On the origin of GeV spectral break for Fermi blazars: 3C 454.3
Shi-Ju Kang, Yong-Gang Zheng, Qingwen Wu, Liang Chen, Yue Yin
aa r X i v : . [ a s t r o - ph . H E ] F e b MNRAS , 1–7 (2021) Preprint 19 February 2021 Compiled using MNRAS L A TEX style file v3.0
On the origin of GeV spectral break for Fermi blazars: 3C 454.3
Shi-Ju Kang, , ★ Yong-Gang Zheng, † Qingwen Wu, ‡ Liang Chen, and Yue Yin School of Physics and Electrical Engineering, Liupanshui Normal University, Liupanshui, Guizhou, 553004, China Department of Physics, Yunnan Normal University, Kunming, Yunnan, 650092, China School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences,80 Nandan Road, Shanghai 200030, China
Accepted 2021 February 16. Received 2021 January 13; in original form 2020 June 21
ABSTRACT
The GeV break in spectra of the blazar 3C 454.3 is a special observation feature that has been discovered by the
Fermi -LAT.The origin of the GeV break in the spectra is still under debate. In order to explore the possible source of GeV spectral break in 3C454.3, a one-zone homogeneous leptonic jet model, as well as the
McFit technique are utilized for fitting the quasi-simultaneousmulti-waveband spectral energy distribution (SED) of 3C 454.3. The outside border of the broad-line region (BLR) and innerdust torus are chosen to contribute radiation in the model as external, seed photons to the external-Compton process, consideringthe observed 𝛾 -ray radiation. The combination of two components, namely the Compton-scattered BLR and dust torus radiation,assuming a broken power-law distribution of emitted particles, provides a proper fitting to the multi-waveband SED of 3C454.3 detected 2008 Aug 3 - Sept 2 and explains the GeV spectral break. We propose that the spectral break of 3C 454.3 mayoriginate from an inherent break in the energy distribution of the emitted particles and the Klein-Nishina effect. A comparisonis performed between the energy density of the ‘external’ photon field for the whole BLR 𝑈 BLR achieved via model fitting andthat constrained from the BLR data. The distance from the position of the 𝛾 -ray radiation area of 3C 454.3 to the central blackhole could be constrained at ∼ . ∼ . 𝑅 BLR , the size of the BLR).
Key words: galaxies: active — galaxies: individual: 3C 454.3 — gamma-rays: galaxies
Blazars are a class of active galactic nuclei (AGN) with a relativis-tic jet pointed within a small observation angle to the line of sightthat can be subdivided into flat-spectrum radio quasars (FSRQs) andBL Lacertae objects (BL Lacs) (Urry & Padovani 1995). The multi-wavelength spectral energy distribution (SED) from the radio to the 𝛾 -ray bands of blazars is mostly caused by the non-thermal radia-tion, where the SED generally exhibits a two-bump framework in thelog 𝜈 − log 𝜈𝐹 𝜈 space. Based on the peak frequency ( 𝜈 Sp ) of the firsthump, blazars are categorized as low (LSP, e.g., 𝜈 Sp < Hz), inter-mediate (ISP, e.g., 10 Hz < 𝜈 Sp < Hz) and high-synchrotron-peaked (HSP, e.g., 𝜈 Sp > Hz) blazars (e.g, Abdo et al. 2010c).It can usually be confirmed that the lower energy bump isgenerally related to the synchrotron (Syn) radiation generated bythe jet’s non-thermal electrons (Urry 1998). However, the ori-gin of the second bump could be considered an open problem.In the leptonic model schemes, the second bump ( 𝛾 -ray) gen-erally is induced by inverse Compton scattering. The seed pho-tons for inverse Compton scattering may be derived from syn-chrotron photons in the jet (synchrotron self-Compton, SSC, process, ★ E-mail: kangshij[email protected] † E-mail: [email protected] ‡ E-mail: [email protected] e.g., Konigl 1981; Marscher & Gear 1985; Ghisellini & Maraschi1989; Maraschi et al. 1992; Konopelko et al. 2003), and/or theexternal photons (external-Compton, EC, process) from outsidethe jet (e.g., Dermer & Schlickeiser 1993; Sikora et al. 1994;Ghisellini & Madau 1996; Böttcher & Dermer 1998). Consider thatthese external photons can be due to the accretion disk (e.g.,Dermer & Schlickeiser 1993), the broad-line region (BLR) (e.g.,Sikora et al. 1994; Ghisellini & Madau 1996), and the moleculartorus (e.g., Błażejowski et al. 2000; Ghisellini & Tavecchio 2008).The SSC model has been extensively employed for fitting the multi-wavelength SED of HSP BL Lacs (e.g., Krawczynski et al. 2004;Zhang et al. 2012), while FSRQs are often better described byan SSC+EC (e.g., Böttcher & Chiang 2002; Ghisellini et al. 2011;Yan et al. 2014; Zhang et al. 2014; Hovatta & Lindfors 2019).The radio source 3C 454.3 is a famous FSRQ at redshift z= 0.859 in the
Fermi Gamma-Ray Space Telescope
Large AreaTelescope (
Fermi -LAT) point source catalogs, named as 1FGLJ2253.9+1608, 2FGL J2253.9+1609, 3FGL J2254.0+1608, and4FGL J2253.9+1609 in the First, Second, Third, and Fourth
Fermi -LAT catalogs (1FGL; Abdo et al. 2010a, 2FGL; Nolan et al. 2012,3FGL; Acero et al. 2015, and 4FGL; Abdollahi et al. 2020), respec-tively. Since the
Fermi Gamma Ray Space Telescope was launchedon June 11, 2008, a new era for studying 𝛾 -ray astronomy has beenstarted. An interesting feature of the 𝛾 -ray spectrum for 3C 454.3 isthe GeV spectral break, which was first detected by Fermi -LAT in © S. J. Kang et al.
Abdo et al. (2009, 2010b), and was further confirmed subsequentlyby Ackermann et al. (2011, 2015) and Stern & Poutanen (2014). The 𝛾 -ray spectrum is characterized by a break around 2 GeV with photonindices of Γ ≃ . ± . Γ ≃ . ± .
25 that are lower andhigher than the break energy, respectively (Abdo et al. 2009).This break is known to occur in both bright FSRQs, and in sev-eral LSP BL Lacs (e.g., Abdo et al. 2010b). The GeV break ener-gies tend to occur in the 1-10 GeV range (e.g., Abdo et al. 2010b;Poutanen & Stern 2010; Harris et al. 2012), and are relatively stable(e.g., Ackermann et al. 2010; Abdo et al. 2011; Stern & Poutanen2011). Such as, the break energy is basically constant ( ∼ a fewGeV) in the flaring state for some sources, specifically for 3C 454.3(Abdo et al. 2011; Pacciani et al. 2014). A minor change in the spec-tral break energy for significant deviations in flux conditions hasbeen detected for 3C 454.3 (Ackermann et al. 2010). According tothe studies performed by Harris et al. (2012), the average spectrumof 3C 454.3 could be optimally fit via a broken power-law function,regardless of the change in the break energy value in accordance withthe energy range that fitting is accomplished.Nowadays, the origin of the GeV break in Fermi blazar spectra(e.g., 3C 454.3) is still a puzzling and unresolved problem. Sev-eral comments that have been presented to address this propertyare 𝛾 − 𝛾 annihilation from He II line photons (Poutanen & Stern2010), inherent electron spectral breaks (Abdo et al. 2009), Ly- 𝛼 dissipation (Ackermann et al. 2010), Klein-Nishina (KN) influencesoccurred when BLR emission is scattered by jet electrons in a near-equipartition method (Cerruti et al. 2013), or a hybrid scattering(e.g., Finke & Dermer 2010; Cerruti et al. 2013; Hunger & Reimer2016). For instance, the origin of the spectral break in 3C 454.3 hasbeen discussed by Abdo et al. (2009). They proposed that the breakin the 𝛾 -ray spectrum is most possibly caused by an intrinsic breakin the energy distribution of the emitting particles near the electronenergies 𝐸 el ∼ 𝑚 𝑒 𝑐 (Abdo et al. 2009).The spectral break can not be due to photon interactions with alocal emission field (Abdo et al. 2009) that needs a jet bulk Lorentzcoefficient lower than that derived from superluminal radio viewingsof 3C 454.3 ( Γ bulk ≃
15, Jorstad et al. 2005), or the extragalacticbackground light (EBL) due to the transparency of the universe to 40GeV photons at 𝑧 . . Fermi -LAT spectrum of 3C 454.3. The mentioned problem was alsofurther discussed by Hunger & Reimer (2016) using a continuous,time-dependent injection, jet model based on Compton scatteringof the external target emission fields of the accretion disk and/orBLR, where the radiation area has been considered inside or beyondthe BLR in the model fitting (e.g., Hunger & Reimer 2016). Also,according to Cerruti et al. (2013) findings, the GeV spectral breakcould be generated by the Klein-Nishina effect when BLR photonsare Compton scattered by a non-thermal, log-parabolic distributedpopulation of electrons in the jet.Since the position of the 𝛾 -ray radiation area in blazars is currentlyobscure, and could be considered an unresolved issue. The radiationarea has been generally considered inside or beyond the BLR in themodel fitting, where the seed photons may originate from the accre-tion disk and/or the BLR and/or the dust torus (e.g., Dermer et al.2014; Finke 2016; Hunger & Reimer 2016 and reference in). We as- sume that the EC caused by the disk emission is negligible in 3C454.3 since it is valid for at least some other bright quasars (e.g., in3C 279, see Lewis et al. 2018). In the current study, we attempt todetermine if the conventional one zone, leptonic model, containingnumerous EC parts, can illustrate the GeV spectral break in 3C 454.3.In this model, the external, soft photons originate in the BLR anddust torus and then are up-scattered through inverse Compton inter-actions with the non-thermal population of electrons, represented bya broken power-law distribution function.The following cosmology is considered throughout 𝐻 =
70 km s − Mpc − , Ω = . Ω Λ = . In the current study, the conventional one-zone synchrotron + inverseCompton model is employed to fit the SED of 3C 454.3, a model thathas been extensively utilized in blazars (see Ghisellini et al. 2010and references in). The model has been employed in our previousworks (see Kang et al. 2014b, 2016; Kang 2017). A homogeneoussphere with radius R installed in a magnetic field B is considered.The homogenous sphere moves relativistically outward with the flowof the jet with a speed of 𝜐 = 𝛽𝑐 (c is the light speed in a vacuum,bulk Lorentz coefficient Γ = / p − 𝛽 ) along the jet direction. TheDoppler factor 𝛿 = [ Γ ( − 𝛽 cos 𝜃 )] − ≈ Γ is selected for the rela-tivistic jet with a narrow observation angle 𝜃 ≤ / Γ . The electronspectrum is chosen as a broken power-law distribution, with indices 𝑝 and 𝑝 , lower and higher than the break energy 𝛾 𝑏 𝑚 𝑒 𝑐 , respec-tively 𝑁 ( 𝛾 ) = (cid:26) 𝑁 𝛾 − 𝑝 , 𝛾 min ≤ 𝛾 ≤ 𝛾 b 𝑁 𝛾 𝑝 − 𝑝 b 𝛾 − 𝑝 , 𝛾 b < 𝛾 ≤ 𝛾 max , (1)where 𝛾 min is the minimum Lorentz factor of electrons, 𝛾 max is themaximum Lorentz factor of electrons, 𝛾 b is the break Lorentz factorfor the electron distribution, which follows from the balance betweenescape and cooling, and 𝑁 is the density normalization coefficient.It is interesting to note that the broken power-law distribution mightmight result from the electrons with a power-law distribution beinginjected into the downstream flow they experience to escape and cool(see Zheng et al. 2018 and references in).Besides, an electron spectrum with a log-parabola distribution (seeMassaro et al. 2004a,b, 2006) produced by stochastic acceleration(e.g., Tramacere et al. 2009, 2011; Chen 2014) is given by 𝑁 ( 𝛾 ) = 𝐾 (cid:18) 𝛾𝛾 (cid:19) − 𝑠 − 𝑏 log (cid:16) 𝛾𝛾 (cid:17) , (2)where 𝑠 is the spectral index, 𝑏 is the spectral curvature parameter, 𝛾 is the peak Lorentz factor, and 𝐾 is the normalization constantof a log parabola shape electron spectrum.According to newly published studies, the 𝛾 -ray radiation area ofblazar jets should be placed at about the outer border of (or beyond)the BLR and in the dust tours (e.g., Böttcher & Els 2016; Kang 2017;Shah et al. 2017; Zheng et al. 2017; MAGIC Collaboration et al.2018; H. E. S. S. Collaboration et al. 2019; Traianou et al. 2020),where portions of both BLR and torus photons should be providedto illustrate the detected 𝛾 -ray spectrum. In the EC procedure, theexternal, soft photons are derived from two radiation zones (e.g.,both BLR and dusty torus, Cerruti et al. 2013; Dermer et al. 2014;Yan et al. 2015; Paliya et al. 2015; Kang 2017). Due to lack of clar-ity of 𝛾 -ray radiation area place, different from the assumptions MNRAS , 1–7 (2021) eV spectral break of 3C 454.3 of Finke & Dermer (2010) and Hunger & Reimer (2016), they con-sidered that the external, seed photons are originated from the ac-cretion disk and BLR. The external, seed photons originate fromboth the dust torus and the whole BLR considered in this work. Asthe same procedure performed by Cerruti et al. (2013), a dual-partCompton-scattering approach is chosen in which the external, seedphotons generally originate from both the BLR and the dust torus.It is assumed that the 𝛾 -ray radiation area is located out of the BLRand within the dusty torus (e.g., Böttcher & Els 2016; Kang 2017;Shah et al. 2017; Zheng et al. 2017; MAGIC Collaboration et al.2018; H. E. S. S. Collaboration et al. 2019; Traianou et al. 2020).The external emission field is indicated via an isotropic blackbodywith the temperature 𝑇 = ℎ𝜈 p /( . 𝑘 𝐵 ) , where the maximum fre-quency of seed photons in the 𝜈 − 𝜈𝐹 𝜈 space is denoted by 𝜈 p (seeKang et al. 2016; Kang 2017 for the details), ℎ is Planck Constant, 𝑘 𝐵 is Boltzmann Constant. Consider that the 𝛾 -ray radiation areais placed out of the BLR and in the dusty torus. Thus, the energydensity value of the BLR 𝑈 BLR is reduced quickly, while the en-ergy density value of the dusty torus 𝑈 torus is approximately keptunchanged (see Ghisellini & Tavecchio 2008, 2009). Accordingly, inthis model, the 𝑈 BLR is considered as an arbitrary free parameterwhile the 𝑈 torus = × − Γ erg cm − (e.g., Cleary et al. 2007)is chosen in the jet co-moving frame. Furthermore, the influencesof Klein-Nishina and the self-absorption (e.g., Rybicki & Lightman1979; Blumenthal & Gould 1970) in the inverse Compton scatteringand synchrotron radiation are appropriately assumed in this work,respectively (see Kang et al. 2016; Kang 2017 for the details). In theSED modeling of Figure 1, the model forecasting is assumed as the in-herent radiation. It is then compared with the observational informa-tion (e.g., Zheng & Zhang 2011; Zheng & Kang 2013; Zheng et al.2013, 2014, 2016; Kang et al. 2012, 2014b,a, 2016; Kang 2017).To constrain the model parameters and obtain a combination oftheir optimal values, a McFit procedure is employed to fit the quasi-simultaneous multi-waveband SED of 3C 454.3 that was given inAbdo et al. (2009). The
McFit procedure is a fitting tool that adoptsa Bayesian Monte Carlo (MC) fitting technique for the confidentfitting of parameters limited by the data even in the presence ofother unconstrained parameters (see Zhang et al. 2015, 2016). Thementioned technique could derive the optimal fitted parameters andtheir corresponding uncertainties through the converged MC chains(see Zhang et al. 2015, 2016 for the details).
The simultaneous multi-wavelength data acquired from high energy 𝛾 -rays ( Fermi -LAT), X-ray, UV and optical (Swift satellite) and radio(IRAM 30 m and Effelsberg 100 m telescopes) for 3C 454.3 extractedwithin the time interval MJD 54685-54690 (2008 August 7-12) andnon-simultaneous mid-IR (infrared radiation) data acquired with theVLT/VISIR instruments in the early 2008 July are gathered fromAbdo et al. (2009) and presented in Figure 1. In the Fermi band ofFigure 1, a spectral break is apparent near 2 GeV, with photon indicesof Γ ≃ . ± . Γ ≃ . ± .
25 lower and higher than thebreak, respectively (Abdo et al. 2009).The one-zone jet model is employed as described in Section 2to regenerate the multi-waveband SED of 3C 454.3. In this model,there exist 10 free parameters in the Syn + SSC + EC (BLR) + EC(torus) model: 𝐵 , 𝛿 , 𝑅 , 𝑝 , 𝑝 , 𝛾 min , 𝛾 max , 𝛾 b , 𝑁 and 𝑈 BLR forthe broken power-law distribution electron spectrum. To decreasethe number of these free parameters, the emitting area radius in thejet frame could be bounded with the minimum variability timescale and redshift with 𝑅 𝛿𝑐𝑡 var /( + 𝑧 ) ∼ . × 𝛿 cm, where theintra-day variation of Fermi 𝛾 -ray band was determined in 3C 454.3(e.g., Weaver et al. 2019; Das et al. 2020). In addition, a typical 𝛾 -ray variability timescale in days was reported in other literature (e.g.,Zhang et al. 2018). A 1-day conservative estimation is assumed andemployed in this work. The maximum electron Lorentz factor isassumed in this work to be 𝛾 max = × ( 𝛾 max ≫ 𝛾 b ) and doesnot have any considerable effect on the fundamental results (e.g.,Kang et al. 2016). The next eight parameters, including 𝐵 , 𝛿 , 𝛾 min , 𝑝 , 𝑝 , 𝛾 b , 𝑁 and 𝑈 BLR , are left free in the fitting.In SED fitting, 23 observational data points could be found, in-cluding 2 UV, 8 X-ray, and 13 𝛾 -ray data points. The observationaluncertainties corresponding to the data samples in the 𝛾 -ray bandsare chosen in the McFit fitting. Unfortunately, since uncertainties arenot available for the UV and X-ray data points acquired by Abdo et al.(2009), two percent of the observational flux is considered as the sys-tematic flux error (e.g., Aleksić et al. 2014; Kang et al. 2016). Now,SED fitting is accomplished according to the
McFit fitting tech-nique within the permissible range of parameters (see Table 1). Theobtained results of the optimal fitting are indicated in Figure 1. Aoptimal combination of model parameters is extracted by the
McFit fitting technique. The obtained best-fit model parameters, as well asuncertainties, are presented in Table 1. The distributions of parametervalues for 3C 454.3 are shown in Figure 2, where the likelihood mapof the parameter-constraint outputs by the
McFit code are indicatedby histograms and contours. The colored contour lines represent atwo-dimensional contour map of the relative marginalization prob-abilities. The red crosses indicate the optimal fitted values and 1 𝜎 error bars.It should be noted that the GeV spectral break of 3C 454.3 couldbe entirely reproduced through the leptonic jet model with the Syn+ SSC + EC (BLR) + EC (torus) model. The value distribution ofall obtained model parameters is usually displayed as a (or approx-imately) normal distribution (see Figure 2). However, the optimalfitted values and uncertainties obtained from the optimal combina-tion of model parameters for all model parameters are not alwaysrelated to peak probabilities in a one-dimensional histogram or two-dimensional contour plot of relative marginalization probabilities(see Zhang et al. 2015). For instance, the best fit of the density nor-malization coefficient 𝑁 and the indices 𝑝 of electron spectrumin particular appear to be on the edge of the considered region. Ascould be seen from Table 1, all the modeling parameters lie withinacceptable ranges. For instance, almost all fitted model parametersare consistent with those obtained with other previous works. Forexample, the Doppler factor 𝛿 ≃ . + . − . is compatible with theDoppler coefficient of 𝛿 = [ Γ ( − 𝛽 cos 𝜃 )] − ≈ . Γ = . ± . 𝜃 = 𝑜 . ± 𝑜 . 𝛾 min = . + . − . , which corresponds to a spe-cific situation of the electrons pre-shocked (e.g., Sari et al. 1998), iscompatible with values from the literature (e.g., Zhang et al. 2014;Kang et al. 2014b; Hovatta & Lindfors 2019). However, the BLR en-ergy density of 3C 454.3 ( 𝑈 BLR = ( . + . − . ) × − erg cm − inthe rest frame) in our modeling is about two orders of magnitude lessthan that of luminous FSRQs, where 𝑈 BLR ∼ . × − erg cm − due to the emission location (see Ghisellini & Tavecchio 2008, 2009for details). MNRAS000
McFit code are indicatedby histograms and contours. The colored contour lines represent atwo-dimensional contour map of the relative marginalization prob-abilities. The red crosses indicate the optimal fitted values and 1 𝜎 error bars.It should be noted that the GeV spectral break of 3C 454.3 couldbe entirely reproduced through the leptonic jet model with the Syn+ SSC + EC (BLR) + EC (torus) model. The value distribution ofall obtained model parameters is usually displayed as a (or approx-imately) normal distribution (see Figure 2). However, the optimalfitted values and uncertainties obtained from the optimal combina-tion of model parameters for all model parameters are not alwaysrelated to peak probabilities in a one-dimensional histogram or two-dimensional contour plot of relative marginalization probabilities(see Zhang et al. 2015). For instance, the best fit of the density nor-malization coefficient 𝑁 and the indices 𝑝 of electron spectrumin particular appear to be on the edge of the considered region. Ascould be seen from Table 1, all the modeling parameters lie withinacceptable ranges. For instance, almost all fitted model parametersare consistent with those obtained with other previous works. Forexample, the Doppler factor 𝛿 ≃ . + . − . is compatible with theDoppler coefficient of 𝛿 = [ Γ ( − 𝛽 cos 𝜃 )] − ≈ . Γ = . ± . 𝜃 = 𝑜 . ± 𝑜 . 𝛾 min = . + . − . , which corresponds to a spe-cific situation of the electrons pre-shocked (e.g., Sari et al. 1998), iscompatible with values from the literature (e.g., Zhang et al. 2014;Kang et al. 2014b; Hovatta & Lindfors 2019). However, the BLR en-ergy density of 3C 454.3 ( 𝑈 BLR = ( . + . − . ) × − erg cm − inthe rest frame) in our modeling is about two orders of magnitude lessthan that of luminous FSRQs, where 𝑈 BLR ∼ . × − erg cm − due to the emission location (see Ghisellini & Tavecchio 2008, 2009for details). MNRAS000 , 1–7 (2021)
S. J. Kang et al.
Figure 1.
The SED of 3C 454.3 (obtained from Abdo et al. 2009 and reproduced by permission of the AAS). The synchrotron, SSC, EC torus , EC
BLR , and totalemission based on the broken power-law electron spectrum are indicated by dotted, dashed, dot-dashed, long-dashed, and solid lines, respectively. The totalemission using the log-parabolic electron spectrum is indicated by long-dashed-dashed (blue) line. The right panel is zoomed in
Fermi -LAT spectrum.
Table 1.
The relevant parameters of 3C 454.3 (Best-fit model and output parameters).broken power-law electron spectrum log-parabolic electron spectrumParameter Parameters range Best-fit model parameters Parameter Parameters range Best-fit model parameters 𝐵 (G) [0.01, 3.85] 1 . + . − . 𝐵 (G) [0.01, 3.85] 1 . + . − . 𝛿 [10.0, 47.0] 22 . + . − . 𝛿 [10.0, 47.0] 23 . + . − . 𝑝 [1.20, 3.50] 2 . + . − . 𝑠 [0.2, 5.90] 2 . + . − . 𝑝 [3.10, 7.86] 4 . + . − . 𝑏 [0.01,2.96] 1 . + . − . 𝛾 min [1.0, 200.0] 118 . + . − . 𝛾 min [1.0, 200.0] 54 . + . − . 𝛾 b ( ) [1.0, 100.0] 9 . + . − . 𝛾 ( ) [1.0, 100.0] 2 . + . − . 𝑁 ( cm − ) [0.01, 15000.0] 2036 . + . − . 𝐾 ( − cm − ) [0.01, 15000] 70 . + . − . 𝑈 BLR ( − erg cm − ) [0.01, 200.0] 46 . + . − . 𝑈 BLR ( − erg cm − ) [0.1, 200.0] 35 . + . − . 𝜒 /dof 76.3/23 84.6/23 𝑟 diss ∼ . 𝑅 BLR ( ∼ . In the context, the one-zone homogeneous leptonic jet model[Syn+SSC + EC (BLR) + EC (torus)] and
McFit technique are em-ployed to fit the quasi-simultaneous multi-waveband SED of 3C454.3, where two EC components are considered in the fitting,namely, both Compton-scattered BLR and dust torus radiations.Combining two EC components provides an appropriate fitting tothe quasi-simultaneous multi-waveband SED of 3C 454.3 and ex-plains the GeV spectral break of 3C 454.3. The GeV spectral breakof 3C 454.3 can be reproduced naturally using the two EC compo-nents (EC
BLR + EC torus ) jet model, considering a broken power-lawdistribution electron spectrum and Klein-Nishina effect. We arguethat the GeV spectral break of 3C 454.3 may originate from an in-herent break in the energy distribution of the emitted particles andthe Klein-Nishina effect. However, although both the electron distri-bution break and the Klein-Nishina affect the resulting shape of the 𝛾 -ray spectrum (e.g., Lewis et al. 2018, 2019), detecting the dom-inant factor based on the current work is complicated and shouldbe further verified in the next work. Based on the energy densitiesof the BLR external photon fields and the scattering distance fromthe central black hole, the position of the 𝛾 -ray emitting area of 3C454.3 could be firmly constrained between the BLR and the dust torus (outside BLR, inside dust torus) (the scattering distance of the 𝛾 -ray radiation area from the central black hole 𝑟 diss is approximatelyseveral times of 𝑅 BLR ). 𝛾 − ray emission region of 3C 454.3 The 𝑈 BLR could be utilized to estimate the position of 𝛾 -ray emis-sion area (see the work performed by Dermer et al. 2014). More-over, the 𝑈 BLR can be estimated from the luminosity of BLR andthe BLR radius estimated from the accretion disk luminosity (e.g.,Ghisellini & Tavecchio 2008). For 3C 454.3, Bonnoli et al. (2011) re-ported the luminosity of the accretion disk 𝐿 disk ≃ . × erg s − and the size of the BLR 𝑅 BLR ≃ × cm ( ≃ × 𝑅 𝐺 ) ob-tained from the relation of Kaspi et al. (2007). Based on the relation-ship between the 𝑈 BLR and 𝑅 BLR (Ghisellini & Tavecchio 2008), 𝑈 BLR ≃ × − erg cm − can be estimated, which is consistentwith that of luminous FSRQs (e.g., Ghisellini & Tavecchio 2008;Dermer et al. 2014). The fitting value of 𝑈 BLR (see Table 1) derivedfrom the modeling procedure is two orders of magnitude less thanthe mentioned estimated amount. This implies that a radiating areais located outside the BLR’s outer boundary, which is compatiblewith the predicted positions for the 𝛾 -ray radiation region in other MNRAS , 1–7 (2021) eV spectral break of 3C 454.3 B R e l a t i v e P r obab ili t y B δ δ B p p δ p p p
110 120 130 140110 120 130 1400.00.20.40.60.81.0 γ min
110 120 130 1401.201.351.501.65 110 120 130 14021.622.423.224.0 110 120 130 1402.62.72.82.9 110 120 130 140 γ min p γ b γ b γ m i n N N γ b
40 60 80 10040 60 80 1000.00.20.40.60.81.0 U BLR
40 60 80 1001.201.351.501.65 40 60 80 10021.622.423.224.0 40 60 80 1002.62.72.82.9 40 60 80 1004.64.85.05.2 40 60 80 100110120130140 40 60 80 100891011 40 60 80 100 U BLR N Figure 2.
Parameter constraints of our model fitting. Histograms and contours show the likelihood map of the parameter-constraint outputs by the
McFit code.Red crosses mark the best-fit values and 1 𝜎 error bars. All parameters are constrained in reasonable ranges (see Table 1). sources (e.g., Dermer et al. 2014; Böttcher & Els 2016; Kang 2017;Zheng et al. 2017).The relation between the 𝑈 BLR and the dissipation distance 𝑟 diss from the central black hole (e.g., Ghisellini & Madau 1996;Ghisellini & Tavecchio 2009) could be approximated as (Sikora et al.2009; Hayashida et al. 2012) 𝑈 BLR ( 𝑟 ) = 𝜏 BLR 𝐿 disk 𝜋𝑅 𝑐 [ + ( 𝑟 diss / 𝑅 BLR ) ] , (3)where 𝜏 BLR is a portion of the disc luminosity reprocessed into BLRemission, where its typical value is 𝜏 BLR = . 𝑟 diss can be calculatedas 𝑟 diss ≃ . 𝑅 BLR ≃ .
78 pc ( ≃ . × 𝑅 𝐺 ), using the 𝑈 BLR derived from the model fitting the SEDs of 3C 454.3. Thisis compatible with previously published work in several blazars(e.g., Finke & Dermer 2010; Dermer et al. 2014; Yan et al. 2015;Paliya et al. 2015; Kang 2017; Zheng et al. 2017). 𝛾 − ray origin of 3C 454.3 In this work, the SED (GeV spectral break) of 3C 454.3 could be wellreproduced via the leptonic jet model with the Syn+ SSC+ EC (BLR)+ EC (torus) model using the electron spectrum with a broken power-law distribution. Cerruti et al. (2013) suggested that the GeV spectralbreak could be produced by the EC dissipation of photons from thedusty torus and BLR, assuming an electron spectrum representedwith a log-parabolic function. The different electron spectra are re-lated to different physical origins. A log-parabolic electron spectrumis produced by stochastic acceleration process (Fermi II process)in the jet (see Massaro et al. 2004a,b, 2006), where the accelerationdominates over radiative cooling (e.g., Tramacere et al. 2009, 2011).However, the electron spectrum with a broken power-law distributionis a steady-state electron spectrum, where no acceleration process inthe jet’s emitting region. There is a balance between the emitting par-ticle cooling and escape rates in the emitting region (e.g., Kardashev1962; Sikora et al. 1994; Inoue & Takahara 1996; Kirk et al. 1998;Ghisellini et al. 1998; Böttcher & Chiang 2002; Chen et al. 2012;Böttcher et al. 2013). The broken energy 𝛾 b of the broken power-lawelectron spectrum is a critical energy due to the balance between the MNRAS , 1–7 (2021)
S. J. Kang et al. emitting particle escape and cooling during the radiation process,where less than this critical energy, the energy loss process is dom-inated by particle escape, and above the critical energy, the energyloss is dominated by cooling (e.g., Finke 2013; Zheng et al. 2018 andreference in). Moreover, the shock acceleration shapes a power-lawparticle distribution (Fermi 1949). Mixing of shocked populationsmay cause the break, or the broken-power law could approximate amore precise functional form.In order to distinguish these two electron spectra, in this work,the fitting results are compared using the two electron spectra witha broken power-law distribution and a log-parabola distribution. Theobtained best-fit model parameters, as well as uncertainties, are alsopresented in Table 1. In addition to the electron spectrum parameters,other jet model parameters (e.g., 𝐵 , 𝛿 , 𝑈 BLR ) using a log-parabolicelectron spectrum are consistent with that of the electron spectrumwith a broken power-law distribution (see Table 1). However, the fit-ted chi-square ( 𝜒 /dof =84.6/23) of the log-parabolic electron spec-trum is larger than that ( 𝜒 /dof =76.3/23) of the electron spectrumwith a broken power-law distribution. These scenarios suggest thatthe broken power-law distribution electron spectrum fits the SEDbetter. In addition, in Figure 1, the SED fitting result (total emis-sion) using the log-parabolic electron spectrum is indicated by thelong-dashed-dashed (blue) line, which exhibits a strong curvaturein the Fermi GeV 𝛾 -ray band. In terms of intuitive phenomenology,the curvature-type radiation particle distribution may be more in-clined to produce a curvature-type radiation photon spectrum (seeMassaro et al. 2004a,b, 2006; Anjum et al. 2020); the broken-typeradiation particle distribution may be more inclined to produce abroken-type radiation photon spectrum. Here, the curvature spectrumcannot effectively produce the 𝛾 -ray spectrum break (see Figure 1).On the contrary, a broken power-law distribution electron spectrumcan effectively generate the 𝛾 -ray spectrum break. Based on the factthat the observed spectrum is broken, not a curvature one, a brokenpower-law electron spectrum, which may be more effectively presentthe observation characteristics. Further study is required to verifywhether this interpretation is suitable for all GeV spectral breaks.We should note that the GeV spectral break may be caused byan inherent break in the emitted electron spectrum, where the breakenergy can be determined by an inherent break in the emitted elec-tron spectrum. By modeling SED 3C 454.3, the break energy 𝛾 𝑏 = . + . − . × of the electron spectrum and Γ (≃ 𝛿 ) = . + . − . are obtained. Assuming the most prominent line of the BLR cloudis derived from the Ly- 𝛼 line, the spectrum is considered as a black-body with an approximated maximum 𝜈 ext ≃ × Γ Hz (e.g.,Ghisellini & Tavecchio 2008). However, it should note that the mostprominent line from the perspective of the gamma-ray emitting re-gion may vary by position with respect to the ionization gradient inthe BLR due to the relativistic effects (see Finke 2016), which mayaffect the blackbody spectrum. According to the Thomson regime orKN regime, the EC maximum frequency 𝜈 pec , thom ≃ 𝛾 Γ 𝜈 ext 𝛿 + 𝑧 ≃ .
98 GeV (4)or 𝜈 pec , kn ≃ √ 𝛾 b 𝑚 𝑒 𝑐 ℎ 𝛿 + 𝑧 ≃ .
20 GeV (5)can be obtained, where 𝑚 𝑒 is the electron mass (e.g., Chen 2018and references therein). The EC peak frequency 𝜈 pec , kn ≃ 𝛼 line, e.g., Ackermann et al.2010; Cerruti et al. 2013) with the energy 𝐸 seed , BLR , generally cre-ates a break ( 𝐸 𝛾 ) at a few GeV (e.g., Abdo et al. 2009; Finke et al.2010), 𝐸 𝛾 ≃ 𝐸 seed , BLR 𝛾 Γ 𝛿 + 𝑧 . (6)However, whether the effect of the electron distribution break or theKlein-Nishina effect on the resulting shape of the 𝛾 -ray spectrumdominating on the physical process is beyond the scope of this work.We leave these issues in the future.We should note that, in this work, we only use the two externalphoton fields jet model to fit the steady-state SED of 3C 454.3 anddo not consider fitting SED (e.g., flare) of other states of 3C 454.3or other GeV-break sources. Based on 3C 454.3 steady-state energyspectrum simulation, we propose and test a possible origin of GeVspectral break that the spectral break (GeV break) of 3C 454.3 mayoriginate from both an inherent break in the energy distribution ofthe emitting particles and Klein-Nishina influence (see Abdo et al.2009 for the related discussions). As future work, this explanation’sapplicability to all GeV-break blazars and all states should be morestudied and tested. ACKNOWLEDGEMENTS
We thank the anonymous editor and referee for very constructive andhelpful comments and suggestions, which greatly helped us to im-prove our paper. This work is partially supported by the National Nat-ural Science Foundation of China (Grant Nos.11763005, 11873043,U1931203, U1831138), the Science and Technology Foundation ofGuizhou Province (QKHJC[2019]1290) and the Research Founda-tion for Scientific Elitists of the Department of Education of GuizhouProvince (QJHKYZ[2018]068).
DATA AVAILABILITY
The data underlying this article will be shared on reasonable requestto the corresponding author.
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