0.2 0 0.2 0.4 0.6 0.8 1
DCC F DCC F DCC F DCC F Time Delay (days)2003-04 -60 -40 -20 0 20 40 60Time Delay (days)2004.0-2007.5
Fig. 17.— Variation of X-ray/optical time lag across overlapping 2 intervals from the begin-ning of the first year to the end of the second, except for the bottom right panel, for whichthe interval is indicated more precisely. Notice the big change between 1998-99 and 2000-2001, when the time delay went from X-ray leading optical to the opposite sense. There is amajor change between 2001-02 and 2003-04 as well, when the time delay went from opticalleading X-ray to the opposite sense. In the last 4 years (bottom right panel) the correlationbecame weaker but maintained the negative time delay. 45 – -0.4-0.2 0 0.2 0.4 0.6 0.8-600 -400 -200 0 200 400 600
DCC F Time Delay (days)
Fig. 18.— Cross-correlation function of the X-ray light curve and the position angle of thejet. Changes in the position angle lead those in the X-ray flux by 80 ±
150 days. 46 – F l u x ( - e r g c m - s - ) F l u x D en s i t y ( m Jy ) YEAR1 2 3 4 5 6 7 8 9 10 11 12 13Optical light curveSum of the flares
Fig. 19.— Smoothed X-ray and optical light curves. Curves correspond to summed fluxafter modeling the light curve as a superposition of many individual flares. Thick horizontalstrips in the X-ray light curve in 2000 correspond to epochs when no data are available.Flare pairs listed in Table 4 are marked with the respective ID numbers. 47 – -0.6-0.4-0.2 0 0.2 0.4 0.6 0.8-500 -400 -300 -200 -100 0 100 200 300 400
DCC F Time Delay (days)
Fig. 20.— Cross-correlation of the X-ray and 43 GHz core light curves. Changes in theX-ray flux lead those in the radio core by 130 +70 − days. 48 – j ν ( a r b i t r a r y un i t s ) γ max =const, a fac =1 γ max =const, a fac =5 0 0.2 0.4 0.6 0.8 1 1.2 20 40 60 80 100 j ν ( a r b i t r a r y un i t s ) Time (days) γ max = γ max (t), a fac =1 20 40 60 80 100Time (days) γ max = γ max (t), a fac =5 Fig. 21.— Simulated synchrotron (solid curve) and SSC (dashed curve) flares. Here allflares are created by an exponential rise and decay in the magnetic field B ( B , N , and R are functions of distance along the jet). In the bottom panels, γ max is increased linearly withtime causing the SSC flux to peak ahead of the synchrotron flux. Flare amplitudes havebeen scaled such that they can be seen on the same plot. Normalization in the two upperpanels is the same and that in the two lower panels is the same. 49 – j ν ( a r b i t r a r y un i t s ) γ max =const, a fac =1 γ max =const, a fac =5 0 0.2 0.4 0.6 0.8 1 1.2 20 40 60 80 100 j ν ( a r b i t r a r y un i t s ) Time (days) γ max = γ max (t), a fac =1 20 40 60 80 100Time (days) γ max = γ max (t), a fac =2 Fig. 22.— Simulated synchrotron (solid curve) and SSC (dashed curve) flares. Here all flaresare created by an exponential rise and decay in the magnetic field N ( B , N , and R arefunctions of distance along the jet). In the bottom panels, γ max is increased linearly withtime causing the SSC flux to peak ahead of the synchrotron flux. Flare amplitudes havebeen scaled such that they can be seen on the same plot. Normalization in the two upperpanels is the same and that in the two lower panels is the same. 50 – F l u x ( - e r g c m - s - ) F l u x ( - e r g c m - s - ) Time (MJD) 2 4 6 8 10 12 14 16 2100 2120 2140 2160 2180 2200Time (MJD)
Fig. 23.— Segments of real light curves (optical: asterisks, X-ray: open circles) over ∼
100 day intervals similar to the length of the simulated light curves. Optical flux density ismultiplied by R band central frequency (4 . ×14