Correlation between optical and γ -ray flux variations in bright flat spectrum radio quasars
MMNRAS , 1–22 (2015) Preprint 7 September 2020 Compiled using MNRAS L A TEX style file v3.0
Correlation between optical and γ -ray flux variations in bright flatspectrum radio quasars Bhoomika (cid:63) , C. S. Stalin , S. Sahayanathan Indian Institute of Astrophysics, Block II, Koramangala, Bangalore 560034, India Astrophysical Sciences Division, Bhabha Atomic Research Centre, Mumbai, India
Last updated 2015 May 22; in original form 2013 September 5
ABSTRACT
Blazars are known to show flux variations over a range of energies from low energy radio to high energy γ -rays. Cross-correlationanalysis of the optical and γ -ray light curves in blazars shows that flux variations are generally correlated in both bands, however,there are exceptions. We explored this optical-GeV connection in four flat spectrum radio quasars (FSRQs) by a systematicinvestigation of their long term optical and γ -ray light curves. On analysis of the four sources, namely 3C 273, 3C 279, PKS1510 −
089 and CTA 102 we noticed different behaviours between the optical and GeV flux variations. We found instances when(i) the optical and GeV flux variations are closely correlated (ii) there are optical flares without γ -ray counterparts and (iii) γ -ray flares without optical counterparts. To understand these diverse behaviours, we carried out broad band spectral energydistribution (SED) modelling of the sources at different epochs using a one-zone leptonic emission model. The optical-UVemission is found to be dominated by emission from the accretion disk in the sources PKS 1510 − γ -ray flux variations are caused by changes in the bulk Lorentz factor ( Γ ), (ii) γ -ray flares without opticalcounterparts are due to increase in Γ and/or the electron energy density and (iii) an optical flare without γ -ray counterpart is dueto increase in the magnetic field strength. Key words: galaxies: active - galaxies: nuclei - galaxies: jets - γ -rays:galaxies Blazars, among the most luminous objects (10 − erg s − ) inthe Universe, are a class of active galactic nuclei (AGN) believed tobe powered by accretion of matter onto super massive black holeswith masses greater than ∼ M (cid:12) situated at the centers of galax-ies (Lynden-Bell 1969; Shakura & Sunyaev 1973). These objectshave relativistic jets oriented close to the line of sight (within a fewdegrees) to the observer and their radiation output is dominated bynon-thermal emission processes (Antonucci 1993; Urry & Padovani1995). They display rapid and large amplitude flux variability overthe entire accessible wavelength band on a range of time scales fromminutes to years (Wagner & Witzel 1995; Ulrich et al. 1997). In addi-tion to flux variations, blazars also show high polarization (Kinmanet al. 1966; Angel & Stockman 1980) and polarization variability(Andruchow et al. 2005; Abdo et al. 2010a; Rakshit et al. 2017; Raniet al. 2018; Pasierb et al. 2020). Blazars are divided into flat spectrumradio quasars (FSRQs) and BL Lac objects (BL Lacs) with FSRQshaving strong emission lines in their optical/infra-red (IR) spectrawhile BL Lacs have either featureless spectra or spectra with weakemission lines, with equivalent widths < (cid:63) E-mail: [email protected] broad line region ( L BLR ) to the Eddington luminosity ( L Edd ) > × − . A two hump structure is evident in the broad band spec-tral energy distribution (SED) of blazars, the low energy componentpeaking in the IR-X-ray band and the high energy component peak-ing in the MeV - GeV band (Fossati et al. 1998; Mao et al. 2016).In the leptonic scenario, the low energy component is attributed tosynchrotron emission process by the relativistic electrons in the jet,while the high energy component is attributed to inverse Compton(IC) process (Abdo et al. 2010d). The seed photons for IC emis-sion could be the synchrotron photons from the jet (synchroton selfCompton SSC; Konigl 1981; Marscher & Gear 1985; Ghisellini &Maraschi 1989) as well as photons exterior to the jet (external comp-ton EC; Begelman et al. 1987). These external photons can be fromthe accretion disk (Dermer & Schlickeiser 1993; Boettcher et al.1997), the BLR (Ghisellini & Madau 1996; Sikora et al. 1994) andthe torus (Błażejowski et al. 2000; Ghisellini & Tavecchio 2008).The observed broad band SED of blazars are generally explainedsatisfactorily by leptonic models, however, there are exceptions,wherein the observed SED is interpreted by hadronic (Mücke et al.2003; Böttcher et al. 2013; Rajput et al. 2019) or lepto-hadronicmodels (Diltz & Böttcher 2016; Paliya et al. 2016). In the hadronicmodels of blazars, the high energy emission is due to synchrotronemission from protons that are accelerated to relativistic energies(Mücke et al. 2003; Aharonian 2000) or from pair cascades initiatedby proton-proton or proton-photon interactions (Mannheim 1993). © 2015 The Authors a r X i v : . [ a s t r o - ph . H E ] S e p Bhoomika et al.
Table 1.
Details of the objects analysed in this work. The mean γ -ray flux in the 100 MeV - 300 GeV band is in units of 10 − ph cm − s − and Γ p is the γ -rayphoton index in the 100 MeV - 300 GeV band. The values of Γ p are from (Ackermann et al. 2015).Name 4FGL name α δ z Γ p γ -ray fluxPKS 1510 −
089 4FGL J1512.8 − − − − Recent observations indicate that a single model might be inade-quate to explain the SED of a source at all times. For example, in thebroad band SED analysis of 3C 279 at various epochs, it has beenfound that leptonic model explains the SED during the March - April2014 flare (Paliya et al. 2015), while the SED during the flare inDecember 2013 is better fit by lepto-hardronic models (Paliya et al.2016). TXS 0506+056 is the first blazar associated with the detectionof neutrinos by the IceCube neutrino observatory on 22 September2017 and this was coincident in direction and time with a γ -ray flarefrom TXS 0506+056. This gives observational evidence of hadronicemission in blazars (IceCube Collaboration et al. 2018). Also, re-cently another blazar has been found to be spatially coincident withthe IceCube neutrino event IC-200107A (Paliya et al. 2020). Thus,it is very clear that we do not yet fully understand the emissionprocesses that contribute to the high energy emission in blazars.Broad band SED modelling of blazars is often used to constrainthe hadronic v/s leptonic scenario for the production of high energy γ -ray emission in them. An alternative to this SED based approachis the one based on carrying out a comparative analysis of the fluxvariations in the optical and γ -ray bands. In the leptonic scenario,as the relativistic electrons in the jets of blazars are responsible forboth the optical and γ -ray emission a close correlation is expectedbetween the optical and γ -ray flux variations (Böttcher 2007). Al-ternatively, in the hadronic model of emission from blazars, thoughthe optical emission is dominated by electron synchrotron, the γ -rayemission could be from proton synchrotron, and therefore, a correla-tion between the optical and γ -ray flux variations may not be expected(Mücke & Protheroe 2001). Thus, by a systematic investigation of thecorrelation between the optical and γ -ray flux variations in a sampleof blazars, it would be possible to constrain the leptonic v/s hardonicemission from blazar jets. An alternative to SED modelling and op-tical - γ -ray studies to distinguish between the leptonic and hadronicscenarios in the high energy emission from FSRQs is through theirX-ray polarization. According to Zhang & Böttcher (2013) X-raypolarization in blazars will be different in these two scenarios. X-ray polarimetric observations in the future from the Imaging X-rayPolarimetry Explorer (IXPE; Weisskopf et al. 2016) will be able toconstrain the origin of high energy emission in blazars.The launch of the Fermi
Gamma-ray Space Telescope (hereinafter
Fermi ; Atwood et al. 2009) in the year 2008 has enabled investiga-tion of the long term γ -ray flux variability characteristics of blazars(Rajput et al. 2020) that dominate the extragalactic γ -ray sky. Priorto Fermi , the availability of long term γ -ray light curves of blazarswere limited. However, today we know about 3000 blazars that aredetected by Fermi (The Fermi-LAT collaboration 2019) and most ofthem have γ -ray light curves spanning more than 10 years suitablefor long term γ -ray variability studies. In support of Fermi , groundbased monitoring observations in the optical and IR are being carriedout by the Small and Moderate Aperture Research Telescope Sys- https://fermi.gsfc.nasa.gov/ssc/data/access/lat/msl_lc/ tem (SMARTS ; Bonning et al. 2009) and the Steward Observatory (Smith et al. 2009). These observations in the optical and IR bandsserve as a valuable data set to study the correlations between theoptical and γ -ray flux variations in blazars. Studies carried out onthese lines have led to varied results. Few studies demonstrated thatthe γ -ray flares in blazars are correlated with optical flares with orwithout lag (Bonning et al. 2009; Chatterjee et al. 2012; Liao et al.2014; Carnerero et al. 2015). However, studies of this kind carried outon more objects have found that the optical and γ -ray flux variationsare not correlated all times and there are objects where γ -ray flaresare detected without an optical counterpart (Vercellone et al. 2011;Dutka et al. 2013; MacDonald et al. 2015). Similarly, prominent opti-cal flares with no corresponding γ -ray flares are also known in someobjects (Chatterjee et al. 2013; Cohen et al. 2014; Rajput et al. 2019).Recently, Liodakis et al. (2019) looked for the presence/absence ofcorrelated optical and γ -ray flux variations in a large sample of Fermi blazars. To further probe the prevalence of anomalous opticaland γ -ray flux variability in blazars and understand their physicalcharacteristics through broad band SED modelling, we carried out asystematic analysis of the γ -ray flux variability of blazars that haveoptical and IR monitoring data available in the archives. Here, wepresent our results on four FSRQs. Results on the BL Lacs analyzedas part of this investigation will be presented elsewhere. In section 2,we provide the details on the selection of the objects for this program.The data used in this work is explained in Section 3 followed by theanalysis in Section 4. The results are presented in Section 5 followedby the summary in the final section. For this work, we first selected all sources that are classified as FSRQsin the third catalog of AGN detected by the large area telescope (LAT)onboard
Fermi (3LAC; Ackermann et al. 2015). For the selectedFSRQs we then looked into their one day binned γ -ray light curvesgiven at the Fermi site and selected those sources that have at leastone flare with the γ -ray flux exceeding 10 − photons cm − s − . Thislead us to a sample of 84 sources. For those 84 sources, we looked atthe archives of SMARTS for the availability of optical and IR dataoverlapping the duration of γ -ray light curves. For 40 out of the 84sources we found data in SMARTS. Of these 40, three sources namely3C 454.3, PKS 1510 −
089 and 3C 279 have the largest number of datapoints in the optical and IR bands with the total exceeding 500. Tothese three, we added two more sources namely CTA 102 and 3C 273due to their high γ -ray activity states (Ciprini 2016; Bastieri 2009).Thus, our final sample for correlated optical - GeV studies consists offive sources. Of these five, results for one source 3C 454.3 is alreadypublished in Rajput et al. (2019). In this work we present our resultson the analysis of the remaining four sources. The details of these http://james.as.arizona.edu/ psmith/Fermi/ https://fermi.gsfc.nasa.gov/ssc/data/access/lat/msl_lc/MNRAS , 1–22 (2015) ptical GeV connection in FSRQs Table 2.
Details of the epochs considered for detailed light curve analysis, SED modelling and spectral analysis. The γ -ray fluxes in the 100 MeV to 300 GeVband are in units of 10 − ph cm − s − and the optical fluxes in the V-band are in units of 10 − erg cm − s − MJD Calendar date Mean fluxName ID Start End Start End γ Optical RemarkPKS 1510 −
089 A 54937 54957 16-04-2009 06-05-2009 2.97 1.07 γ -ray flare with no optical flareB 54951 54971 30-04-2009 20-05-2009 2.26 1.94 γ -ray flare and optical flareC 55757 55777 15-07-2011 04-08-2011 1.10 0.66 γ -ray flare with no optical flareD 56062 56162 15-05-2012 23-08-2012 0.44 0.62 Quiescent stateE 57105 57125 24-03-2015 13-04-2015 3.12 0.95 γ -ray flare with no optical flareF 57157 57177 15-05-2015 04-06-2015 3.17 2.30 γ -ray flare and optical flare3C 273 A 55265 55285 10-03-2010 30-03-2010 1.53 16.9 γ -ray flare with no optical flareB 56450 56550 07-06-2013 15-09-2013 0.40 16.7 Quiescent state3C 279 A 55290 55390 04-04-2010 13-07-2010 0.26 0.14 Quiescent stateB 56742 56762 26-03-2014 15-04-2014 2.21 2.15 γ -ray flare with no optical flareC 57178 57198 05-06-2015 25-06-2015 3.94 1.42 γ -ray flare with no optical flareD 57828 57848 16-03-2017 05-04-2017 2.33 4.25 optical flare but no γ -ray flareCTA 102 A 55840 55940 06-10-2011 14-01-2012 0.31 0.39 Quiescent stateB 57740 57750 18-12-2016 28-12-2016 10.3 44.5 γ -ray flare and optical flare four sources are given in Table 1. A brief description about them aregiven below: − It was identified as a quasar firstly by Bolton & Ekers (1966) with avisual magnitude of 16.5 mag. It is one of the most variable FSRQsin the 3FGL catalog. Located at a redshift of z = 0.361 (Tanner et al.1996), it is powered by a black hole of mass 5.4 × M (cid:12) andaccretes at the rate of 0.5 M (cid:12) /year (Abdo et al. 2010e). It has beendetected at very high energies by HESS (H. E. S. S. Collaborationet al. 2013) and MAGIC (Major Atmospheric Gamma-Ray Imag-ing Cherenkov; Aleksić et al. 2014). This source has been studiedfor multi-wavelength flux variability (Prince et al. 2017; Nalewajko2013) as well as subjected to few SED modelling studies (Princeet al. 2019; Nalewajko et al. 2012). Considering radio observationswith the VLBA coupled with optical long term monitoring data Wuet al. (2005) argued for the presence of a binary black hole in PKS1510 −
3C 273, the first quasar discovered by Schmidt (1963) at a redshift z =0.158 has a large scale radio jet with a projected size of 57 kpc (Harris& Krawczynski 2006). It was the first quasar that was discovered inthe γ -ray band in the energy range of 50 −
500 MeV (Swanenburget al. 1978). It was later detected by the Energetic Gamma- RayExperiment Telescope (EGRET; Hartman et al. 1999) and then by
Fermi . It has been studied for flux variations in the optical (Xionget al. 2017) and also has been found to show dramatic variations inthe γ -ray band from Fermi observations (Abdo et al. 2010c). The γ -ray outburst in 2009 was explained by a time dependent one zonesynchrotron self-Compton model (Zheng et al. 2013). At a redshift of z = 0.536 (Lynds et al. 1965), 3C 279 was amongthe blazars that were discovered as emitters of γ -rays by EGRET(Hartman et al. 1992). In the GeV-TeV range it was first detectedby the ground based atmospheric Cherenkov experiment MAGIC(MAGIC Collaboration et al. 2008). It has been recently suggestedthat 3C 279 hosts a supermassive black hole binary at its center (Qian et al. 2019). The source is found to show flux variations overa range of wavelengths such as radio (Pauliny-Toth & Kellermann1966), optical (Oke 1967) and γ -rays (Hartman et al. 1992). It hasalso been studied for correlated variations over different wavebands(Chatterjee et al. 2008). Fermi observations have revealed minutescale flare in this source with a shortest flux doubling time scalelesser than 5 minutes during the outburst in 2015 (Hayashida et al.2017). In addition to flux variability studies, it has also been studiedvia broad band SED modelling during various activity states. Theflares at different epochs of the source were explained by leptonicprocess (Paliya et al. 2015; Shah et al. 2019), lepto-hardonic process(Paliya et al. 2018) as well as hadronic processes (Petropoulou et al.2017). These observations and subsequent modelling clearly indicatethat the same emission mechanisms are not responsible for the highenergy emission we receive from the source at all times.
This FSRQ at a redshift of z = 1.037 (Schmidt 1965) is highlypolarized (Moore & Stockman 1981) and variable in the opticalband (Maraschi et al. 1986). It was detected in the γ -ray band bothby EGRET (Fichtel et al. 1994) and Fermi (Abdo et al. 2009). It hasbeen studied for flux variations across different wavebands (Kaur &Baliyan 2018) and minute like time scales of variability were detectedin the optical (Osterman Meyer et al. 2009) and γ -ray bands (Shuklaet al. 2018). Our aim in this work is to characterize the connection between opticaland γ -ray flux variations in FSRQs. Therefore, primarily data in boththe optical and γ -ray bands are needed. However, for broad band SEDmodelling, data from other wavelength regions are also required.Thus, for this work we used all the publicly available data in the IR,optical, UV, X-rays and γ -rays that span a period of 10 years between08 August 2008 and 08 August 2018. Optical polarimetric data ifavailable during the above period was also used. MNRAS , 1–22 (2015)
Bhoomika et al.
Figure 1.
Light curves of the source PKS 1510 − γ -ray light curve (in units of 10 − ph cm − s − ), the second panel fromthe top is the X-ray light curve (in units of counts/sec), the next two panels are the optical (in units of 10 − erg cm − s − ) and the IR (in units of 10 − erg cm − s − ) light curves and the bottom panel is the optical V-band polarization. The peak of either the optical or γ -ray light curve is shown by red dotted lines,while the two black solid lines on either side of the red line correspond to a width of 10 days each. The two blue lines show the quiescent period of 100 days.For the γ -ray light curve, upper limits are not shown and only points with TS > We used the
Swift -UV-Optical Telescope (UVOT) for data in theUV and optical bands. They were analyzed using the online tool .To generate the light curve the magnitudes thus obtained and uncor-rected for Galactic reddening were then converted to fluxes usingthe zero points taken from Breeveld et al. (2011). However correc-tions due to galactic absorption were applied to generate the averagedata points for SED analysis. In addition to the optical data from Swift -UVOT, we also used optical data in the V-band from bothSMARTS and the Steward Observatory, while the IR observations inthe J and K-bands were taken from SMARTS. Optical polarizationdata whereever available were taken from the Steward Observatory.The details of the instrument and the data reduction procedures forSMARTS can be found in Bonning et al. (2012), while the details onthe observations and reductions of data from Steward Observatorycan be found in Smith et al. (2009). We used data from the X-ray telescope (XRT) on board
Swift coveringthe energy range from 0.3 −
10 keV (Burrows et al. 2005; Gehrelset al. 2004). The data that spans about 10 years and covering theperiod August 2008 to August 2018 were taken from the archivesat HEASARC . The data were analyzed by the instrument pipleinefollowing standard procedures. For light curve analysis, we used thedata collected using both window timing (WT) and photon counting(PC) modes. For spectral analysis of the sources PKS 1510 − γ -ray flaring state we used the WT mode data due tothe non availability of PC mode data. The XRT data were processedwith the xrtpipeline task using the latest CALDB files availablewith version HEASOFT-6.24. We used the standard grade selection0-12 and the calibrated and cleaned events were added to generatethe energy spectra. For PC mode, we extracted the source spectrafrom a circular region of radii 60 (cid:48)(cid:48) , and the background spectra wereselected from the region of radii 80 (cid:48)(cid:48) away from the source. In WTmode, for the source we used a circular region of 60 (cid:48)(cid:48) radii while https://heasarc.gsfc.nasa.gov/docs/archive.htmlMNRAS000
10 keV (Burrows et al. 2005; Gehrelset al. 2004). The data that spans about 10 years and covering theperiod August 2008 to August 2018 were taken from the archivesat HEASARC . The data were analyzed by the instrument pipleinefollowing standard procedures. For light curve analysis, we used thedata collected using both window timing (WT) and photon counting(PC) modes. For spectral analysis of the sources PKS 1510 − γ -ray flaring state we used the WT mode data due tothe non availability of PC mode data. The XRT data were processedwith the xrtpipeline task using the latest CALDB files availablewith version HEASOFT-6.24. We used the standard grade selection0-12 and the calibrated and cleaned events were added to generatethe energy spectra. For PC mode, we extracted the source spectrafrom a circular region of radii 60 (cid:48)(cid:48) , and the background spectra wereselected from the region of radii 80 (cid:48)(cid:48) away from the source. In WTmode, for the source we used a circular region of 60 (cid:48)(cid:48) radii while https://heasarc.gsfc.nasa.gov/docs/archive.htmlMNRAS000 , 1–22 (2015) ptical GeV connection in FSRQs MJD(Days) +5.493e4 F g a mm a
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Figure 2.
Multi-wavelength light curves for epochs A (top left), B (top right), C (bottom left) and D (bottom right) for the source PKS 1510 − γ -ray fluxes are in units of 10 − ph cm − s − . The optical fluxes are in units of 10 − erg cm − s − and the IR fluxes are in the units of 10 − erg cm − s − . The vertical dotted line shows the peak of the optical/ γ -ray flare. MNRAS , 1–22 (2015) Bhoomika et al.
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Figure 3.
Muti-wavelength light curves for the source PKS 1510 −
089 during epochs E (left) and F (right). Symbols and lines are as in Fig. 2. for the background we used the region between 80 (cid:48)(cid:48) and 120 (cid:48)(cid:48) radiicentered around the source. We combined the exposure maps using
XIMAGE and created the ancillary response files using xrtmkarf . Forfitting the data within XSPEC (Arnaud 1996), we used an absorbedsimple power law model with the Galactic neutral hydrogen columndensities of N H = 6.89 × cm − , 2.21 × cm − , 4.81 × cm − and 1.68 × cm − from Kalberla et al. (2005) for the sourcesPKS 1510 − χ statistics within XSPEC and the uncertainties were calculated atthe 90% confidence level. γ -ray data We analyzed 10 years of γ -ray data from the LAT instrument onboard Fermi during the period 08 August 2008 to 08 August 2018to generate the one day binned γ -ray light curve. The LAT is animaging high energy γ -ray telescope, sensitive in the energy rangefrom 20 MeV −
300 GeV. The field of view of the LAT instrumentis 20% of the sky and it scans continuously, covering the wholesky every three hours (Atwood et al. 2009). We used fermipy toanalyze the 10 years of γ -ray data. Fermipy is a python softwarepackage that provides a high-level interface for LAT data analysis(Wood et al. 2017). We used Pass 8 data for the analysis wherethe photon-like events are classified as ’evclass=128, evtype=3’with energy range 0.1 (cid:54) E (cid:54)
300 GeV. A circular region of interest(ROI) of 15 ◦ was chosen with a zenith angle cut of 90 ◦ in orderto remove Earth limb contamination. We used the latest isotropicmodel "iso_P8R2_SOURCE_V6_v06" and the Galactic diffuse emission model "gll_iem_v06" for the analysis. The recommendedcriteria "(DATA_QUAL>0)&&(LAT_CONFIG==1)" was used forthe good time interval selection. In the generation of γ -ray lightcurves, we considered the source to be detected if the test statistics(TS) is > σ detection (Mattox et al. 1996). Analysis for the presence or absence of correlation between opticaland γ -ray flares requires identification of flares in optical and/or γ -ray light curves. Due to large gaps and/or less number of points in theoptical light curves it is not possible to automatically identify epochs(through cross-correlation analysis) on the presence or absence ofcorrelated optical and γ -ray flux variations. Therefore, flares fordetailed analysis were selected visually as follows. Multi-wavelengthlight curves that span the 10 year period were first generated for eachobject. In that, optical and γ -ray light curves were visually inspectedfor the presence of sharp peaks above their base flux levels. Onceidentified, expanded multiwavelength light curves were generated fora total duration of 20 days, centered at the optical and/or γ -ray flares.In an epoch when a γ -ray flare or an optical flare is identified, weimposed the condition of having data in multiple wavelengths suchas γ -rays, X-rays, UV, optical and IR so as to constrain both the lowenergy and high energy hump in the SED analysis. These conditions MNRAS , 1–22 (2015) ptical GeV connection in FSRQs Figure 4.
Multi-wavelength light curves of the source 3C 273. The panels and the vertical lines are as in Fig.1 lead to the identification of few flares. Of these we concentrated onlyon some epochs for each object. − The multi-wavelength light curves that include γ -ray, X-ray, UV,optical and IR are given in Fig. 1. The figure also includes polarizationmeasurements. Inspection of the light curves indicates that the sourcehas displayed varied activity levels that includes both flaring andquiescent periods. From visual inspection of the light curves weselected 6 epochs (A, B, C, D, E and F) in the source for studying thecorrelations between optical and γ -ray variations. These epochs wereidentified by the presence of optical and/or γ -ray flares in the lightcurves and a quiescent state in both the optical and γ -ray bands. Asummary of these epochs is given in Table 2 and the multi-wavelengthlight curves covering a shorter duration during these epochs areshown in Fig. 2 and Fig. 3. More details on these six epochs aregiven below: Epoch A:
During this epoch, the γ -ray has increased in flux by afactor of about 10, while the optical and the IR J and K-band fluxeshave not shown any variability and are indeed steady. There is alsoa hint that the X-ray flux from the source is non-variable, however,due to the lack of data during part of the γ -ray flare, no conclusivestatement could be made on the nature of X-ray flux variations. Theoptical polarization too has not shown noticeable variability during the steady optical/IR brightness state of the source. We conclude thatin this epoch we observed a γ -ray flare with no optical counterpart. Epoch B:
During this epoch, the optical flux has increased by a factorof 6, while the flux variations in the IR band are at a reduced level.There is also a hint of a very low amplitude γ -ray flare during thepeak of the optical flare, but it is very small. The lack of X-ray dataand optical polarization data during the epoch of the optical flareprevents us to make any statement on the nature of X-ray variationsas well as the degree of optical polarization during this epoch. Thusin this epoch the source has shown correlated optical and γ -ray fluxvariations, though the amplitude of variations in the γ -ray band ismuch lower than that of the optical and IR bands. Epoch C:
The flux variations noticed in this epoch is similar to thatobserved during epoch A. A minor flare is observed in the γ -rayband, but the source is stable in the X-ray, optical and IR bands. Wedo not have optical polarization data during the γ -ray flare for anidea on the nature of optical V-band polarization. Thus, during thisepoch, the source has shown a γ -ray flare without a counterpart inthe low energy X-ray, optical and IR bands. Epoch D:
During this period, the source is in the quiescent state inall the energy bands analyzed here.
Epoch E:
During this epoch, the source has shown a strong γ -rayflare, however, such a flare is not seen in the X-ray, optical and IRbands. Here too, optical polarization data is not available during theperiod of the γ -ray flare. Thus, in this epoch, the source has shown MNRAS , 1–22 (2015)
Bhoomika et al.
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Figure 5.
Light curves of 3C 273 for epoch A (left panel) and epoch B (right panel). The γ -ray fluxes are in units of 10 − ph cm − s − and the optical and IRfluxes are in units of 10 − erg cm − s − . The vertical dotted line shows the peak of the γ -ray flare. a γ -ray flare without similar flaring in the other wavelengths such asX-rays, optical and IR. Epoch F:
A weak γ -ray flare is seen in the source during this period.Simultaneous to the γ -ray flare, there is an indication of a minoroptical flare which is also accompanied by an increase in the degreeof optical polarization. There is paucity of X-ray and IR data duringthe peak of the γ -ray flare. Thus, the optical and γ -ray flux variationsare closely correlated during this epoch. We show in Fig. 3 the multi-wavelength light curves for the source 3C273. The source is mostly quiescent during the period 2008 to 2018August except for few instances where it has flared in the γ -ray band.We identified two epochs in this source for studying the correlationbetween optical and γ -rays. The details of these two epochs are givenin Table 2. They are also marked in Fig. 4, and an expanded versionof these two epochs is given in Fig. 5. Epoch A:
There is a prominent γ -ray flare during this epoch, whereinthe γ -ray flux has increased by a factor of two at the peak of the γ -rayflare. During the peak of the γ -ray flare, the X-ray, optical and IRbrightness do not show significant changes. Also, the source lacksoptical polarization data during the peak of the γ -ray flare. The sourcehas thus shown a γ -ray flare without an optical counterpart in thisepoch. Epoch B:
During this epoch the source is found to be in the quiescentstate in all the wavebands namely γ -rays, X-ray, optical and IR. The source is also weakly polarized in the optical V-band during thisperiod. We show in Fig. 6 the multi-wavelength light curves. From visualinspection, we identified four epochs in this source for studying thecorrelation between optical and γ -ray flux variations. We give inTable 2 the summary of those four epochs. An expanded view of themulti-wavelength flux variations in the source is shown in Fig. 7.Below, we summarize the salient aspects of these four epochs. Epoch A:
In this epoch the source is in the quiescent state. In theone day binned γ -ray light curve the source is below the detectionlimit for many days during this 100 days period. Also, in the X-ray,optical and IR bands, the source is non-variable during this period.However, during the middle of this epoch, the optical polarizationincreased by a factor of about 5 from ∼
6% to ∼ Epoch B:
During this epoch, the source has shown a minor flare inthe γ -ray band with no corresponding flare in the optical, IR andX-ray bands. Polarization data is not available during the peak ofthe γ -ray flare thereby making it impossible to know the polarizednature of the source. By comparing the multi-wavelength light curvesduring this epoch, we conclude that the source showed a γ -ray flarewithout an optical counterpart. Epoch C:
During this epoch, a strong γ -ray flare was observedwherein the γ -ray flux increased by a factor of about 3. During the MNRAS000
During this epoch, a strong γ -ray flare was observedwherein the γ -ray flux increased by a factor of about 3. During the MNRAS000 , 1–22 (2015) ptical GeV connection in FSRQs Figure 6.
The light curves of the source 3C 279 in different wavelengths. The panels and the dashed lines are as in Fig. 1. peak of the γ -ray flare, X-ray too showed a flare, however, in theoptical and IR bands, the source was found to be stable with no signsof flux variability. An interesting behaviour displayed by this sourceis an apparent negative correlation of γ -ray and X-ray flux variationsto the optical polarization. During the epoch when the γ -ray andX-ray were at their peaks, the optical polarization was low, and itgradually increased when the X-ray and γ -ray fluxes declined. Epoch D:
During this epoch, the source showed a prominent opticaland IR flare. The flare was found be be asymmetric with a fast riseand slow decay. During the epoch of the optical and IR flare thesource did not show any variation in the γ -ray band. Due to the lackof polarization data during the peak of the optical and IR flare, wecould not make any statement on the optical polarization state duringthe time of the optical and IR flare. Thus this epoch is a clear exampleof the source showing an optical flare without a γ -ray counterpart. The source was found to be in a steady and low brightness stateduring most of the time between 2008 August to 2018 August, exceptfor a spectacular γ -ray flare in the beginning of 2016. The multi-wavelength light curves are shown in Fig. 8. We have identified 2epochs in this source for studying the correlation between optical and γ -ray variations. A summary of these two epochs is given in Table2 and expanded plots of these two epochs are shown in Fig. 9. Moredetails on these two epochs are given below. Epoch A:
During this epoch the source was in the quiescent state inall the wavebands considered in this work.
Epoch B:
The source showed a major γ -ray flare during this epoch.This flaring in the γ -ray band was also accompanied by flaring be-haviour in the X-ray and optical wavelengths. The nature of IR fluxduring this period is uncertain due to the non-availability of IR dataduring this flaring period. Thus, during this epoch, the source showedcorrelated flux variations in the optical and γ -ray bands. Blazars show spectral variations in addition to flux variations. Tocharacterize the spectral variability of the blazars studied here, welooked for variations in the V − J color against the V-band brightness.This spectral analysis was done for all the epochs in the sourcesPKS 1510 − γ -ray flux variations were explored in Section 4.1. Suchspectral analysis was not carried out for the source CTA 102 dueto the lack of J-band data. Spectral variations were characterized bylinear least squares fit to the colour-magnitude diagram by takinginto account the errors in both the colour and magnitude. A sourceis considered to have shown colour variation if the Spearman rankcorrelation coefficient is > . < − < − MNRAS , 1–22 (2015) Bhoomika et al.
MJD(Days) F g a mm a
1e 5 1 day binned F X r a y XRT PC modeXRT WT mode MJD(Days) F O p t i c a l
1e 10 STEWARD VSMARTS V MJD(Days) F I R
1e 10 SMARTS JSMARTS K P . D . ( % ) Pol. Degree MJD(Days) +5.674e4 F g a mm a
1e 5 1 day binned +5.674e4 F X r a y XRT PC modeXRT WT mode MJD(Days) +5.674e4 F O p t i c a l
1e 10 STEWARD VSMARTS V MJD(Days) +5.674e4 F I R
1e 10 SMARTS JSMARTS K +5.674e4 P . D . ( % ) Pol. DegreeMJD(Days) +5.717e4 F g a mm a
1e 5 1 day binned +5.717e4 F X r a y XRT PC modeXRT WT mode MJD(Days) +5.717e4 F O p t i c a l
1e 10 STEWARD VSMARTS V MJD(Days) +5.717e4 F I R
1e 10 SMARTS JSMARTS K
10 15 20 25MJD(Days) +5.717e4 P . D . ( % ) Pol. Degree MJD(Days) +5.782e4 F g a mm a
1e 5 1 day binned+5.782e4 F X r a y XRT PC modeXRT WT modeMJD(Days) +5.782e4 F O p t i c a l
1e 10 STEWARD VSMARTS VMJD(Days) +5.782e4 F I R
1e 10 SMARTS JSMARTS K
10 15 20 25MJD(Days) +5.782e4 P . D . ( % ) Pol. Degree
Figure 7.
Multi-wavelength light curves of the source 3C 279 for epoch A (top left), epoch B (top right), epoch C (bottom left) and epoch D (bottom right). Theoptical and IR light curves have units of 10 − erg cm − s − , while the γ -ray light curves have units of 10 − ph cm − s − . The dashed lines indicate the peak ofthe optical/ γ -ray flare.MNRAS000
Multi-wavelength light curves of the source 3C 279 for epoch A (top left), epoch B (top right), epoch C (bottom left) and epoch D (bottom right). Theoptical and IR light curves have units of 10 − erg cm − s − , while the γ -ray light curves have units of 10 − ph cm − s − . The dashed lines indicate the peak ofthe optical/ γ -ray flare.MNRAS000 , 1–22 (2015) ptical GeV connection in FSRQs Figure 8.
Long term light curves of the source CTA 102 in different wavelengths. Details in this figure are similar to that of Fig. 1. behaviour. In the source 3C 273, during epoch A, we found thesource to show a RWB trend. For the source 3C 279, we foundBWB behaviour during epochs B and D. This indicates that thespectral variations shown by FSRQs are complex and a FSRQ maynot show the same spectral variability pattern at all times. The colourmagnitude diagram for the sources PKS 1510 − γ -ray spectra To study the intrinsic distribution of electrons in the jets that areinvolved in the γ -ray emission process, we generated γ -ray spectrafor all the selected epochs (as detailed in Section 4.1) of the foursources. We fitted the γ -ray spectra with the two models namely(i) the simple power law (PL) model and (ii) the log-parabola (LP)model. For PL model we used the following dN ( E )/ dE = N ◦ ( E / E ◦ ) Γ PL (1)where N ◦ is the normalization of the energy spectrum and E ◦ is thescaling factor and Γ PL is the photon index.The LP model has the following form (Nolan et al. 2012) dN ( E )/ dE = N ◦ ( E / E ◦ ) − α − β ln ( E / E ◦ ) (2)where, dN/dE is the number of photons in cm − s − MeV − , α isphoton index at E ◦ , β is the curvature index that defines the curvaturearound the peak, E is the energy of the γ -ray photon, N ◦ is thenormalization and E ◦ is the scaling factor. To test the model that well describes the γ -ray spectra (PL againstLP), as well as the presence of curvature, we used the maximumlikelihood estimator gtlike . Following Nolan et al. (2012), we cal-culated the curvature of the test statistics as T S curve = 2(log L LP - log L PL ). Here L represents the likelihood function. We used thethreshold T S curve > 16 for the presence of a statistically significantcurvature in the γ -ray spectra, (at the 4 σ level; Mattox et al. 1996).We found that for all the epochs, the γ -ray spectra is well fit by theLP model except for the quiescent epoch of the source 3C 273 whichis well fit by the PL model. The results of the γ -ray spectral analysisare given in Table 3. One example of the PL model that best fits thedata (for the source 3C 273 at Epoch B) and another example of aLP model that best fits the data (for the source 3C 279 at Epoch C)is shown in Fig. 11. The sources studied here showed various characteristics in their op-tical and γ -ray flux variations. There are instances when (a) opticaland γ -ray flux variations are correlated, (b) there is an optical flarewithout a γ -ray counterpart and (c) there is a γ -ray flare without anoptical counterpart. To further characterize the nature of the sourcesduring the various epochs, we constructed their broad band SED dur-ing these epochs and studied them using simple one zone leptonicemission model. To obtain the SEDs in UV, optical and IR, all photo-metric measurements during each epoch were averaged filter wise to MNRAS , 1–22 (2015) Bhoomika et al.
MJD(Days) F g a mm a
1e 5 1 day binned F X r a y XRT PC modeXRT WT mode MJD(Days) F O p t i c a l
1e 10 STEWARD V MJD(Days) F I R
1e 11 SMARTS J P . D . ( % ) Pol. Degree MJD(Days) +5.774e4 F g a mm a
1e 5 1 day binned +5.774e4 F X r a y XRT PC modeXRT WT mode MJD(Days) +5.774e4 F O p t i c a l
1e 10 STEWARD V MJD(Days) +5.774e4 F I R
1e 11 SMARTS J +5.774e4 P . D . ( % ) Pol. Degree
Figure 9.
The left and right panels show the multi-wavelength light curves of the source CTA 102 for epoch A and B respectively. The dashed line shows thepeak of the γ -ray flare. The optical and γ -ray fluxes are in units of 10 − erg cm − s − and 10 − ph cm − s − respectively. Table 3.
Details of the PL (Eq. 1) and LP (Eq. 2) model fits for the different epochs of the sources PKS 1510 − Γ PL is thephoton index from PL fitting, α and β the photon index and curvature index from LP fit to the spectra, TS is the test statistics, Log L is the log-likelihood, and T S curve is the curvature of the test statistics defined as 2(log L L P - log L PL ). For all the epochs in the sources PKS 1510 − Γ PL Flux TS − Log L α β
Flux TS − Log L TS curve
PKS 1510-089A -2.41 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±000
PKS 1510-089A -2.41 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±000 , 1–22 (2015) ptical GeV connection in FSRQs V - J PKS 1510-089(Epoch A)
PKS 1510-089(Epoch E)
PKS 1510-089(Epoch F) V - J
3C 273(Epoch A)
3C 279(Epoch B)
14 15V magnitude2.22.32.42.52.6
3C 279(Epoch D)
Figure 10.
Colour-magnitude relations. From the left, the top panels are for the source PKS 1510 − Energy[GeV]10 E d N / d E [ e r g c m s ] Epoch B(Quie) logparabola fitpowerlaw fit 10 Energy[GeV]10 E d N / d E [ e r g c m s ] (Epoch C) logparabola fitpowerlaw fit Figure 11.
Observed and model fits to the γ -ray spectra of the source 3C 273 for epoch B (left panel) and of 3C 279 for epoch C (right panel). get one photometric point per epoch. In the case of X-ray and γ -raybands, all the data in each epoch were used to generate the averageX-ray and γ -ray spectra.Modelling the time averaged spectral energy distribution duringvarious epochs under different emission mechanisms can help us tounderstand the physical conditions in the source. The γ -ray emissionfrom FSRQs is generally interpreted as the external Compton scat- tering of thermal IR photons (Shah et al. 2019; Rajput et al. 2019)and hence the broad band SEDs are modeled using synchrotron, syn-chrotron self Compton and external Compton emission processes.The details of the model are given in Sahayanathan et al. (2018) andthe best fit physical parameters of the sources are obtained by fittingthe broad band SED using χ minimization technique. We added12% systematics to the data in order to account for the emission MNRAS , 1–22 (2015) Bhoomika et al. model related uncertainties. There are twelve free parameters in ourmodel, of which six parameters govern the electron energy distri-bution, namely electron energy index before the break (p), electronenergy index after the break (q), the break Lorentz factor ( γ b ), mini-mum Lorentz factor of the electron distribution ( γ min ), the maximumLorentz factor of the electron distribution ( γ max ) and the electronenergy density ( U e ). The other six parameters in the model are themagnetic field (B), size of the emission region (R), Lorentz factor( Γ ), jet viewing angle ( θ ), external photon field temperature (T) andthe fraction of the external photons that take part in the EC process(f). In order to investigate the different flaring behaviour betweenoptical and γ -ray, firstly we fitted the quiescent epoch to obtain theparameters for all the sources. From the observed SED, we couldobtain the high and low energy spectral indices, the synchrotron fluxin the optical, the SSC and EC fluxes in the X-ray and γ -ray energiesrespectively. Consistently for the model fit, we chose five free param-eters namely p, q, U e , Γ and B while the other parameters were frozento typical values. The adopted values of the seven frozen parametersfor the four sources are given in Table 4. In Table 5 and Figure12 toFigure 16, we summarize the results of the fitting. From the residualsgiven in the bottom panel of the Figures for some sources, it is clearthe optical data is steeper and deviate significantly from the best fitmodel. This suggests the presence of more than one emission com-ponent at optical/UV energies.To account for the deviation of the model from the optical spectra,we modified the model by including the emission from the accretiondisk. The thermal emission from the disk is decided by two parame-ters, namely the central black hole mass and the mass accretion rate(Shakura & Sunyaev 1973; Jolley & Kuncic 2008). The mass of theblack hole is obtained from Chen (2018) and the accretion rate isfitted to reproduce the optical spectra. This procedure significantlyimproved the resultant χ and the best fit parameters are given inTable 5. The model spectrum along with the observed data are givenin Fig. 12 to 16 . Through this exercise we also demonstrate thecapability to extract the accretion disk component from the broad-band SED through a realistic spectral modelling involving differentemission mechanisms. γ -ray spectra The high energy γ -ray spectra of FSRQs and low synchrotron peakedBL Lacs deviate from the power law behaviour and are phenomeno-logically better represented either as a broken power law (BPL) or aLP model. Such departures from simple PL fits noted as a commonfeature in FSRQs firstly in the early observations from Fermi -LAT(Abdo et al. 2010b) are now observed in the high energy spectra ofseveral FSRQs (Harris et al. 2014; Paliya et al. 2015; Rajput et al.2019; Sahakyan 2020). The cause of the spectral curvature seen inthe γ -ray spectra from Fermi -LAT is still not known. Several scenar-ios, both intrinsic and extrinsic origins are proposed in the literatureto explain the break in the γ -ray spectrum of FSRQs.One of the causes could be due to the attenuation of γ -rays byphoton-photon pair production within the BLR due to HeII recombi-nation and HI recombination. In this scenario termed as the doubleabsorber model (Poutanen & Stern 2010), one expects to see a breakaround 4 − −
30 GeV. Such anobservation would imply absorption of γ -rays by BLR photons andthe γ -ray production site must lie within the BLR. However, observa-tions do not support the double absorber model (Harris et al. 2012). Alternatively, the break in the GeV spectra of FSRQs can happenby Klein-Nishina effect on the inverse Compton scattering of BLRphotons by relativistic jet electrons with a curved distribution (Cer-ruti et al. 2013). But, from an analysis of the γ -ray spectra of a largenumber of blazars, Costamante et al. (2018) found that in FSRQs,the observed γ -ray spectra is not by IC scattering of BLR photonsand the γ -ray emission site lies outside the BLR.Apart from the above, the break in the γ -ray spectra of FSRQs canalso happen due to intrinsic effects because of the electrons in therelativistic jets of these sources either having a cut-off in their energydistribution or a log-parabola energy distribution. In this work, theSEDs of all the sources in the different epochs are well modelled byIC scattering of the photons from the obscuring torus, and the γ -rayemission region lies outside the BLR where IC takes place in theThomson regime. The results of the γ γ -ray spectra of all the sources studied here are better described by theLP model than the PL model. In this work, the γ -ray spectra of allthe sources at all the epochs are better described by the LP modelexcept for epoch B of 3C 273, which is well fit by the PL model.The parameters α and β in the LP model fits to the data carry veryimportant information on the characteristics of the γ -ray spectra. Inthis model, α gives the slope of the spectra and β is a measure of thecurvature in the spectra. A smaller value of α and β implies a harderspectrum with a mild curvature. Any changes in the value of α and β during different epochs is a measure of the changes in the γ -rayspectral shape. The dependence of α and β values against the fluxesof the sources are given in Fig. 17. For all the sources we found thespectra to harden with increasing flux. We found decreasing as wellas increasing trend of β with flux. The variation in the γ -ray spectralshape can be associated with the shift in IC peak frequency. Thisis evident from the results of our SED analysis. Our model fits tothe observed SED also gives the IC peak frequency (see Table 5).Analysis of the IC peak indicates that as the IC peak shifts towardslower energies, the spectrum is harder and the curvature ( β ) is sharperwhich too demonstrates that the γ -ray spectral variation is closelyrelated to the changes in the IC peak. Alternatively, γ -ray spectralvariation can also be attributed to the changes in the location of the γ -ray emission region during different activity states of the sources(Coogan et al. 2016). Besides, since the γ -ray emission in FSRQs isdue to EC scattering of the external target photons, the γ -ray peakenergy will depend on the dominant external photon frequency. Ifthe target photon field is the IR emission from the dusty torus, thenthe temperature of the dust emission will depend on the location ofthe emission region from the central black hole (Dermer et al. 2014;Ghisellini & Tavecchio 2009). The capability of
Fermi to scan the sky once in three hours and sup-porting ground based monitoring observations in the optical band hasenabled one to study close correlations between flux variations in theGeV band and other low energy bands. From multiband observationsof the blazar 3C 454.3 over a period of about 5 months, Bonning et al.(2009) found close correlation between the optical and GeV band fluxvariations. This argues for co-spatiality of the optical and GeV emis-sion regions. This correlation is also easily understood in the onezone leptonic emission model, wherein relativistic electrons in thejet produce optical emission by synchrotron process, and the samerelativistic electrons produce γ -ray emission by inverse Comptonprocess. However, analysis of the same source by Rajput et al. (2019) MNRAS , 1–22 (2015) ptical GeV connection in FSRQs noticed that the optical and GeV flux variations are not correlated atall times. Such mismatch between optical and GeV flux variations arealso known in few other blazars such as PKS 0208 − − − −
75 (Dutka et al. 2013), PKS1510 −
089 (MacDonald et al. 2015) and PKS 2155 −
304 (Wierzchol-ska et al. 2019). From the analysis of multi-band light curves ofthe sources, we found instances where the optical and γ -ray fluxvariations are closely correlated, cases where there are optical flareswithout γ -ray counterpart and instances when there are γ -ray flareswithout optical counterparts. Thus, it is evident that the correlationsbetween the optical and GeV flux variations in Fermi blazars arecomplex. Recently, from correlation analysis between the optical and γ -ray light curves of 178 blazars, Liodakis et al. (2019) found thatstatistically about 50% of their optical flares have no GeV counter-parts and this fraction is less in the case of γ -ray flares, i.e., about20% of γ -ray flares have no optical counterparts. While in the lep-tonic scenario a close correlation between optical and GeV variationsis expected, the results found in this work as well as the other recentresults by Rajput et al. (2019) and Liodakis et al. (2019) indicate thatcorrelated variability analysis between the optical and GeV bandsmay also not be definitive in constraining the leptonic v/s hadronicscenario for the high energy emission process in blazars. Most ofthe correlation studies between different energy bands of the blazarsindicate positive correlation. But there are exceptions and cases ofanticorrelation are also found for some sources (Chatterjee et al.2013; Cohen et al. 2014; Dutka et al. 2013; MacDonald et al. 2015;Rajput et al. 2019). We found various behaviours between optical and γ -ray energy bands for our selected sample of sources. We lookedfor a correlation between the optical (V-band) and γ -rays for all theepochs considered here. Fig. 18 shows only the epochs where thecorrelation is significant at the 90% level. We converted the γ -rayfluxes from ph cm − s − to erg cm − s − at 100 MeV (Singal et al.2014) to match the optical flux units. The results of the fit are givenin Table 7. The fit takes into account the uncertainty in both opticaland γ -rays. For the source PKS 1510 −
089 during epochs B and Fthe optical and γ -ray flares are correlated. During this epoch Γ islarger than that of the quiescent period. This has given rise to in-creased flare in optical and γ -rays. The difference in the amplitudeof variations between optical and γ -ray flares during epochs B and Fmust be due to a combination of Γ and B. For epochs A, C and E themagnetic field is lower than the quiescent period by a factor of 1.2- 1.5. This has led to decreased optical variations. At the same time Γ has increased from 1.1 - 1.7 times the quiescent period leading toincreased γ -ray flare, but no corresponding optical flare (see Fig. 2and Fig. 3).In the source 3C 273, using our criteria, we were able to identifyone quiescent period and one flaring period. At epoch A, the bulkLorentz factor increased compared to the quiescent state B, whetherthe magnetic field is nearly the same (Table 5). It is natural to expectincreased optical and γ -ray flares during epoch A, but we found a γ -ray flare without an optical counterpart. This absence in opticalflux variations might be due to sub-dominant optical synchrotronemission compared to the prominent accretion disk emission. Theprominent accretion disk component is very well evident in the broadband SED both in the quiescent and active states (Fig. 14).In the source 3C 279, we identified four epochs, A,B, C and D ofwhich during epoch A, the source was quiescent while it was activeduring the other epochs. During epoch D, magnetic field is about1.5 times larger than the quiescent period leading to larger opticalsynchrotron emission. At the same epoch, Γ has increased fromabout 7 to 12. This explains the increased γ -ray and optical flaring in epoch D. During epochs B and C, Γ has increased relative to thequiescent state giving rise to larger γ -ray fluctuations. During epochB, magnetic field is marginally larger than the quiescent period, whilethe particle density is lower than the quiescent period. However, inepoch C, the magnetic field and particle density is lower and higherrespectively than the quiescent period. The interplay between lowmagnetic field and high particle density and vice versa could leadto lower optical variations. This could be the reason for γ -ray flareswithout optical counterparts in epochs B and C in 3C 279. The lowenergy peak of the SED during all epochs in 3C 279 is dominated bysynchrotron emission from the relativistic jet.In CTA 102, we found one flaring epoch when the optical and γ -ray seems to be correlated. Many short term flares with opticaland γ -ray counterparts are seen during this epoch. For SED analysiswe considered only 10 days due to the availability of γ -ray, X-rayand optical data points for SED modelling. During Epoch B, Γ wasnearly four times greater than the quiescent epoch. The magneticfield during epoch B and the quiescent period agree with each otherwithin errors (see Table 5). This increase in Γ relative to the quiescentepoch is the cause of the increased γ -ray flare and optical flare duringepoch B. Prominent accretion disk component is visible in the SEDduring the quiescent phase, however, this is not evident in the flaringepoch B (Fig. 16). This is also reflected in the high accretion ratefound during the quiescent epoch A and a negligibly small accretionrate during epoch B.In the SED analysis carried out in this work, the viewing angleis fixed at 2 ◦ for all the sources. Radio observations indicate thatthe average viewing angle of the sources studied here is lesser than2 ◦ except for 3C 273, where it is around 6 ◦ (Jorstad et al. 2017).Similarly, according to Hovatta et al. (2009) the average viewingangle is around 3.5 ◦ for the sources except CTA 102 for which it is3.7 ◦ . Thus the values of viewing angle available in the literature ofthese source is generally low and not too different from the constantvalue of 2 ◦ used for all the sources. However, to ascertain the effectviewing angle can have on the Γ obtained from SED analysis, werepeated the SED analysis for different values of θ such as 0.5, 1.0,1.5, 2.5 and 3.0 degrees. A similar fit statistics was obtained for allcases with considerable increase in the Γ suggesting a degeneracy.The plot between Γ v/s θ for the source PKS 1510 −
089 is shownin the Figure 19. We found that as θ increases, Γ too increased.No significant changes were noticed in the other parameters, andthe changes are consistent within the errors. The choice of viewingangle do not alter our conclusions since the Lorentz factor obtainedfor different epochs still follow the same trend. This trend is alsofound in other sources. To further verify the degeneracy between thebulk Lorentz factor and the viewing angle we continued the fittingprocedure with the constant Γ , which is fixed at 15 and repeated theSED fitting for all the sources with the inclusion of the accretion diskcomponent. The results of the SED fitting at constant Γ are givenin Table 6. We found minimal change in the parameters comparedto their values given in Table 5. It shows that the adopted θ valuesdirectly impact the predicted Γ or vice-versa and this is true for all thesources and at all epochs. Recent study from radio observations ofthe source S5 0716 + 714 by Kravchenko et al. (2020) also shows thatthe variation in Γ occurs due to the change in θ . This indicates that thechanges in the γ -ray flux states of a source is largely associated withthe changes in the Γ of the jet, as well as θ . Though various physicalprocesses have been proposed to explain the uncorrelated opticaland GeV flux variations in blazars in the literature, our analysis ofthe broad band SED of the four FSRQs studied in this work ondifferent epochs is consistent with leptonic processes in the jets ofthese sources. MNRAS , 1–22 (2015) Bhoomika et al.
Table 4.
Values of the parameters that were frozen during the model fits tothe observed SEDs. Here, R is the size of the emission region in units of 10 cm, and the temperature T is in Kelvin.Object R γ min γ max γ b T(K) fPKS 1510 −
089 7.9 40 2 × × × × It is argued that FSRQs generally show a RWB trend (Sarkar et al.2019), while BL Lacs show a BWB trend (Gaur et al. 2019). If thesetwo classes of blazars indeed show a distinct colour magnitude rela-tion, it leads to hypothesize that the jets are fundamentally differentbetween FSRQs and BL Lacs. However, with the availability of moredata it is now known that blazars show different types of colour vari-ability in the optical - IR bands. Blazars are found to show BWBtrend (e.g., Stalin et al. 2009), RWB trend (e.g., Sarkar et al. 2019),both BWB and RBW trends (Rajput et al. 2019) as well as weak/nospectral change with brightness (Raiteri et al. 2003). The dominanceof the more variable red synchrotron emission over the less variablethermal emission from the accretion disk could lead to a RWB trend(Sarkar et al. 2019). Alternatively, a BWB trend can happen due toincreased variations at shorter wavelengths (Stalin et al. 2009). Inthe one zone leptonic emission model this can be explained via theinjection of fresh electrons with high energy leading to a BWB trend(Kirk et al. 1998; Mastichiadis & Kirk 2002). Alternatively, accord-ing to Papadakis et al. (2007) and Villata et al. (2004) a BWB trendcan also happen due to changes in the Doppler factor. We examinedthe colour variations during all the epochs and considered a sourceto show colour variation only when the Spearman rank correlationcoefficient is > < − < −
089 significant colour variations wereobserved during epoch A,E and F. While during epochs A and E, wefound a RWB trend, during epoch R, we found a BWB trend. Theobserved colour variation in the optical band has no direct relationto the presence or absence of correlated variation between opticaland γ -ray bands. Our results clearly indicate that FSRQs show bothBWB and RWB behaviours. We carried out detailed investigations of the correlation between op-tical and GeV flux variations in four FSRQs namely PKS 1510 − γ -ray spectra and (d) analysis of optical-IR colourvariations. The results of those analysis are summarized below:(i) All the four FSRQs studied here, namely PKS 1510 − γ -rays are closely correlated, (b) epochs when there are optical flareswithout γ -ray and (c) epochs when there are γ -ray flares withoutoptical counterparts. From our one zone leptonic model fit to theobserved SED of all such epochs in the sources, we found that theregions giving rise to optical and γ -ray flares are co-spatial.(ii) SED analysis indicates that the optical emission is often wellexplained by synchrotron emission process and the γ -ray emission is well explained by EC process with the seed photons from the torus.A Prominent accretion disk component is seen in the synchrotronpart of the SEDs in PKS 1510 − γ -rayflux variations are caused by increase in the bulk Lorentz factor (b) γ -ray flares with no optical counterparts are due to an increase in thebulk Lorentz factor and/or increase in the electron number densityand (c) an optical flare with no γ -ray counterpart is due to an increasein the magnetic field.(iv) The γ -ray spectra of the sources during various epochs arewell represented by the LP model(v) Varied colour behaviours such as BWB trend and RWB trendare seen in our sample of sources. ACKNOWLEDGMENTS
The multiwavelength data underlying this article are publicly avail-able from the
Fermi-LAT , Swift-XRT and Swift-UVOT , SMARTS and Steward observatory . REFERENCES
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Model fits to the broad band SED during epoch A and B for the source CTA 102. The lines and symbols are as in Fig. 12
Table 5.
Results of the broad band SED analysis of the sources at different epochs for the constant viewing angle θ =2 ◦ .Bulk Lorentz Low energy High energy Eletron energy Magnetic Accretion IC peakName Epoch factor particle index particle index density (cm − ) field (Gauss) rate (MeV) χ /dofPKS 1510 −
089 A (with out AD) 10.29 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±000
089 A (with out AD) 10.29 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±000 , 1–22 (2015) ptical GeV connection in FSRQs Table 6.
Results of the broad band SED analysis on the sources at different epochs for the constant Bulk Lorentz factor Γ = 15.Viewing Low energy High energy Eletron energy Magnetic AccretionName Epoch Angle particle index particle index density (cm − ) field (Gauss) rate χ /dofPKS 1510 −
089 A 2.97 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± PKS 1510-089Least square fit ph cm s )0.0000.0250.0500.0750.1000.125 2.42.62.83.0
3C 273Least square fit ph cm s )0.00.10.20.32.02.12.22.32.42.5
3C 279Least square fit ph cm s )0.060.080.10 1.82.02.22.42.6 CTA 102Least square fit ph cm s )0.0250.0000.0250.0500.0750.100 Figure 17.
Variations of the parameters α and β with flux for the sourcesPKS 1510 −
089 (top left), 3C 273 (top right), 3C 279 (bottom left) and CTA102 (bottom right). l o g ( F [ e r g c m s ]) Epoch CEpochE F Optical [erg cm s ])9.69.49.29.08.8 Epoch A F Optical [erg cm s ])10.09.59.08.58.0 l o g ( F [ e r g c m s ]) Epoch BEpoch C
Figure 18.
Optical flux v/s γ -ray flux for the sources PKS 1510 −
089 (topleft), 3C 273 (top right) and 3C 279 (bottom left) respectively.
Table 7.
Results of the linear least squares fit to the optical and γ -ray fluxmeasurements, during different epochs for the sources PKS 1510-089, 3C273, and 3C 279. Here R and P are the Spearman rank correlation coefficientand the probability for no correlation respectively.Object Epoch Slope Intercept R PPKS 1510 −
089 C 3.23 ± ± ± ± ± ± ± ± ± ± , 1–22 (2015) Bhoomika et al. B u l k L o r e n t z F a c t o r () PKS 1510-089
Epoch AEpoch BEpoch CEpoch DEpoch EEpoch F
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