# Modeling the Broadband Emission of 3C 454.3

N. Sahakyan,1,2,3
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
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The results of a long-term multiwavelength study of the powerful flat spectrum
radio quasar 3C 454.3 using Fermi-LAT and Swift XRT/UVOT data are reported. In
the $\gamma$-ray band, Fermi-LAT observations show several major flares when
the source flux was $>10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$; the peak
$\gamma$-ray flux above $141.6$ MeV, $(9.22\pm 1.96)\times 10^{-5}\>{\rm
photon\>cm^{-2}\>s^{-1}}$ observed on MJD 55519.33, corresponds to $2.15\times
10^{50}\>{\rm erg\>s^{-1}}$ isotropic $\gamma$-ray luminosity. The analysis of
Swift XRT and UVOT data revealed a flux increase, although with smaller
amplitudes, also in the X-ray and optical/UV bands. The X-ray emission of 3C
454.3 is with a hard spectral index of $\Gamma_{\rm X}=1.16-1.75$, and the
flux in the flaring states increased up to $(1.80\pm 0.18)\times 10^{-10}{\rm
erg\>cm^{-2}\>s^{-1}}$. Through combining the analyzed data, it was possible
to assemble 362 high-quality and quasi-simultaneous spectral energy
distributions of 3C 454.3 in 2008-2018 which all were modeled within a one-
zone leptonic scenario assuming the emission region is within the broad line
region, involving synchrotron, synchrotron self-Compton and external Compton
mechanisms. Such an extensive modeling is the key for constraining the
underlying emission mechanisms in the 3C 454.3 jet and allows to derive the
physical parameters of the jet and investigate their evolution in time. The
modeling suggests that during the flares, along with the variation of emitting
electron parameters, the Doppler boosting factor increased substantially
implying that the emission in these periods has most likely originated in a
faster moving region.

###### keywords:

quasars: individual: 3C 454.3 – galaxies: jets – gamma-rays: galaxies –
X-rays: galaxies

††pubyear: 2015††pagerange: Modeling the Broadband Emission of 3C
454.3–Modeling the Broadband Emission of 3C 454.3

##  1 Introduction

Blazars are a subclass of active galactic nuclei with a jet pointing or making
a small angle with respect to the observer (Urry & Padovani, 1995). These jets
are strong sources of electromagnetic radiation ranging from radio to high
energy (HE; $>100$ MeV) and very high energy $\gamma$-ray bands (see Padovani
et al. 2017 for a recent review). This emission is characterized by rapid and
high-amplitude variability in almost all wavelengths, the most extreme being
at $\gamma$-ray band (e.g., order of minutes, Ackermann et al., 2016; Foschini
et al., 2011; Foschini et al., 2013; Nalewajko, 2013; Brown, 2013; Rani et
al., 2013a; Saito et al., 2013; Hayashida et al., 2015; Shukla et al., 2018).
Blazars are dominant sources in the extragalactic $\gamma$-ray sky and have
been observed even at very high redshifts (e.g., Ackermann et al., 2017;
Sahakyan et al., 2020). The recent studies of 4FGL J1544.3-0649 reveal the
possible existence of transient blazars; being undecteable in the X-ray and
$\gamma$-ray bands, 4FGL J1544.3-0649 for a few months rose to be one of the
brightest known X-ray blazars (Sahakyan & Giommi, 2021). If 4FGL J1544.3-0649
does not indeed represent an isolated case but rather a common phenomenon,
this would have a non-negligible role in the multimessenger astrophysics.
The broadband spectral energy distribution (SED) of blazars is characterized
by two broad humps, one at optical/UV/X-ray bands and the other in the HE
$\gamma$-ray band (see Padovani et al. 2017 for a recent review). It is
believed that the first peak (low energy component) is mostly due to
synchrotron emission from relativistic electrons, whereas the origin of the
second component is highly debatable. Within conventional leptonic scenarios,
this component is produced when the synchrotron emitting electrons inverse
Compton up scatter the photons of internal (synchrotron self Compton (SSC)
Ghisellini et al., 1985; Bloom & Marscher, 1996; Maraschi et al., 1992) or
external (external inverse Compton (EIC) Błażejowski et al., 2000; Ghisellini
& Tavecchio, 2009; Sikora et al., 1994) origin. The nature of the external
photon fields depends on the distance of the emitting region from the central
black hole (Sikora et al., 2009) and can be dominated either by the photons
directly emitted from the accretion disk (Dermer & Schlickeiser, 1993; Dermer
et al., 1992) or disk photons reflected from the broad-line region (BLR;
Sikora et al., 1994) or IR photons emitted from the dusty torus (Błażejowski
et al., 2000). Recently, after associating TXS 0506+056 with the
IceCube-170922A neutrino event (IceCube Collaboration et al., 2018a, b;
Padovani et al., 2018), it is more evident that the HE component could be
initiated by the interaction of energetic protons when they are effectively
accelerated in the blazar jets. The HE component can be either from proton
synchrotron emission (Mücke & Protheroe, 2001) or from secondary particles
from pion decay (Mannheim, 1993; Mannheim & Biermann, 1989; Mücke & Protheroe,
2001; Mücke et al., 2003; Böttcher et al., 2013). In the latter case, blazars
are also sources of very high energy neutrinos (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).
Based on the properties observed in the optical band, blazars are classified
as Flat Spectrum Radio Quasars (FSRQs) when the emission lines are stronger
and quasar-like or BL Lacs when these lines are weak or absent (Urry &
Padovani, 1995). Alternatively, blazars are FSRQs when the luminosity of the
broad emission lines (or accretion disk) measured in Eddington units is
$L_{\rm BLR}/L_{\rm Edd}\geq 5\times 10^{-4}$, otherwise they are BL Lacs
(Ghisellini et al., 2011; Sbarrato et al., 2012a). Depending on the position
of the synchrotron component peak ($\nu_{\rm s}$), the blazars are further
classified as low synchrotron peaked (LSP) sources, when $\nu_{\rm s}<10^{14}$
Hz, intermediate synchrotron peaked (ISP) and high synchrotron peaked (HSP)
sources when $10^{14}<\nu_{\rm s}<10^{15}$ Hz and $\nu_{\rm s}>10^{15}$ Hz,
respectively (Padovani & Giommi, 1995; Abdo et al., 2010b). However, sometimes
the synchrotron peak of HSPs can reach $\sim$1 keV, ($\sim 2\times 10^{17}$
Hz) or beyond, showing an extreme behaviour (e.g. Giommi et al., 1999;
Costamante et al., 2001; Biteau et al., 2020). Such behaviour was first
observed during the flare of Mkn 501 when the synchrotron peak reached $\sim
100$ keV (Pian et al., 1998), and then many such objects were identified in
the X-ray observations. For example, during the flares of 1ES 1218+304 the
X-ray spectral index hardened to $\Gamma\leq 1.80$, shifting the peak towards
higher energies (Sahakyan, 2020a). In this classification, FSRQs usually have
a synchrotron peak at $\nu_{\rm s}<10^{14}$ Hz, so they are LSPs.
The BL Lac and FSRQ SEDs demonstrate different properties. In FSRQs, the
strong external photon fields which are weak or absent in the case of BL Lacs,
modify the HE component: these external photons are seen relativistically
boosted in the comoving frame of the jet and can dominate over the internal
synchrotron photon fields, giving rise to the EIC component (e.g., Gasparyan
et al., 2018; Sahakyan & Gasparyan, 2017). Therefore, in FSRQs the luminosity
of the second component is usually larger, i.e. shows a larger Compton
dominance (Sikora et al., 1994) due to the presence of external seed photons.
The shape of this component depends on the distribution of up-scattering
photons which in its turn is defined by the distance of the emitting region
from the central black hole. So, the modeling of the SED or features in the
$\gamma$-ray spectrum (e.g., break or cut-off) can help to localize the
emission region (e.g., Poutanen & Stern, 2010; Aleksić et al., 2011; Sahakyan,
2020b).
3C 454.3 is a typical FSRQ at $z=0.859$ harboring a black hole with a mass
estimated to be $1.5\times 10^{9}\>M_{\odot}$ (Woo & Urry, 2002; Liu et al.,
2006). This source was extensively studied in the multiwavelength band over
the last two decades (e.g., Giommi et al., 2006). However, after the prominent
optical outburst in 2005 with a peak optical brightness of $R=12$ mag, the
source remained active showing several bright flares, it has become a target
of multiwavelength studies (Raiteri et al., 2008, 2011; Pacciani et al., 2010;
Abdo et al., 2011, 2009; Ackermann et al., 2010; Jorstad et al., 2013; Amaya-
Almazán et al., 2021). This multiwavelength campaigns provided unprecedented
information on this source. For example, Bonning et al. (2009) studying the
multiwavelength data observed during the high flux state in July 2008, showed
that the emissions in IR, optical, UV, and $\gamma$-ray bands are well
correlated while the X-ray flux is correlated with none of these fluxes. These
features in the multiwavelength variability can be naturally explained within
the EIC scenario. However, Bonnoli et al. (2011) found that the optical, X-ray
and $\gamma$-ray fluxes correlate during the extreme brightening of 3C 454.3
in the first week of December 2009. In the $\gamma$-ray band the source was
first detected by EGRET on the Compton Gamma-Ray Observatory (Hartman et al.,
1993) and then extensively monitored by AGILE and Fermi large area telescope
(Fermi-LAT) since 2007. The AGILE observations have shown that the 3C 454.3
was in active $\gamma$-ray state in several occasions (Donnarumma et al.,
2009; Pacciani et al., 2010; Vercellone et al., 2011). In 2010 during the
exceptional bright $\gamma$-ray flare Fermi-LAT detected a flux above $\sim
10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$ from 3C 454.3 which corresponds to
$\sim 10^{50}\>{\rm erg\>s^{-1}}$ isotropic luminosity, making 3C 454.3 one of
the brightest $\gamma$-ray sources in the sky (Abdo et al., 2011). During the
flaring of 3C 454.3, different extraordinary changes in terms of spectral and
temporal properties were reported in the multiwavelength context and
especially in the $\gamma$-ray band. For example, Abdo et al. (2009) found
that the $\gamma$-ray spectrum of 3C 454.3 steepens above $\sim 2$ GeV and it
is better explained by a broken power-law with photon indices of $\sim 2.3$
and $\sim 3.5$ below and above the break, respectively. This turnover in the
spectrum was interpreted by the spectral break in the electron distribution;
however, Finke & Dermer (2010) interpreted the break to be due to the inverse
Compton scattering of accretion disk and BLR photons.
In this paper, the evolution of the multiwavelength SED of 3C 454.3 during
2008-2018 as well as the spectral changes in different bands are investigated.
These changes in the SED are expected to arise from the variation of the
parameters of the emitting electrons or the physical parameters of the
emission region (Paggi et al., 2011), so, they directly define the physical
processes taking place in the jet as well as the state of the plasma in it.
For this reason, in the period from 2008 to 2018, as many SEDs of 3C 454.3 as
possible that can be constructed with contemporaneous data from the radio to
HE bands have been modeled within a leptonic scenario. More explicitly, these
SEDs are modeled assuming the low energy component is due to synchrotron
emission whereas the second component is due to SSC and/or EIC by the same
electrons. Through such modeling the jet parameters are estimated for
different periods allowing to investigate their variation which could help to
investigate the changes in the jet of 3C 454.3 as well as to understand the
origin of the flares. 3C 454.3 was selected because of i) the availability of
rich multiwavelength data (e.g., more than 465 observations with Neil Gehrels
Swift Observatory (hereafter Swift) and continuous monitoring by Fermi-LAT)
and ii) its large amplitude variability in almost all wavelengths.
In the current paper the origin of the multiwavelength emission from 3C 454.3
is investigated using the multiwavelength data accumulated during 2008-2018.
The paper is structured as follows. Section 2 presents the multiwavelength
data analyzed in the current study. The evolution of SED in time is presented
in Section 3. The modeling of SEDs is presented in Section 4 and the
discussions in Section 5. The conclusion is given in Section 6.

Figure 1: The multiwavelength light curve of 3C 454.3 between May 01, 2007 and
August 04, 2018. From top to bottom: adaptively binned $\gamma$-ray light
curve ($>141.6$ MeV), 3-day binned $\gamma$-ray light curve ($>100$ MeV),
Bayesian block representation of the $\gamma$-ray light curve, 2.0-10 keV
X-ray flux, 0.3-10.0 keV X-ray photon index, flux in V, B, and U filters and
flux in W1, M2 and W2 filters.

##  2 Multiwavelenth Observations

3C 454.3, being among the brightest $\gamma$-ray blazars, was frequently
monitored in different energy bands. Here, the emission of 3C 454.3 in the
optical/UV, X-ray and $\gamma$-ray bands is investigated using the data from
Fermi-LAT, Swift UVOT and XRT telescopes.

###  2.1 Fermi-LAT data

Fermi-LAT on board the Fermi Gamma-ray Space Telescope is a pair-conversion
telescope sensitive to $\gamma$-rays in the energy band from $20$ MeV to $500$
GeV. Scanning the entire sky every $\sim 3$ hours, it provides the deepest
view of the $\gamma$-ray sky (Atwood et al., 2009).
In the current study, the publicly available Fermi-LAT data accumulated
between August 4, 2008 and August 4, 2018 are used. The Pass 8 (P8R3) Fermi-
LAT events in the energy range from 100 MeV to 500 GeV extracted from a
$12^{\circ}$ region of interest (ROI) around the $\gamma$-ray position of 3C
454.3 (RA $=343.497$ and Dec $=16.149$) have been analyzed using Fermi
ScienceTools (1.2.1) and the P8R3_ SOURCE_ V2 instrument response functions
(IRFs). With the help of gtselect tool the front and back events of type 3 and
event class $128$ coming from zenith angles smaller than $90^{\circ}$, to
reduce contamination by photons from Earth’s atmosphere, were selected.
Instead, the good time intervals are selected with gtmktime tool using the
filter expression (DATAQUAL $>$0) and (LAT CONFIG$==$1). The events are binned
within a $16.9^{\circ}\times 16.9^{\circ}$ square region with a stereographic
projection into $0.1^{\circ}\times 0.1^{\circ}$ pixels and into 37 equal
logarithmically spaced energy bins with the help of gtbin tool. Then, an
exposure map in the ROI with $22^{\circ}$ radius was computed using tasks
gtltcube and gtexpmap. The background point sources from the Fermi-LAT fourth
source catalog (4FGL; Ajello et al., 2020) within ROI+5 from the position of
3C 454.3 were all included in the model file with the same spectral models as
in the catalog. The normalization and spectral parameters of the sources
within the ROI were set as free parameters, while that of the sources outside
ROI were fixed to the catalog values. The model file contains the standard
templates describing the diffuse emission from the Galaxy (gll_ iem_ v07) and
the isotropic $\gamma$-ray background (iso_ P8R3_ SOURCE_ V2_ v1). The
normalization of both components is considered as a free parameter in the
analysis. Initially, the binned likelihood analysis is applied to the full
time data set using the gtlike tool.
In the light curve calculations (shorter periods), the flux and photon index
are estimated applying unbinned likelihood analysis. The photon indexes of all
sources except 3C 454.3 are fixed, only keeping free the normalization of the
sources within the ROI. As no variability is expected from background models,
their normalization was fixed. Since the likelihood fitting is performed for
short periods, the spectrum of 3C 454.3 was modeled as a power-law (PL) with
the normalization and photon index as free parameters. The significance of the
source emission in each interval is evaluated using test statistics defined as
$TS=2log(L_{1}/L_{0})$, where $L_{0}$ and $L_{1}$ are the likelihoods of the
model without source (null hypothesis) and the alternative likelihood (with
source), respectively.
3C 454.3 is a well known strongly variable $\gamma$-ray blazar, so the light
curve is computed in two different ways. Initially, the light-curve with 3-day
binning was calculated (Fig. 1 panel b), but at this fixed time binning the
fast variation of the flux will be smoothed out and the true increase or the
variation of the flux cannot be investigated. In the case of short time
intervals, the flux can be estimated only in the active state when the source
is bright. Thus, in order to have a deeper and detailed view of the
$\gamma$-ray flux variation, the light curve was generated with the help of
the adaptive binning method (Lott et al., 2012). In this case, the bin width
is defined by requiring a constant relative flux uncertainty, so the time bins
are longer during low flux levels and narrower when the source is in flaring
state. The light curve generated by this method is a powerful tool for
investigation of the flux variations in short time scales and identification
of flaring periods as well as it contains maximum possible information on the
flux variation (e.g., see Gasparyan et al., 2018; Sahakyan et al., 2018;
Zargaryan et al., 2017; Baghmanyan et al., 2017; Britto et al., 2016; Rani et
al., 2013b).
The adaptively binned light curve with 20% uncertainty and above $E_{0}=141.6$
MeV (for $E_{0}$ see Lott et al., 2012) is in Fig. 1 panel a) showing the
complex behavior of 3C 454.3 in 2008-2018. The source is so bright that the
flux and photon index were estimated in 11698 time intervals providing a
possibility to investigate the $\gamma$-ray flux changes also in hour scales.

Figure 2: The distribution of the $\gamma$-ray flux estimated in adaptively
binned intervals. The red line shows the fit with three Gaussian functions.

The source exhibited several substantial $\gamma$-ray flaring events during
the considered period. In the low state (e.g., MJD 55800-56140) the
$\gamma$-ray flux is of the order of $\simeq 5\times 10^{-8}\>{\rm
photon\>cm^{-2}\>s^{-1}}$, however, during the flares the flux was above
$10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$. The major $\gamma$-ray flaring
activity was observed during MJD 55517-55522 when the highest $\gamma$-ray
flux of $(9.22\pm 1.96)\times 10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$ above
141.6 MeV was observed on MJD 55519.3 with $15.6\sigma$ significance which is
$1844$ times higher than the lowest $\gamma$-ray flux. Interestingly, there
are in total 1657 time intervals when the source flux was above $10^{-5}\>{\rm
photon\>cm^{-2}\>s^{-1}}$ which were observed in different periods, showing
that from time to time the source was in a powerful $\gamma$-ray emitting
state. Fig. 2 shows the distribution of the $\gamma$-ray flux of 3C 454.3
estimated in 11698 intervals. The distribution shows three peaks which
characterize different states of the source. The fit of these peaks with three
Gaussian functions is shown with red line in Fig. 2. The first peak is at
$1.71\times 10^{-6}\>{\rm photon\>cm^{-2}\>s^{-1}}$ which is the average
$\gamma$-ray flux of the source. The other two peaks are at $9.32\times
10^{-6}\>{\rm photon\>cm^{-2}\>s^{-1}}$ and $3.9\times 10^{-5}\>{\rm
photon\>cm^{-2}\>s^{-1}}$, respectively, when the source was in an active
$\gamma$-ray emitting state. Especially interesting are the periods when the
flux exceeded the third peak; for example, in 72 intervals the source was in a
hyperactive state when the $\gamma$-ray flux varied within $(5.01-9.22)\times
10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$, corresponding to an apparent
isotropic $\gamma$-ray luminosity of $(0.88-5.69)\times 10^{50}\>{\rm
erg\>s^{-1}}$, which is the range of the highest $\gamma$-ray luminosity
observed from blazars so far. It is interesting to note that the 3C 454.3 flux
was $>10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$ for 30.8 days in total ($\sim
0.84$ % of the considered ten years). This once more confirms that 3C 454.3 is
extremely variable in the $\gamma$-ray band.

Figure 3: Photon index versus flux. Left panel: The $\gamma$-ray photon index
vs. the flux during the major $\gamma$-ray flare (MJD 55400-55800) estimated
in 3-day bins. Right panel: The X-ray photon index vs. the flux during MJD
55400-55600.

The evolution of the $\gamma$-ray photon index in the considered ten years was
also investigated. Unlike the fast $\gamma$-ray flux variation, the photon
index does not vary significantly. It is hard to investigate the photon index
variation when adaptive bins are considered, as the time intervals are short
and the photon index is estimated with large uncertainty; the simple
$\chi^{2}$ test results in $\chi^{2}/dof\simeq 1.01$ with a probability of
$P(\chi^{2})=0.12$, implying a relatively constant photon index. Instead, in
the light curve with 3-day bins, the accumulation time is enough for precise
estimation of the photon index showing that it varies as well. Considering
only the intervals when TS $>$ 16, the hardest photon index of $1.87\pm 0.04$
was observed on MJD $56559.16\pm 1.5$ with $47.5\sigma$. The source flux was
$(2.54\pm 0.15)\times 10^{-6}\>{\rm photon\>cm^{-2}\>s^{-1}}$, implying the
source was in an average $\gamma$-ray emitting state. Furthermore, the
$\gamma$-ray photon index correlation was investigated. The correlation of the
photon index and the flux is expected when the accelerated electrons are
cooled down; the photon index is controlled by acceleration or cooling times,
and depending on which of them is dominating, the photon index at the peak
flux either softens or hardens (Kirk et al., 1998). Photon index hardening is
observed for some blazars and radio galaxies when they get brighter (e.g., see
Abdo et al., 2010a, c; Ackermann et al., 2010; Baghmanyan et al., 2017). In
the long time scale, any trend will be smoothed out because of the mix of
different flux levels, so the spectral variability and flux correlation was
investigated using the data around the major $\gamma$-ray flare (MJD
55400-55800). The $\gamma$-ray photon index versus flux estimated in 3-day
bins is presented in Fig. 3 (left panel) and the possible correlation is
investigated using the linear-Pearson correlation test. The test yielded
$r_{p}=-0.41$, implying a negative correlation between the flux and photon
index, i.e., the flux increases with decreasing (hardening) photon index. It
should be noted that a very moderate harder when brighter trend was measured
using daily bins for the period covering the outbursts in 2009 December and
2010 April (Ackermann et al., 2010).

###  2.2 Swift XRT

The Swift satellite with three instruments on board, the UV and Optical
Telescope (UVOT, Roming et al., 2005), the X-Ray Telescope (XRT, Burrows et
al., 2005) sensitive to the 0.3-10.0 keV band, and the Burst Alert Telescope
(BAT, Barthelmy et al., 2005) sensitive to the 15-150 keV band is an ideal
instrument for simultaneous observation of blazars in the X-ray, Optical, and
UV bands. 3C 454.3 was monitored by Swift 465 times during 2005 - 2016. In the
current study the data collected by XRT and UVOT instruments has been
analyzed.
The XRT data were taken both in photon counting mode (PC) or windowed timing
mode (WT) with the single exposure ranging from 0.22 to 14.35 ks for a total
exposure of $\sim 0.76$ Ms. All the XRT data were processed using
Swift$\\_$xrtproc which is an automatic tool for XRT data analysis developed
within the Open Universe initiative 111https://openuniverse.asi.it (Giommi et
al. (2020), Giommi et al. 2021, submitted). The raw event files (Level1) were
reduced, calibrated and cleaned via the XRTPIPELINE script by applying the
standard filtering criteria and the latest calibration files of CALDB. The
source counts were extracted from a circular region of a radius of $\sim 20$
pixels ($47^{{}^{\prime\prime}}$) centered on the position of 3C 454.3, while
the background counts are taken from an annular ring centered at the source,
with inner and outer radii of $\sim 51$ pixels ($120^{{}^{\prime\prime}}$) and
$\sim 85$ pixels ($200^{{}^{\prime\prime}}$), respectively. For some
observations, the source count rate was above $0.5\>{\rm counts\>s^{-1}}$ and
the data were significantly affected by the pile-up in the inner part of the
point-spread function. These pile-up effects were removed by excluding events
within the circle the radius of which is defined by the count rate and varying
within $3$-$6$-pixels. The ungrouped data were loaded in XSPEC (vesiopn 12.11)
for spectral fitting using Cash statistics (Cash, 1979). The individual
spectra were fitted adopting absorbed PL and log-parabola models with the
galactic absorption column density of $6.78\times 10^{20}\>{\rm cm^{-2}}$
222https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3nh/w3nh.pl.
Fig. 1 d) shows the 2.0-10.0 keV X-ray flux variation during 2007-2016. The
X-ray variation over different observations is evident, the lowest flux being
$(7.47\pm 0.59)\times 10^{-12}{\rm erg\>cm^{-2}\>s^{-1}}$ and the highest
$(1.80\pm 0.18)\times 10^{-10}{\rm erg\>cm^{-2}\>s^{-1}}$. The source was
observed many times around the major $\gamma$-ray brightening, showing the
X-ray flux increased between MJD 55517-55520 when in seven observations the
flux was above $\sim 10^{-10}{\rm erg\>cm^{-2}\>s^{-1}}$. Another period of
bright X-ray emission was observed in MJD 55166-55174 when again the X-ray
flux was $>10^{-10}{\rm erg\>cm^{-2}\>s^{-1}}$. The X-ray flux varies albeit
with lower amplitude also during the $\gamma$-ray flaring period in MJD
56800-57800.
Fig. 1 e) shows the variation of X-ray photon index measured in the $0.3-10$
keV band. The X-ray photon index is around $\sim 1.5$ and does not show
substantial variation over different observations. However, occasionally
harder or softer indexes are observed; the softest index of $1.75\pm 0.04$ was
observed on MJD 56829.60 while the hardest, $1.16\pm 0.20$, on MJD 54831.70.
The photon index variation versus the flux is investigated using the data
around the flares at MJD 55130-55250 and MJD 55400-55600. In the latter case,
the linear-Pearson correlation test shows no correlation, while a negative
correlation ($r_{p}=-0.60$) is found during the first flare (Fig. 3 right
panel). Along with the increase of the flux, the photon index hardens to $\sim
1.35$.

Table 1: Results of the $\gamma$-ray spectrum fitting with different models (PLEC and LP). Period | Flux1 | $\Gamma/\alpha$ | $E_{\rm cut}^{2}$ | $\beta$ | $\sigma$ | $\sqrt{2(\Delta\mathcal{L})}$
---|---|---|---|---|---|---
54719.82 - 54730.50 | $3.94\pm 0.44$ | $2.15\pm 0.05$ | $4.03\pm 1.00$ | \- - | 93.31 | 31.47
54808.37 - 54850.18 | $0.82\pm 0.05$ | $2.21\pm 0.06$ | $3.61\pm 0.96$ | \- - | 63.71 | 26.53
54955.18 - 54990.41 | $0.85\pm 0.12$ | $2.13\pm 0.06$ | $3.20\pm 0.81$ | \- - | 60.30 | 30.53
55051.41-$55065.48^{*}$ | $1.27\pm 0.05$ | $2.14\pm 0.07$ | \- - | $0.18\pm 0.04$ | 52.42 | 26.09
55104.72 - 55118.41 | $3.10\pm 0.09$ | $2.25\pm 0.06$ | $3.13\pm 0.79$ | \- - | 79.08 | 30.29
55160.50 - 55166.10 | $7.84\pm 0.20$ | $2.13\pm 0.04$ | $5.05\pm 1.18$ | \- - | 95.78 | 35.89
55177.89-$55182.82^{*}$ | $6.94\pm 0.22$ | $2.08\pm 0.04$ | \- - | $0.11\pm 0.02$ | 94.54 | 31.36
55213.93 - 55223.36 | $5.06\pm 0.13$ | $2.22\pm 0.05$ | $3.34\pm 0.76$ | \- - | 85.59 | 37.13
55246.42 - 55264.45 | $3.06\pm 0.07$ | $2.25\pm 0.05$ | $3.83\pm 0.94$ | \- - | 96.03 | 29.57
55280.79 -$55288.24^{*}$ | $5.79\pm 0.19$ | $2.19\pm 0.04$ | \- - | $0.11\pm 0.02$ | 92.52 | 25.52
55303.44 - 55308.62 | $7.48\pm 0.19$ | $2.17\pm 0.05$ | $4.11\pm 1.08$ | \- - | 88.65 | 26.90
55371.82 - 55414.87 | $1.53\pm 0.04$ | $2.20\pm 0.05$ | $2.75\pm 0.52$ | \- - | 88.15 | 52.14
55414.87 - 55422.58 | $2.71\pm 0.30$ | $2.07\pm 0.09$ | $1.67\pm 0.43$ | \- - | 59.08 | 28.70
55464.76 - 55480.30 | $2.29\pm 0.38$ | $2.03\pm 0.08$ | $1.70\pm 0.35$ | \- - | 68.19 | 34.55
55480.30 - 55494.20 | $3.71\pm 0.41$ | $2.27\pm 0.05$ | $4.06\pm 1.03$ | \- - | 98.09 | 30.11
55494.20 -$55500.87^{*}$ | $5.80\pm 0.18$ | $2.23\pm 0.05$ | \- - | $0.12\pm 0.02$ | 87.34 | 28.15
55502.06 - 55510.51 | $10.54\pm 0.17$ | $2.13\pm 0.02$ | $10.55\pm 2.13$ | \- - | 143.97 | 45.78
55517.05 - 55518.06 | $48.96\pm 1.03$ | $2.01\pm 0.03$ | $8.81\pm 1.97$ | \- - | 143.71 | 40.02
55518.06 - 55518.68 | $62.37\pm 1.27$ | $2.11\pm 0.03$ | $6.28\pm 1.42$ | \- - | 146.21 | 37.83
55519.59 - 55520.19 | $73.59\pm 1.79$ | $2.09\pm 0.04$ | $6.40\pm 1.68$ | \- - | 128.32 | 26.71
55520.19 - 55520.80 | $52.29\pm 1.34$ | $1.98\pm 0.04$ | $6.91\pm 1.57$ | \- - | 88.00 | 39.00
55521.30 -$55523.00^{*}$ | $24.94\pm 0.72$ | $2.10\pm 0.04$ | \- - | $0.09\pm 0.02$ | 114.86 | 27.45
55523.00 - 55525.35 | $21.23\pm 0.45$ | $2.14\pm 0.04$ | $6.76\pm 1.65$ | \- - | 104.34 | 32.77
55529.04 - 55530.56 | $20.31\pm 0.57$ | $2.13\pm 0.04$ | $5.82\pm 1.61$ | \- - | 74.78 | 25.08
55541.35 - 55542.68 | $14.88\pm 0.48$ | $2.09\pm 0.06$ | $3.75\pm 1.03$ | \- - | 85.26 | 25.91
55543.94 - 55545.30 | $17.02\pm 0.49$ | $2.08\pm 0.05$ | $4.23\pm 1.10$ | \- - | 94.92 | 28.50
55549.00 - 55553.46 | $18.28\pm 0.30$ | $2.15\pm 0.02$ | $9.17\pm 1.83$ | \- - | 131.45 | 47.50
55587.20 - 55628.06 | $2.93\pm 0.07$ | $2.30\pm 0.03$ | $5.76\pm 1.15$ | \- - | 119.14 | 44.66
56657.96 - 56744.44 | $0.95\pm 0.03$ | $2.24\pm 0.08$ | $4.69\pm 2.05$ | \- - | 75.02 | 28.73
56829.85 - 56832.09 | $11.95\pm 0.31$ | $1.84\pm 0.03$ | $14.94\pm 3.54$ | \- - | 114.77 | 37.68
56857.26 -$56863.64^{*}$ | $2.12\pm 0.15$ | $1.89\pm 0.08$ | \- - | $0.22\pm 0.05$ | 40.56 | 27.77
57267.66 - 57278.13 | $2.84\pm 0.16$ | $2.12\pm 0.06$ | $3.06\pm 0.80$ | \- - | 72.78 | 27.99
57287.48 -$57301.85^{*}$ | $2.98\pm 0.10$ | $2.23\pm 0.05$ | – | $0.12\pm 0.03$ | 81.17 | 25.05
57326.85 -$57333.30^{*}$ | $3.25\pm 0.16$ | $2.06\pm 0.07$ | \- - | $0.19\pm 0.04$ | 60.43 | 28.34
57400.81 - 57409.39 | $4.33\pm 0.12$ | $1.99\pm 0.05$ | $2.90\pm 0.54$ | \- - | 88.21 | 56.42
57431.33 -$57456.50^{*}$ | $1.26\pm 0.21$ | $2.78\pm 0.10$ | \- - | $0.16\pm 0.03$ | 60.63 | 29.99
57558.20 - 57562.21 | $7.40\pm 0.38$ | $1.83\pm 0.07$ | $4.67\pm 1.34$ | \- - | 55.20 | 26.14
57562.21 - 57562.71 | $16.42\pm 0.76$ | $1.77\pm 0.08$ | $3.86\pm 1.11$ | \- - | 64.92 | 27.05
57563.01 - 57564.33 | $17.18\pm 0.50$ | $1.87\pm 0.04$ | $5.52\pm 1.17$ | \- - | 89.99 | 47.61
57607.08 - 57635.05 | $2.37\pm 0.21$ | $2.20\pm 0.04$ | $5.41\pm 1.24$ | \- - | 97.19 | 35.48
57743.77 - 57763.90 | $1.64\pm 0.05$ | $2.13\pm 0.05$ | $3.66\pm 0.88$ | \- - | 76.37 | 34.49
1 The flux in units of $10^{-6}\>{\rm photon\>cm^{-2}\>s^{-1}}$. |  |  |  |  |  |
1 The cut-off energy in GeV. |  |  |  |  |  |

###  2.3 Swift UVOT

Simultaneously with XRT, 3C 454.3 was observed with the UVOT instrument in six
filters, V (500-600 nm), B (380-500 nm), U (300-400 nm), W1 (220-400 nm), M2
(200-280 nm) and W2 (180–260 nm). All the single observations were processed.
The source counts were extracted from a circular region of
$5^{{}^{\prime\prime}}$ around the source, while the background - from a
$20^{{}^{\prime\prime}}$ region away from the source not containing any
significant pixel. The source magnitudes and fluxes were extracted using
uvotsource. Magnitudes are corrected for the galactic extinction (Schlafly &
Finkbeiner, 2011) which were then converted to fluxes using the central
wavelength values for each filter from Poole et al. (2008).
Fig. 1 panels f) and g) show the light curves in optical and UV bands
(separating V, B, U and W1, M2 and W2 filters for clarity). On the low state
the optical/UV flux of the source is at the level of $(7-8)\times
10^{-12}\>{\rm erg\>cm^{-2}\>s^{-1}}$ which increases above $\sim 3\times
10^{-11}\>{\rm erg\>cm^{-2}\>s^{-1}}$ during the flares. The flux increased in
all six filters with different amplitudes: the highest flux of $(1.16\pm
0.03)\times 10^{-10}\>{\rm erg\>cm^{-2}\>s^{-1}}$ was observed on MJD 53507.85
before the Fermi-LAT operation (not shown in Fig. 1). This coincides with the
exceptional optical outburst observed in spring 2005 (Villata et al., 2006).
The flux increased almost to the same level, $(1.03\pm 0.03)\times
10^{-10}\>{\rm erg\>cm^{-2}\>s^{-1}}$, also in $B$ band on MJD 56832.89.
During the $\gamma$-ray major brightening around MJD 55500 and the flare in
MJD 56800-57800, the UV flux in all bands substantially increased, being above
$\sim 5\times 10^{-11}\>{\rm erg\>cm^{-2}\>s^{-1}}$.
The visual inspection of the light curves shown in Fig. 1 suggests that the
flares in different bands are nearly correlated or appear with small legs. A
cross correlation analysis of the 3C 454.3 emission in different bands has
been performed in Amaya-Almazán et al. (2021) where a detailed comparison of
the emission in various bands is provided (see Table 2 and 3 in Amaya-Almazán
et al., 2021).

Figure 4: The $\gamma$-ray SEDs of 3C 454.3 in different periods. Panels a)
and b) PLEC and LP spectral modeling (blue shaded area) versus PL model (gray
shaded area), respectively. Panels c) and d) the periods with hard
$\gamma$-ray spectra. The spectral points have been obtained by running gtlike
tool for smaller energy intervals.

##  3 Evolution of Spectral Energy Distribution

The data presented in the previous section provide a detailed view of the
long-term emission of 3C 454.3. The temporal evolution of the SEDs is
investigated by generating SEDs with simultaneous or quasi simultaneous data.
The SEDs are constructed in the following manner: for each interval the
$\gamma$-ray data are plotted together with the Swift UVOT, XRT or, if
available, archival data extracted from the ASI Space Science Data Centre
(ASI/SSDC) 333https://tools.ssdc.asi.it/SED/. The archival data observed both
at low and high frequencies are included, allowing to constrain the SEDs from
$10^{6}$ Hz to $10^{26}$ Hz. The intervals are selected based on the
$\gamma$-ray data as the source is being continuously monitored since 2008.
Yet, in the ideal case, the $\gamma$-ray spectral points should be generated
for all adaptively binned intervals and compared with the Swift observations.
However, for short intervals, in the $\gamma$-ray band the spectrum will
extend only up to moderate energies of $\sim 1$ GeV not enough for theoretical
modeling. So, in order to overcome the problem of low statistics, the
adaptively binned light curve is divided into piecewise constant blocks
(Bayesian blocks) by optimizing a fitness function (Scargle et al., 2013).
This gives the optimal segmentation of the data into time intervals during
which the data are statistically consistent with a constant flux. These blocks
provide an objective way to detect significant local variations in the light
curve. In this way, the $\gamma$-ray emitting intervals with the same flux
level (weather flaring or constant) will be selected and separated. These
intervals are shown in Fig. 1 c panel. By this statistical method, the
selected intervals will be longer, allowing to calculate the $\gamma$-ray
spectra up to reasonable energies necessary for theoretical modeling.
The Bayesian block algorithm applied to the adaptively binned light curve
produces 388 intervals each with a constant flux level. Similarly, Bayesian
blocks are computed also for the 3-day binned light curve, which in general
produces similar results although with less intervals. In order to have a more
detailed view of the SEDs evolution, the blocks from adaptively binned light
curve are considered. The spectrum in each Bayesian block is computed by
applying unbinned likelihood analysis assuming the spectrum of 3C 454.3 is a
PL with the normalization and index as free parameters. Then, the SEDs are
calculated by fixing the source PL index and running gtlike separately for 4
to 7 energy bins (depending on the source significance) of equal width in log
scale.
The resultant SED evolution in time (SED/ligh curve animation) can be found in
youtube.com/wNLVj3W6ZFg showing dramatic changes in the broadband spectrum of
3C 454.3 during 2008-2018. The flux amplification is nearly of two orders of
magnitude in the optical/UV bands while in the X-ray band it is of two-three
orders of magnitude. The major changes are observed in the $\gamma$-ray band
when the flux changes by four orders of magnitude. Similar changes of the flux
in the optical/UV and X-ray bands show that, perhaps, in these bands the same
component is contributing, whereas in the $\gamma$-ray band another component
is dominating. This fits well in the synchrotron and SSC/EIC scenario for the
broadband emission from 3C 454.3.

Figure 5: The cut-off energy versus the $\gamma$-ray flux (left panel) and
photon index (right panel).

###  3.1 Gamma-ray spectrum evolution in time

The periods when the $\gamma$-ray spectrum deviates from the simple PL model
(red bowtie) can be identified in the time evolution of the multiwavelength
SEDs. In order to identify whether the curvature is statistically significant,
alternative fits with functions in the form of $dN/dE\sim
E_{\gamma}^{-\alpha}\>\times Exp(-E_{\gamma}/E_{cut})$ (power-law with
exponential cut-off [PLEC]) and $dN/dE\sim(E_{\gamma}/E_{\rm
br})^{-(\alpha+\beta log(E_{\gamma}/E_{\rm br}))}$ (log-parabola [LP]) were
applied. These models are compared with PL modeling by applying a log
likelihood ratio test where the significance is $2(\mathcal{L_{\rm
PLEC/LP}}-\mathcal{L_{\rm PL}})$. In the 388 Bayesian blocks, there are 41
intervals when the significance of the curvature was $>5\sigma$. These periods
are given in Table 1 for each interval, providing the $\gamma$-ray flux,
photon index, cut-off energy or $\beta$ if the model is LP, detection
significance and curvature significance.
In all the periods, both PLEC and LP provide a statistically better
representation of the data and only in nine periods (marked with $*$) only LP
modeling was preferred over the simple PL model. In all the periods, the
detection significance of the source was $>40\>\sigma$, convincingly high to
test the curvature. In these periods the $\gamma$-ray spectrum is soft with a
photon index of $1.98-2.30$, except for five intervals when it was $<1.90$.
Fig. 4 a) and b) panels show the 3C 454.3 spectra during two periods (with a
high significance of the curvature) where the PLEC and LP are compared with PL
model. Interestingly, curved spectra were observed also when the source was in
active and hyperactive states (MJD 55502-55554 in Table 1). The spectrum in
the hyperactive state with a flux of $(7.36\pm 0.18)\times 10^{-5}\>{\rm
photon\>cm^{-2}\>s^{-1}}$ is shown in Fig. 4 b).
The cut-off energy variation versus the $\gamma$-ray flux and photon index is
shown in Fig. 5. No strong cut-off energy variation is found as compared to
the flux, i.e., the flux varies by a factor of $\sim 90$, whereas the cut-off
energy only by $\sim 5$. Similarly, as the photon index occasionally can be as
hard as $\simeq 1.77$, the break energy remains relatively constant. This is
in agreement with the previous studies of 3C 454.3 (e.g., Abdo et al., 2011;
Ackermann et al., 2010). The highest cut-off energy of $E_{\rm cut}=14.95\pm
3.54$ GeV has been observed on MJD 56829.85-56832.09 when the source was in a
bright $\gamma$-ray emission state with a flux of $(1.19\pm 0.03)\times
10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$ and the $\gamma$-ray photon index was
$1.84\pm 0.03$.
Interestingly, there are periods when the $\gamma$-ray spectrum substantially
hardened shifting the peak of the second emission component towards higher
energies. The spectrum of 3C 454.3 in such two periods in shown in Fig. 4
panels c) and d). In the first period (panel c), even if the $\gamma$-ray
spectrum is initially hard, it starts to curve above a few GeV, and the LP
model better explains the data. On the other hand, the $\gamma$-ray spectrum
measured during MJD 56558.21-56561.37 is with a photon index of $1.84\pm 0.04$
and extends above $\sim 10$ GeV with $51.50\sigma$. Additional periods with
harder $\gamma$-ray photon index of $1.88\pm 0.06$, $1.89\pm 0.07$ and
$1.89\pm 0.06$ were observed during MJD 56834.20-56834.91, 56916.17-56916.64
and 56827.09-56827.52, respectively. Although, these are short intervals as
compared with the period in Fig. 4 d) and the spectra were measured up to
$\sim 10$ GeV, the hardening of the spectrum is evident.

##  4 Origin of multiwavelength emission

The multiwalength data obtained in Section 2 provide unprecedented detailed
information on the emission spectrum of 3C 454.3 over different years. Yet,
the large amount of the available data allows to investigate not only the
emission in different states but also, through theoretical modeling, the
evolution of different components of the SEDs. By modeling single snapshot
SEDs constrained by (quasi) contemporaneous data, the main parameters
describing the jet can be estimated, whereas modeling of the SEDs of the same
source observed in different periods can provide a clue on the changes in the
jet over different periods. Such an interpretation of the data is the backbone
of any model aiming to self-consistently explain blazar emission. Thus, in all
the periods shown in the SED/light curve animation when the data in the
optical/UV, X-ray and $\gamma$-ray bands are available (362 periods) have been
modeled and the corresponding parameters estimated.
The double-peaked SED of 3C 454.3 is modeled within a homogeneous one-zone
leptonic scenario where the low energy component is interpreted as synchrotron
emission of relativistic electrons, while the second component is due to
inverse Compton up-scattering of various photon fields. The seed photons come
from the jet itself (SSC model e.g., Maraschi et al., 1992; Bloom & Marscher,
1996) and those from the accretion disk (external Compton scattering of direct
disk radiation, EC disk; Dermer et al., 1992) or those reflected from the BLR
clouds (EC BLR; Sikora et al., 1994) or those of the dusty torus (Błażejowski
et al., 2000), depending on the location of the emission region along the jet.
However, the observed high energetics of 3C 454.3 as well as the short time
variability in the $\gamma$-ray band suggest that the emission region is
located close to the blazar central black hole where the dominant photon
fields are those from the accretion disk and BLR. Similar assumption was made
in Vercellone et al. (2010), and Finke & Dermer (2010) demonstrated that the
combination of those two photon fields can explain the sharp break in the SED
of 3C 454.3 and it gives a better fit to the quasi-simultaneous radio,
optical/UV, X-ray and $\gamma$-ray data.
In this scenario, the emission is produced in a spherical blob of the jet with
a size of $R$ filled with uniform magnetic field $B$ that moves with a Lorentz
factor of $\Gamma$ at a small angle to the observer. The emission from the
blob is enhanced by $\delta\simeq\Gamma$ for small angles. The emission region
is filled with a population of non-thermal electrons which have a broken
power-law distribution in the form of

$N(\gamma^{\prime})=\left\\{\begin{array}[]{ll}N^{\prime}_{e}\gamma^{\prime-
p_{1}}&\mbox{$\gamma^{\prime}_{\rm{min}}\leq\gamma^{\prime}\leq\gamma^{\prime}_{\rm{br}}$}\\\
N^{\prime}_{e}{\gamma^{\prime}_{br}}^{p_{2}-p_{1}}\gamma^{\prime-
p_{2}}&\mbox{$\gamma^{\prime}>\gamma^{\prime}_{\rm{br}}$}\\\
\end{array},\right.$ (1)

where $p_{1}$ and $p_{2}$ are the low and high indexes of electrons
correspondingly below and above the break energy $\gamma^{\prime}_{\rm{br}}$,
$\gamma^{\prime}_{\rm min}$ is the minimum electron energy in the jet frame.
$N^{\prime}_{e}$ is connected with the total energy of electrons $U_{\rm
e}=m_{e}\>c^{2}\int_{\gamma^{\prime}_{\rm min}}^{\gamma^{\prime}_{\rm
max}}\\!\gamma^{\prime}\>N(\gamma^{\prime})\,\mathrm{d}\gamma^{\prime}$ which
scales with the magnetic field energy density $B^{2}/8\pi$.
It is assumed that the emission region is within the BLR, at a distance of
$10^{17}$ cm. Bonnoli et al. (2011) derived that for 3C 454.3 the BLR is
located at a distance of $\sim 6\times 10^{17}$ cm. Therefore, the BLR is
modeled as a spherical shell with a lower boundary of $R_{\rm in}\simeq
4.9\times 10^{17}$ cm and an outer boundary of $R_{\rm out}=1.2\times R_{\rm
in}\simeq 5.9\times 10^{17}$ (Donea & Protheroe, 2003) and which reflects 10%
of the disk luminosity $L_{\rm disk}$. The disk emission is approximated as a
mono-temperature black body.
In order to reduce the number of free parameters, it is assumed that the
emission region size is $R=5\times 10^{15}$ cm which corresponds to hour scale
variability as observed in the $\gamma$-ray band. Next, in order to constrain
the source parameters (e.g., the disk luminosity), the SED observed in MJD
54808.37-54750.83, where the disk contribution in the optical/UV band (blue
bump) can be seen, is modeled. The fitting is performed with the open source
package JetSet (Massaro et al., 2006; Tramacere et al., 2011, 2009).
The SED well reproduced by the applied model is shown in Fig. 6 (upper panel).
The sum of all components is shown in blue, while the disk component is in
magenta peaking at $3.02\times 10^{4}$ K ($6.3\times 10^{14}$ Hz) with the
luminosity of $L_{\rm disk}=4.57\times 10^{46}\>{\rm erg\>s^{-1}}$ similar to
the values usually estimated for 3C 454.3. The X-ray emission is dominated by
the contribution from SSC (green) while the EC of disk and BLR components
(light blue and red, respectively) dominate at higher energies. The fitting
resulted in $\delta\simeq 16.9$ which is typical for the bright blazars and
$\gamma^{\prime}_{\rm min}=5.88$ implying that all electrons are cooling in
the emitting region. The PL indexes of electrons change from 1.34 to 3.51 at
the break energy of $240.7$.

Figure 6: Upper panel: The multiwavelength SED during MJD 54808.37-54750.83.
Fermi-LAT, Swift XRT and UVOT data are in red, blue and light blue,
respectively. The VLBI radio data are from Vercellone et al. (2010). Middle
panel: The multiwavelength SED during the bright period in MJD
55519.59-55520.19. Lower panel: The summary of all components from the
modeling of all SEDs with contemporaneous data collected during 2008-2018.

When modeling the SEDs in other periods, the disk luminosity and temperature
are fixed to the values obtained from the fitting of the SED in MJD
54808.37-54750.83. The other model parameters ($N^{\prime}_{e}$, $p_{1}$,
$p_{2}$, $\gamma^{\prime}_{\rm min}$, $\gamma^{\prime}_{\rm br}$, $\delta$ and
$B$) have been then estimated by fitting the SEDs. The SEDs modeling animation
is available here youtube.com/dAqVjpO5Nb4. The synchrotron/SSC components
account for the data up to the X-ray band and, in principle, SSC could extend
to HEs. However, as demonstrated in Finke & Dermer (2010), the SSC component
cannot explain the sharp break observed in the $\gamma$-ray band and in such
case the strong contribution from BLR photons should be neglected. Considering
inverse Compton scattering of only BLR photons, which have a narrower
distribution than the SSC component starts to decrease and cannot explain the
Fermi-LAT data. Instead, the HE spectrum can be well reproduced when
considering the joint contribution from EC of disk and BLR photons. The EC
disk component dominates in the sub-GeV band, while the contribution of EC BLR
is significant at HEs. However, the $\gamma$-ray data can be explained also
when considering the joint inverse Compton scattering of BLR and torus photons
(e.g., see Kang et al., 2021).
The modeling of the SED during the bright period in MJD 55519.59-55520.19 is
shown in Fig. 6 (middle panel). In this active emission state, the source flux
from radio to X-ray bands increased nearly by an order of magnitude while in
the $\gamma$-ray band by nearly two orders of magnitude. As compared with the
results of the modeling of the SED in MJD 54808.37-54750.83, the parameters
describing the emitting electrons did not vary substantially (e.g.,
$p_{1}=1.19$, $p_{2}=3.77$ and $\gamma^{\prime}_{\rm{br}}=271.7$ were
estimated in MJD 55519.59-55520.19), but a higher $\delta\simeq 50.8$ was
estimated. This implies that the flaring activity was caused by the changes in
the bulk Lorentz factor of the emitting region.

Figure 7: The evolution of model free parameters estimated by modeling the
SEDs. a) and b) the PL indexes of electrons before and after the break,
respectively. c) the Doppler boosting factor changes in 2008-2018. d) and e)
the break and minimum energy of emitting electrons in different periods. f)
the change of magnetic field in the emitting region.

The evolution of model parameters is shown in Fig. 7. The photon indexes
(panel a and b) are defined by different data sets and vary in the range of
$p_{1}=0.77-1.97$ and $p_{2}=2.71-5.98$. The emission in the X-ray band is due
to inverse Compton up-scattering of synchrotron photons in the Thomoson regime
and the PL index of the emitting electrons is defined by the X-ray data.
Similarly, the $\gamma$-ray data which are due to inverse Compton scattering
of disk and BLR photons are defining $p_{2}$. The modeling shows that the
$p_{1}$-$p_{2}>1.4$, so the index change is significantly larger than that
expected from the standard cooling break. The break energy (panel d in Fig. 7)
is in the range of $107.07-1220.58$ defining the low and high energy peaks to
be at $\sim 3\times 10^{12}$ Hz and $10^{22}$ Hz, respectively, which is
characteristic for FSRQs. The minimum electron energy varies in the range of
$2.03$-$48.88$ which is shown in panel e) of Fig. 7. Along with $p_{1}$ this
minimal energy is defined by the SSC modeling of the X-ray data.The magnetic
field in the jet is in the range from $1.43$ to $9.19$ G (lower panel of Fig.
7) and the amplitude of its variation is lower than that of the parameters
describing the emitting electrons. This implies that the observed flares are
likely due to the changes in the emitting electrons rather than in the
emitting region plasma.

##  5 Discussion

The broadband monitoring of 3C 454.3 in 2008-2018 reveals an interesting and
complicated behaviour in all the considered bands. The highest amplitude
flares are observed in the $\gamma$-ray band when the flux in several
occasions was above $10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$ which corresponds
to an apparent isotropic $\gamma$-ray luminosity exceeding $10^{50}\>{\rm
erg\>s^{-1}}$ (for the 5.49 Gpc distance to 3C 454.3). In these active states,
in the proper frame of the jet, the total power emitted in the $\gamma$-ray
band would be $L_{\rm em,\gamma}=L_{\rm\gamma}/2\>\delta^{2}\simeq
10^{47}\>(\delta/20)^{-2}\>{\rm erg\>s^{-1}}$ which by nearly an order of
magnitude exceeds the disk luminosity $L_{\rm d}$ in agreement with the
results of Ghisellini et al. (2014).
The $\gamma$-ray photon index of 3C 454.3 varies as well; occasionally the
photon index can be as hard as $1.87\pm 0.04$ measured during a 3-day period.
During this period, the highest energy event with $E_{\rm\gamma}=14.92$ GeV
has been observed in MJD 56559.89 within a circle of $0.006^{\circ}$ around 3C
454.3, with the probability of 0.99987 being associated with it (computed with
gtsrcprob tool). Such hardening of the $\gamma$-ray spectrum is unusual for
FSRQs which are characterized by a soft $\gamma$-ray photon index (e.g., the
mean of FSRQ photon index distribution is $2.2$ in 4FGL). However, during the
$\gamma$-ray flares, occasional hardening of the the $\gamma$-ray photon index
of FSRQs have been already observed (e.g., see Pacciani et al., 2014;
Gasparyan et al., 2018; Sahakyan, 2020b; Paliya et al., 2019; Angioni et al.,
2019). In some periods the $\gamma$-ray spectrum of 3C 454.3 deviates from the
simple PL model and PLEC and LP models give a better explanation to the
overall spectrum. Such modification of the spectrum was observed when the
$\gamma$-ray emission of the source was in an average or active emitting
state, but unlike the strong changes in the flux ($\sim 90$ times), the cut-
off energy is within $2-10$ GeV.
In the X-ray band 3C 454.3 behaves like a classical FSRQ with a hard X-ray
photon index of $\sim 1.5$. Unlike the changes in the X-ray flux, which can
increase up to $10^{-10}{\rm erg\>cm^{-2}\>s^{-1}}$, the photon index is
relatively constant. The linear-Pearson correlation test reveals a negative
correlation ($r_{\rm p}=-0.60$) between the flux and photon index during the
flare at MJD 55130-55250. In the optical/UV band 3C 454.3 is in an active
state after the large outburst in 2005: in several occasions the flux was as
high as $10^{-10}\>{\rm erg\>cm^{-2}\>s^{-1}}$. The available optical/UV data
allows to shape the peak of the low energy component to be around
$10^{13}\>{\rm Hz}$ and unlike the increase of the flux it remains relatively
constant. In the past, short transition of the low energy component to higher
frequencies during the flares was observed in several FSRQs (e.g., see
Cavaliere & D’Elia, 2002; D’Ammando et al., 2011; Sbarrato et al., 2012b;
Giommi et al., 2012; Cutini et al., 2014). For 3C 454.3, in this band either
the contribution of the disk is observed or, when the synchrotron jet emission
dominates during the flares, it corresponds to the falling part of the low
energy component which consequently defines the HE tail of the electron
distribution. This implies that even during the flares, the processes limiting
the maximum energy of the accelerated electrons (e.g., cooling or a limit from
the accelerator size) do not change and produce the same effect on the
electron acceleration.
The multiwavelength SEDs observed in various periods during the considered ten
years are well modeled within one-zone leptonic model taking into account the
inverse Compton scattering of synchrotron, disk and BLR photons. The adopted
model with physically realistic parameters can satisfactorily reproduce the
observed SEDs; the models obtained in 362 periods are in Fig. 6 (lower panel)
which shows the multiwavelength behaviour of 3C 454.3 in 2008-2018. It is
evident that the broadband emission varies significantly, except for the radio
band which is most likely produced from electrons in more extended regions.
This is more evident when comparing the SEDs in the upper and middle panels of
Fig. 6 where two different emission states of the source are shown. Unlike the
changes in the flux, the peak of both components remains relatively stable.
Within the adopted scenario, this could be interpreted by strong cooling of
the electrons, i.e., due to the existence of dense photon fields (internal and
external), the injected particles cool down, limiting their maximum energy,
thus affecting the emission of photons. The different rising and decaying
spectra of both components are most likely related with the initial injection
(cooling) of electrons.
The modeling reveals that the emitting electrons initially are distributed
with a hard PL index with a mean of $p_{\rm 1,mean}=1.27$ which substantially
hardens to $p_{\rm 2,mean}=3.87$. The break energy varies in the range of
$107.08-1220.58$ and is defined by the interplay between the particle
acceleration and cooling times. The electron cooling time is defined as

$t_{\rm cool}=\frac{3\>m_{e}c\>(1+z)}{4\sigma_{\rm T}\>u_{\rm
tot}^{\prime}\>\gamma_{\rm e}^{\prime}}$ (2)

where $u_{\rm tot}^{\prime}=u_{\rm B}+u_{\rm SSC}+u_{\rm disc}+u_{\rm BLR}$.
The densities of disk and BLR photons are constant whereas $u_{\rm B}$ and
$u_{\rm SSC}$, which depend on the synchrotron and SSC components, vary in
different periods (Fig. 6 lower panel). Thus, the small variation of the break
energy (see Fig. 7) is defined by the changes in $u_{\rm B}$ and $u_{\rm
SSC}$. Yet, in the vast majority of cases the ratio of $u_{\rm SSC}/u_{\rm B}$
is $\geq 1$ implying that the SSC cooling cannot be neglected, so the
nonlinear effects are important for the formation of particle distribution,
i.e., $\gamma_{\rm br}$ and $p_{2}$. Because of these nonlinear effects the
difference between $p_{1}$ and $p_{2}$ is larger than that expected from
traditional cooling break ($\Delta p=1$). Alternatively, large $\Delta p$
could be due to the nature of the injection process or due to the
inhomogeneities in the source (Reynolds, 2009).
In the modeling, some SEDs can be modeled only when considering very hard
electron spectra; $p_{1}$ is $0.77-1.97$. This index depends on the
combination of the data in the X-ray and $\gamma$-ray bands and sometimes
because of their hard photon indexes, $p_{1}<1$ is required. In the fast
electron cooling regime, a much softer $\gamma^{-2}$ spectrum will be formed
below $\gamma_{\rm min}$, whereas in the slow cooling regime the hard spectrum
of electrons may be due to their initial injection. However, the PL index of
$\leq 1.0$ is challenging for many particle acceleration scenarios. The
diffuse shock acceleration of particles can form a spectrum as hard as $-1$
depending on the parameters of the shocks (e.g., Summerlin & Baring, 2012).
Similarly, a very hard electron spectrum will be formed in the relativistic
magnetic reconnection (Zenitani & Hoshino, 2001; Guo et al., 2014; Sironi &
Spitkovsky, 2014; Werner et al., 2016) only under extremely high magnetization
conditions ($\geq\>100$).

Figure 8: Upper panel: The distribution of Doppler boosting factor. Lower
panel: The distribution of the jet luminosity in the form of electrons (red)
and magnetic field (blue).

The distribution of Doppler boosting factor is presented in the upper panel of
Fig. 8 which has a peak at $\delta\simeq 20$ which is characteristic for
bright FSRQs (Ghisellini & Tavecchio, 2015). However, in some periods
substantially higher values for $\delta$ are estimated: there are 26 periods
when $\delta>35$. As can be seen from Fig. 7 (panel c), high $\delta$ were
estimated around MJD 55500 when the source was in a bright $\gamma$-ray
emission state. For example, the highest $\delta=54.8$ was estimated in MJD
55518.68-55519.10 when the $\gamma$-ray flux was as high as $(5.97\pm
0.14)\times 10^{-5}\>{\rm photon\>cm^{-2}\>s^{-1}}$ and that in the X-ray
band- $(1.59\pm 0.07)\times 10^{-10}\>{\rm erg\>cm^{-2}\>s^{-1}}$. So, in this
period the emission region has a larger Doppler boosting factor which results
in a strong increase in the Compton dominance (hence an increase of the HE
component) as the external photon density in the comoving frame of the jet
depends on the Doppler boosting factor. This faster moving emitting region
could be either re-accelerated during the propagation or could be newly
injected and emits close to the central source. Another possibility for the
Doppler boosting factor increase can be due to geometrical effects, i.e, when
the jet regions may have different orientations; e.g., jets in a jet (Giannios
et al., 2009) or twisted inhomogeneous jet model (Raiteri et al., 2017). So,
during the flares the photons may be produced in a region viewed at smaller
angles as compared to the entire jet, which increases the Doppler boosting
factor.
The modeling provides also information on the power of the jet. The
distribution of the jet luminosities in the form of magnetic field and
electron kinetic energy computed as $L_{B}=\pi cR_{b}^{2}\Gamma^{2}U_{B}$ and
$L_{e}=\pi cR_{b}^{2}\Gamma^{2}U_{e}$ is given in Fig. 8 (lower panel).
$L_{\rm e}$ is in the range of $(0.79-9.35)\times 10^{44}\>{\rm erg\>s^{-1}}$
while $L_{\rm B}$ in $(0.12-5.07)\times 10^{44}\>{\rm erg\>s^{-1}}$, implying
the system is not far from the equipartition condition. The peak of $L_{\rm
e}$ is around $3\times 10^{44}\>{\rm erg\>s^{-1}}$ and $L_{\rm B}$ is at
$1.2\times 10^{44}\>{\rm erg\>s^{-1}}$. For the majority of SEDs, the jet is
slightly particle-dominated with $L_{\rm e}/L_{\rm B}\geq 1$ and only in a few
periods when the low energy components exceed the X-ray flux $L_{\rm e}/L_{\rm
B}<1$. The total jet luminosity defined as $L_{\rm tot}=L_{\rm e}+L_{\rm
B}+L_{\rm p}+L_{\rm rad}$ (Ghisellini & Celotti, 2001), where $L_{\rm p}$ and
$L_{\rm rad}$ are the power carried by the cold protons and the produced
radiation, respectively, is $\leq 2.08\times 10^{46}\>{\rm erg\>s^{-1}}$,
being smaller than the total Eddington luminosity of $1.9\times 10^{47}\>{\rm
erg\>s^{-1}}$ for the black hole mass of $1.5\times 10^{9}\>M_{\odot}$ in 3C
454.3.

##  6 Conclusions

In this paper the broadband emission from 3C 454.3 during 2008-2018 is
investigated. In this period the source was in active emission state
displaying extraordinary flares in the $\gamma$-ray band. In several occasions
the $\gamma$-ray flux exceeded $5\times 10^{-5}\>{\rm
photon\>cm^{-2}\>s^{-1}}$ corresponding to an apparent isotropic $\gamma$-ray
luminosity of $>\>10^{50}\>{\rm erg\>s^{-1}}$. Similarly, the source was
active (although with lower amplitude) also in the X-ray and optical/UV bands.
The multiwavelength SEDs of 3C 454.3 (in 362 periods) constrained with
contemporaneous data collected during 2008-2018 have been modeled within a
one-zone leptonic scenario taking into account the inverse Compton scattering
of synchrotron, disk and BLR reflected photons. Through the modeling, the main
parameters describing the jet in different periods have been estimated
providing an insight into the jet evolution in 2008-2018. It is shown that
during the large $\gamma$-ray flares the Doppler boosting factor substantially
increased which points that the emission during the flares comes most likely
from a region which either moves faster or has a different geometrical
orientation.

## Acknowledgements

I thank the anonymous referee for constructive comments. I acknowledge the use
of data, analysis tools and services from the Open Universe platform, the
Astrophysics Science Archive Research Center (HEASARC) and the Fermi Science
Tools.
This work was supported by the Science Committee of RA, in the frames of the
research project No 20TTCG-1C015.
This work used resources from the ASNET cloud and the EGI infrastructure with
the dedicated support of CESGA (Spain).

## Data availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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