Multiwavelength Photometric and Spectropolarimetric Analysis of the FSRQ 3C 279
V. M. Patiño-Álvarez, S. Fernandes, V. Chavushyan, E. López-Rodríguez, J. León-Tavares, E. M. Schlegel, L. Carrasco, J. Valdés, A. Carramiñana
MMNRAS , 1–31 (2016) Preprint 6 June 2018 Compiled using MNRAS L A TEX style file v3.0
Multiwavelength Photometric and SpectropolarimetricAnalysis of the FSRQ 3C 279
V. M. Pati˜no- ´Alvarez , (cid:63) , S. Fernandes , V. Chavushyan , E. L´opez-Rodr´ıguez ,J. Le´on-Tavares , E. M. Schlegel , L. Carrasco , J. Vald´es , A. Carrami˜nana Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany Instituto Nacional de Astrof´ısica ´Optica y Electr´onica (INAOE), Apartado Postal 51 y 216, 72000 Puebla, M´exico University of Texas at San Antonio, Department of Physics and Astronomy, One UTSA Circle, San Antonio Texas, 78249 TX, USA SOFIA Science Center, NASA Ames Center, Mountain View, CA, USA Centre for Remote Sensing and Earth Observation Processes (TAP). Flemish Institute for Technological Research (VITO),Boeretang 282, 2400 Mol, Belgium.
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
In this paper, we present light curves for 3C 279 over a time period of six years;from 2008 to 2014. Our multiwavelength data comprise 1 mm to gamma-rays, withadditional optical polarimetry. Based on the behaviour of the gamma-ray light curvewith respect to other bands, we identified three different activity periods. One of theactivity periods shows anomalous behaviour with no gamma-ray counterpart associ-ated with optical and NIR flares. Another anomalous activity period shows a flare ingamma-rays, 1 mm and polarization degree, however, it does not have counterparts inthe UV continuum, optical and NIR bands. We find a significant overall correlation ofthe UV continuum emission, the optical and NIR bands. This correlation suggests thatthe NIR to UV continuum is co-spatial. We also find a correlation between the UVcontinuum and the 1 mm data, which implies that the dominant process in produc-ing the UV continuum is synchrotron emission. The gamma-ray spectral index showsstatistically significant variability and an anti-correlation with the gamma-ray lumi-nosity. We demonstrate that the dominant gamma-ray emission mechanism in 3C 279changes over time. Alternatively, the location of the gamma-ray emission zone itselfmay change depending on the activity state of the central engine.
Key words: galaxies: active galaxies: jets gamma-rays: galaxies quasars: indi-vidual (3C 279)
Blazars, active galactic nuclei with a relativistic jet pointingalmost directly into our line of sight (Urry & Padovani 1995),are the dominant population of gamma-ray sources in thesky, as seen by the Fermi Gamma-ray Telescope (Nolan et al.2012). Blazars are highly variable at all frequencies, withnon-thermal emission spanning over 10 decades in energy.According to the behaviour of their optical spectra, blazarsare divided into BL Lac objects (BL Lacs) and flat spectrumradio quasars (FSRQs).Some objects exhibit a high degree of linear polarizationat optical wavelengths (e.g. Blinov et al. 2015, and referencestherein), however, this can also be a function of the activity (cid:63)
E-mail: [email protected] state of the source (e.g. Itoh et al. 2015; Carnerero et al.2015; Bhatta et al. 2015, and references therein).3C 279, an FSRQ at z = 0 . c (cid:13) a r X i v : . [ a s t r o - ph . H E ] J un Pati˜no- ´Alvarez et al. that the continuum spectra from 2006-2007 correspond toa power-law with α = − .
6. They also found co-rotation ofthe optical EVPA and VLBA core polarization PA , whichshowed that the optical and radio emission were co-spatialwithin the uncertainties of their measurements. B¨ottcher &Principe (2009) found a possible signature of a decelerat-ing jet through a plasmoid evolution simulation by fittingto R -band, V -band, and I -band light curves from January2006.Hayashida et al. (2012) report that, at radio wave-lengths, the variability for this source appears to be muchless rapid compared to the gamma-ray and optical bands;and the excess variance ( F var , Vaughan et al. 2003) in theradio regime is quite modest (for instance at 37, 15 and 5GHz). (Hayashida et al. 2015) reported rapid gamma-rayvariability of 3C 279 during 2013-2014.By analyzing multiwavelength observations and theSED of 3C 279 at three different epochs, Aleksi´c et al. (2011)found that the Very High Energy (VHE) γ -ray emission de-tected in 2006 and 2007 by MAGIC challenge the standardone-zone model, based on relativistic electrons in a jet scat-tering Broad Line Region (BLR) photons. Instead, they ex-plored a two-zone model, where the VHE γ -ray emittingregion is located just outside the BLR, while the standardoptical-to-X-ray and the γ -ray emitting region is still insidethe BLR, as well as a lepto-hadronic model, with both mod-els fitting the data reasonably well. Aleksi´c et al. (2014a)found a cutoff in the GeV range of the high energy SED ofthis source. This finding hints that the gamma-ray emissionis coming from an inner region of the blazar, and thereforeinternally absorbed in the MAGIC energy range.Janiak et al. (2012) modeled the time lag observed be-tween optical R -band and gamma-rays in 3C 279, duringthe flare of February 2009 (lasting ∼
10 days). Their modelshowed that the flare was produced at a distance of a fewparsecs from the central black hole; however, this is not theonly possible model. Discerning between modeling such lagsassuming single dissipative events (as Janiak et al. 2012),or two-dissipative-zones scenarios is not an easy task. Thedata available and the cadence of the multiwavelength lightcurves do not yet allow distinguishing which mechanism isdominant in a given source (Janiak et al. 2012).Lindfors et al. (2006) studied the synchrotron flaring be-haviour of 3C 279, using data covering 10 years of monitor-ing from optical to radio frequencies. The authors found thatduring high gamma-ray states, an early-stage shock compo-nent is normally present; while in low gamma-ray states, thetime since the onset of the last synchrotron outburst is sig-nificantly longer. They proposed that this supports the ideathat gamma-ray flares are associated with the early stagesof shock components propagating in the jet.Despite those studies, a general consensus about thelocation of the gamma-ray production zone in 3C 279 doesnot yet exist.To study the stratification of the emission regions fordifferent wavelengths in 3C 279, we study multiwavelengthlight curves from 1 mm to gamma-rays, comprising a time-frame of six years, with an unprecedented cadence. We alsowish to investigate the dominant emission mechanism forthese wavelengths.We arrange this paper as follows: Section 2 describesthe observations used to carry out this work. Section 3 de- scribes briefly the cross-correlation analysis between the dif-ferent light curves. In Section 4 we address the variability ofthe different bands and the activity periods we identify. Wepresent in Section 5 our results and discussion. We summa-rize our conclusions in Section 6.
We obtained data from a variety of bands, including opticaland near-infrared (NIR) photometry, optical spectra, mil-limeter, gamma-rays, X-rays, and spectropolarimetry. Thesedatasets originate from a variety of sources. The light curvesfrom the data are shown in Fig. 3.
To identify the emission mechanism of the source, we usedoptical ( V -band) and Near-Infrared (NIR, J - H - and K -band) photometry.We retrieved 263 V -band photometric points fromThe Steward Observatory Monitoring Program (Smithet al. 2009) and 550 V -band photometric points from theSMARTS project (Bonning et al. 2012). The NIR photo-metric data points are from the Observatorio Astrof´ısicoGuillermo Haro (OAGH) at Cananea, Sonora, Mexico us-ing the Cananea Near-Infrared Camera (CANICA, Car-rami˜nana et al. 2009) and from the SMARTS project. Weobtained the J -band photometric points from the OAGH(66 points) and the SMARTS project (545 points). The H -band photometric points were observed at the OAGH (70points). The K -band photometric points were retrieved fromthe SMARTS project (487 points). To compare the opticaland NIR amplitude variations with those observed at otherwavelengths in linear scale, the optical and NIR photom-etry data have been converted to mJy. We converted thephotometric data from magnitudes to fluxes using the abso-lute calibration of the photometry ( f ) from Carrasco et al.(1991). The optical spectra used in this work come from three dif-ferent sources: 252 optical spectra were taken at the Stew-ard Observatory as part of the Ground-based Observa-tional Support of the Fermi Gamma-ray Space Telescopeat the University of Arizona monitoring program. Theoptical spectra were taken with the SPOL CCD Imag-ing/Spectropolarimeter (Smith et al. 2009). The data in thearchive at the University of Arizona include flux calibratedspectra for 3C 279, which have already been reduced; de-tails on the observational setup and reduction process arepresented in Smith et al. (2009). The spectral coverage isfrom 4000 to 7500 ˚A. The resolution ranges from 15-25 ˚A,depending on the slit width used for the observation. In thiswork, we only use spectra that have been calibrated againstthe V -band magnitude. Steward Observatory data is bro-ken up into observing cycles separated by several months. http://james.as.arizona.edu/ ∼ psmith/ Fermi/MNRAS000
To identify the emission mechanism of the source, we usedoptical ( V -band) and Near-Infrared (NIR, J - H - and K -band) photometry.We retrieved 263 V -band photometric points fromThe Steward Observatory Monitoring Program (Smithet al. 2009) and 550 V -band photometric points from theSMARTS project (Bonning et al. 2012). The NIR photo-metric data points are from the Observatorio Astrof´ısicoGuillermo Haro (OAGH) at Cananea, Sonora, Mexico us-ing the Cananea Near-Infrared Camera (CANICA, Car-rami˜nana et al. 2009) and from the SMARTS project. Weobtained the J -band photometric points from the OAGH(66 points) and the SMARTS project (545 points). The H -band photometric points were observed at the OAGH (70points). The K -band photometric points were retrieved fromthe SMARTS project (487 points). To compare the opticaland NIR amplitude variations with those observed at otherwavelengths in linear scale, the optical and NIR photom-etry data have been converted to mJy. We converted thephotometric data from magnitudes to fluxes using the abso-lute calibration of the photometry ( f ) from Carrasco et al.(1991). The optical spectra used in this work come from three dif-ferent sources: 252 optical spectra were taken at the Stew-ard Observatory as part of the Ground-based Observa-tional Support of the Fermi Gamma-ray Space Telescopeat the University of Arizona monitoring program. Theoptical spectra were taken with the SPOL CCD Imag-ing/Spectropolarimeter (Smith et al. 2009). The data in thearchive at the University of Arizona include flux calibratedspectra for 3C 279, which have already been reduced; de-tails on the observational setup and reduction process arepresented in Smith et al. (2009). The spectral coverage isfrom 4000 to 7500 ˚A. The resolution ranges from 15-25 ˚A,depending on the slit width used for the observation. In thiswork, we only use spectra that have been calibrated againstthe V -band magnitude. Steward Observatory data is bro-ken up into observing cycles separated by several months. http://james.as.arizona.edu/ ∼ psmith/ Fermi/MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 Our observational time-frame contains 6 Steward data cy-cles, and our activity periods contain from 1 to 3 Stewardcycles.We obtained 17 optical spectra from the spectroscopicmonitoring program being carried out at the Instituto Na-cional de Astrof´sicia ´Optica y Electr´onica (INAOE) 2.1-mtelescope at OAGH in Mexico (for details see Pati˜no- ´Alvarezet al. 2013a), and the 2.1-m telescope at the ObservatorioAstron´omico Nacional at San Pedro Martir (OAN-SPM),Baja California, Mexico. After each object exposure, He-Ar lamp spectra were taken to allow wavelength calibra-tion. Spectrophotometric standard stars were observed everynight (at least two per night) in order to perform flux cali-bration. The spectrophotometric data reduction was carriedout using the IRAF package . The image reduction processincluded bias and flat-field corrections, cosmic ray removal,2D wavelength calibration, sky spectrum subtraction, andflux calibration. The 1D spectra were subtracted taking anaperture of 6 arcsec around the peak of the spectrum pro-file. The observational log for the observations in OAGH andOAN-SPM is shown in Table 1. From a visual inspection ofthe data, we determined that there is an agreement betweenthe spectra obtained from the Steward Observatory, OAGH,and OAN-SPM.All spectra were shifted into the rest frame of the source.We applied a cosmological correction to the monochromaticflux of the form (1 + z ) . 3C 279 has a high galactic lat-itude, therefore no corrections were necessary for galacticinterstellar extinction and reddening. When we performedsubtraction of the Fe II emission usually found around theMg II λ λ − λ V -band fluxin mJy and the λ V -band and spectral observations inthe same night. We have also added 5 per cent to the uncer-tainty in the continuum emission to take into account theflux calibration error (Paul Smith, Private Communication).We fit the data with a linear regression taking into accountthe uncertainty in both quantities using the IDL task FI-TEXY . The linear fit obtained yields the relationship:Flux = ( − . ± . . ± . × Flux V (1)Both quantities in Eq. 1 are given in mJy. Fig. 2 showsthe flux correlation and fit to the data. After applying thistransformation to the V -band data points, we ended up with844 data points for UV-continuum. http://iraf.noao.edu/ http://idlastro.gsfc.nasa.gov/ftp/pro/math/fitexy.pro Wavelength (Å) F l ux ( · - e r g c m - s - Å - ) Figure 1.
Mean spectrum of 24 high S/N ratio spectra taken atSteward Observatory. The spectrum (in black) is in rest frame,and has the continuum subtracted. The fitted Fe II emission tem-plate (Vestergaard & Wilkes 2001) is shown in red. As can beseen, the UV Fe II emission is negligible.
Flux V (mJy) F l ux ( m J y ) Figure 2.
Correlation between the V -band flux and the 3000˚A continuum flux. The 1 mm data were obtained at the SMA on Mauna Kea(Hawaii) from 2008 August 19 to 2014 May 20. 3C 279 isincluded in an ongoing monitoring program at the SMA todetermine the fluxes of compact extragalactic radio sourcesthat can be used as calibrators at mm wavelengths. We ob-tained 365 fluxes from this monitoring program. Data fromthis program are updated regularly and are available at theSMA website . Details of the observations and data reduc-tion can be found in Gurwell et al. (2007). http://sma1.sma.hawaii.edu/callist/callist.htmlMNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al.
Table 1.
Observational log of the spectra taken in OAGH and OAN-SPM.UT Date Observatory Grating Resolution (˚A) Seeing Exposure Time (s)2011 Jan 30 OAGH 150 l/mm 15.4 2.5” 3 × × × × × × × × × × × × × × × × × × The X-ray data were retrieved from the public database ofthe Swift-XRT . The Swift-XRT data were processed usingthe most recent versions of the standard Swift tools: SwiftSoftware version 3.9, FTOOLS version 6.12 and XSPEC ver-sion 12.7.1. Light curves are generated using xrtgrblc version1.6. Circular and annular regions are used to describe thesource and background areas, respectively, and the radii ofboth depend on the current count rate. In order to handleboth, piled-up observations and cases where the sources landon bad columns, PSF correction is handled using xrtlccorr(Full details of the reduction procedure can be found in Stroh& Falcone 2013). The gamma-ray light curve from 0.1 to 300 GeV was builtby using data from the Fermi Large Area Telescope (LAT).It was reduced and analyzed with the Fermi Science Toolsv9r33p0. The Region of Interest (ROI) was selected as 15 ◦ in radius, centred at the position of 3C 279. The minimi-sation was done through a maximum likelihood algorithm,and we modelled our source spectra as a log-parabola. Weincluded all sources within 15 ◦ of 3C 279, extracted from the2FGL catalog (Nolan et al. 2012), with their normalisationand spectral indices kept free. The currently recommendedCALDB set of the instrument response functions, along withthe latest diffuse and isotropic background model files wereapplied to this analysis. In order to generate the spectralmodels and produce the gamma-ray light curve, modifiedversions of the user-contributed software were used. Weadopted a time bin of 7 days for our light curve fluxes to http://fermi.gsfc.nasa.gov/ssc/data/analysis/user/ increase S/N ratio and kept only the fluxes from time binswith a TS >
25. Upper limits were not calculated for thebins with TS <
25, because they are not suitable for cross-correlation analysis. The low number of discarded bins en-sures that we do not introduce a bias due to gaps in thegamma-ray light curve.
The polarization spectra were also taken from the StewardObservatory monitoring program. From their archive, we re-trieved 322 Stokes q and u spectra and 256 total flux spectrawhich were used for the present analysis. The Steward Ob-servatory monitoring program divides their observing timeinto cycles, which correspond to observing runs of ∼
10 dayseach month.Using the q and u spectra from the Steward Observa-tory database, we estimate the degree and position angle ofpolarization as a function of time. To avoid the noisy edgesof the spectra below 5000 ˚A and above 7000 ˚A, we only usedata in the wavelength range of λλ q and u spectra are the wavelength-calibrated andnormalised linear polarization parameters as a function ofwavelength. The normalized linear Stokes polarization pa-rameters are defined as q = Q/I and u = U/I . Where Qand U are the linear Stokes polarization parameters and Ithe total intensity. In spectral form this is q ( λ ) = Q ( λ ) /I ( λ )and u ( λ ) = U ( λ ) /I ( λ ). We use the calibrated total flux spectra, along with the q and u spectra to determine the polarized flux. There areonly calibrated total flux spectra for a subset of the q and u spectra. There are 66 nights where the V -band magnitude of MNRAS000
10 dayseach month.Using the q and u spectra from the Steward Observa-tory database, we estimate the degree and position angle ofpolarization as a function of time. To avoid the noisy edgesof the spectra below 5000 ˚A and above 7000 ˚A, we only usedata in the wavelength range of λλ q and u spectra are the wavelength-calibrated andnormalised linear polarization parameters as a function ofwavelength. The normalized linear Stokes polarization pa-rameters are defined as q = Q/I and u = U/I . Where Qand U are the linear Stokes polarization parameters and Ithe total intensity. In spectral form this is q ( λ ) = Q ( λ ) /I ( λ )and u ( λ ) = U ( λ ) /I ( λ ). We use the calibrated total flux spectra, along with the q and u spectra to determine the polarized flux. There areonly calibrated total flux spectra for a subset of the q and u spectra. There are 66 nights where the V -band magnitude of MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 F l ux ( · - ph c m - s - ) F l ux ( · - e r g c m - s - ) F l ux ( · - e r g c m - s - Å - ) F l ux ( m J y ) F l ux ( m J y ) F l ux ( J y ) C oun t R a t e ( c s - ) Steward - Polarized ll l Figure 3.
Multiwavelength light curves of 3C 279. The band of observation and the origin of the data is labeled inside each panel. Inthe fourth panel, the points represent the observed spectra, as well as the points obtained using the relationship between the V -bandand the 3000 ˚A continuum.MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. the comparison star used to calibrate the total flux spectrawas not measured due to non-photometric conditions.
We estimate the linear degree of polarization as a functionof wavelength (polarization spectrum) as p ( λ ) = (cid:112) q ( λ ) + u ( λ ) . (2)To determine if there was a wavelength dependence inthe degree of polarization in the range λλ λλ q and u spectra, the lineardegree of polarization is defined as (Stokes 1852) P = (cid:112) q + u . (3)Since the definition of the degree of polarization squaresand sums q and u values, a Rician statistical bias is intro-duced into the estimate that causes an overestimation in thevalue of the degree of polarization (Serkowski 1958, 1962;Wardle & Kronberg 1974; Clarke et al. 1993). We estimatethe corrected degree of polarization as in Serkowski (1958)and Wardle & Kronberg (1974) P = (cid:112) < q ( λ ) > + < u ( λ ) > − σ P . (4)For each observation we use the median values of the q and u spectra to estimate the degree of polarization. σ p isthe error in P and is defined in equation 5.The ratio P/σ p is an estimation of the accuracy of P values (Simmons & Stewart 1985; Smith et al. 2007). Forratio values greater than 3, the polarization measurementsare very accurate (Smith et al. 2007). For our data set, P/σ p >>
3, indicating our estimations are highly signifi-cant. The Rician statistical bias has a greater effect on thevalue of the degree of polarization when the ratio
P/σ p is lessthan approximately 3. For over 99 per cent of the data set,the per cent difference between corrected and uncorrectedvalues is less than 1 per cent. We do not report estimationsof P where P/σ p is less than 1, as this means the error in P is larger than P itself. We consider this to be an unreliablemeasurement with very low signal to noise.We estimate the error in P using root-mean-squared(rms) values of the q and u observations binned from λλ q and u estimations. Therefore, theyare a measure of the error of the q and u observations.We estimate the error in P with the rms values of q and u following a method suggested by Paul Smith (Private Communication). Equation 5 is a result of propagation oferrors from binning of the data. From the propagation oferrors, the σ P is a single rms value, in this case the rms of aStokes parameter binned from λλ / √ N . Here, N is the number of observations. N = 500 because we bin the data from 5000 - 7000 ˚A andthe resolution of the spectrograph is 4˚A/pixel.Our adopted relationship to estimate the error in P is σ P = MAX ( rms q , rms u ) √ N . (5)Simply put, we take the larger of the q and u rms val-ues and divide by square root of N. We take the maximumrms value of the two Stokes parameters as a conservativeapproach to estimating the error. As in the case of P , we determine from a linear fit to the po-sition angle of polarization ( PA ) spectra that a single valuecould characterize each observation. We estimate the PA be-tween λλ P A = 12 arctan (cid:32) < u ( λ ) >< q ( λ ) > (cid:33) . (6)In the definition of the PA based on the polarizationellipse (Jones 1941; Stokes 1852), there is no distinctionbetween nπ multiplicative factors of the PA (Adam 1963).Therefore, there is an nπ ambiguity in all PA estimations.We apply a shifting method commonly used to correct forthe ambiguity (e.g. Sasada et al. 2011, Sorcia et al. 2013 ) toour data. The shifting method applies corrections to adja-cent PA values in the light curve and makes the assumptionthat variations in the PA over those adjacent points shouldbe less than ∼ ◦ apart.In the literature, there is great variation in time be-tween adjacent points, from the order of days to months.Clearly, the shorter the time between the adjacent points,the more viable the assumption is. Therefore, the methodis most accurate for densely sampled data sets. Some au-thors use as little as five days as a limit over which to applythe shifting method (Jorstad 2009; Carnerero et al. 2015).The data we use is only very densely sampled ( ∼ ∼ ∼ PA , not theintrinsic values themselves. The original calculated PA canbe recovered by applying nπ shifts to all of the data points tolie in the original calculated PA range. We take the contin-uation of long-term trends in our data over longer cadenceobservations and gaps in data as significant, assuming nolarge variations in PA between time bins. This analysis isconsistent with earlier works where the authors follow con-sistent trends of PA swings in their analysis over less denselysampled data (Marscher et al. 2008).One caution to the shifting method is that it can in-troduce shifts where there might not be a true shift present.This happens where adjacent points are close to ∼ ◦ apartand could be greater or less than ∼ ◦ within error limits. MNRAS000
P/σ p is lessthan approximately 3. For over 99 per cent of the data set,the per cent difference between corrected and uncorrectedvalues is less than 1 per cent. We do not report estimationsof P where P/σ p is less than 1, as this means the error in P is larger than P itself. We consider this to be an unreliablemeasurement with very low signal to noise.We estimate the error in P using root-mean-squared(rms) values of the q and u observations binned from λλ q and u estimations. Therefore, theyare a measure of the error of the q and u observations.We estimate the error in P with the rms values of q and u following a method suggested by Paul Smith (Private Communication). Equation 5 is a result of propagation oferrors from binning of the data. From the propagation oferrors, the σ P is a single rms value, in this case the rms of aStokes parameter binned from λλ / √ N . Here, N is the number of observations. N = 500 because we bin the data from 5000 - 7000 ˚A andthe resolution of the spectrograph is 4˚A/pixel.Our adopted relationship to estimate the error in P is σ P = MAX ( rms q , rms u ) √ N . (5)Simply put, we take the larger of the q and u rms val-ues and divide by square root of N. We take the maximumrms value of the two Stokes parameters as a conservativeapproach to estimating the error. As in the case of P , we determine from a linear fit to the po-sition angle of polarization ( PA ) spectra that a single valuecould characterize each observation. We estimate the PA be-tween λλ P A = 12 arctan (cid:32) < u ( λ ) >< q ( λ ) > (cid:33) . (6)In the definition of the PA based on the polarizationellipse (Jones 1941; Stokes 1852), there is no distinctionbetween nπ multiplicative factors of the PA (Adam 1963).Therefore, there is an nπ ambiguity in all PA estimations.We apply a shifting method commonly used to correct forthe ambiguity (e.g. Sasada et al. 2011, Sorcia et al. 2013 ) toour data. The shifting method applies corrections to adja-cent PA values in the light curve and makes the assumptionthat variations in the PA over those adjacent points shouldbe less than ∼ ◦ apart.In the literature, there is great variation in time be-tween adjacent points, from the order of days to months.Clearly, the shorter the time between the adjacent points,the more viable the assumption is. Therefore, the methodis most accurate for densely sampled data sets. Some au-thors use as little as five days as a limit over which to applythe shifting method (Jorstad 2009; Carnerero et al. 2015).The data we use is only very densely sampled ( ∼ ∼ ∼ PA , not theintrinsic values themselves. The original calculated PA canbe recovered by applying nπ shifts to all of the data points tolie in the original calculated PA range. We take the contin-uation of long-term trends in our data over longer cadenceobservations and gaps in data as significant, assuming nolarge variations in PA between time bins. This analysis isconsistent with earlier works where the authors follow con-sistent trends of PA swings in their analysis over less denselysampled data (Marscher et al. 2008).One caution to the shifting method is that it can in-troduce shifts where there might not be a true shift present.This happens where adjacent points are close to ∼ ◦ apartand could be greater or less than ∼ ◦ within error limits. MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 This could create false positive shifts in the PA . Poor sam-pling can also affect the interpretation of the results, becausefalse positives can be detected. Careful study of how theshifting method corrects for the nπ ambiguity in each dataset is essential. The PA trends uncovered by correcting the nπ ambiguity are used to probe magnetic field orientationshifts over time, locations of polarized emission sites, and PA behaviour during flares (e.g. Abdo et al. 2010a; Kiehlmannet al. 2013).We estimate the error in the PA in the limit of P >>σ P , as is characteristic of our data set, as (Serkowski 1962;Wardle & Kronberg 1974) σ PA = 28 . ◦ ∗ σ P P . (7)The variability of P and PA , compared to the gamma-rays and the UV continuum is shown in Fig. 4.The Steward Observatory bins their data from λλ q and u Stokes spectra. The rms values contain infor-mation about the error as they take into account the photoncounting statistics for the wavelength range of λλ We carried out the Cross-Correlation analysis using threedifferent methods: The Interpolation Method (ICCF,Gaskell & Sparke 1986), the Discrete Cross-CorrelationFunction (DCCF, Edelson & Krolik 1988) and the Z-Transformed Discrete Correlation Function (ZDCF, Alexan-der 1997). We used modified versions of these methods as de-scribed in Pati˜no- ´Alvarez et al. (2013b). The correlations be-tween gamma-rays, X-rays, UV continuum, optical V -band,NIR JHK -bands and polarization ( P and PA ), were ana-lyzed using cross-correlation analysis. The resulting lags ob-tained from the cross-correlation analysis between the differ-ent light curves are summarized in Table 2, and the figuresare presented in Appendix A.The confidence intervals (at 90 per cent) in the lagsare calculated using an equation obtained by Monte Carlosimulations of different types of time series as explained inPati˜no- ´Alvarez (2012). The simulations show that the maincontributor to the uncertainty in the lag obtained by thecross-correlation analysis is the sampling mean of the differ-ent light curves involved. The reason we needed simulationsto obtain the uncertainty in the lag is because the usual er-ror reported in the literature varies with the method used. The uncertainty in the ICCF is not well defined in the liter-ature. One method involves fitting a Gaussian to the peakof the cross-correlation function and taking the standarddeviation as uncertainty. However, this does not take intoconsideration the properties of the individual light curves.The DCCF uncertainty usually presented in the literatureis based on the bin size selected prior to the analysis, whichhas the same problem as the ICCF. The error defined for theZDCF by Alexander (1997) is a fiducial interval. However,a fiducial interval is not the same as a confidence interval,a fact that is also mentioned in the paper. The significancelevels are what best represent the level of certainty in thecross-correlation coefficient results. Our cross-correlation fig-ures show significance levels in the correlation coefficient at90, 95, and 99 per cent, also calculated from Monte Carlosimulations (Emmanoulopoulos et al. 2013), as well as theconfidence intervals in the lags.As can be seen in Table 2, the V -band, the J -bandand the UV Continuum emission are simultaneous. Becauseemission in the λ V - and NIR JHK -bandsare simultaneous; any correlation with other bands is alsovalid for these bands. The simultaneity of these bands im-plies the emission regions for these bands are co-spatial (e.g.Marscher 1996; Marscher & Travis 1996; Rani et al. 2013).On the other hand, the correlations involving the 1mmemission were analyzed using the Spearman Correlation Co-efficient, in order to discern if the emission in the V -bandand the 1 mm light curves have a common origin, as sug-gested by Aleksi´c et al. (2014b). Given the high cadenceof observations in the V -band, we obtained approximate V -band fluxes at the observation times of the 1 mm light curvevia linear interpolation. We calculated the Spearman corre-lation coefficient for these two bands and found a correla-tion coefficient of R = 0 .
65, with a probability of obtainingthis correlation by chance p << .
01. This low value allowsus to confirm a significant correlation. We repeat this pro-cedure for the rest of the bands used in this work, beingcareful of taking the light curve with the highest cadence asreference. We also made sure that only interpolated valueswere taken into account during the correlation (i.e. no ex-trapolation). We found a positive and significant correlationbetween the 1 mm emission and the following bands: 3000˚A continuum ( R = 0 . J -band ( R = 0 . K -band( R = 0 . R = − . H -band ( R = 0 . P ( R = − . PA ( R = 0 . R = 0 . H -band, is dueto the low number of observations on the H -band comparedto the 1 mm light curve. Based on the behaviour of the gamma-rays with respect tothe UV, optical and NIR, we separated the entire time rangeinto three different activity periods: A flaring period in mul-tiple bands, with counterparts in gamma-rays; a flaring pe-riod in multiple bands with no counterparts in gamma-rays;and another flaring period in multiple bands with appar-
MNRAS , 1–31 (2016)
Pati˜no- ´Alvarez et al. F l ux ( × - ph c m - s - ) P O p ti ca l ( % ) -300-200-1000100200300 P A O p ti ca l ( ° ) Fermi
LAT (0.1-300 GeV)Steward ll l ll ll F l ux ( × - e r g c m - s - Å - ) F l ux ( × - e r g c m - s - ) Steward ll F l ux ( × - ph c m - s - ) Figure 4.
The behaviour of the polarimetric observations ( P , PA , Polarized Flux) compared with the gamma-rays and the UV-continuumfor 3C 279. We labelled each panel with the band of observation and the origin of the data. Table 2.
Cross-Correlation results for the entire time-range and the defined activity periods. All correlationsare at a confidence level > P and P A , but we found no significant correlation with any of the other light curves.Bands Full Time-Range Period A Period B Period C J -band vs. H -band 0.0 ± ± ± ± J -band vs. K -band -0.1 ± ± ± ± V -band 0.0 ± ± ± ± J -band 0.2 ± ± ± ± V -band vs. J -band 0.0 ± ± ± ± ± ± J -band vs. X-rays -65.1 ± ± V -band vs. X-rays -67.7 ± ± ± ± ± ± ≥000
Cross-Correlation results for the entire time-range and the defined activity periods. All correlationsare at a confidence level > P and P A , but we found no significant correlation with any of the other light curves.Bands Full Time-Range Period A Period B Period C J -band vs. H -band 0.0 ± ± ± ± J -band vs. K -band -0.1 ± ± ± ± V -band 0.0 ± ± ± ± J -band 0.2 ± ± ± ± V -band vs. J -band 0.0 ± ± ± ± ± ± J -band vs. X-rays -65.1 ± ± V -band vs. X-rays -67.7 ± ± ± ± ± ± ≥000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 ent counterparts in gamma-rays. We also performed cross-correlation analysis on each individual activity period, forall the light curves. For the polarimetric quantities we de-fine the continuum levels of the P as the per centage thatbest describes the level that is returned to, after flaring ac-tivity. The continuum level of the PA is the angle that thefluctuations rotate about or return to, after some varyingtime-frame or amplitude swing. Hereafter, all the dates wepresent are in the format JD = JD − (cid:48) (cid:48) This period ranges from JD = 4650 − V -band),UV continuum, and NIR emission ( J -, H - and K -bands). Inthe 1 mm light curve we observe a response to each of theseflares, however, the amplitude of the 1 mm flares is not ashigh as in the other wavelengths. The cross-correlation forthis period shows a delay of 0.7 ± P in the firstSteward cycle is the largest for the entire data set. The max-imum and minimum values for P are 34.5 per cent and 1.6per cent, respectively. This corresponds to a spread of 32.9per cent, and the drop from the maximum to the minimumoccurs over 29 days. This behaviour occurs during flaringactivity in other wavebands, as discussed in Section 4. The PA behaviour during this time exhibits 4 small scale swings( ∼ ◦ ).We observed five clear flares in P (in this context a flareis a local maximum in the P light curve). Flaring time-scalesof P range from 40 to 85 days and the change of P duringflaring was as high as an order of magnitude increase.The P flare around JD = 5330 is superseded by twoapparent large swings in PA with a delay of approximately50 days: ∼ ◦ southward and ∼ ◦ northward, then ∼ ◦ southward and ∼ ◦ northward. In a recent pa-per on the polarimetric behaviour of 3C 279 (Kiehlmannet al. 2016), this PA behaviour is not observed. The cadenceof data in that paper is much higher, therefore we believethese swings could be artifacts resulting from poor samplingin that portion of the light curve. This exemplifies the reasonwhy care must be taken with the shifting method and thedangers of shifting over large time gaps. In the Kiehlmannet al. (2016) paper, a southward rotation of the PA is re-ported over this time period, which is consistent with ourdata.The polarized flux follows the trend of P taking intoaccount the continuum flux level. At the beginning of theactivity period, P is high and the continuum is decreasing,thus the polarized flux is high, but decreasing. When the P drops, so does the polarized flux. The PA during this begin-ning period is oscillating around an increasing PA continuumvalue. There is a small amplitude flare in the continuum anda large amplitude flare in the gamma-rays as P drops to aminimum, around JD = 4900, as such, the polarized fluxis at a minimum.The third Steward cycle in this activity period has high levels of P variability associated with several flares in theUV continuum. The UV-mm flares have been previouslydiscussed, but the P during the largest flare in this cycleis near the maximum of the polarized flux over the entiretime-frame, suggesting simultaneous flaring in P . Precedingthis flare is the beginning of a large swing in PA that oc-curs over approximately 200 days. Over the cycle, there is ageneral northward rotation, but at JD = 5650 it rotatessharply southward. The extent of the swing is not known forsure, because there is an observational gap in the middle ofthe swing. However, after the gap, the PA is rotating sharplynorthward, returning to the continuum PA level. The returnto the continuum level happens to coincide with the maxi-mum of the largest UV flare. Such a large long-term swingin PA during a large flare in the UV suggests that a fea-ture is moving along a helical magnetic field, as proposed byKiehlmann et al. (2016).In Activity Period A, the continuum P level fromJD = 4800 − <
10 per cent, until JD =5300, where it increases until JD = 5500. It drops backdown to a low level for the rest of the activity period. Wefound a beginning trend of a northward rotation of the con-tinuum PA followed by a swing to a southward rotation atapproximately JD = 4900, which coincides with a flare in P , but no concurrent multiwavelength counterparts. There isa northward rotation of the continuum PA in Steward cycle3, but the time of the swing occurs during an observationalgap. At the very end of the third steward cycle, we observea swing to southward rotation, which also happens to coin-cide with a flare in P and no concurrent multiwavelengthcounterparts. This period ranges from JD = 5850 − V -band, with clear counterparts in the UV spectralcontinuum and NIR bands. We also observe an increase inthe 1 mm emission corresponding with each of these flares.The highest levels of 1 mm emission over the entire time-frame of our observations occurs during this activity period.There are increases in polarization degree coincident withthese flares; this might indicate that these flares have a non-thermal origin. However, there are no counterparts to anyof these flares in the gamma-rays. This kind of behaviourhas only been reported once by (Chatterjee et al. 2013) onthe source PKS 0208-512. In the previous case, the reportedperiod of low gamma-ray flux is ∼
150 days, while the periodwe observe in 3C 279 is ∼
500 days.We analyze the polarimetric behaviour over the twoSteward cycles that make up this time period. The P ishighly variable during this period, and we find correlationswith the high levels of activity in the other emission bandsover this time-frame. There is a clear general northward ro-tation of the PA at the beginning, flattening out at the end.There are two high amplitude swings in the PA on the orderof at least ∼ ◦ . This period contains the minimum valueof P for all of the activity periods, 1.4 per cent at JD =6008. Due to the gaps in P data, we observed few clear flaresin P , but we compared local minima and estimated flaringtime-scales that range from 8 to 83 days. We were able to MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. F l ux F l ux P o l a r i ze d F l ux P O p t ( % ) -200-1000100200 P A F l ux C oun t R a t e Steward, OAGH - l ll ll ll Figure 5.
Activity period A. The gamma-rays, UV, optical andNIR are well correlated and simultaneous. The units are the sameas in Fig. 3. confirm the existence of flares by noting the concurrent ris-ing and falling trends in the P light curve.Similarly to activity period A, we observed flares thathad an order of magnitude increases and decreases in P .The second Steward cycle in this period shows some of thehighest amplitude P flares over the time-frame, while theother emission bands show low amplitude flares. There isalso a jump in the continuum P level during this time pe-riod at approximately JD = 4600. This can be explainedby an increase in the Lorentz factor, since the gamma-raysbase level changes, which indicates a change in the domi-nant emission process (Ghisellini & Celotti 2001). Due tothe high amplitude flares of P , the polarized flux increasesas a general trend.The continuum P level is low, < = 6400, where it jumps to approximately10 per cent. The continuum level of PA rotates northwardthroughout the activity period. We note that the swing tonorthward rotation from the southward rotation observed atthe end of activity period A must have occurred during theobservational gap between periods. At the end of Stewardcycle 5, the PA becomes roughly constant at approximately ∼ ◦ . The point where the PA becomes constant is coinci-dent with the jump in the base level of the P . This could bedue to a strengthening magnetic field forcing a well orderedmagnetic field topology. F l ux F l ux P o l a r i ze d F l ux P O p t ( % ) -200-1000100200 P A F l ux C oun t R a t e Steward, OAGH - l ll ll ll Figure 6.
Activity period B. We do not observe a counterpart ingamma-rays to flares in the UV, optical and NIR. The units arethe same as in Fig. 3.
This period ranges from JD = 6400 − ± ± MNRAS000
This period ranges from JD = 6400 − ± ± MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 tween the X-rays and the NIR, optical V, and UV bands, at ∼ −
64 days; meaning the X-rays precede the other bands.The cross-correlation between the X-rays and gamma-raysfor this period, shows a delay of 1.3 ± . ± . P we observe a dip over a time-scale of ∼
183 days,with the minimum at the middle of the time period. Thecontinuum level of P starts at approximately the same levelas the end of activity period B, then begins to increase afterJD = 6700. The P drops from 20 per cent to 5 per centduring the dip which occurs over the first 30 days of the cy-cle, while the recovery occurs over approximately 150 days.In the observed emission bands, there is large amplitude flar-ing activity throughout the period. Thusly, even though P dips at the beginning of the cycle and then recovers, thepolarized flux increases over the activity period.The continuum level of the PA is nearly constant arounda value of approximately ∼ ◦ . We observed two small am-plitude swings in PA (on the order of ∼
10 degrees), first fromnorthward to southward movement, and then back to north-ward. The swing back to northward occurs at the minimum P value of the dip. The standard deviation from the meanvalue of the PA is 6.4 degrees, which implies these swingsare deviations from a constant PA continuum. The polar-ized flux increases for the duration of the activity period;even though the P dips at the same time the UV continuumflares, so that the rising UV flux coincides with falling P and falling UV flux coincides with rising P . We will discussthis and multiwavelength behaviour correlations further inSection 5. F l ux F l ux P o l a r i ze d F l ux P O p t ( % ) P A F l ux F l ux C oun t R a t e Steward, OAGH - l ll ll ll Figure 7.
Activity period C. We found a delay between gamma-rays and the UV continuum. This delay is different than the onefound in Period A. The units are the same as in Fig. 3.
Overall, the continuum level of P remains lower than 5 percent, except for JD = 5300 − = 6400until the end of the observational time-frame, where it isapproximately 10 per cent. The continuum level of the PA is characterized by four swings. There is a predominantlynorthward rotation throughout the time period, with thesouthward rotations lasting 400 and 100 days. The constanttrend at the end of the observational time-frame is approx-imately 400 days long. Two of the swings in PA occur si-multaneously with flares in P , while the other inferred twoswings occur during observational gaps. The beginning ofthe constant trend in the continuum level of the PA coin-cides with the jump in the P continuum at JD = 6400. Micro-variability occurs on the short time-scale bins ofaround 10 days that make up each Steward observation cy-cle. We analyze the micro-variability over the entire data set,as there are no observed trends in behaviour that are morecommon or rare in any specific activity period. There is awide range of behaviour and we do not observe consistentlysimilar correlated behaviour between P and PA . We observe MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. G a mm a - R a y S p ec t r a l I nd e x Figure 8.
Gamma-ray spectral index over the entire observationperiod. variability in P on the order of a few days with changes in P from 3 to 10 per cent. We also observed PA swings lastinga few days with changes that ranged from ∼ P and PA behave chaotically or randomly on this timescale.This leads us to speculate that stochastic processes such asturbulence could be responsible for the small amplitude vari-ability (Jones et al. 1985; Marscher 2014; Kiehlmann et al.2016). We created a plot of the behaviour of the gamma-ray spec-tral index as a function of time over the entire time-frameof study (see Fig. 8). We use time bins of 7 days; for eachtime bin, we fit 3C 279 spectra as a power-law of the form dNdE = N (cid:32) EE (cid:33) − γ (8)where N is the prefactor, γ is the gamma-ray spectralindex, and E is the energy scale.We test the variability of the gamma-ray spectral indexby fitting a constant value to the calculated spectral indicesover our entire observational period. Under the assumptionthat the gamma-ray spectral index can be represented bya constant value, the best fit shows a chi-square value of χ = 646. Taking into account the degrees of freedom of thefit (N dof = 277), the probability of getting this χ value bychance (estimated with IDL routine MPCHITEST (Mark-wardt 2009)) is P < × − . Such a small probabilitycorresponds to a variability signal of over 11-sigma, thus werejected the hypothesis that the gamma-ray spectral indexdid not vary over the last six years.The variability of the gamma-ray spectral index implieschanges of the energy distribution of the electron populationresponsible for the Inverse Compton effect. The softening of
47 47.5 48 48.5log L γ (erg s -1 )22.53 G a mm a - R a y S p ec t r a l I nd e x Figure 9.
Gamma-ray luminosity vs. the gamma-ray power-lawspectral index. The red line represents the result of the linearfitting performed using the IDL task FITEXY. the spectrum may imply either cooling of the pre-existingelectron population (by synchrotron emission); or the injec-tion of a less energetic electron population to the pre-existingone. The hardening of the spectrum implies an injection ofan energetic electron population (i.e. more energetic thanthe pre-existing one). This result is important in the con-text of a variable SED since the synchrotron spectrum ofthe source will also be affected.Using a sample of 451 blazars, Fan et al. (2012) showedthat there is an anti-correlation between the gamma-ray lu-minosity and spectral index averaged over two years. Be-cause of this, we decided to explore the variability behaviourof 3C 279 in the gamma-ray spectral index vs. gamma-rayluminosity plane. We calculate the gamma-ray luminosityusing equations 1 and 2 from Ghisellini et al. (2009). By ap-plying the Spearman Rank Correlation test we found thatthere is a significant anti-correlation with a correlation co-efficient of -0.28, and a probability of getting this result bychance of ∼ − . We also used the IDL routine FITEXY toconfirm the anti-correlation. We found a statistically signif-icant linear anti-correlation (see Fig. 9), with a probabilityof obtaining the χ value by chance << .
01. This confirmsthe result from the Spearman Rank Correlation test.
We analyze the multiwavelength variability of 3C 279 over atime-frame of six years, using light curves of multiple emis-sion bands from 1 mm up to gamma-rays. We summarizeour results as follows.(i) We identify the simultaneity of the UV λ V -band, and the NIR J -, H -and K -bands, using three cross-correlation analysis meth-ods as described in Section 3. This correlation allowed us tospeculate that the emission from the middle UV range to theNIR are emitted from the same region. We propose that thisemission region is the jet itself or a moving feature along the MNRAS000
We analyze the multiwavelength variability of 3C 279 over atime-frame of six years, using light curves of multiple emis-sion bands from 1 mm up to gamma-rays. We summarizeour results as follows.(i) We identify the simultaneity of the UV λ V -band, and the NIR J -, H -and K -bands, using three cross-correlation analysis meth-ods as described in Section 3. This correlation allowed us tospeculate that the emission from the middle UV range to theNIR are emitted from the same region. We propose that thisemission region is the jet itself or a moving feature along the MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 jet via synchrotron emission. The variable and high P foundin the observations discards the accretion disk as the mainemission source (big blue bump) and further supports thehypothesis of these bands being dominated by synchrotronemission.(ii) We find a significant correlation between the V -bandand the 1 mm emission for the entire time range of the ob-servations used in this paper, with a Spearman correlationcoefficient of 0.65, and a probability of obtaining this corre-lation by chance of P << .
01. This indicates that the op-tical V -band emission should be dominated by non-thermalemission from the jet. The correlation found between the UVcontinuum, V -band, and NIR bands, strongly suggests thatthe emission from these bands is dominated by non-thermalemission. We conclude that the jet dominates the emissionat these wavelengths.(iii) The cross-correlation analysis on the gamma-raysand the UV continuum (therefore, all the way to the NIR)for period A shows a delay of 0.7 ± V -bandand 1 mm emission, we attribute the UV continuum mainlyto emission from the jet. Since our cross-correlation analysisis consistent with no delay between the gamma-ray emissionand the UV, we postulate that they are co-spatial. A correla-tion between jet emission and gamma-ray emission supportsthe hypothesis that the primary high-energy component isInverse Compton emission arising from seed photons in thejet. Therefore, the SSC model better describes our data.It is worth clarifying that we are not concluding that thegamma-ray emission can be explained solely by SSC, as it islikely that we have a contribution from both, SSC and EIC;our results only show that the dominant contribution to thegamma-ray emission is the SSC component.It is important to take into account that even when thereare EIC models that show significant correlations and shortdelays between the optical and gamma-ray bands, thesemodels have the optical total flux dominated by a sourceexternal to the jet (not just the seed photons being domi-nated by the external source, there is a difference betweenthe two scenarios). The rise of polarised flux during thisperiod indicates that the optical total flux is dominated bysynchrotron emission. In the cases where optical total flux isdominated by the same source of seed photons for gamma-rays, a correlation is of course expected. The short delaysusually suggest that the gamma-ray emission region is inthe vicinity of the black hole (e.g. inside the BLR, with atypical radius of 10 - 10 cm, consistent with the models where the shortest delays are obtained). In this case, theshort delay makes total sense.With this in mind, we make an estimation of the shortestexpected delay for EIC in 3C 279, as the light travel time forthe BLR size. B¨ottcher & Els (2016) calculates the radiusof the BLR for 3C 279 as 2 . × cm, which translates to88.8 light days. Taking into account the cosmological timedilation we have an expected time delay of 136.4 days. Evenassuming that the calculation of B¨ottcher & Els (2016) over-estimates the radius by one order of magnitude, this stillleaves us with a minimum delay for EIC that is too largeto be compatible with the observed delay between gamma-rays and UV/Optical/NIR, discarding the possibility of EICbeing the dominant component of gamma-ray emission forPeriod A.(iv) We report period B as an anomalous activity periodin 3C 279 observed from JD ∼ λ V - and NIR bands, as well as thehighest flux levels of 1 mm emission during our entire time-range. However, there is no counterpart in the gamma-rayemission to any of these flares. This was previously reportedby Pati˜no- ´Alvarez et al. (2015). This kind of behaviour hasbeen reported only for one other source. Chatterjee et al.(2013) reported an anomalous flare for the source PKS 0208-512, which was proposed to be caused by a change in themagnetic field in the emitting region without any change indoppler factor or the number of emitting electrons.A possible explanation for this behaviour is a change inopacity in the jet to gamma-ray emission. An ejection of acomponent into the jet is one of the ways flares are created,this could increase the bulk Lorentz factor of the gamma-rayemission region. The increase in the bulk Lorentz factor ofthe jet leads to an increment in the interaction cross-sectionof the electron-positron pair production in the gamma-rayemitting region. This would lead to an increased rate ofgamma-ray absorption that would naturally lead to a lackof observed gamma-ray emission. We consider this to bethe most likely scenario given the evidence that many flaresin AGN with relativistic jets have been linked with ejectedcomponents into the jet (Arshakian et al. 2010; Le´on-Tavareset al. 2010, 2013). In Appendix B, we present theoretical cal-culations of the cross-sections for the inverse Compton scat-tering, and for the electron-positron pair production; andhow the cross-sections change with increasing Lorentz fac-tor. In Appendix B3, we mention a few works whose con-clusions closely relate to the conclusion of this work regard-ing the absorption of gamma-rays via electron-positron pairproduction (Protheroe 1986; Mastichiadis 1991; Zdziarski &Krolik 1993; Petry et al. 2000).Another possibility is the absorption of gamma-rays bythe broad line region. There are multiple works that, viamodelling, show that high energy photons surrounded bythe intense radiation field of the BLR are prone to γγ ab-sorption (e.g., Donea & Protheroe 2003; Reimer 2007; Liuet al. 2008; Sitarek & Bednarek 2008; B¨ottcher et al. 2009;Tavecchio & Mazin 2009; B¨ottcher & Els 2016; Abolmasov& Poutanen 2017, and references therein). Despite the dif-ference in physical parameters and assumptions used in theworks mentioned before, the conclusion is nonetheless thesame, the BLR is an efficient γγ absorber. This has alsobeen considered by several studies as a counter-argument MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. for the gamma-ray emission zone being located inside theBLR in FSRQ (e.g., Tavecchio et al. 2011).(v) At the start of activity period C, from JD ∼ P ; however, we do not find any counterpart inthe spectral range from UV to NIR. Hayashida et al. (2015)described the behaviour of the gamma-ray flares occurringin this time period and modelled the SED of 3C 279 dur-ing the different flares with a leptonic model (Synchrotron+ SSC + EIC). It is clear from the SED models that theEIC dominates the emission over the SSC at the energiesof Fermi-LAT. Such behaviour has been reported before forthe source PKS 1510-089 (Dotson et al. 2015), where theysuggest that the GeV variability is due to an increase of theexternal photon field.In the time range from JD ∼ ± ≥ σ ) between the gamma-raysand the optical R-band, as well as the R-band and radio at37 and 95 GHz. This apparent discrepancy between their re-sults and ours can be reconciled by considering the differenttime frames used in the two studies: Ramakrishnan et al.(2016) used a time consisting of parts of periods B and C.Cross-Correlating time periods where the dominant emis-sion mechanism changes, leads to a diminished significanceof the correlation coefficient.(vi) In general, we can see from the data that polarimetricvariability is common in the active and inactive states ofthe multiwavelength emission of 3C 279. We do not observeany trends of P variability amplitude or timescale in anyparticular activity state or time-frame. It seems that duringsome time periods, P behaves chaotically or randomly, andthis is seen during the quiescent periods of emission in theother bands.We present two main results from our polarimetric ob-servations. Firstly, the behaviour of activity period C is ofspecial interest and secondly, a general result that differenttimescales of variability can distinguish stochastic versus de-terministic variability behaviour.The behaviour of the P A and P during Period C is uniquefor the observational time-frame. P shows a dip at the start of this period, followed by a slow steady increase. The P A is roughly constant during the entire time period, which im-plies that the magnetic field topology is unchanging dur-ing this high level of flaring activity in the other bands (atleast in the optical emitting region). Given the gamma-rayactivity observed during this period, which is often associ-ated with magnetic field topology variability (Marscher &Jorstad 2010), this behaviour indicates that the source ofseed photons for gamma-rays is external to the jet, as con-cluded previously using other observational evidence. Thechanges in polarization degree along with the flaring in theNIR-UV can be explained by transverse shocks in the jet,with a well ordered magnetic field, that does not change themagnetic field topology. Rather, energy is injected by the ac-celeration of particles across the shocks (Marscher & Gear1985; Lyutikov et al. 2004; Nalewajko & Begelman 2012).A chaotic or random behaviour is most easily explainedby invoking a highly variable magnetic field topology andstrength in different regions of the jet, most likely from tur-bulence and instabilities (Jones et al. 1985; Ferrari 1998;Marscher 2014; Kiehlmann et al. 2016) or moving compo-nents (Blinov et al. 2016). Also, during high activity peri-ods where non-thermal emission is involved, the ’active’ ordeterministic P behaviour is superimposed on a ’quiescent’behaviour which is predominantly stochastic (e.g. Marscher2014; Kiehlmann et al. 2016). The data show this effectduring flaring events where the behaviour in P and PA ismore pronounced, indicating the dominance of a determinis-tic component which we deem to be directly related to syn-chrotron emission. While there is little evidence for differenttime-scales of variability, Kiehlmann et al. (2016) also reportthat the changes in the direction of the polarization are dueto deterministic processes. They find that a smooth 360 ◦ swing observed in the data, is not consistent with stochas-tic processes; leading to the conclusion that deterministicprocesses are mainly responsible for this behaviour.(vii) We test the gamma-ray power-law spectral index forvariability by fitting a constant value. The result of the fitshows a χ = 646 . dof = 277, the probability ofgetting this χ value by chance is P ∼ × − , whichmeans that the gamma-ray power-law spectral index in 3C279 has been variable with a significance of over 11- σ overthe past six years. We believe our results conclusively showthat the gamma-ray power-law spectral index has varied overthe studied time-frame. Fan et al. (2012) previously reportedthat spectral index variability is associated with gamma-rayflux variability. Our data supports this, as the source wasvery variable in gamma-ray flux over the time-frame of thestudy. Vercellone et al. (2010) found a trend which suggeststhat a harder gamma-ray SED is observed when an objectis brighter, from a study of the source 3C 454.3, using AG-ILE data. Fan et al. (2012) reported as well that the spectralindex flattened (i.e. a harder spectrum) with higher gamma-ray luminosity for a sample of 451 blazars, using the aver-age of the first two years of Fermi observations found in the2FGL Catalog (Nolan et al. 2012). The trend we find be-tween the gamma-ray spectral index and gamma-ray fluxvariability over the time-frame of study matches the onesmentioned above (see Fig. 9). The physical interpretationof spectral index changes is related to the cooling dynam-ics of emitting particles and the accretion regimes of theobject (Abdo et al. 2010b; Ghisellini et al. 2009). However, MNRAS000
01. This indicates that the op-tical V -band emission should be dominated by non-thermalemission from the jet. The correlation found between the UVcontinuum, V -band, and NIR bands, strongly suggests thatthe emission from these bands is dominated by non-thermalemission. We conclude that the jet dominates the emissionat these wavelengths.(iii) The cross-correlation analysis on the gamma-raysand the UV continuum (therefore, all the way to the NIR)for period A shows a delay of 0.7 ± V -bandand 1 mm emission, we attribute the UV continuum mainlyto emission from the jet. Since our cross-correlation analysisis consistent with no delay between the gamma-ray emissionand the UV, we postulate that they are co-spatial. A correla-tion between jet emission and gamma-ray emission supportsthe hypothesis that the primary high-energy component isInverse Compton emission arising from seed photons in thejet. Therefore, the SSC model better describes our data.It is worth clarifying that we are not concluding that thegamma-ray emission can be explained solely by SSC, as it islikely that we have a contribution from both, SSC and EIC;our results only show that the dominant contribution to thegamma-ray emission is the SSC component.It is important to take into account that even when thereare EIC models that show significant correlations and shortdelays between the optical and gamma-ray bands, thesemodels have the optical total flux dominated by a sourceexternal to the jet (not just the seed photons being domi-nated by the external source, there is a difference betweenthe two scenarios). The rise of polarised flux during thisperiod indicates that the optical total flux is dominated bysynchrotron emission. In the cases where optical total flux isdominated by the same source of seed photons for gamma-rays, a correlation is of course expected. The short delaysusually suggest that the gamma-ray emission region is inthe vicinity of the black hole (e.g. inside the BLR, with atypical radius of 10 - 10 cm, consistent with the models where the shortest delays are obtained). In this case, theshort delay makes total sense.With this in mind, we make an estimation of the shortestexpected delay for EIC in 3C 279, as the light travel time forthe BLR size. B¨ottcher & Els (2016) calculates the radiusof the BLR for 3C 279 as 2 . × cm, which translates to88.8 light days. Taking into account the cosmological timedilation we have an expected time delay of 136.4 days. Evenassuming that the calculation of B¨ottcher & Els (2016) over-estimates the radius by one order of magnitude, this stillleaves us with a minimum delay for EIC that is too largeto be compatible with the observed delay between gamma-rays and UV/Optical/NIR, discarding the possibility of EICbeing the dominant component of gamma-ray emission forPeriod A.(iv) We report period B as an anomalous activity periodin 3C 279 observed from JD ∼ λ V - and NIR bands, as well as thehighest flux levels of 1 mm emission during our entire time-range. However, there is no counterpart in the gamma-rayemission to any of these flares. This was previously reportedby Pati˜no- ´Alvarez et al. (2015). This kind of behaviour hasbeen reported only for one other source. Chatterjee et al.(2013) reported an anomalous flare for the source PKS 0208-512, which was proposed to be caused by a change in themagnetic field in the emitting region without any change indoppler factor or the number of emitting electrons.A possible explanation for this behaviour is a change inopacity in the jet to gamma-ray emission. An ejection of acomponent into the jet is one of the ways flares are created,this could increase the bulk Lorentz factor of the gamma-rayemission region. The increase in the bulk Lorentz factor ofthe jet leads to an increment in the interaction cross-sectionof the electron-positron pair production in the gamma-rayemitting region. This would lead to an increased rate ofgamma-ray absorption that would naturally lead to a lackof observed gamma-ray emission. We consider this to bethe most likely scenario given the evidence that many flaresin AGN with relativistic jets have been linked with ejectedcomponents into the jet (Arshakian et al. 2010; Le´on-Tavareset al. 2010, 2013). In Appendix B, we present theoretical cal-culations of the cross-sections for the inverse Compton scat-tering, and for the electron-positron pair production; andhow the cross-sections change with increasing Lorentz fac-tor. In Appendix B3, we mention a few works whose con-clusions closely relate to the conclusion of this work regard-ing the absorption of gamma-rays via electron-positron pairproduction (Protheroe 1986; Mastichiadis 1991; Zdziarski &Krolik 1993; Petry et al. 2000).Another possibility is the absorption of gamma-rays bythe broad line region. There are multiple works that, viamodelling, show that high energy photons surrounded bythe intense radiation field of the BLR are prone to γγ ab-sorption (e.g., Donea & Protheroe 2003; Reimer 2007; Liuet al. 2008; Sitarek & Bednarek 2008; B¨ottcher et al. 2009;Tavecchio & Mazin 2009; B¨ottcher & Els 2016; Abolmasov& Poutanen 2017, and references therein). Despite the dif-ference in physical parameters and assumptions used in theworks mentioned before, the conclusion is nonetheless thesame, the BLR is an efficient γγ absorber. This has alsobeen considered by several studies as a counter-argument MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. for the gamma-ray emission zone being located inside theBLR in FSRQ (e.g., Tavecchio et al. 2011).(v) At the start of activity period C, from JD ∼ P ; however, we do not find any counterpart inthe spectral range from UV to NIR. Hayashida et al. (2015)described the behaviour of the gamma-ray flares occurringin this time period and modelled the SED of 3C 279 dur-ing the different flares with a leptonic model (Synchrotron+ SSC + EIC). It is clear from the SED models that theEIC dominates the emission over the SSC at the energiesof Fermi-LAT. Such behaviour has been reported before forthe source PKS 1510-089 (Dotson et al. 2015), where theysuggest that the GeV variability is due to an increase of theexternal photon field.In the time range from JD ∼ ± ≥ σ ) between the gamma-raysand the optical R-band, as well as the R-band and radio at37 and 95 GHz. This apparent discrepancy between their re-sults and ours can be reconciled by considering the differenttime frames used in the two studies: Ramakrishnan et al.(2016) used a time consisting of parts of periods B and C.Cross-Correlating time periods where the dominant emis-sion mechanism changes, leads to a diminished significanceof the correlation coefficient.(vi) In general, we can see from the data that polarimetricvariability is common in the active and inactive states ofthe multiwavelength emission of 3C 279. We do not observeany trends of P variability amplitude or timescale in anyparticular activity state or time-frame. It seems that duringsome time periods, P behaves chaotically or randomly, andthis is seen during the quiescent periods of emission in theother bands.We present two main results from our polarimetric ob-servations. Firstly, the behaviour of activity period C is ofspecial interest and secondly, a general result that differenttimescales of variability can distinguish stochastic versus de-terministic variability behaviour.The behaviour of the P A and P during Period C is uniquefor the observational time-frame. P shows a dip at the start of this period, followed by a slow steady increase. The P A is roughly constant during the entire time period, which im-plies that the magnetic field topology is unchanging dur-ing this high level of flaring activity in the other bands (atleast in the optical emitting region). Given the gamma-rayactivity observed during this period, which is often associ-ated with magnetic field topology variability (Marscher &Jorstad 2010), this behaviour indicates that the source ofseed photons for gamma-rays is external to the jet, as con-cluded previously using other observational evidence. Thechanges in polarization degree along with the flaring in theNIR-UV can be explained by transverse shocks in the jet,with a well ordered magnetic field, that does not change themagnetic field topology. Rather, energy is injected by the ac-celeration of particles across the shocks (Marscher & Gear1985; Lyutikov et al. 2004; Nalewajko & Begelman 2012).A chaotic or random behaviour is most easily explainedby invoking a highly variable magnetic field topology andstrength in different regions of the jet, most likely from tur-bulence and instabilities (Jones et al. 1985; Ferrari 1998;Marscher 2014; Kiehlmann et al. 2016) or moving compo-nents (Blinov et al. 2016). Also, during high activity peri-ods where non-thermal emission is involved, the ’active’ ordeterministic P behaviour is superimposed on a ’quiescent’behaviour which is predominantly stochastic (e.g. Marscher2014; Kiehlmann et al. 2016). The data show this effectduring flaring events where the behaviour in P and PA ismore pronounced, indicating the dominance of a determinis-tic component which we deem to be directly related to syn-chrotron emission. While there is little evidence for differenttime-scales of variability, Kiehlmann et al. (2016) also reportthat the changes in the direction of the polarization are dueto deterministic processes. They find that a smooth 360 ◦ swing observed in the data, is not consistent with stochas-tic processes; leading to the conclusion that deterministicprocesses are mainly responsible for this behaviour.(vii) We test the gamma-ray power-law spectral index forvariability by fitting a constant value. The result of the fitshows a χ = 646 . dof = 277, the probability ofgetting this χ value by chance is P ∼ × − , whichmeans that the gamma-ray power-law spectral index in 3C279 has been variable with a significance of over 11- σ overthe past six years. We believe our results conclusively showthat the gamma-ray power-law spectral index has varied overthe studied time-frame. Fan et al. (2012) previously reportedthat spectral index variability is associated with gamma-rayflux variability. Our data supports this, as the source wasvery variable in gamma-ray flux over the time-frame of thestudy. Vercellone et al. (2010) found a trend which suggeststhat a harder gamma-ray SED is observed when an objectis brighter, from a study of the source 3C 454.3, using AG-ILE data. Fan et al. (2012) reported as well that the spectralindex flattened (i.e. a harder spectrum) with higher gamma-ray luminosity for a sample of 451 blazars, using the aver-age of the first two years of Fermi observations found in the2FGL Catalog (Nolan et al. 2012). The trend we find be-tween the gamma-ray spectral index and gamma-ray fluxvariability over the time-frame of study matches the onesmentioned above (see Fig. 9). The physical interpretationof spectral index changes is related to the cooling dynam-ics of emitting particles and the accretion regimes of theobject (Abdo et al. 2010b; Ghisellini et al. 2009). However, MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 Abdo et al. (2010b) reported that the spectral index doesnot generally change with gamma-ray flux variability for alarge sample of
Fermi -LAT sources. They also report a weaktrend in some sources, where the spectral index decreaseswhen the source is brighter. They mention that their ob-servation of nearly constant spectral index does not excludefine variability over short periods of time (such as during aflare). We have shown that the gamma-ray spectral index of3C 279 not only varies during our observational time-frame(see Fig. 8), including periods of flaring activity, but alsothat there is a statistically significant harder-when-brightertrend (see Fig. 9).
In this paper, we also discuss the observed simultaneity ofthe continuum emission from UV to NIR. This implies thatthe emission from these bands is co-spatial during the en-tire time-frame of our study. We also discuss our conclusionthat this continuum is produced by synchrotron emission.The main supporting evidence of this is the dominance of asingle component over a wide wavelength range. Synchrotronemission is one process capable of such behaviour and is themost probable of the emission processes that are inherentto AGN. The non-thermal origin of the emission implies thejet is the source of the emission. It follows that synchrotronemission dominates the part of the spectrum that we con-clude is co-spatial.The flaring we report in activity period A (JD =4650 − = 5850 − = 6400 − ii λ ii λ ACKNOWLEDGMENTS
We thank the anonymous referee for their positive, con-structive and helpful comments. We are thankful to P.Smith for his help on the polarimetry analysis. This workwas supported by CONACyT research grants 151494 and280789 (M´exico). V. P.-A. acknowledges support from theCONACyT program for Ph.D. studies. V.P.-A. and V.C.are grateful to UTSA for their hospitality during theirstay. S.F. acknowledges support from the University ofTexas at San Antonio (UTSA) and the Vaughan fam-ily, support from the NSF grant 0904421, as well as theUTSA Mexico Center Research Fellowship funded by theCarlos and Malu Alvarez Fund. This work has receivedcomputational support from Computational System Biol-ogy Core, funded by the National Institute on MinorityHealth and Health Disparities (G12MD007591) from the Na-tional Institutes of Health. Data from the Steward Observa-tory spectro-polarimetric monitoring project were used; thisprogram is supported by Fermi Guest Investigator grantsNNX08AW56G, NNX09AU10G, and NNX12AO93G. 1 mmflux density light curve data from the Submillimeter Arraywas provided by Mark A. Gurwell. The Submillimeter Ar-ray is a joint project between the Smithsonian AstrophysicalObservatory and the Academia Sinica Institute of Astron-omy and Astrophysics and is funded by the SmithsonianInstitution and the Academia Sinica.
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APPENDIX A: CROSS-CORRELATION FIGURES
MNRAS000
MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 Figure A1.
Cross-correlation functions obtained for the full time-frame of study presented in this work. Bands involved and methodused are shown in each panel. Confidence levels at 90% , 95% and 99% are drawn.MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al.
Figure A2.
Continuation of Fig. A1. Middle panels show the discrepancy in results between the ICCF and the ZDCF methods (is thesame case for the DCCF), that is mentioned in Table 2. MNRAS000
Continuation of Fig. A1. Middle panels show the discrepancy in results between the ICCF and the ZDCF methods (is thesame case for the DCCF), that is mentioned in Table 2. MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 Figure A3.
Same as Fig. A1 for the Period A (JD = 4650 − , 1–31 (2016) Pati˜no- ´Alvarez et al.
Figure A4.
Continuation of Fig. A3. MNRAS000
Continuation of Fig. A3. MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 Figure A5.
Same as Fig. A1 for the Period B (JD = 5850 − , 1–31 (2016) Pati˜no- ´Alvarez et al.
Figure A6.
Continuation of Fig. A5. MNRAS000
Continuation of Fig. A5. MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 Figure A7.
Same as Fig. A1 for the Period C (JD = 6400 − ≥ , 1–31 (2016) Pati˜no- ´Alvarez et al.
Figure A8.
Continuation of Fig. A7. MNRAS000
Continuation of Fig. A7. MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 APPENDIX B: THEORETICAL STUDY OF THE GAMMA-RAY OPACITY IN THE JET OF 3C 279B1 Cross-Section Calculations
B1.1 Electron-Positron Pair Production
The creation of a pair of positive and negative electrons must be interpreted as a transition of an ordinary electron from astate of negative energy to a state of positive energy. The energy necessary to create a pair of free electrons is larger than2 m e c (where m e is the electron mass and c is the speed of light in vacuum). It can be supplied through the absorption of a γ -quantum or by impact of a particle with kinetic energy greater than 2 m e c . Energy and momentum conservation, however,are only possible if another particle is present (for instance, a nucleus). Thus pairs will be created by γ -rays or fast particlesin passing through matter. We consider the most importance case; that is the creation of pairs by γ -rays in the presence of anucleus with charge Z (atomic number).Denoting the energy and momentum of the two electrons by E + , (cid:126)p + , E − , (cid:126)p − , the process in question is the following:a γ -quantum passing through the Coulomb field of the nucleus is absorbed by an electron in the negative state E = − E + , (cid:126)p = (cid:126)p + , then the electron going over into a state of positive energy E − , (cid:126)p − .This process is closely related to the Bremsstrahlung process. The reverse process to the creation of a pair is obviouslythe transition of an ordinary electron in the presence of a nucleus from a state with energy E = E − to a state E = − E + emitting a light quantum, k = E − E = E + + E − (B1)Given that we can see the pair production as a modified version of a Bremsstrahlung process, from Heitler (1954) weobtain the general expression for the Bremsstrahlung differential cross-section as dσ = αZ e π d Ω d Ω k kdk (cid:12)(cid:12)(cid:12)(cid:12)(cid:88) (cid:18) ( u ∗ u (cid:48) )( u (cid:48)∗ α (cid:48) u (cid:48)(cid:48) ) E − E (cid:48) + ( u ∗ α (cid:48) u (cid:48)(cid:48) )( u (cid:48)(cid:48)∗ u ) E − E (cid:48)(cid:48) (cid:19)(cid:12)(cid:12)(cid:12)(cid:12) (B2)Where the u terms refer to matrix elements for the Coulomb interaction matrix, e is the charge of the electron, α is thefine-structure constant and d Ω refers to a differential of solid angle.Pair production differs from ordinary Bremsstrahlung only in that the energy in the final state is negative. Now, thematrix elements for the reverse process are the conjugate complex expressions of those for the direct process. We can thereforetake the cross-section for the creation of a pair directly from the Bremsstrahlung expression. In calculating this, however, wemust insert a density function ρ F for the final state. Since in the case of pair production we have in the final state a positiveand a negative electron, from Heitler (1954) our density function is given by ρ F = ρ E + ρ E − dE + (B3)Furthermore, we have now to divide by the velocity of the incident light quantum (i.e. by c ). Thus, the differentialcross-section has to be multiplied by ρ E + ρ E − dE + ρ E ρ k dk p E = p − dE + k dk (B4)Since (cid:126)p = (cid:126)p − , (cid:126)p = − (cid:126)p + , the angles θ , θ , φ , denoting the direction of the electron in the initial and final state, areconnected with the angles θ + , θ − , φ + , denoting the direction of the positive and negative electron, by θ + = π − θ, θ − = θ , φ + = π + φ (B5)Then putting E = E − , E = − E + , (cid:126)p = (cid:126)p − , (cid:126)p = (cid:126)p + (B6) MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. and inserting Eqs. B4, B5 and B6 in the formula B2, we obtain the differential cross-section for the creation of a pair (cid:126)p + , (cid:126)p − : dσ = − αZ e π p + p − dE + k sin θ + sin θ − dθ + dθ − dφ + q ×× (cid:26) p sin θ + ( E + − p + cos θ + ) (4 E − q ) + p − sin θ − ( E − − p − cos θ − ) (4 E − q )++ 2 p + p − sin θ + sin θ − cos φ + ( E − − p − cos θ − )( E + − p + cos θ + ) (4 E + E − + q − k ) −− k p sin θ + + p − sin θ − ( E − − p − cos θ − )( E + − p + cos θ + ) (cid:27) (B7)where q = ( (cid:126)k − (cid:126)p + − (cid:126)p − ) (B8)Integrating over the angles, the cross-section for the creation of a positive electron with energy E + and a negative onewith energy E − then becomes σ E + dE + = σ p + p − k dE + (cid:26) − − E + E − p + p − p p − ++ µ (cid:18) E + (cid:15) − p + (cid:15) + E − p − (cid:15) + (cid:15) − p + p − (cid:19) + L (cid:20) k p p − ( E E − + p p − ) −− E + E − p + p − − µ k p + p − (cid:18) E + E − − p − p − (cid:15) − + E + E − − p p (cid:15) + + 2 kE + E − p p − (cid:19)(cid:21)(cid:27) (B9)where (cid:15) + = 2 log (cid:18) E + + p + µ (cid:19) , L = 2 ln (cid:18) E + E − + p + p − + µ µk (cid:19) σ = Z r s (B10)In the extreme relativistic case where all energies are large compared with the rest energy of the electron (which appliesto our case) Eq. B9 becomes σ E + dE + = 4 σdE + E + E − + E + E − k (cid:20) ln (cid:18) E + E − kµ (cid:19) − (cid:21) (B11)Applying equipartition, i.e. E + = E − = E /
2, this equation reduces to σ E + = Z r α (cid:26) (cid:20) ln (cid:18) E mc (cid:19)(cid:21) − (cid:27) (B12) B1.2 Inverse Compton Effect
The process we discuss here is the following: A primary light quantum k collides with a free electron which we can assumeto be initially at rest: p = 0 , E = µ ( µ = mc ) (B13)The general case p (cid:54) = 0 can be obtained from the special case of Eq. B13 by a Lorentz transformation. In the final statethe light quantum has been scattered, so that we have a quantum k instead of k . Since the momentum is conserved in theinteraction of light with free electrons, in the final state the electron has a momentum p (energy E ) p = k − k (B14)The conservation of energy states that E + k = k + µ (B15) MNRAS000
The process we discuss here is the following: A primary light quantum k collides with a free electron which we can assumeto be initially at rest: p = 0 , E = µ ( µ = mc ) (B13)The general case p (cid:54) = 0 can be obtained from the special case of Eq. B13 by a Lorentz transformation. In the final statethe light quantum has been scattered, so that we have a quantum k instead of k . Since the momentum is conserved in theinteraction of light with free electrons, in the final state the electron has a momentum p (energy E ) p = k − k (B14)The conservation of energy states that E + k = k + µ (B15) MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 According to Eqs. B14 and B15 the frequency of the scattered quantum cannot be the same as that of the primaryquantum. Using the relativistic relation between momentum and energy p = E − µ and denoting the angle between k and k by θ , we obtain from Eqs. B14 and B15 k = k µµ + k (1 − cos θ ) (B16)which is the well-known formula for the frequency shift of the scattered radiation. In the relativistic case, the frequencyshift increases with the angle of scattering θ .An electron moving with relativistic velocity with a given momentum p can exist in four states, corresponding to the factthat the electron may have either of two spin directions and also a positive or negative energy: E = ± (cid:112) ( p + µ ) (B17)Now, we calculate the transition probability by constructing the transition matrix. The compound matrix element, whichdetermines the transition probability is then given by K FO = (cid:88) (cid:18) H FI H IO E O − E I + H FII H IIO E O − E II (cid:19) (B18)where (cid:80) denotes the summation over all four intermediate states, i.e. over both spin directions and both signs of theenergy. E O , E I , ... represent the total energies in the initial and the intermediate states. The energy differences occurring inthe denominator of Eq. B18 are given by E O − E I = µ + k − E (cid:48) E O − E II = µ + k − ( E (cid:48)(cid:48) + k + k ) = µ − E (cid:48)(cid:48) − k (B19)where E (cid:48) , E (cid:48)(cid:48) represent the energy of the electron in the states I, II, E (cid:48) = ± (cid:112) ( p (cid:48) + µ ) , E (cid:48)(cid:48) = ± (cid:112) ( p (cid:48)(cid:48) + µ ) (B20)If we denote the Dirac amplitudes of the electron with the momenta p , p , p (cid:48) , p (cid:48)(cid:48) by u , u , u (cid:48) , u (cid:48)(cid:48) and the componentsof the matrix vector α in the direction of the polarization of the two light quanta k and k simply by α and α , respectively,from Heitler (1954), the matrix elements for the transitions O → I , etc., are given by H FI = − e (cid:115)(cid:18) π (cid:125) c k (cid:19) ( u ∗ αu (cid:48) ) , H IO = − e (cid:115)(cid:18) π (cid:125) c k (cid:19) ( u (cid:48)∗ α u ) H FII = − e (cid:115)(cid:18) π (cid:125) c k (cid:19) ( u ∗ α u (cid:48)(cid:48) ) , H IIO = − e (cid:115)(cid:18) π (cid:125) c k (cid:19) ( u (cid:48)(cid:48)∗ αu ) (B21)The transition probability per unit time for our scattering process is, w = 2 π (cid:125) | K FO | ρ F (B22)where ρ F denotes the number of final states per energy interval dE F . By conservation of momentum the final state isdetermined completely by the frequency of the scattered quantum k and the angle of scattering. Therefore we have ρ F dE F = ρ k dk (B23)where ρ k denotes the number of states for the scattered quantum per energy interval dk . It would be incorrect, however,to equate the energy intervals dk and dE F . Since the final energy is given as a function of k and θ by E F = k + (cid:112) ( p + µ ) = k + ( k + k − k k cos θ + µ ) (B24)we obtain (cid:18) ∂k∂E F (cid:19) θ = Ekµk (B25) MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. and hence ρ F = ρ k (cid:18) ∂k∂E F (cid:19) θ = d Ω k (2 π (cid:125) c ) Ekµk (B26) d Ω is the element of solid angle for the scattered quantum. Collecting our formulae B18, B19, B21, B22, B26 and dividingby the velocity of light, we obtain the differential cross-section for the scattering process, dσ = e Ek µk d Ω (cid:26) (cid:88) (cid:20) ( u ∗ αu (cid:48) )( u (cid:48)∗ α u ) µ + k − E (cid:48) + ( u ∗ α u (cid:48)(cid:48) )( u (cid:48)(cid:48)∗ αu ) µ − k − E (cid:48)(cid:48) (cid:21)(cid:27) (B27)By evaluating the matrix elements in Eq. B27, we obtain for the summationΣ = 12 µ (cid:20) ( u ∗ αK (cid:48) α u ) k − ( u ∗ α K (cid:48)(cid:48) αu ) k (cid:21) (B28)This can be further simplified by using the wave equation for u , [( α p ) + βµ ] u = E µ . Since p = 0, E = µ ,(1 − β ) u = 0.However, this equation can only be used only when β acts directly on u . Now β anticommutes with α and α and hencethe terms 1 + β vanish and we obtainΣ = 12 µ (cid:26) u ∗ (cid:20) e e ) + 1 k α ( α k ) α + 1 k α ( α k ) α (cid:21) u (cid:27) (B29)The differential cross-section (B27) is proportional to the square of (B29). The value that Eq. B29 takes depends on thespin directions of the electron in the initial and final states. We are not, however, interested in the probability of finding theelectron with a certain spin after the scattering process. We shall therefore sum dφ over all spin directions of the electronafter the scattering process and shall average over the spin directions in the initial state. We must also take into account thatthe number of electrons available for the scatter is proportional to the atomic number ( Z ) of the most abundant elements,because those atoms will be the electron donators for the enviroment. Doing this, the differential cross-section now becomes dσ = 14 Zr d Ω k k (cid:20) k k + kk − Θ (cid:21) (B30)Eq. B30 represents the Klein-Nishina formula (Klein & Nishina 1929) for our specific problem.It is convenient to consider the scattered radiation as composed of two linearly polarized components, one perpendicularand one parallel. Denoting the directions of polarization of k and k by e and e respectively, we can choose the followingdirections for e : • Perpendicular: e perpendicular to e , cos Θ = ( e e ) = 0 • Parallel: e and e in the same plane (i.e. in the ( k , e ) plane),cos Θ = 1 − sin θ cos φ Where φ is the angle between the ( k , k ) plane and the ( k , e ) plane; and θ the angle of scattering ( k , k ).To obtain finally the total intensity scattered into an angle θ we have to take the sum dφ = dφ ⊥ + dφ (cid:107) . Also, substitutingthe fact that Γ = k µ , the differential cross-section becomes: dσ = Zr d Ω 1 + cos θ − cos θ )] (cid:26) (1 − cos θ ) (1 + cos θ )[1 + Γ(1 − cos θ )] (cid:27) (B31)To obtain the total scattering we have to integrate over all angles (solid angles and θ ); this yields to σ IC = 2 πZr (cid:26) (cid:20) − ln(1 + 2Γ) (cid:21) + 12Γ ln(1 + 2Γ) − (cid:27) (B32) MNRAS000
The process we discuss here is the following: A primary light quantum k collides with a free electron which we can assumeto be initially at rest: p = 0 , E = µ ( µ = mc ) (B13)The general case p (cid:54) = 0 can be obtained from the special case of Eq. B13 by a Lorentz transformation. In the final statethe light quantum has been scattered, so that we have a quantum k instead of k . Since the momentum is conserved in theinteraction of light with free electrons, in the final state the electron has a momentum p (energy E ) p = k − k (B14)The conservation of energy states that E + k = k + µ (B15) MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 According to Eqs. B14 and B15 the frequency of the scattered quantum cannot be the same as that of the primaryquantum. Using the relativistic relation between momentum and energy p = E − µ and denoting the angle between k and k by θ , we obtain from Eqs. B14 and B15 k = k µµ + k (1 − cos θ ) (B16)which is the well-known formula for the frequency shift of the scattered radiation. In the relativistic case, the frequencyshift increases with the angle of scattering θ .An electron moving with relativistic velocity with a given momentum p can exist in four states, corresponding to the factthat the electron may have either of two spin directions and also a positive or negative energy: E = ± (cid:112) ( p + µ ) (B17)Now, we calculate the transition probability by constructing the transition matrix. The compound matrix element, whichdetermines the transition probability is then given by K FO = (cid:88) (cid:18) H FI H IO E O − E I + H FII H IIO E O − E II (cid:19) (B18)where (cid:80) denotes the summation over all four intermediate states, i.e. over both spin directions and both signs of theenergy. E O , E I , ... represent the total energies in the initial and the intermediate states. The energy differences occurring inthe denominator of Eq. B18 are given by E O − E I = µ + k − E (cid:48) E O − E II = µ + k − ( E (cid:48)(cid:48) + k + k ) = µ − E (cid:48)(cid:48) − k (B19)where E (cid:48) , E (cid:48)(cid:48) represent the energy of the electron in the states I, II, E (cid:48) = ± (cid:112) ( p (cid:48) + µ ) , E (cid:48)(cid:48) = ± (cid:112) ( p (cid:48)(cid:48) + µ ) (B20)If we denote the Dirac amplitudes of the electron with the momenta p , p , p (cid:48) , p (cid:48)(cid:48) by u , u , u (cid:48) , u (cid:48)(cid:48) and the componentsof the matrix vector α in the direction of the polarization of the two light quanta k and k simply by α and α , respectively,from Heitler (1954), the matrix elements for the transitions O → I , etc., are given by H FI = − e (cid:115)(cid:18) π (cid:125) c k (cid:19) ( u ∗ αu (cid:48) ) , H IO = − e (cid:115)(cid:18) π (cid:125) c k (cid:19) ( u (cid:48)∗ α u ) H FII = − e (cid:115)(cid:18) π (cid:125) c k (cid:19) ( u ∗ α u (cid:48)(cid:48) ) , H IIO = − e (cid:115)(cid:18) π (cid:125) c k (cid:19) ( u (cid:48)(cid:48)∗ αu ) (B21)The transition probability per unit time for our scattering process is, w = 2 π (cid:125) | K FO | ρ F (B22)where ρ F denotes the number of final states per energy interval dE F . By conservation of momentum the final state isdetermined completely by the frequency of the scattered quantum k and the angle of scattering. Therefore we have ρ F dE F = ρ k dk (B23)where ρ k denotes the number of states for the scattered quantum per energy interval dk . It would be incorrect, however,to equate the energy intervals dk and dE F . Since the final energy is given as a function of k and θ by E F = k + (cid:112) ( p + µ ) = k + ( k + k − k k cos θ + µ ) (B24)we obtain (cid:18) ∂k∂E F (cid:19) θ = Ekµk (B25) MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. and hence ρ F = ρ k (cid:18) ∂k∂E F (cid:19) θ = d Ω k (2 π (cid:125) c ) Ekµk (B26) d Ω is the element of solid angle for the scattered quantum. Collecting our formulae B18, B19, B21, B22, B26 and dividingby the velocity of light, we obtain the differential cross-section for the scattering process, dσ = e Ek µk d Ω (cid:26) (cid:88) (cid:20) ( u ∗ αu (cid:48) )( u (cid:48)∗ α u ) µ + k − E (cid:48) + ( u ∗ α u (cid:48)(cid:48) )( u (cid:48)(cid:48)∗ αu ) µ − k − E (cid:48)(cid:48) (cid:21)(cid:27) (B27)By evaluating the matrix elements in Eq. B27, we obtain for the summationΣ = 12 µ (cid:20) ( u ∗ αK (cid:48) α u ) k − ( u ∗ α K (cid:48)(cid:48) αu ) k (cid:21) (B28)This can be further simplified by using the wave equation for u , [( α p ) + βµ ] u = E µ . Since p = 0, E = µ ,(1 − β ) u = 0.However, this equation can only be used only when β acts directly on u . Now β anticommutes with α and α and hencethe terms 1 + β vanish and we obtainΣ = 12 µ (cid:26) u ∗ (cid:20) e e ) + 1 k α ( α k ) α + 1 k α ( α k ) α (cid:21) u (cid:27) (B29)The differential cross-section (B27) is proportional to the square of (B29). The value that Eq. B29 takes depends on thespin directions of the electron in the initial and final states. We are not, however, interested in the probability of finding theelectron with a certain spin after the scattering process. We shall therefore sum dφ over all spin directions of the electronafter the scattering process and shall average over the spin directions in the initial state. We must also take into account thatthe number of electrons available for the scatter is proportional to the atomic number ( Z ) of the most abundant elements,because those atoms will be the electron donators for the enviroment. Doing this, the differential cross-section now becomes dσ = 14 Zr d Ω k k (cid:20) k k + kk − Θ (cid:21) (B30)Eq. B30 represents the Klein-Nishina formula (Klein & Nishina 1929) for our specific problem.It is convenient to consider the scattered radiation as composed of two linearly polarized components, one perpendicularand one parallel. Denoting the directions of polarization of k and k by e and e respectively, we can choose the followingdirections for e : • Perpendicular: e perpendicular to e , cos Θ = ( e e ) = 0 • Parallel: e and e in the same plane (i.e. in the ( k , e ) plane),cos Θ = 1 − sin θ cos φ Where φ is the angle between the ( k , k ) plane and the ( k , e ) plane; and θ the angle of scattering ( k , k ).To obtain finally the total intensity scattered into an angle θ we have to take the sum dφ = dφ ⊥ + dφ (cid:107) . Also, substitutingthe fact that Γ = k µ , the differential cross-section becomes: dσ = Zr d Ω 1 + cos θ − cos θ )] (cid:26) (1 − cos θ ) (1 + cos θ )[1 + Γ(1 − cos θ )] (cid:27) (B31)To obtain the total scattering we have to integrate over all angles (solid angles and θ ); this yields to σ IC = 2 πZr (cid:26) (cid:20) − ln(1 + 2Γ) (cid:21) + 12Γ ln(1 + 2Γ) − (cid:27) (B32) MNRAS000 , 1–31 (2016) ultiwavelength Analysis of the FSRQ 3C 279 Figure B1.
Cross-Sections ( σ ) calculated as function of the Lorentz factor (Γ) for two cases. Left panel: The dominant element in themedium is Carbon. Right panel: The dominant element is Oxygen. Figure B2.
Ratio of the PP to ICS cross-sections calculated as function of the Lorentz factor (Γ) for two cases. Left panel: The dominantelement in the medium is Carbon. Right panel: The dominant element is Oxygen.
B1.3 Cross-Sections Comparison
The cross-sections of both processes, electron-positron Pair Production (PP) and Inverse Compton Scattering (ICS) werecalculated for a wide range of Lorentz factors. In the case of the pair production, the pair production referred is that from theproduced electrons and positrons. We should take into account that both of these quantities depend on the atomic numberof the most abundant element, in the case of the ICS as donators of electrons, and in the case of the PP, as the nucleus thatgives place to the reaction. The calculated cross-sections for both processes can be seen in Fig. B1.For a better appreciation of how the cross-section vary with respect to each other, Fig. B2 shows the ratio of the cross-sections as a function of the Lorentz factor.
B2 Lorentz Factor of the electrons radiating optical emission
The frequency at which the maximum of the synchrotron emission is located, can be found as ν max = 0 . ν c , ν c = c πρ Γ (B33)where ν c is the critical frequency, c is the speed of light in vacuum, Γ is the Lorentz factor of the emitting electron, and MNRAS , 1–31 (2016) Pati˜no- ´Alvarez et al. ρ is the curvature radius.The MOJAVE collaboration measured values of apparent velocity ( β app ) for 3C 279 at different epochs (see Lister et al.2009; Hovatta et al. 2014; Homan et al. 2015; Lister et al. 2016), from which we can calculate Lorentz Factors. We first correctthe apparent velocity by orientation, assuming a jet viewing angle of 2.4 degrees (Hovatta et al. 2009), and then calculate theLorentz factors of the radio emitting electrons. The Lorentz factors obtained are in the range of 1 . − . ∼ −
711 for the optical emitting electrons.As we can see from Fig. B2, the cross-section of the PP is similar to that of the ICS for the lower Lorentz factorsobtained, while it can trump the ICS when looking at the higher Lorentz factors obtained. This supports our hypothesis thatthe electron-positron pair production can produce gamma-ray opacity in the source 3C 279. Unfortunately, all the observationsused above were taken prior to the time-frame of this study.
B3 Comparison with the litetrature
To the knowledge of the authors, there is no work that directly computes the dependence of the cross sections for the twoaforementioned processes to the Lorentz factor. However, there are a number of works whose conclusions closely relate to theconclusion of this work regarding the absorption of gamma-rays via electron-positron pair production.Protheroe (1986) proved that the mean interaction length of electrons for Compton scattering increases with the electronenergy (and therefore the Lorentz factor); which means that Compton interactions are less frequent the higher the energy(and Lorentz factor) of the electron. However, it is also worth mentioning that the calculations were made for interactionwith the photon field of the CMB, and not that of an AGN.Mastichiadis (1991) talks about the triplet pair production ( γe → e ), and how its cross-section increases as ∼ ln (cid:18) γ(cid:15) m e c (cid:19) ,while the cross-section for Compton scattering decreases as ∼ m e c γ(cid:15) . Even when the process is not exactly the same that westudy in this work, this is in general agreement with our results, further supporting the idea of gamma-ray absorption at highLorentz factors.Zdziarski & Krolik (1993) study the gamma-ray emission of the blazar Mrk 421, in which they calculate the gamma-rayopacity due to pair production; and even when the opacity on this source should be lower than 1 in order for theirinterpretation of the spectrum to hold (at least at the observation time), they speculate that internal absorption by pairproduction may be the cause of the absence of TeV gamma-rays in other blazars. They also performed calculations showingthat for a Lorentz factor of 700, and fast emission region expansion ( β exp (cid:38) . MNRAS000