Multi-band Cross-correlated Radio Variability of the Blazar 3C 279

We present the results of our study of cross-correlations between long-term multi-band observations of the radio variability of the blazar 3C 279. More than a decade (2008-2022) of radio data were collected at seven different frequencies ranging from 2 GHz to 230 GHz. The multi-band radio light curves show variations in flux, with the prominent flare features appearing first at higher-frequency and later in lower-frequency bands. This behavior is quantified by cross-correlation analysis, which finds that the emission at lower-frequency bands lags that at higher-frequency bands. Lag versus frequency plots are well fit by straight lines with negative slope, typically ~-30 day/GHz. We discuss these flux variations in conjunction with the evolution of bright moving knots seen in multi-epoch VLBA maps to suggest possible physical changes in the jet that can explain the observational results. Some of the variations are consistent with the predictions of shock models, while others are better explained by a changing Doppler beaming factor as the knot trajectory bends slightly, given a small viewing angle to the jet.

The broad-band spectral energy distribution (SED) of blazars spans the radio to -ray bands and contains a double-hump structure (e.g.Fossati et al. 1998).The matter composition inside the blazar jets and the dominant particle population responsible for the observed emission in both humps is still not certain (Böttcher 2019).However, most blazar studies consider the particles to include ultrarelativistic electrons and either positrons (leptonic scenario) or protons (hadronic scenario) to be the primary emitters (Böttcher et al. 2013).In either scenario, the first hump of the SED, which peaks between the infrared (IR) and X-ray bands is explained by synchrotron emission (Blumenthal & Gould 1970) originating from leptons in the relativistic jet (Abdo et al. 2010;Böttcher et al. 2013;Böttcher 2019, and references therein).
One of the most effective ways to understand jet emission and its dynamics is to study the changes in physical properties of blazars required to produce multi-frequency light-curve variations.
In this regard, cross-correlation techniques can be an efficient method to extract the temporal trends of observed variability and to identify plausible connections across various blazar emission bands (e.g., Liodakis et al. 2018, and references therein).It has been noticed from such multi-band observations that the variability patterns in different wavebands are sometimes correlated, but often not (e.g., Hayashida et al. 2012;Böttcher 2019, and references therein).Understanding the physical origin of the variability behaviour of blazars is one of the major open questions in the field of AGN research.Multi-band cross-correlation studies help in constraining the radiative mechanism and the location of the emission region, and in understanding whether or not the emission processes at various energy bands are connected.
3C 279 is a FSRQ ( = 0.5362) (Marziani et al. 1996) containing a black hole with mass in the range of (3-8) × 10 8 ⊙ (Gu et al. 2001;Woo & Urry 2002).The presence of apparent superluminal motion of radio knots in this source was first reported by Cohen et al. (1971).The radio morphology of 3C 279 exhibits a bright stationary compact core and a thin jet then consisting of six knots aligned with position angle (PA) ∼ 205 • and extending out 4.7 ′′ (De Pater & Perley 1983).The source has often been observed with high resolution very long baseline interferometry (VLBI), which reveals the presence of a single-sided jet extending southwest on parsec scales with bright knots expelled from the core region.The features in the jet display various projected apparent speeds and polarization angles (e.g., Unwin et al. 1989;Wehrle et al. 2001;Jorstad et al. 2005;Chatterjee et al. 2008).Polarimetric studies using observations from the Very Long Baseline Array (VLBA) at 43 GHz have found the electric field vector usually to be oriented along the jet direction on pc to kpc scales, indicating that the magnetic field is mainly perpendicular to the relativistic jet (Jorstad et al. 2005).During the last decade, several intensive MW studies of 3C 279 have examined cross-correlated variability in an effort to understand the emission mechanism in this FSRQ.Such intensive studies have shown that the broad-band emission of 3C 279 displays complex behaviour, with variability ranging over time scales from minutes to years across the electromagnetic bands (e.g., Hayashida et al. 2012;Fuhrmann et al. 2014;Patiño-Álvarez et al. 2017;Prince 2020;Rajput et al. 2020, and references therein).
The prime motivation of this work is to search for correlations between the different radio frequency emissions of 3C 279 using long-term observations.A few earlier studies have discussed multi-frequency radio cross-correlations of 3C 279 (Wang et al. 2008;Deng et al. 2008;Yuan 2012).However, they included observations covering a much shorter or non-overlapping time of observations and also less dense coverage of frequency bands than presented in this work.These studies suggested that emission at lower-frequency bands lags that of the higher-frequency ones.However, it is vital to check the significance of such a pattern with more extended long-term observations comprising abundant data covering a broad range of frequencies.The presence of positive (or negative) correlations between the different radio emission bands could significantly constrain the origin of the radio variability and identify plausible physical scenarios.For example, this study can investigate whether the radio variability in this blazar is always consequence of a shock wave propagating down an adiabatic, conical, relativistic jet (e.g., Marscher & Gear 1985;Hughes et al. 1989).In addition, we can address the importance of changes in synchrotron self-absorption (SSA) opacity between the higher and lower frequency emission (Aller et al. 1985a).Furthermore, the study can allow an assessment of the extent to which bends in the jet flow affect the flux density as the Doppler factor changes.
To understand the physical processes responsible for the observed blazar emission, it is important to observe the changes in the radio jet and relate them to multi-wavelength variability (e.g., Fuhrmann et al. 2014;Weaver et al. 2022, and references therein).
In this work, we present a long-term (∼14 years) multi-band radio cross-correlation study of 3C 279.Our study includes radio data ranging from 2.25 GHz to 230 GHz, with observations spanning from August 2008 to October 2022.This is first multi-band radio cross-correlation study on 3C 279 using more than a decade of observations made at seven different radio bands.
In our study, the data were collected from six radio observatories, which include unpublished measurements we made at the RATAN-600 and the Xinjiang Astronomical Observatory-Nanshan station radio telescopes (XAO-NSRT) along with archival data, the bulk of which were taken by our groups.These observations were made at 7 different frequency bands.Details of the radio data and the analysis are described in Section 2. In Section 3 and Section 4 we present and discuss the results, respectively.Our conclusions are provided in Section 5.The XAO-NSRT is operated by the Urumqi observatory, which uses the 26-m parabolic antenna of the Nanshan radio telescope, China (Sun et al. 2006;Marchili et al. 2010, and references therein).This facility consists of a single-beam dual-polarization receiver, constructed by the Max-Planck-Institut für Radioastronomie (MPIfR), with central frequency of 4.80 GHz and bandwidth of 600 MHz.

Radio telescopes and observations
The flux density was measured in cross-scan mode, with each scan comprised of eight sub-scans (four in azimuth and four in elevation) over the source position.The data were acquired in this fashion at C-band (4.8 GHz) and K-band (23.6 GHz).The XAO-NSRT data used in this work were reduced by following the data calibration and reduction procedures as explained in Section 2 of Marchili et al. (2011); see also Marchili et al. (2012) and Liu et al. (2015).
The radio telescope RATAN-600 (Parĳskĳ 1993) has a 600-m circular multi-element antenna that provides measurements of 1-22 GHz broad-band spectra simultaneously (within 1-2 min) when a source moves along the focal line where the receivers are located.
The angular resolution depends on the antenna elevation angle, and its values along RA (FWHM RA ) and Dec (FWHM Dec ) calculated for an average Dec value ( ∼ 30  (1977) and Perley & Butler (2013;2017).The measurements of the calibrators were corrected for linear polarization and angular size according to the data from Ott et al. (1994) and Tabara & Inoue (1980).
The RATAN-600 measurements were processed using the automated data reduction system (Kovalev et al. 1999;Tsybulev 2011;Udovitskiy et al. 2016;Tsybulev et al. 2018) and the Flexible Astronomical Data Processing System (FADPS) standard package modules (Verkhodanov 1997) for the broad-band RATAN continuum radiometers.Some of the RATAN-600 measurements are presented in the on-line catalogue BLcat4 .It should be noted that all RATAN-600 data, except those at 1.25 GHz, were used in the present work.The data at 1.25 GHz were not included due to sparser coverage at this frequency band, which made them inadequate for detailed comparisons with other bands.

Very Long Baseline Array Observations
We

Cross-correlation analysis
We carried out cross-correlation between different radio light curves using the z-transformed discrete correlation function (ZDCF) method (Alexander 1997;2013).This method is applicable to both evenly and unevenly sampled data, but is particularly appropriate when the observed data are unevenly sampled and sparse.The ZDCF binning algorithm adopts the same idea as that of the discrete correlation function (DCF) developed by Edelson & Krolik (1988).However, in ZDCF, the statistical significance for each bin is made sufficiently high by varying that bin's width.Consider that there are pairs of flux densities { , } at a particular time-lag bin.Then the crosscorrelation function (CCF) at the lag is calculated using the correlation coefficient (Alexander 2013) where , represent the mean bin values and , correspond to the standard deviations, (2) 2 is defined similarly.However, such usage of the sample variance could be inaccurate due to the high skewness of the sample distribution of (Alexander 2013).If and are drawn from a bivariate normal distribution, then one can convert to an approximately normally distributed random variable, Fisher's (Alexander 2013, and the references therein).Defining where is the unknown population correlation coefficient of the bin.
Transforming back to , the error interval (±1 ) is calculated as where ( ) is the variance of .In the ZDCF, equal population binning is considered rather than binning by equal Δ .Obtaining convergence for -transform requires the minimum number of points per bin ( min ) to be 11.Also, to avoid bias, the dependent pairs (e.g., , , , for the case of estimation of time difference in , ) are dropped.We made use of the openly available FORTRAN 95 routine5 for the specific procedure explained in Alexander (1997) to carry out the cross-correlation.While performing the ZDCF analysis, we chose the default min = 11 for each bin.We used 1000 Monte Carlo runs for error estimation of the coefficients.Also, we did not consider the points for which the lag was zero.
To estimate the significance of a DCF peak, we followed the method described in Max-Moerbeck et al. (2014).For this, we simulated a total of 1000 light curves at each frequency band with the same power spectral density and the flux distribution function of the original light curve using the algorithm provided by Emmanoulopoulos et al. (2013), as realized by the DELightcurveSimulation code (Connolly 2015)6 .Further, from the distribution of the DCF between simulated light curve pairs (using the same method as for the real data), the thresholds for 1 , 2 and 3 significance were calculated at each lag.We only consider the significant DCF peak closer to zero lag and discard any peaks near the edges of the temporal span considered.The peaks present at large values of might be due to the several smaller fluctuations present in the light curves (e.g., Meyer et al. 2019;Max-Moerbeck et al. 2014).Also, we notice that the overlap between the light curves is smaller for larger values of , hence we consider these peaks less credible.After identifying a significant DCF peak, to estimate the exact location of cross-correlation function peak with corresponding uncertainties, we implement the maximum likelihood method of Alexander (2013) by using the openly available FORTRAN 95 routine (PLIKE) 7 .We note that this method estimates a fiducial interval rather than the traditional confidence interval.The approach taken here is similar to Bayesian statistics, where the normalized likelihood function (i.e.fiducial distribution) is interpreted as expressing the degree of belief in the estimated parameter, and the 68 percent interval around the likelihood function's maximum represents the fiducial interval.Here a positive lag for a DCF tagged as 'light curve 1 versus light curve 2' means that the emission in light curve 2 lags that of light curve 1, while a negative lag means 2 leads 1.

Decade-long multi-band radio light curve of 3C 279
Using the more than decade-long radio observations from various observatories, we have created a multi-band radio light curve of 3C 279 (Fig. 1).
We have merged the observations from different observatories in order to construct a complete light curve in each radio band.In Figure 1, the light curve at 2.5 GHz is the result of merging the observations from RATAN-600 at 2.25 GHz and F-GAMMA at 2.64 GHz; the light curve at 4.8 GHz combines data from RATAN-600 at 4.7 GHz, F-GAMMA at 4.8 GHz, XAO-NSRT at 4.8 GHz, & UMRAO at 4.8 GHz; the light curve at 8 GHz comes from merging observations from RATAN-600 at 8.2 GHz, F-GAMMA at 8.35 GHz, and UMRAO at 8.0 GHz; the light curve at 11 GHz combines the observations from RATAN-600 at 11.2 GHz & F-GAMMA at 10.45 GHz; finally, the light curve at 23 GHz combines our observations from RATAN-600 at 22.3 GHz and XAO-NSRT at 23.6 GHz with those of F-GAMMA at 21.7 GHz.The long term light curves data at 43 GHz and 230 GHz are taken from VLBA and SMA, respectively.The mean cadence of these merged light curves at different frequency bands is provided in Table 1.We note that outliers/very short-term fluctuations are present in the original light curves at 23 and 230 GHz, which may be caused by turbulence or some other fast random process.Since these short time-scale fluctuations do not play a significant role in the ZDCF correlations, we have smoothed the original light curves at 23 and 230 GHz using the median smoothing algorithm (with data points = 5) available in the SPMF open-source data mining library8 (Fournier-Viger et al. 2016).This provides for a clearer representation of longer term variation patterns.
From visual inspection of the multi-band radio light curves of 3C 279 (Fig. 1), we noticed that the most prominent peak in the emission first occurs around MJD 56100 (22 June 2012) at higher radio frequencies (230 GHz and 43 GHz).The emission amplitude typically declines with decreasing frequency.Such a trend was also reported by Larionov et al. (2020) for 3C 279.However, they did not report any cross-correlation study on the different radio light curves.
Visual inspection suggests that the radio emission at lower-frequency bands usually lags behind that at the higher-frequency bands.To quantify the lags/leads between different radio light curves, we carried out cross-correlation analyses.

Intra-band radio cross-correlation
Adopting the ZDCF cross-correlation methodology, as explained in Section 2.3, we carried out intra-band cross-correlations between all possible combinations of light curves.The cross-correlation plots (21 combinations) are shown in Figure 2. The peak DCF value and the corresponding lag with 1 error are provided in Table 3. From these cross-correlation results (Fig. 2 and Table 3), we find that the lower frequency light curve lags behind the higher frequency one for nearly for every pair.The information on lags/leads and the DCF values for all the combinations of light curves are given in Table 3.

Connection between lag and frequency
We next carried out an investigation of the connection/dependency of the observed lags with the radio emission at different frequencies.We used the estimated lag values quoted in Table 3 and plotted lags versus frequency for each radio band against the rest of the bands (Fig. 3).
To derive an empirical relationship between lag and frequency, we fitted a straight line defined as: where is the lag value of particular frequency data ( ) with respect to the other frequency bands ( ).The slope and intercept values are denoted by and , along with the associated uncertainties as and , respectively.The straight-line fits are shown as solid red lines in Figure 3.These relations between lag and frequency for  6) -( 12)).

DISCUSSION
This work presents a systematic study of the multi-band crosscorrelated radio variability of the blazar 3C 279.For this, we used the radio observations made over more than a decade from various radio telescopes spanning frequency bands from 2 GHz to 230 GHz.

Comparison with earlier studies
A few multi-frequency radio cross-correlation studies for 3C 279 have been reported earlier (Wang et al. 2008;Deng et al. 2008;Yuan 2012).However, these studies include observations covering shorter and/or non-overlapping periods of observations; they also employ fewer frequency bands than presented in this work.2008) suggested that the jet magnetic field primarily determines the observed time lag between bands arising from synchrotron radio emission.If the magnetic field strength is weak, then, because of the slower cooling of synchrotron radiation at lower frequencies, the observed time lag will be longer in the lower than in the higher-frequency bands.Such weak magnetic fields could arise either due to the location of the emitting region being far away from the central black hole or by weaker magnetic field compression by the shock waves in the emitting region.Deng et al. (2008) carried out a cross-correlation between the Metsähovi radio light curves at 22 GHz and 37 GHz (data time period: 1980-2005).Their results showed that there is a strong correlation between the two radio frequencies.Using the DCF technique, they found that 37 GHz light curve leads the 22 GHz by ∼ 140 days.However, with the ZDCF method they found the 22 GHz data leading the 37 GHz by ∼ 168 days and they stated that their results were not reliable because of large uncertainties.
Yuan (2012) presented cross-correlation results using light curves at 4.8 GHz, 8 GHz, and 14.5 GHz (data time period: 2009 September to 2010 July).Since the data length in this work was quite short (only ∼ 9 months), no significant time lags between the three frequency bands were found.
A standard explanation of time lags at lower frequencies is in terms of differing opacities.One sees more deeply into the source at higher frequencies -there is greater synchrotron self-absorption at the lower frequencies -so changes in emission at higher frequencies are observed earlier, and are less smeared out, than those at lower frequencies.Alternatively, even if none of the bands are self-absorbed, the lags and broadening of the flare/outburst profile in the light curve (especially at the lower frequencies) can be understood if the higherfrequency radiation is emitted closer to the site of particle acceleration at, for example, a shock front.In this case, the lower-frequency emission emerges from more diffuse regions further from the shock, producing the major flux changes, hence variations are delayed and broadened (e.g., Marscher & Gear 1985;Hughes et al. 1989).

Evolution of Core and Knots
To understand the relevance of the evolution of the radio core and the individual knots to the observed features in our work, we have analyzed the results of the VLBA study carried out by Weaver et al. (2022).These authors presented the kinematics of parsec-scale jets of a sample of -ray bright blazars monitored with the VLBA at 43 GHz, covering observations from 2007 June to 2018 December.They found that the jet of 3C 279 during this time span consisted of the "core," A0, and 17 moving features (C24, C25, C26, C27, C28, C29, C30 (which includes C30a and C30b), C31, C32, C33, C34, C35, C36, C37, C38 and D3).Three "quasi stationary" features tagged as A1, A2, and A3 are also present.Using the data provided in Weaver et al. (2022), we have created light curves for the core and individual knots, as displayed in Figure 4. From Figure 4, we find that knot C31 is main component involved in the outburst from MJD ∼ 55200 to ∼ 56300 − a span of about 3 years.(It should be noted that C31 was probably blended with the core A0 during the first part of the outburst.) The flux density of C31 dropped very abruptly (over ∼ 100 days) from MJD ∼ 56200 to ∼ 56300 to end the outburst.This could be due to radiative energy losses, perhaps in combination with adiabatic expansion, which would lower the maximum electron energy as well as the magnetic field, so that the cutoff frequency decreases to < 43 GHz.In order to verify that the knots in fact expanded during the outburst, we fit a least-squares straight line to the angular size vs. time for C31 and C32 (shown in Fig. 5).
Although there are apparently random fluctuations about the straight lines, likely owing to the difficulty of measuring angular sizes from the VLBA data, it is apparent that both knots C31 and C32 expanded during the outburst.
The MJD ∼ 55200 to ∼ 56300 outburst peaked at around the same time at 23, 11, and 8 GHz (Fig. 1).This could have occurred if the peak was caused by the Doppler factor reaching a maximum and then decreasing with time, so that the fluxes at all frequencies of the flare decreased together.At 43 GHz, the peak flux occurred before (Fig. 1) than at 23, 11, and 8 GHz, so the temporal evolution at this higher frequency is due to something else, probably either energy losses (as described above) or an optically thick-to-thin transition.The position angle vs. time plot (see Fig. 6 of Weaver et al. 2022) shows that the direction of knot C31 changes rapidly late in the outburst, so a changing Doppler factor is a reasonable hypothesis.The Doppler beaming factor is given by where and respectively are the magnitude (in units of the speed of light) and angle (relative to the line of sight) of the velocity of the knot, and Γ ≡ (1 − 2 ) −1/2 is the Lorentz factor.The apparent speed in light units in the sky plane, after removal of the redshift dependence, is We can combine these equations to solve for the angle : The flux density of a knot with a spectral index of 0 (i.e., observed at the spectral peak) depends on the Doppler factor as ∝ 3 .The increase in flux density by a factor of ∼ 4 between MJD 55800 and 56230 could have corresponded to an increase in the Doppler factor by a factor of 1.6.From the data presented in Weaver et al. (2022), we find that the apparent speed of knot C31 varied from 4.2 from MJD 55600 to 55900, to 1.7 from MJD 55950 to 56100, to 16 after MJD 56200.The second of these intervals included the peak in flux.This, plus the relatively low apparent speed implies that was very close to zero, so that ∼ 2Γ if Γ >> 1. Equation 15 then becomes ≈ 0.5 app Γ −2 .We then find that the flux variation can be explained if knot C31 maintained a constant Lorentz factor of 30Γ 30 and the trajectory bent from = 0.13 • Γ −1 30 (MJD 55600-55900) to = 0.086 • Γ −1 30 (MJD 55950-56100) and then to = 0.77 • Γ −1 30 (after MJD 56200).We conclude that, because of the high Lorentz factor of the jet flow in 3C 279, a very slight bending of the trajectory of a knot is sufficient to cause a major outburst after the knot separates from the core.
The outburst from MJD ∼ 56500 to ∼ 57000 was significant only at frequencies ≤ 23 GHz.Hence, it is not apparent on the 43 GHz images.From the light curves for the core and individual knots (Fig. 4), we noticed that the knots C32 and C33 both appear to be involved during this outburst and exhibited a low-amplitude flare at 43 GHz.To verify the expansion of the knot during an outburst (as explained above) and to obtain a clearer trend of such expansion, we only considered the knot C32.This is because the data were more extensive for knot C32 compared to the sparser observations for knot C33.Since we have verified that knot C32 expanded during the outburst, an interesting question is whether the adiabatic or synchrotron stage of the expanding shock model of Marscher & Gear (Marscher & Gear 1985) fits the maximum flux vs. frequency dependence of this section of the light curve at frequencies ≤ 23 GHz.To investigate this, we have estimated the peak flux of the outburst at each frequency with the quiescent flux subtracted.The quiescent flux was considered as the average value during the quiescent period before the flux started to rise, i.e., the minimum flux level between MJD 55000 and 55500.The details on the time period of consideration for the quiescent flux level and the maximum peak flux of the outburst at different frequencies are provided in Table 4. Further, using these values, a plot of maximum flux with subtracted quiescent flux vs. frequency is plotted in Figure 6.
The Marscher & Gear (MG Marscher & Gear 1985) shock-in-jet model predicts a dependence of the maximum flux density observed at frequency during an outburst to be ∝ , where depends on the dominant process by which the radiating electrons lose energy.In order to calculate from the equations of (Marscher & Gear 1985), we adopt = 2.2 as the slope of the energy distribution of electrons accelerated at the shock front (see, e.g., Sironi et al. 2015), and a magnetic field strength that depends on radius as ∝ −1 .The shock is assumed to expand only transverse to the jet initially, but may become a plasmoid that expands longitudinally as well during late stages.As derived from Table 4 and displayed in Figure 6, the value of changes from 1 = −0.37 ± 0.20 as the peak flux moves from 23 to 11 GHz, then 2 = 0.03 ± 0.31 from 11 to 8 GHz, and 3 = 1.15 ± 0.11 from 4.8 to 2.5 GHz.The prediction of MG is = −0.15during the synchrotron-loss stage, consistent within the uncertainties with 2 and within 1.1 of 1 .The MG value for the later, adiabatic-loss stage is = 0.51, which is a considerably weaker dependence than 3 .It is closer to the value = 0.93 predicted by the MG adiabatic-loss stage if the expansion is in all three dimensions instead of only laterally.The early observed value, 1 , with the peak flux density increasing as the frequency decreases, is in the same sense as the Compton stage of MG, but much weaker.However, MG assumed that the seed photons for Compton scattering are from synchrotron radiation within the shock.If, instead, the seed photons are from regions outside the jet (e.g., the broad emission-line region (Hayashida et al. 2012)), the Compton losses probably decay more slowly than adopted by MG, with the absolute value of lower than derived by MG.Another possibility is that the Doppler factor increased during the early stages of the outburst, causing to rise more rapidly as the peak frequency decreased than predicted by the MG synchrotron-loss stage.

CONCLUSIONS
We have conducted a detailed analysis of quasi-simultaneous multiband radio flux observations of the blazar 3C 279.Our data cover the period of 2008 to 2022 at seven different frequencies ranging from 2.5 GHz to 230 GHz.Some of the data were collected from public archives; new observations from various radio telescopes are listed in Table 1.The summary and conclusions from our study are as follows: 1. Overall, the multi-band radio light curves exhibit flux variations with prominent outbursts occurring first at higher-frequency and later at lower-frequency bands.Such a trend was further quantified using cross-correlation analysis, indicating that the emission at lower-frequency bands lags that at higher-frequency bands.As is typical for blazars, the flux changes at the higher frequencies lead those at lower frequencies (e.g., Raiteri et al. 2001;2003;Gupta et al. 2012;Kutkin et al. 2014;Gaur et al. 2015;and references therein).The plots of lag versus frequency are well fit by straight lines with a negative slope, typically ∼ −30 day GHz −1 .This observational trend possibly favours scenarios where time lags at lower frequencies are due to different opacities, as greater synchrotron self-absorption could occur at the lower frequencies than at the higher ones.Thus, measurements of the light curve time lag in radio bands are a useful way to examine the properties of the opaque apparent base of AGN jets.Under the shocked jet scenario, frequency-dependent radiative loss timescales could also play a role, especially at high radio frequencies (e.g., Marscher & Gear 1985;

Figure 1 .
Figure 1.Multi-band radio lightcurve of 3C 279.For clearer visual presentation, the individual light curves are shown with offsets, which are provided in the inset label.The solid black and thin blue slanted lines connect the peaks of the first and second outbursts, respectively.

Figure 2 .Figure 3 .
Figure 2. Cross-correlation plots between different combinations of radio bands.Here the positive lag for DCF tagged as 'frequency 1 Vs frequency 2' means light curve 2 variations lag those of light curve 1.The blue coloured contours from dark to light represent the 1 , 2 and 3 significance levels, respectively.
Wang et al. (2008) carried out cross-correlations using radio light curves at 8 GHz (data time period: 1965 to 2000), 22 GHz (data time period: 1980 to 2005) and 37 GHz (data time period: 1980 to 2005).They found that the 8 GHz variations lag behind those at 22 GHz by ∼ 69 days, and 22 GHz data lag behind 37 GHz by ∼ 33 days.Wang et al. (

Figure 4 .Figure 5 .
Figure 4. Light curves of individual components of 3C 279 based on VLBA images at 43 GHz.

Table 1 .
Radio observatory data used in this work

Table 2 .
RATAN-600 radiometer parameters: central frequency 0 , bandwidth Δ 0 , detection limit for sources per transit Δ .FWHM RA×DEC is the average angular resolution along RA and Dec.
antenna throughout the daily rotation of the Earth and the horizontal location of all input horns in the frequency bands from 1 to 22 GHz in the focal plane of the antenna.We used the following six flux density secondary calibrators:3C 48,  3C 138, 3C 147, 3C 161, 3C 286, and NGC 7027.The flux density values were calculated based on the scales provided byBaars et al.
• ) and are presented in Table 2.The observations were carried out with six-frequency radiometers at 1.25 (0.96 earlier), 2.25, 4.7 (3.9 earlier), 8.2, 11.2, and 22.3 GHz.The observations of 3C 279 and astronomical flux density calibrators were made at their upper culminations.The objects were scanned with a fixed

Table 3 .
ZDCF Results for Radio Lightcurves

Table 4 .
Maximum flux information for the second outburst.