# Modeling the time variable spectral energy distribution of the blazar CTA
102 from 2008 to 2022

N. Sahakyan1,2,3, D. Israyelyan1, G. Harutyunyan1,4, S. Gasparyan1, V.
Vardanyan1, M. Khachatryan1
1ICRANet-Armenia, Marshall Baghramian Avenue 24a, Yerevan 0019, Armenia
2ICRANet, P.zza della Repubblica 10, 65122 Pescara, Italy
3 ICRA, Dipartimento di Fisica, Sapienza Universita‘ di Roma, P.le Aldo Moro
5, 00185 Rome, Italy
4 Byurakan Astrophysical Observatory, Aragatsotn reg., Armenia E-mail:
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present long-term multiwavelength observations of blazar CTA 102
($z=1.037$). Detailed temporal and spectral analyses of $\gamma$-ray, X-ray
and UV/optical data observed by Fermi-LAT, Swift XRT, NuSTAR and Swift-UVOT
over a period of 14 years, between August 2008 and March 2022, was performed.
We found strong variability of source emission in all the considered bands,
especially in the $\gamma$-ray band it exhibited extreme outbursts when the
flux crossed the level of $10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$. Using the
Bayesian Blocks algorithm, we split the adaptively binned $\gamma$-ray light
curve into 347 intervals of quiescent and flaring episodes and for each period
built corresponding multiwavelength spectral energy distributions (SEDs),
using the available data. Among the considered SEDs, 117 high-quality (quasi)
contemporaneous SEDs which have sufficient multiwavelength data, were modeled
using JetSeT framework within a one-zone leptonic synchrotron and inverse
Compton emission scenario assuming the emitting region is within the broad-
line-region and considering internal and external seed photons for the inverse
Compton up-scattering. As a result of modeling, the characteristics of the
relativistic electron distribution in the jet as well as jet properties are
retrieved and their variation in time is investigated. The applied model can
adequately explain the assembled SEDs and the modelling shows that the data in
the bright flaring periods can be reproduced for high Doppler boosting and
magnetic field. The obtained results are discussed in the context of particle
cooling in the emitting region.

###### keywords:

quasars: individual: CTA 102– radiation mechanisms: non-thermal – galaxies:
jets – X-rays: galaxies- - gamma-rays: galaxies

††pubyear: 2022††pagerange: Modeling the time variable spectral energy
distribution of the blazar CTA 102 from 2008 to 2022–Modeling the time
variable spectral energy distribution of the blazar CTA 102 from 2008 to 2022

##  1 Introduction

Active galactic nuclei powered by supermassive black holes with masses of
$10^{6}$-$10^{10}\>M_{\odot}$ are the most luminous persistent objects in the
extragalactic sky. In some AGNs a relativistic jet is formed perpendicular to
the accretion disc plane and it plays a crucial role in blazar
classifications. According to the unification scheme developed by Urry &
Padovani (1995), an AGN is called a blazar when the jet is closely aligned
with the line of sight of the observer. Blazars are characterized by high
radio and optical polarization, apparent superluminal motion along with high-
amplitude variability in all accessible bands of the electromagnetic spectrum.
Usually, this variability is unpredictable and only for a few objects periodic
variability is observed (e.g., see Ackermann et al., 2015; Ren et al., 2022).
Blazars are usually believed to be persistent sources, however recently a
blazar showing a transient behaviour was observed. Namely, 4FGL J1544.3-0649
was never detected in the X-ray and $\gamma$-ray bands until May 2017 when it
rose above the detectability level and for a few months became one of the
brightest X-ray blazars (Sahakyan & Giommi, 2021). Blazar emission is
dominated by non-thermal emission from the jet which is significantly Doppler
amplified since the jet with superluminal motion is viewed at small angles.
Because of this, blazars even at higher redshift are observed (e.g., see
Sahakyan et al., 2020).

The emission from blazars is observed in a wide frequency range, from radio to
high energy (HE; $>100$ MeV) and very high energy (VHE; $>100$ GeV)
$\gamma$-ray bands (Padovani et al., 2017) displaying a double hump structure
in their broadband spectral energy distribution (SED). The first component
(low-energy) usually peaks between far infrared and X-rays while the second
component (HE) is observed between X-rays and VHE $\gamma$-rays. The low-
energy component is explained by the synchrotron emission of jet-accelerated
electrons under the magnetic field while the origin of the HE component is
discussed within leptonic and hadronic models, depending on the type of
emission initiating particles, $e^{-}e^{+}$ pairs or hadrons. According to the
widely discussed leptonic scenario, the HE component is due to inverse Compton
upscattering of photons by energetic electrons. Most common scenarios used in
the literature are synchrotron self-Compton (SSC) model and the external
Compton (EIC) model. According to the first scenario, the internal synchrotron
photons are up-scattered to higher energies (Ghisellini et al., 1985; Bloom &
Marscher, 1996; Maraschi et al., 1992) whereas the latter model assumes the
photons are produced external to the jet (Błażejowski et al., 2000; Ghisellini
& Tavecchio, 2009; Sikora et al., 1994). In alternative hadronic or lepto-
hadronic scenarios, the protons co-accelerated with the electrons make a non-
negligible contribution to the HE component. This contribution can be either
directly from proton synchrotron radiation (Mücke & Protheroe, 2001) or from
secondaries produced in the proton-photon interactions or photo-pair
productions (Mannheim, 1993; Mannheim & Biermann, 1989; Mücke & Protheroe,
2001; Mücke et al., 2003; Böttcher et al., 2013; Petropoulou & Mastichiadis,
2015; Gasparyan et al., 2022). Lately, the hadronic models (especially lepto-
hadronic Gasparyan et al., 2022) have become more attractive after the
detection of VHE neutrinos spatially coinciding with the direction of known
blazars (IceCube Collaboration et al., 2018a, b; Padovani et al., 2018). The
initial association between TXS 0506+056 and IceCube-170922A event provided
first multimessenger picture of blazar and opened a wider perspective for
theoretical studies (Ansoldi et al., 2018; Keivani et al., 2018; Murase et
al., 2018; Padovani et al., 2018; Sahakyan, 2018; Righi et al., 2019; Cerruti
et al., 2019; Sahakyan, 2019; Gao et al., 2019; Gasparyan et al., 2022). The
assumption that blazars are neutrino sources was further strengthened by the
observation of multiple neutrino events from the direction of PKS 0735+178
when the source was undergoing a major flaring activity in the optical/UV,
X-ray and $\gamma$-ray bands (Sahakyan et al., 2022).
Commonly, the blazars are grouped based on their optical spectral properties.
Namely, Flat Spectrum Radio Quasars (FSRQs) which show strong optical lines
and BL Lacertae type objects (BL Lacs) which have very faint optical emission
lines. Blazars are further classified based on the observed SEDs. Namely,
based on the frequency where the synchrotron component peaks ($\nu_{\rm p}$),
blazars are separated into low, intermediate and high-energy peaked sources
(Padovani & Giommi, 1995; Abdo et al., 2010); low synchrotron peaked sources
(LSPs or LBLs) when $\nu_{\rm p}<10^{14}$ Hz, intermediate synchrotron peaked
sources (ISPs or IBLs) when $10^{14}\>{\rm Hz}\><\nu_{\rm p}<10^{15}$ Hz and
high synchrotron peaked sources (HSPs or HBLs) when $\nu_{\rm p}>10^{15}$ Hz.
However, recently Giommi & Padovani (2021) showed that there are strong
similarities between the properties of IBLs and HBLs and they show large
differences from LBLs, so the classification can be refined into LBLs and
intermediate-high-energy-peaked objects (IHBLs) when $\nu_{\rm p}$ is below or
above $10^{13.5}$ Hz.
CTA 102 is a FSRQ with a redshift of $z=1.037$ (Schmidt, 1965). Harboring a
black hole with a mass of $8.5\times 10^{8}\>{\rm M_{\rm BH}}$ (Zamaninasab et
al., 2014), CTA 102 is one of the brightest FSRQs observed in the HE
$\gamma$-ray band. It was initially observed by the Compton Gamma Ray
Observatory mission having estimated a $\gamma$-ray flux of $(2.4\pm
0.5)\times 10^{-7}\>{\rm photon\>cm^{-2}\>s^{-1}}$ (Nolan et al., 1993). Then,
CTA 102 was scanned continuously by the Fermi Large Area Telescope (Fermi-LAT)
since mid-2008, initially showing that the source is relatively weak in the
$\gamma$-ray band. However, from 2016 to 2017 it underwent an unprecedented
outburst in all the wavebands (Casadio et al., 2015; Balonek et al., 2016;
Chapman et al., 2016; Popov & Bachev, 2016; Ciprini, 2016; Bulgarelli et al.,
2016; Ciprini, 2017; Becerra et al., 2016; Minervini et al., 2016; Carrasco et
al., 2016). For example, in the $\gamma$-ray band its flux was as high as
$(3.55\pm 0.55)\times 10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$ (Gasparyan et
al., 2018) and in some active $\gamma$-ray periods its spectrum also deviated
from simple power-law model (Sahakyan, 2020). During the $\gamma$-ray flares,
the source was so bright that variability was investigated down to minute
scales (Shukla et al., 2018). In December 2016, the source was also in an
extreme optical and near-IR out-bursting state when the brightness increased
up to six magnitudes with respect to the faint state of the source (Raiteri et
al., 2017). Various theoretical models were used to explain the flaring
behaviour of CTA 102 which includes an inhomogeneous curved jet with different
jet regions changing their orientation and consequently the Doppler factors
(Raiteri et al., 2017), or a superluminal component crossing a recollimation
shock (Casadio et al., 2019), or lepto-hadronic processes when the gas cloud
penetrates the jet (Zacharias et al., 2017, 2019) or the activities were
interpreted as change of the location of the emission region (e.g., Gasparyan
et al., 2018; Prince et al., 2018; Sahakyan, 2020), etc.

Due to the long-lasting and peculiar multiwavelength flaring activity, CTA 102
was frequently observed in different bands and became one of the most-studied
blazars (Li et al., 2018; Kaur & Baliyan, 2018; D’Ammando et al., 2019; Meyer
et al., 2019; Chavushyan et al., 2020; Acharyya et al., 2021; Roy et al.,
2021; Kim et al., 2022; Geng et al., 2022). Although many studies have been
conducted which lead to a better understanding of the CTA 102 jet, it is up to
now not clear the origin of the multiwavelength flares of CTA 102, especially
the changes in the jet that have led to prolonged flaring activities.

The monitoring of CTA 102 during its unprecedented outburst with various
instruments resulted in accumulation of an extensive data set. In addition,
before and after the outburst the source was also monitored in the
$\gamma$-ray band with Fermi-LAT and observed in the optical/UV and X-ray
bands by Neil Gehrels Swift Observatory (Gehrels et al., 2004), (hereafter
Swift). This can be combined with other available data to build the broadband
SEDs of CTA 102 in various (flaring or quiescent) periods with (quasi)
contemporaneous data. These SEDs with various spectral properties represent an
ample variety of source emission in different states and their modeling is
crucial for understanding of the physical processes and their changes in time.
In the broadband SEDs of blazars the changes are expected to be due to the
variation of the parameters of the emitting electrons or the physical
parameters of the emission region. Therefore, the modeling of the SEDs in
different periods allows to connect the observational properties with the
physical processes at work in jets. For example in Sahakyan (2021) and
Sahakyan & Giommi (2022) the modeling of a large number of contemporaneous
SEDs of 3C 454.3 and BL Lac allowed to estimate the main parameters describing
the emitting electrons and the emission region and investigate their evolution
in time which was crucial for understanding of the observed spectral changes
in them.

Motivated by the availability of multiwavelength data from CTA 102
observations before, during and after the large outburst, for furthering our
knowledge of the emission processes dominating in the jet of CTA 102 we
performed an intense broadband study of CTA 102 using the data accumulated
during 2008-2022. We have systematically investigated the spectral and
variability properties of the source emission in the optical/UV, X-ray and
$\gamma$-ray bands. We performed a deep investigation of the origin of the
source emission in various periods by generating as many SEDs of CTA 102 as
possible that can be constructed with contemporaneous data and modeling them
within the leptonic scenario. The paper is structured as follows. The
broadband data analyses are described in Section 2. The multiwavelength
variability is explored in Section 3. The modeling of broadband SED is
described in Section 4. We present the discussion and results in Section 5 and
the conclusions in Section 6.

##  2 Multiwavelength observations of CTA 102

Exhibiting interesting multiwavelength properties, CTA 102 was frequently
observed in different bands. Below we report the data analyzed in this paper
or extracted from public archives which was used in the current study.

###  2.1 Fermi-LAT observations of CTA 102

Operating since 2008, Fermi-LAT provides an exceptional view of the
$\gamma$-ray sky, imaging the entire sky every three hours (Atwood et al.,
2009). In the current paper the Fermi-LAT data accumulated between 04 August
2008 and 04 March 2022 in the 100 MeV–300 GeV range were downloaded and
analyzed using the Fermi ScienceTools version 2.0.8 and P8R3_SOURCE_V3
instrument response function. Events were extracted from a region of interest
(ROI) with a $12^{\circ}$ radius centered on the source position (RA: 338.15,
DEC: 11.73). As recommended by the Fermi-LAT team, the cut evclass = 128 and
evtype=3 was applied to select events with higher probability of being
photons. Whereas, the filter ${\rm(DATA\\_QUAL>0)\&\&(LAT\\_CONFIG==1)}$ was
applied to update the good time interval based on spacecraft specifications. A
maximum zenith angle cut of $>90^{\circ}$ is applied to reduce the
contamination from Earth limb $\gamma$-rays. The model file was generated
based on Fermi-LAT fourth source catalog Data Release 3 (4FGL-DR3; Ajello et
al., 2020; Abdollahi et al., 2022) which includes point sources within the ROI
and standard Galactic (gll_ iem_ v07) and the isotropic (iso_P8R3_SOURCE_
V3_v1) diffuse emission components. The spectral parameters of the background
sources falling between $12^{\circ}$ and $12^{\circ}$+$5^{\circ}$ were fixed
to the values published in the 4FGL-DR3 catalog, while the parameters of the
other sources (within $12^{\circ}$) and background models were left free. The
best match between the source parameters and the data was obtained by applying
standard binned likelihood analysis with gtlike tool.

After analyzing the data accumulated in the whole time interval, light curves
were computed with different time bins to investigate the variability in the
$\gamma$-ray band. Initially, the entire period was divided into three-day
intervals (1653 in total) and for each single period the flux, photon index
(CTA 102 spectrum was modeled with power-law distribution) and the Test
Statistics (TS, defined as twice the difference between the log-likelihoods of
the model computed with and without including the source; Mattox et al., 1996)
were estimated.

Next, for a deeper investigation of the $\gamma$-ray flux variability, the
light curve was generated with the help of the adaptive binning method (Lott
et al., 2012). As distinct from the fixed time interval light curve where the
longer bins will smooth out the fast variation and in short time intervals the
flux can be estimated only in the bright state of the source, in the
adaptively binned light curve the bin width is defined by requiring a constant
relative flux uncertainty above an optimal energy, so the time bins are longer
during low flux levels and narrower when the source is in flaring state. This
allows to track the evolution of the $\gamma$-ray flux in time, extract
maximum possible information and identify flaring periods (e.g., see Gasparyan
et al., 2018; Sahakyan et al., 2018; Sahakyan & Gasparyan, 2017; Zargaryan et
al., 2017; Baghmanyan et al., 2017; Britto et al., 2016; Rani et al., 2013).

The spectral changes in the $\gamma$-ray band were further investigated by
producing the source spectrum in different periods. For this purpose, the
adaptively binned light curve is divided into piece-wise constant blocks
(Bayesian blocks Scargle et al., 2013) representing optimal segmentation of
the data into time intervals during which the flux is constant. By this
approach, the considered period is divided into 347 intervals with the same
flux level, whether flaring or quiescent. The spectrum of CTA 102 in each of
the selected period is computed by applying unbinned likelihood analysis and
running gtlike separately for 5 (when the source is in average or quiescent
state) or 7 energy bins (when the source is in flaring state) of equal width
in log scale.

Figure 1: The multiwavelength light curve of CTA 102 between 2007 and 2022. a)
Adaptively binned $\gamma$-ray light curve ($>166.3$ MeV) with the Bayesian
blocks, b) 3-day binned $\gamma$-ray light curve, c) 2.0-10 keV X-ray flux, d)
0.3-10.0 keV X-ray photon index, e) flux in V, B, and U filters, f) flux in
W1, M2 and W2 filters and g) V-band and R-band fluxes. The periods for which
the SEDs have been modeled are highlighted in gray.

###  2.2 Swift observations of CTA 102

In the optical/UV and X-ray bands there are available a total of 146
observations of CTA 102 with Swift XRT/UVOT instruments. All the XRT
observations were individually downloaded and analyzed using Swift_xrtproc
pipeline (Giommi et al., 2021). This tool developed within the Open Universe
Initiative downloads the raw data and calibration files from one of the
official Swift archives, processes it using the XRTPIPELINE task for each
snapshot and for the entire Swift observation, applies pile-up correction when
the source count rate is above $0.5\>{\rm counts\>s^{-1}}$ and generates
source (from a circle with a radius of 20 pixels centered at the position of
the source) and background (an annular ring centered at the source) spectral
files. It performs a spectral fitting with XSPEC (version 12.12.0) on the
ungrouped data using Cash statistics (Cash, 1979), modeling CTA 102 spectrum
as a power-law and a log-parabola. As a result, the tool generates SED data
and estimates the flux and photon index in various bands. More details on
Swift_xrtproc are given in Giommi et al. (2021).

The Swift-UVOT data in three optical filters (V, B, and U) and three UV
filters (W1, M2, and W2) were downloaded and reduced using HEAsoft version
6.29 with the latest release of HEASARC CALDB. The source counts were
extracted from a region of 5 arcsec radius centered at the source and the
background counts from a region of 20 arcsec centered away from the source.
uvotsource tool was used to obtain the magnitude which was corrected for
reddening and galactic extinction using the reddening coefficient $E(B-V)$
from the Infrared Science Archive
111http://irsa.ipac.caltech.edu/applications/DUST/.

###  2.3 NuSTAR observations of CTA 102

NuSTAR with two focal plane modules (Harrison et al., 2013), FPMA and FPMB,
observed CTA 102 in the hard X-ray (3-79 keV) band on December 30, 2016 for a
total exposure of 26.2 ksec. The NuStar data was processed with NuSTAR_
Spectra script which is a shell script based on the NuSTAR Data Analysis
Software (NuSTARDAS) that automatically downloads calibrated and filtered
event files from the SSDC repository, generates scientific products and
carries out a complete spectral analysis. It uses nuproducts to generate the
spectra from source counts extracted from a circular region whose radius is
set to a value that is optimised depending on the source count rate
($30^{\prime\prime}$ in this case), while the background counts are from an
annulus centered on the source. With the XSPEC, the spectral analysis is
performed adopting Cash statistics for the energy range from 3 keV up to the
maximum energy where the signal is still present, typically between 20 and 79
keV. NuSTAR_ Spectra script is presented and described in Middei et al.
(2022).

###  2.4 Archival optical data

In order to monitor the flux changes in the optical band, the light curves
from several public archives were used. Namely, the optical data (V- and R-
band) from Steward Observatory (Smith et al., 2009), V-band data from the All-
Sky Automated Survey for Supernovae (ASAS-SN) 222https://asas-sn.osu.edu/
(Kochanek et al., 2017) and the V-band data from the Catalina Sky Survey (CSS;
Drake et al., 2009) were downloaded from the public archives.

##  3 Multiwavelength variability

The multiwavelength light curve of CTA 102 is shown in Fig. 1. The adaptively
binned light curve above $166.3$ MeV in Fig. 1 panel a) shows the continuous
observation of the source in the $\gamma$-ray band and reveals the complex
flux changes. During the considered periods several outbursts are observed.
Until April 2011 the source flux was constant, not exceeding $10^{-7}\>{\rm
photon\>cm^{-2}\>s^{-1}}$. The first flare (when $F_{\rm\gamma}>15\times
F_{\rm\gamma,min}$) occurred in April-June 2011 (MJD 55680-55730), when the
flux increased up to $(2.55\pm 0.62)\times 10^{-6}\>{\rm
photon\>cm^{-2}\>s^{-1}}$. Other enhancements were observed between September-
October 2012 (MJD 56180-56230) and between March-April 2013 (MJD 56380-56400).
Yet, a major flaring activity, when the source flux increased above
$10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$, was observed between December 2015-
March 2016 (MJD 57370-57470). Then, the source entered a prolonged out-
bursting state between November 2016 -June 2017 (MJD 57710-57910) when the
highest flux of $(2.64\pm 0.60)\times 10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$
above $166.3$ MeV was observed on MJD 57738.5. Another brightening of the
source (although with lower amplitude) was observed between November
2017-March 2018 (MJD 58080-58180). During the considered period, the
$\gamma$-ray flux of CTA 102 was above $10^{-5}\>{\rm
photon\>cm^{-2}\>s^{-1}}$ for 121.1 hours in total. The ratio between the
highest and lowest fluxes is $\simeq 1137$ which again shows the high-
amplitude variation of the $\gamma$-ray flux. The overall trends revealed in
the $\gamma$-ray light curve generated by the adaptive binning method are also
visible in the 3-day light curve (panel b) Fig. 1) but, as expected, the
intra-day flux variability is smoothed out.

Together with the $\gamma$-ray flux, the photon index varies as well. The
hardest photon index is $\Gamma_{\gamma}=1.52\pm 0.12$ observed on MJD 57752.5
when the source was in bright $\gamma$-ray state with a flux of $(1.02\pm
0.20)\times 10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$. The distribution of
photon index estimated in all adaptively binned intervals is shown in Fig. 2
(light magenta). The mean of the photon index distribution $2.31$ is the same
as the time-averaged photon index of the source in 4FGL DR3 ($\sim 2.3$).
However, there are 353 periods when the photon index was significantly hard
($<1.9$) which means that the peak of the HE component moved to HEs. In Fig.
2, the blue area corresponds to photon index distribution only when the
$\gamma$-ray flux was $10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$ which shows
that in some of the bright states the photon index of the source was also
hard.

Figure 2: The distribution of the $\gamma$-ray photon index estimated in the
adaptively binned intervals. The light red area shows the total distribution,
while the blue is only when the $\gamma$-ray flux was above $10^{-5}\>{\rm
photon\>cm^{-2}\>s^{-1}}$.

The X-ray flux ($2-10$ keV) variation in time is shown in Fig. 1 panel c).
There is significant variability of the X-ray flux in different XRT
observations. During the prolonged flaring in the $\gamma$-ray band, the
source was also in an active X-ray emission state, when the X-ray flux reached
${\rm F_{X-ray}[2-10\>keV]}=(5.77\pm 0.63)\times 10^{-11}\>{\rm
erg\>cm^{-2}\>s^{-1}}$. The NuSTAR observation shows that the source flux in
the 3-10 keV band is $(4.46\pm 0.02)\times 10^{-11}\>{\rm
erg\>cm^{-2}\>s^{-1}}$ in agreement with the X-ray flux observed by Swift XRT
on the same day (${\rm F_{X-ray}[2-10\>keV]}=(5.30\pm 0.47)\times
10^{-11}\>{\rm erg\>cm^{-2}\>s^{-1}}$). As the X-ray band corresponds to the
rising part of the HE component, the flux in the 10-30 keV band increases
being $(9.04\pm 0.05)\times 10^{-11}\>{\rm erg\>cm^{-2}\>s^{-1}}$. Also, the
Swift XRT and NuSTAR observations reveal similar photon indexes in the 0.3-10
keV and 3-30 keV bands, $1.25\pm 0.08$ and $1.30\pm 0.01$, respectively.

In Fig. 1 panels e), f) and g), the flux variation in the optical/UV band is
shown. In the optical band, the source’s emission follows the same trend as in
the $\gamma$-ray and X-ray bands. Namely, Swift UVOT, ASAS-SN, Steward (V and
R band) and CSS observations show that the flux was relatively constant up to
MJD 56000 and then increased several times around MJD 56200. However, long-
lasting flaring activity was observed between MJD 57400-58000 when the flux in
the optical band, as observed with all the considered instruments, was above
$10^{-11}\>{\rm erg\>cm^{-2}\>s^{-1}}$. The highest flux of $(6.38\pm
0.19)\times 10^{-10}\>{\rm erg\>cm^{-2}\>s^{-1}}$ was observed in the V-band
on MJD 57751.84 by Swift UVOT. The Swift UVOT observations show that between
MJD 57718-57768 (November 2016-January 2017), the source was in an extreme
bright state in the optical/UV band when the flux was above $10^{-10}\>{\rm
erg\>cm^{-2}\>s^{-1}}$. This is in agreement with the results obtained from
CTA 102 monitoring by the Whole Earth Blazar Telescope (WEBT) (Raiteri et al.,
2017). The ASAS-SN monitoring of the source shows that another flaring
activity was observed on MJD 58741 and then the source’s emission in the
optical band was on its regular level.

##  4 Broadband SED modeling

One of the ways for investigation of the underlying physical processes in the
jet is through broadband SED modeling. The SEDs constrained with
contemporaneous or quasi-contemporaneous data contain valuable information on
the emitting particle spectrum and on the condition of the plasma inside the
jet. The evolution of the CTA 102 SEDs in time (SED/light curve animation) is
shown here youtube.com/jFNkI_psAjo. These SEDs were generated by plotting the
$\gamma$-ray spectra for each of the Bayesian blocks shown in Fig. 1 together
with the data available in all other energy bands. In a visually effective
way, the temporal changes in the CTA 102 spectra can be seen by going from one
to another interval. This animation shows the high-amplitude and spectral
changes in different periods, demonstrating dramatic changes of the CTA 102
during the prolonged out-bursting period.

In FSRQs, such as CTA 102, a one-zone synchrotron/synchrotron-self Compton
(SSC) with an external radiation component is expected to produce the
broadband emission. The origin of the external photons depends on the location
of the emitting region (Sikora et al., 2009) and photons directly emitted from
the disc (Dermer & Schlickeiser, 1993; Dermer et al., 1992), emitted from the
BLR (Sikora et al., 1994) or emitted from the dusty torus (Błażejowski et al.,
2000) can inverse Compton up-scatter and explain the second component in the
broadband SED. In the current study we assume that the emitting region is at
$10^{17}$ cm distance from the black hole within the BLR and the external
photons are the photons emitted from the BLR. The SED modeling when different
locations of the emitting region are considered is presented in Gasparyan et
al. (2018) and Sahakyan (2020).

Here, we consider a one-zone leptonic model of jet emission, assuming the
accelerated electrons (protons) are injected in the spherical region of radius
$R$. This magnetized region with a field strength of $B$ moves along the jet
with a bulk Lorentz factor of $\Gamma_{\rm jet}$ at an angle of $\theta$
relative to the observer’s line of sight. As the jet is almost aligned to the
observer (small $\theta$), the emission is Doppler boosting by a beaming
factor of $\Gamma_{\rm jet}=\delta$. It is assumed that the spectrum of the
injected electrons is described by a power-law with an exponential cutoff
energy distribution defined as

$\displaystyle N(\gamma_{\rm e})=N_{0}\>\gamma_{\rm e}^{-p}\>Exp(-\gamma_{\rm
e}/\gamma_{\rm cut}),\>\>\>\>\>\>\>\gamma_{\rm e}>\gamma_{\rm min}$ (1)

where $\gamma_{\rm cut}$ and $\gamma_{\rm min}$ are the cut-off and minimum
energy of the electrons, respectively, and $p$ is the power-law index of the
electron energy distribution. The normalization constant $N_{0}$ defines the
energy density of the electrons: $U_{\rm e}=m_{\rm e}c\int\gamma_{\rm
e}N(\gamma_{\rm e})d\gamma_{\rm e}$.

In this scenario, the first peak in the SED is described by synchrotron
radiation as a consequence of the interaction of relativistic electrons inside
the emitting region with the magnetic field. Instead, the second peak (from
X-ray to HE $\gamma$-rays) is formed by the contribution of inverse Compton
scattering of synchrotron (SSC) and BLR emitted (EIC) photons. The BLR radius
and luminosity of CTA 102 are $R_{\rm BLR}=6.73\times 10^{17}\>{\rm cm}$ and
$L_{\rm BLR}=4.14\times 10^{45}\>{\rm erg\>s^{-1}}$ (Pian et al., 2005),
respectively, and the BLR is modeled as a spherical shell with a lower
boundary of $R_{\rm in,BLR}=0.9\times R_{\rm BLR}=6.06\times 10^{17}$ cm and
an outer boundary of $R_{\rm out,BLR}=1.2\times R_{\rm BLR}=8.08\times
10^{17}$ cm. Assuming that the 10% of the disc luminosity is reprocessed into
BLR radiation, the disc luminosity would be $L_{\rm disc}=4.14\times
10^{46}\>{\rm erg\>s^{-1}}$.

Figure 3: The multiwavelength SED of CTA 102 during MJD 56196.7-56202.3
constructed with the data from Swift UVOT, XRT and Fermi-LAT. The disc, SSC,
EIC-BLR and the sum of all components are in dashed pink, dot-dashed orange,
dot-dot-dashed purple and solid blue lines, respectively.

To model the broadband SED, a publicly available code, JetSet was used
(Massaro et al., 2006; Tramacere et al., 2009, 2011; Tramacere, 2020). JetSet
fits the numerical models to observed data and is able to find the optimal
values of parameters best describing the data. The multiwavelength SED of CTA
102 constrained with contemporaneous data observed during MJD 56196.7-56202.3
and modeled with JetSet is shown in Fig. 3. The dashed violet line shows the
disc thermal emission approximated as a black body. The power-law index of the
emitting electrons is $p=1.61$ while the minimum and cut-off energies are
$\gamma_{\rm min}=51.3$ and $\gamma_{\rm cut}=685.6$, respectively. The
synchrotron emission of these electrons in the magnetic field of $B=4.43$ G
extends up to $10^{16}$ Hz explaining the observed data in the optical/UV
bands. Then, the SSC component takes into account the X-ray data (dot-dashed
orange curve in Fig. 3) dominating only up to $10^{22}$ Hz, failing to explain
the $\gamma$-ray data. Instead, the inverse Compton upscattering of the BLR
photons that have higher mean energy and number density in the jet frame can
explain the $\gamma$-ray data (dot-dot-dashed purple curve in Fig. 3). The
modeling allows to estimate the jet parameters such as size of the emission
region, $R=2.03\times 10^{15}$ cm and the Doppler factor $\delta=29.8$. The
size of the emission region corresponds to the flux variability of the order
of $1.3$ hours, consistent with the rapid multi-band variability of CTA 102.

The modeling of the single snapshot SED shown in Fig. 3 permits to identify
the parameters of the emitting region and the jet for a given period. However,
in order to deeply investigate the multiwavelength emission processes in CTA
102 something beyond the single-epoch SED modeling is required. In Sahakyan
(2021) and Sahakyan & Giommi (2022) the multiwavelength emission from 3C 454.3
and BL Lac was investigated by modeling as many contemporaneous SEDs as
possible constrained during the considered periods. As compared with the
single snapshot SED modeling, the advantage of such an approach is that it
allows to follow the changes also in the parameters over time, thus get a clue
on the evolution of the processes that have lead to the emission in different
states (e.g., flares). In addition, such modeling has diagnostic applications,
i.e., by fitting many SEDs it is possible to identify periods when the source
was characterized with peculiar emission properties that are not possible to
explain within the considered model.

In order to model the SEDs of CTA 102 in different periods, from the SEDs
generated for each Bayesian block there were selected all the periods with
sufficient multiwavelength data, i.e., when the optical/UV data at least in
two filters is available together with the $\gamma$-ray and X-ray data. In
Fig. 1 the selected periods are shown in gray. As a result high-quality SEDs
in 117 periods were assembled which represent various emitting sates of CTA
102 including periods when it was in a prolonged flaring state in the
$\gamma$-rays. Therefore, this allows to understand the physical processes
dominating in the jet of the source in its quiescent and flaring states. All
the selected SEDs are modeled within the same one-zone scenario described
above.

##  5 Results and Discussion

In this section, the implications of the data analysis are discussed, and the
results from the broadband spectral fitting are presented. In the optical/UV,
X-ray and $\gamma$-ray bands, CTA 102 exhibits complex flux changes showing
multiple flaring periods. The highest amplitude changes are observed in the HE
$\gamma$-ray band where the $\gamma$-ray luminosity of the source varies from
$8.50\times 10^{46}\>{\rm erg\>s^{-1}}$ to $7.55\times 10^{50}\>{\rm
erg\>s^{-1}}$ (assuming a distance of $7.1$ Gpc) which makes CTA 102 one of
the brightest sources in the extragalactic $\gamma$-ray sky.

The visual inspection of the multiwavelength light curves in Fig. 1 shows that
fluxes in different bands change almost simultaneously. Possible correlation
or anticorrelation between the fluxes in different bands shows whether or not
the emission is produced by the same population of the particles and related
mechanisms. In the case of one-zone leptonic scenario considered here, when
the optical/UV photons are from synchrotron emission of the electrons while
the emission in the X-ray and $\gamma$-ray bands is from the inverse Compton
scattering of internal and external photon fields by the electrons in the same
emitting region, one expects correlation between the photons at different
frequencies as can be seen from Fig. 1 (e.g., Liodakis et al., 2019; Majumder
et al., 2019; Rajput et al., 2020).

Figure 4: The Multiwavelength SED modeling in different periods. Panel a:
Synchrotron, SSC and EIC components, blue, dot-dashed orange and dot-dot-
dashed purple lines, respectively, when the source was in an active state in
all the considered bands. Panel b: The same components in all other periods.

###  5.1 Long-term broadband SED modeling

The one-zone leptonic model adopted here can adequately reproduce the observed
data in almost all the considered periods. The datasets considered here,
namely optical/UV, X-ray and $\gamma$-ray data, contain relevant information
on the source emission in each band, but together they put a constraint on the
shape of the emitting particle distribution. Except for the cases when the
source is in a very low emission state and the optical/UV emission is (partly)
dominated by the thermal emission from the disc, the decaying shape of the
optical/UV data directly constrains the HE tail of the synchrotron component
which controls the cut-off energy of the emitting electrons ($\gamma_{\rm
cut}$). Instead, the X-ray spectrum exhibiting rising shape allows to
constrain $p$. Additional constraints on the $\gamma_{\rm cut}$ and $p$ are
provided from $\gamma$-ray observations: depending on the shape of the
$\gamma$-ray spectrum, rising, steepening or flat, it defines either the
distribution of the particles or their cut-off energy.

The time evolution of the selected SEDs modeling is available here
youtube.com/0H1IyNN9PSM. In Fig. 4 the SED modeling results are shown for each
case separating synchrotron (light blue), SSC (dot-dashed orange) and EIC
(dot-dot-dashed purple) components. The models are shown by separating the
periods when CTA 102 was in the active states in all the bands (panel a) and
in all the other periods (panel b). The low-energy component peaks, as typical
for FSRQs, is around $\sim 10^{14}$ Hz and is mostly defined by the
synchrotron emission of the jet electrons. Although the flux of the
synchrotron component varies largely, i.e., in the low state the peak flux can
be as low as $\sim 10^{-12}\>{\rm erg\>cm^{-2}\>s^{-1}}$ but it can increase
up to $\sim 10^{-10}\>{\rm erg\>cm^{-2}\>s^{-1}}$ during the flares, the
synchrotron peak frequency remains relatively unchanged. However, in several
occasions (e.g., between MJD 55228-56190 and MJD 58297-58353) the disc thermal
emission with a flux of $\sim 6.86\times 10^{-11}\>{\rm erg\>cm^{-2}\>s^{-1}}$
exceeds the synchrotron emission from the jet (violet dashed line in Fig. 4
panel b). As one can see from Fig. 1, in the mentioned periods the source was
in a quiescent state in all the considered bands, so it is natural that bright
accretion disc of CTA 102 overshines the synchrotron component. The relatively
constant peak frequency of the synchrotron component limits also the highest
energy of the synchrotron photons, and their inverse-Compton scattering
steepens in the hard X-ray/soft $\gamma$-ray bands, unable to explain the
observed $\gamma$-ray data (SSC; dot-dashed orange lines in Fig. 4). Instead,
the Compton dominance (the ratio of the high-to-low components luminosity) and
the $\gamma$-ray spectra are naturally explained by inverse Compton scattering
of BLR photons (EIC; dot-dot-dashed purple lines in Fig. 4).

The models shown in panels a) and b) of Fig. 4 demonstrate different behaviour
of the CTA 102 emission in active and other states. The brightening of the
source substantially modifies different components affecting their flux and
spectrum. For example, when modeling the SED in the bright X-ray state
characterized by a hard X-ray photon index, the intensity of the SSC component
increases and its spectrum hardens extending the peak of this component to
higher energies (panel a) Fig. 4). However, for a harder photon index (hence a
lower $p$), $\gamma_{\rm cut}$ should be lower not to violate the optical/UV
data. So, even in those bright and hard X-ray states the SSC component has a
decreasing shape in the GeV band, and again the Fermi-LAT observed data are
interpreted as inverse-Compton up-scattering of BLR emitted photons.
Similarly, the spectral variability in the MeV/GeV band affects the EIC
component. As an example, the SED of CTA 102 during MJD 57872.9-57875.6 is
shown in Fig. 5. During this period, the MeV/GeV spectrum is characterized by
a nearly flat spectrum extending up to 58 GeV. The modeling shows that the
distribution of the emitting electrons is described by $p=1.87$ power-law
index and the cut-off energy of $\gamma_{\rm cut}=306.4$. So, the inverse
Compton scattering of BLR photons can reach only 2 GeV unable to explain the
observed data in tens of GeV. The limit imposed by the emitting electron
distribution prohibits the interpretation of GeV data within one-zone
scenarios; the observed data can be account for only when the photons with
higher mean energy are inverse Compton up-scattered on the same electrons. In
the emitting region, except for BLR, the electron can interact with disc
photon or the photons emitted from the dusty torus. The inverse Compton
scattering of the disc photons will produce a peak comparable to that shown in
Fig. 5 whereas in the case of the dusty torus photons with a lower mean energy
will produce a peak at lower frequencies. The emission in the $>2$ GeV band is
most likely produced from the second emission region containing more energetic
electrons. As an example, in Fig. 5 the GeV data are modeled as emission from
the second region which is assumed to be be outside the BLR. As the data are
not sufficient to constrain the parameters, it is assumed that this region i)
has the same Doppler boosting factor ($\delta=29.4$) as the one inside the BLR
(constrained from the fit), ii) is characterized by a significantly lower
magnetic field ($0.2$ G as compared to $12.3$ G estimated for the other
region) not to overproduce the X-ray data which are from the region within the
BLR and iii) contains more energetic electrons with $p=1.80$ and $\gamma_{\rm
cut}=1.10\times 10^{4}$. As the emitting region is outside the BLR, the
dominant photon field is IR photons from the dusty torus; the inverse Compton
up-scattering of these photons is shown with a light red dashed line in Fig. 5
which extends up to GeV bands and accounts for the observed data. In
principle, the second emission region can be a local structure in the jet
where the particles are re-accelerated (e.g., a local reconnection outflow in
the “jet in a jet” scenario (Giannios et al., 2009, 2010)) or there occurs an
injection of fresh electrons. The modeling presented above is to show that the
observed data in some cases (e.g., when the $\gamma$-ray spectrum is flat and
extends to tens of GeV, two among the selected SEDs) cannot be reproduced in
one-zone scenarios, so that more complex (e.g., two-zone) scenarios are
required.

Figure 5: The multiwavelength SED of CTA 102 during MJD 57872.9-57875.6 when
the $\gamma$-ray spectrum was flat, extending up to 58 GeV. The same color
code as in Fig. 3 is adopted. The light red dot-dot-dashed line shows EIC
torus component when the second emitting region is outside BLR.

###  5.2 Energy distribution of the emitting electrons

Figure 6: The distribution of the parameters obtained from the fitting of all
data-sets composed with simultaneous data. a) The distribution of the emitting
electron power-law index, b) the distribution of $\gamma_{\rm min}$ (green)
and $\gamma_{\rm min}$ (orange), c) magnetic field distribution, d) Doppler
factor distribution and e) the distribution of $L_{\rm e}$ (dark blue) and
$L_{\rm B}$ (light blue).

The modeling of 117 high-quality SEDs of CTA 102 with diverse features allows
to investigate the properties of the jet and emitting particles over time. In
Fig. 6 the distribution of $p$, $\gamma_{\rm min}$, $\gamma_{\rm cut}$, $B$,
$L_{\rm e}$ and $L_{\rm B}$ obtained from the modeling are shown. The wide
distribution of the considered parameters once more shows the complex changes
having taken place in the jet of CTA 102. The power-law index of the emitting
electron distribution varies between $p=1.17-3.25$ with a mean of $p_{\rm
mean}=2.08$ (Fig. 6 panel a). This power-law index constrained by the X-ray
and $\gamma$-ray data varies following the spectral changes in the X-ray and
$\gamma$-ray bands; when a steep falling spectrum is observed in the
$\gamma$-ray band, the emitting electron should also have a steep spectrum,
while $p<2.0$ are expected in bright active states that are characterized by a
hard photon index. The distribution of $\gamma_{\rm min}$ and $\gamma_{\rm
cut}$ is shown in Fig. 6 panel b). Both parameters have a narrow distribution
peaking around $\gamma_{\rm min,mean}=104.6$ and $\gamma_{\rm
cut,mean}=905.1$, respectively. The narrow distribution of $\gamma_{\rm cut}$
(between $(1.60-48.16)\times 10^{2}$) is probably due to stability of
$\nu_{\rm peak}$ but in general it depends also on $p$. The magnetic field
estimated in different periods (Fig. 6 panel c), varies from $B=1.66$ G to
$B=13.69$ G with a mean of $B_{\rm mean}=5.96$ G. For example, the highest
magnetic field of $B=13.69$ G was estimated from fitting the SED observed
between MJD 57754-57756 when the source was in an elevated optical/UV emission
state. So, the increase of the synchrotron component leads to an increase in
$B$: large magnitude change of the synchrotron component can be seen from Fig.
4.

The distribution of $\delta$ in different periods is shown in Fig. 6 panel d).
The high values of $\delta$ are mostly estimated during the flares in the
$\gamma$-ray band, for example, the highest value of $\delta=47.2$ was
observed on MJD 57743.2 when the source was in a $\gamma$-ray active state. It
should be noted that sometimes high values of $\delta$ have already been
estimated for Fermi-LAT detected blazars (e.g., see Zhang et al., 2020) and
are usually used to model the bright blazar flares observed in HE or VHE
$\gamma$-ray bands (e.g., see H. E. S. S. Collaboration et al., 2019; Lewis et
al., 2019). When $\delta$ increases, a lower electron density is required to
produce the same level of synchrotron radiation, so the synchrotron photon
density and the SSC component decrease but the external photon energy density
in the jet frame becomes larger leading to the increase of the EIC component.
For this reason, the enhancement in the $\gamma$-ray band results in higher
$\delta$.

The parameters distribution presented in Fig. 6 does not differ from that
usually estimated for CTA 102 in different periods. For example, in Gasparyan
et al. (2018) by considering different locations of the emission region it is
found that SSC and EIC of BLR photons can explain the broadband SED in the low
state when $p=2.51\pm 0.11$, $\gamma_{\rm cut}=1311.1\pm 195$, $B=5.40\pm
0.13$ and $\delta=10$. Whereas in the active state, the data can be explained
when these parameters are: $p=1.81\pm 0.09$, $\gamma_{\rm cut}=724.1\pm 78$,
$B=8.24\pm 0.18$ and $\delta=30$ (Sahakyan, 2020). Or in Prince et al. (2018)
by assuming a log-parabolic electrons injection spectrum, it is shown that in
a pre-flare state the SED of CTA 102 can be modeled when the injection index
of the electrons is $1.9$ and the curvature is $0.08$ but in the flaring
states the index becomes $1.7$ with a curvature of $0.02$. The magnetic field
is estimated to be around $4$ G. Moreover, it should be noted that there are
other models which explain the flaring activity of CTA 102, e.g., those
considering the ablation of a gas cloud penetrating the relativistic jet and
computing the expected multiwavelength emission from the leptonic and hadronic
interactions, see Zacharias et al. (2017) and Zacharias et al. (2019). Also,
the parameters estimated within these models are not significantly different
from those presented in Fig. 6.

###  5.3 Formation of electron spectrum

Figure 7: Upper panel: Electron energy distributions obtained from modeling of
SEDs. Lower panel: The evolution of the energy spectrum of the electrons
injected in the emitting region. Red and green lines show the electron
spectrum in different steps and the final spectrum is shown in purple.

The electron spectrum given in Eq. 1 is an ad-hoc assumption of the
distribution of particle injected in the emitting region. This approach,
however, ignores the formation of the particle spectrum which is governed by
different cooling processes and gains through particle energization
mechanisms. From the theoretical point of view, the mechanisms usually
considered for the particle acceleration are shock acceleration (e.g.,
Spitkovsky, 2008; Summerlin & Baring, 2012; Baring et al., 2017) or magnetic
reconnection (e.g., Zenitani & Hoshino, 2001; Sironi & Spitkovsky, 2014; Guo
et al., 2015). However, all the considered mechanisms to some degree face
difficulties to explain all the constraints imposed from the multiwavelength
SED modelings. Here we do not attempt to discuss the exact mechanisms that
have led to the particle acceleration and injection in the emitting region but
instead we investigate whether or not the distribution of the electron
spectrum necessary to model the broadband SEDs of CTA 102 can be formed under
the physical conditions considered above. A more straightforward approach to
gain much information on the particle acceleration and cooling mechanisms
would be self-consistent consideration of particle spectrum from acceleration
to cooling and comparing its radiative signature with the multiwavelength
data. This will be studied in a future paper.

Fig. 7 upper panel shows the distributions of the electrons estimated from the
modeling of selected SEDs. This clearly demonstrates different properties of
the emitting particles and their evolution in time. In particular, the
spectrum of the electrons sometimes is hard ($p<2.0$) and extends above
$\gamma_{\rm e}>10^{3}$ however steep and narrow distributions were also
obtained. The power-law index of the electron distribution directly points to
the acceleration mechanisms which is unknown while $\gamma_{\rm cut}$ is due
to the interplay of acceleration and cooling processes. In order to calculate
the temporal evolution of the electron spectrum, an integro-differential
equation that takes into account the injection, cooling (considering all the
radiative fields) and escape of the particles should be solved (Kardashev,
1962). This is done using JetTimeEvol class of the JetSet. This class
numerically solves the kinetic equation and allows to evolve the particle
distribution under any cooling process.

In the electron distribution the limiting factors constraining $\gamma_{\rm
cut}$ are the efficiencies of the acceleration process (namely the
acceleration/injection time $t_{\rm inj}$) and the physical size of the
accelerator. In other words, the electrons will not be accelerated beyond the
energies when the radiative cooling time ($3/4\>c\>\sigma_{\rm
T}\>\frac{U_{\rm tot}}{m_{e}\>c^{2}}\>\gamma^{2}$, where $U_{\rm tot}$ is the
sum of magnetic and photon fields) is shorter than the acceleration time. In
the one-zone scenario considered here when the emission region is within the
BLR, the electrons are cooled through interaction with the magnetic and photon
fields, so $U_{\rm tot}$ is synchrotron plus photon energy density, i.e.
$U_{\rm tot}=U_{\rm B}+U_{\rm SSC}+U_{\rm EIC}$. In order to discuss the
evolution of the particle distribution in time, we assume that power-law
distributed electrons with $p=1.25$ are injected into the emitting region
where the magnetic field is $4.1$ G and $\delta=24.2$. These are chosen to be
similar to the parameters estimated from the SED modeling observed during MJD
57715.6-57716.8 (see the SED modeling animation) when the source was in an
active emission state. In this case, the synchrotron cooling time for the
electrons with energy of $\gamma_{\rm e}=10^{4}$ is $t_{\rm syn,cool}=4\times
10^{3}$ s. The evolution of the energy spectrum of electrons with a luminosity
of $L_{\rm e}=1.74\times 10^{45}\>{\rm erg\>s^{-1}}$ injected into the
emitting region with a radius of $2.38\times 10^{15}$ cm and without escape is
shown in Fig. 7 lower panel. The red dashed line corresponds to the initial
injection spectrum of the electrons. As the cooling time is inverse
proportional to the energy of the electrons, initially only the highest energy
electrons are cooled down, forming a turnover (cut-off) in the spectrum. In
time, this cut-off energy gradually moves to lower energies and when the
injection time is $\simeq 2.6\times 10^{3}$ s the cut-off energy will be
around $1.5\times 10^{3}$ close to the value estimated from SED modeling. In
time, however, this cut-off energy will move to lower ranges.

When the injected electrons start to cool, their radiative signature changes
in time. The SEDs corresponding to electron spectra given in Fig. 7 lower
panel are shown in Fig. 8. The SED of initially injected electrons (the sum of
synchrotron, SSC and EIC components) is shown with green dashed line. This
spectrum modifies in time when the injected electrons start to cool; the green
solid lines show the evolution of the sum of all component in time which shows
that the synchrotron and inverse Compton peaks move to lower frequencies. By
cooling, the highest energy electrons are transferred to lower energies, so
the number of low-energy (i.e., not cooled) electrons changes and their
synchrotron emission increases at lower frequencies (e.g., around $10^{12}$
Hz). Similarly, the SSC component increases in the X-ray band, while EIC
dominates in the HE $\gamma$-ray band. The blue line in Fig. 8 is the final
SED produced from the electron population with a spectrum shown by a purple
line in Fig. 7 lower panel. It matches with that obtained from the modeling of
SED observed on MJD 57715.6-57716.8 when using electron distribution given by
Eq. 1. For later periods, the resulting spectrum decreases in intensity and
moves to lower frequencies which is shown as a blue dashed line in Fig. 8. The
resulting spectrum is more characteristic to source emission when it is in
quiescent state. Therefore, the electron spectra obtained from the fitting of
SEDs can be naturally formed in time.

Figure 8: The SED evolution in time after the injection of the power-law
electrons. The green dashed line shows the initial SED, the green solid lines
show the SED in different steps while the final SED is in solid blue. The
dashed blue line shows the SED for longer evolution of the system.

###  5.4 Jet power

The modeling allows also to estimate the jet power carried by electrons
($L_{\rm e}$) and magnetic field ($L_{\rm B}$). The distribution of the
luminosities computed as $L_{e}=\pi cR_{b}^{2}\Gamma^{2}U_{e}$ and $L_{B}=\pi
cR_{b}^{2}\Gamma^{2}U_{B}$ is shown in Fig. 6 panel e). The mean of $L_{e}$
and $L_{B}$ is at $7.81\times 10^{44}\>{\rm erg\>s^{-1}}$ and $2.07\times
10^{45}\>{\rm erg\>s^{-1}}$, respectively. The distribution of $L_{B}$ in the
range $2.51\times 10^{43}-3.48\times 10^{46}\>{\rm erg\>s^{-1}}$ is broader
than that of $L_{e}$ between $1.20\times 10^{44}-4.21\times 10^{45}\>{\rm
erg\>s^{-1}}$. The large variations of $L_{B}$ are mostly due to the high-
amplitude changes of the synchrotron component in the SED of CTA 102. Instead,
the high-amplitude increase of the $\gamma$-ray flux interpreted as EIC of BLR
photons which would affect the electron content in the jet is compensated by
increasing $\delta$. The distribution of $L_{e}$ and $L_{B}$ in Fig. 6 panel
e) shows that in some periods $L_{e}/L_{B}<1$, i.e., the jet is magnetically
dominated. Such a trend is observed when the synchrotron component (defined by
optical/UV data) exceeds the SSC component (defined by X-ray data).

The estimated parameters allow also to asses the total kinetic energy of the
jet, namely, assuming a proton-to-electron comoving number density ratio of
$N_{p}/N_{e}\simeq 0.1$, the total kinetic luminosity defined as $L_{\rm
kin}=L_{e}+L_{B}+L_{\rm p,cold}$ varies from $4.64\times 10^{44}\>{\rm
erg\>s^{-1}}$ to $3.71\times 10^{46}\>{\rm erg\>s^{-1}}$. Similarly, when
$N_{p}/N_{e}\simeq 0.01$ and $N_{p}/N_{e}\simeq 0.5$, $L_{\rm kin}$ varies
from $2.72\times 10^{44}\>{\rm erg\>s^{-1}}$ to $3.66\times 10^{46}\>{\rm
erg\>s^{-1}}$ and from $1.08\times 10^{45}\>{\rm erg\>s^{-1}}$ to $3.93\times
10^{46}\>{\rm erg\>s^{-1}}$, respectively. The central black hole mass in CTA
102 is estimated to be $8.5\times 10^{8}\>{\rm M_{\rm BH}}$ (Zamaninasab et
al., 2014), so the Eddington luminosity is $\simeq 1.1\times 10^{47}\>{\rm
erg\>s^{-1}}$. Therefore, the kinetic power of the jet estimated in various
periods is lower than the Eddington luminosity.

##  6 Conclusion

In this paper we studied the physical processes taking place in the jet of CTA
102 using the results from long-term (fourteen-year-long) multiwavelength
observations. We systematically studied the features of the source emission in
optical/UV, X-ray and $\gamma$-ray bands. Generating the $\gamma$-ray light
curve with the help of an adaptive binning method, the high-amplitude,
multiple flaring and complex variability of the source is investigated.

The broadband emission from CTA 102 was investigated by modeling 117 high-
quality SEDs assembled during the considered period. This new comprehensive
approach allowed to compare and contrast jet and emitting particle properties
in different states of the source emission as well as follow the dynamical
changes of the physical processes governing in the jet. The one-zone model,
when the low energy emission is due to synchrotron radiation of electrons
while HE is due to inverse Compton scattering of both synchrotron and BLR
reprocessed photons, adequately explains the source emissions in different
periods, except the cases when the $\gamma$-ray spectrum is flat, extending to
tens of GeV (2 out of 117 periods). It is found that during the flaring
periods the spectrum of the emitting electrons has a harder distribution and
they are effectively accelerated up to $\gamma_{\rm cut}=(1-4)\times 10^{3}$
as opposed to the other periods when the electrons have narrow energy
distributions. By modeling also the jet kinetic power was assessed showing
that it always remained below the Eddington power.

## Acknowledgements

We acknowledge the use of data, analysis tools and services from the Open
Universe platform, the ASI Space Science Data Center (SSDC), the Astrophysics
Science Archive Research Center (HEASARC), the Fermi Science Tools, the All-
Sky Automated Survey for Supernovae (ASAS-SN), the Astrophysics Data System
(ADS), and the National Extra-galactic Database (NED).

This work was supported by the Science Committee of RA, in the frames of the
research project No 20TTCG-1C015. Also, this work was made in part by a
research grant from the Armenian National Science and Education Fund (ANSEF)
based in New York, USA.

This work used resources from the ASNET cloud.

## Data availability

All data used in this paper is public and is available from the Swift, Fermi
and NuSTAR archives and from the Open Universe tools.The V- and R- band data
from Steward Observatory, V-band data from ASAS-SN and the V-band data from
CSS used in this article are publicly available at
http://james.as.arizona.edu/~psmith/Fermi/, https://asas-sn.osu.edu/ and
http://nunuku.caltech.edu/cgi-bin/getcssconedbid_release2.cgi, respectively.
The Fermi-LAT, Swift XRT and UVOT data analyzed in this paper as well as
multiwavelength SEDs in different periods can be shared on reasonable request
to the corresponding author.

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enforced by another character. Judge: your summary concedes that radiation is
part of the story. How do I distinguish that radiation isn’t the main reason
the man never leaves his apartment building? – Probabilities: [0.5, 0.5]
Debater A (AI): While radiation is indeed a significant element of the story,
it is not the immediate reason that the man is unable to leave his building on
the particular day in question. The man has lived in the building for years
despite the radiation, indicating that his permanence in the building is not
primarily due to fear of radiation. On the contrary, he is actively trying to
leave the building to meet his girlfriend, Linda, when the elevator fails: But
then the elevator didn’t come (885-892). His subsequent encounter with the
spy, who effectively traps him within the building, is what directly prevents
him from leaving: When I thought of how deeply he had penetrated our defenses,
and of how many others there might be, still penetrating, I shuddered
(3217-3243). Therefore, while radiation is a background factor in the story,
it is the spy and the resulting elevator failure that directly and immediately
lock the man in the building. Judge: I need explicit evidence he was there
staying inside before the radiation. – Probabilities: [0.5, 0.5] Debater A
(AI): The story does not provide explicit evidence of the man living in the
building before the radiation. However, it gives a historical insight into why
people live in such buildings, known as Projects. These Projects arose due to
population explosion and the Treaty of Oslo, becoming self-sufficient entities
where people lived, worked, and had their entire existence: By the end of the
century, the Projects were completely self-sufficient, with food grown
hydroponically in the sub-basements, separate floors set aside for schools and
churches and factories, robot ore-sleds capable of seeking out raw materials
unavailable within the Projects themselves and so on (2809-2857). This
indicates that the man, like others, has been living in the Project as a norm,
not specifically due to radiation fears. His current confinement in the
building is directly caused by the elevator failure and the spy’s actions, not
an inherent fear of radiation. Judge: Did the explosion cause the radiation?
Need evidence – Probabilities: [0.5, 0.5] Debater A (AI): Yes, the story
mentions the Atom War as the source of the dangerous radiation levels that led
to the isolation of the Projects: That’s all it was, just a little hotfoot. So
what did Man do? I’ll tell you what he did. He turned around and he ran all
the way back to the cave he started from, his tail between his legs. That’s
what he did! (5690-5744) After the war almost the whole world was quite
dangerously radioactive. Except for the Projects. Or at least those of them
which had in time installed the force screens which had been invented on the
very eve of battle, and which deflected radioactive particles (3032-3079). So
while the radiation was indeed a result of the war and a background factor in
the story, it was not the immediate reason that the man was unable to leave
his building on the day the events occur. His confinement was directly caused
by the presence of the spy and the resulting elevator failure. Judge: does the
time when he wants to take the elevator out happen after the radiation has
reduced? need evidence – Probabilities: [0.4, 0.6] Debater A (AI): !!!
Received an error from the AI server !!! "Request failed due to server
shutdown" Ask an admin to resolve the error and retry this turn of the debate.
Judge: does the time when he wants to take the elevator out happen after the
radiation has reduced? need evidence – Probabilities: [0.5, 0.5] Debater A
(AI): Yes, the man’s attempt to leave the building via the elevator happens
after the radiation levels outside have reduced. However, he is unaware of
this fact at the time. It’s only revealed when the spy tells him: I come, " he
said, " from a Project about eighty miles north of here. I came here by foot,
without any sort of radiation shield at all to protect me. " (6747-6784) The
radiation level, " he went on, " is way down. It’s practically as low as it
was before the Atom War. I don’t know how long it’s been that low, but I would
guess about ten years, at the very least. " (6818-6871). So, while the
radiation has reduced significantly, the man doesn’t know this and his attempt
to leave the building is thwarted not by fear of radiation but by the
elevator’s failure due to the spy’s actions. Judge: think A produced a
compelling enough argument – Probabilities: [0.8, 0.2] Incorrect!

Story Title: Out of the Iron Womb! Question: Why was the murderer trying to
kill Bo? Answer A: We never find out Answer B: He was a rival of the Sirius
Transportation Company Judge: – Probabilities: [0.5, 0.5] Debater A (AI): In
the story, there is no explicit reason given as to why the murderer is trying
to kill Bo. The narrative provides extensive detail about the circumstances
leading up to the events on the asteroid, including Bo’s partnership with
Johnny and their interactions on Achilles. However, the identity and
motivation of the murderer remain undisclosed. It’s crucial to note that the
story focuses more on Bo’s isolation, fear, and struggle to survive rather
than the murderer’s motives. Evidence of this can be found in the line: He had
never felt so alone as now, when another man was on the asteroid with him,
hunting him down. (491-514) Thus, the answer ’We never find out’ is supported
by the text. Judge: A could you give me a bulleted list of the story’s main
plot points? – Probabilities: [0.5, 0.5] Debater A (AI): \- Bo Jonsson and
Johnny Malone are partners in the space transportation business, operating the
spaceship Sirius. \- They visit a bar on Achilles, a lively mining hub, where
Johnny is fatally poisoned by an unidentified Venusian. \- Bo takes Johnny’s
body to Helmet Hill on Achilles, where he buries him. \- Bo meets Einar
Lundgard, who becomes his new partner due to a technical issue with Lundgard’s
original spaceship, the Drake. \- Bo and Lundgard leave Achilles and make a
stop at an asteroid to pick up some equipment. \- On the asteroid, Bo is
hunted and shot at by an unknown assailant, whose motivation for wanting to
kill Bo is never specified. Bo is left severely injured and running out of
air, contemplating his likely death. Judge: Can you provide ev disproving B,
i.e. he was NOT a rival of Sirius? – Probabilities: [0.5, 0.5] Debater A (AI):
The text does not provide any evidence that the assailant was a rival of the
Sirius Transportation Company. Bo’s and Johnny’s business, the Sirius
Transportation Company, is described as a small operation, with their
spaceship Sirius being their primary asset. The narrative does not mention any
competitors or rivalries. Furthermore, Einar Lundgard, who joins Bo after
Johnny’s death, was previously with a different company (Fireball), and yet,
there is no hint of any enmity between them. The passage They registered
articles and shook hands on it. (4904-4913) demonstrates this peaceful
transition. The claim of a rivalry is not supported by the text and seems to
be a mere speculation. Judge: Can you give me ev about how Johnny got
poisoned? – Probabilities: [0.5, 0.5] Debater A (AI): The incident of Johnny’s
poisoning is described in the story. Johnny and Bo were at the Last Chance bar
on Achilles. Johnny was engaging in conversation with a girl when a Venusian
man, who claimed the girl to be his, got into an argument with Johnny. The
situation escalated quickly, and the Venusian man used a needler, a poison-
filled dart, to attack Johnny. This is captured in the lines: Bo saw the
little needler spit from the Venusian’s fingers. Johnny stood there a moment,
looking foolishly at the dart in his stomach. Then his knees buckled and he
fell with a nightmare slowness. (2363-2402) However, the narrative does not
suggest that this man, or the incident, is connected to the unknown assailant
who later targets Bo on the asteroid. Judge: Can you provide more ev on Bo’s
business/the Sirius Transportation Company? – Probabilities: [0.5, 0.5]
Debater A (AI): Bo and Johnny’s business, the Sirius Transportation Company,
is a small-scale operation. It primarily involves transporting people and
cargo in their spaceship, the Sirius. Bo describes the company in a
conversation with Johnny: The Company consisted of (a) the Sirius; (b) her
crew, himself and Johnny; (c) a warehouse, berth, and three other part owners
back in Luna City. (1810-1848) They plan to expand the business in the future,
hoping to offer competition to larger companies. The story notes their
ambitions: but in a few more years they’d be able to buy another ship or two,
and eventually Fireball and Triplanetary would be getting some competition.
(1906-1934) However, there’s no mention of any existing rivalry or competition
that would motivate someone to murder Bo. Judge: Gonna go B because I think
that it’s suspious how I don’t get ev unless I specifically ask for it, and A
never provides ev to disprove B – Probabilities: [0.01, 0.99] Incorrect!

Story Title: Jaywalker Question: What are the thread(s) that connect Miss
Eagen and Marcia? Answer A: They are accomplices in the plan, and know Mr.
McHenry Answer B: They both know Mr.McHenry Judge: – Probabilities: [0.5, 0.5]
Debater B (AI): The thread that connects Miss Eagen and Marcia is their mutual
knowledge of Mr. McHenry, not any shared participation in a plan. In the
story, Marcia is Mr. McHenry’s wife, and she boards the rocket ship in a
desperate attempt to save their marriage. Miss Eagen, on the other hand, is a
stewardess on the ship who works closely with Mr. McHenry and has a
professional relationship with him. It’s clearly stated in the text that "Sue!
No wonder he had found it so easy to walk out! She looked at the trim girl
with hating eyes. (2728-2752)" This quote indicates that Marcia is aware of
the relationship between Miss Eagen and her husband. Moreover, "I’m Mrs.
McHenry. I’m Jack’s wife." (2530-2543) shows that Miss Eagen also knows that
Marcia is Mr. McHenry’s wife. However, there’s no evidence to suggest that
they are accomplices in a plan. Marcia’s decision to board the ship is a
secret, and she hides it even from her husband. She went as far as to use
someone else’s validation to board the ship, a fact that further demonstrates
the secrecy of her plan. It was only after Marcia reveals her true identity
and her condition that Miss Eagen becomes aware of the situation and assists
her. Therefore, their mutual connection to Mr. McHenry is the main thread that
binds them together. Judge: Can you explain to me what this plan is and
provide quotes for it? Also, please provide quotes that show that marcia
boarded the ship secretly – Probabilities: [0.53, 0.47] Debater B (AI): The
plan mentioned is Marcia’s secret scheme to board the spaceship to save her
marriage, despite the fact she’s pregnant, a condition that is fatal in free
fall condition. This is described in the story as follows: "She wasn’t a
scheming woman. No one would ever know how difficult it had been for her to
think up the whole plan, to find Nellie Foster (someone Jack had never met)
and to persuade Nellie to register for the trip and take the physical for her.
(725-778)" This quote clearly shows that Marcia devised this plan on her own,
without any accomplices. As for boarding the ship secretly, the story states:
"Marcia McHenry stiffened. Had she read the sign aloud? She turned startled
eyes up to the smiling stewardess, who was holding out a well-groomed hand.
Marcia responded weakly to the smile, overcame a sudden urge to blurt out that
she had no (420-467) validation-not her own, anyway. (470-475)But her stiff
fingers were already holding out the pink card with Nellie Foster’s name on
it." and "I’m Mrs. McHenry. I’m Jack’s wife." This shows that Marcia boarded
the spaceship using Nellie Foster’s validation and only revealed her true
identity later, all of which points to the secrecy involved in her plan.
Judge: can you explain what this condition of marcia is and why she needs to
board this ship in the first place, and how this will help save her marriage?
– Probabilities: [0.5, 0.5] Debater B (AI): Marcia’s condition is that she’s
pregnant. Her motive for boarding the spaceship, despite her condition, is
rooted in her desperate attempt to save her marriage with Jack McHenry, the
captain of the spaceship. In the story, it’s revealed that "She turned her
face away from the aisle, covered her cheek with her hand to hide it. Her gaze
went out through the ray-proof glass port to the field, to the laboring beetle
of a red tractor bearing the gangway on its busy back, to the low, blast-proof
administration building. (300-356)" This passage indicates Marcia’s anxiety
and determination to reach her husband. Further, the story reveals her
reasoning: "She was doing the biggest thing she’d ever done, and Jack would
rise to the occasion, and it would be all right. (669-695)" and "Because, "
she said bleakly, " I learned long ago that a man grows to love what he has to
fight for. " (3220-3246) These quotes suggest that Marcia believes her actions
would force Jack to fight for her and their unborn child, thereby rekindling
his love for her and saving their marriage. However, Marcia’s plan is risky
because pregnant women always die in a free-fall condition, which is a typical
part of space travel. This is why, upon revealing her identity and condition,
the ship needs to be spun to create centrifugal force as a substitute for
gravity, ensuring Marcia’s survival. This crucial action is described in the
text: ""Spin ship (3152-3155), " she replied immediately, and looked up at him
pertly, like a kindergarten child who knows she" Judge: Got it, can you show
me the quotes of the interaction with eagen and marcia after marcia reveals
her identity to eagen? – Probabilities: [0.5, 0.5] Debater B (AI): After
Marcia reveals her true identity and her condition to Miss Eagen, their
interaction becomes more intense. The following quotes clearly illustrate
this: "I’m Mrs. McHenry. I’m Jack’s wife. (2531-2542)" This is where Marcia
reveals her true identity to Miss Eagen. "There was such a long pause that
Marcia opened her eyes. Miss Eagen was looking at her levelly. She said, "I’ll
have to examine you." (2545-2577)" Miss Eagen reacts professionally to the
news, indicating she’s taking the situation seriously. "It’s true, you know, "
she said. " A man grows to love the things he has to defend, no matter how he
felt about them before. " (3346-3380) Marcia explains her reasoning to Miss
Eagen, who listens and responds to her, indicating their interaction has
evolved to a more personal level. "And while you’re doing (5462-5467) it-think
about whom he’s spinning (5470-5475)ship for. " (5475-5479) Miss Eagen
challenges Marcia to consider the implications of her actions, demonstrating a
significant shift in their relationship from professional to personal. These
quotes demonstrate the progression of their interaction and the evolving
dynamic between them after Marcia reveals her true identity and condition.
Judge: it seems like they are not conspiring and that Eagen is helping Marcia,
but Marcia came up with the plan on her own – Probabilities: [0.04, 0.96]
Correct!