Jet Radiation Properties of 4C +49.22: from the Core to Large-scale Knots

The substructures of large-scale jets in radio-loud active galactic nuclei (AGNs), i.e., knots, hotspots, and lobes, have been resolved in the radio, optical, and X-ray bands (see Harris & Krawczynski 2006 for a review). This presents an opportunity to reveal the jet properties from the radio core to the large-scale knots. This is helpful for revealing jet formation and propagation, composition, particle acceleration, and radiation mechanisms, etc. (e.g., Zargaryan et al. 2017). Observations using very long baseline interferometry (VLBI) in multi-epoch measurements of sub-parsec scale jets suggest that AGN jets start out highly relativistic with a Lorentz factor of tens (Jorstad et al. 2005; Lister et al. 2016), and it was proposed that the jets are still mildly relativistic at the kiloparsec scale (e.g., Arshakian & Longair 2004; Mullin & Hardcastle 2009). Convincing evidence for jet deceleration and transverse motions in M87 is presented by measuring its kiloparsec-scale proper motions with the Hubble Space Telescope and the parsec-scale proper motions with VLBI, and the apparent velocity that is still superluminal in its outer jet (Meyer et al. 2017). The broadband spectral energy distributions (SEDs) of the radiation from both the radio core and large-scale jet for radio-loud AGNs show that their origin is non-thermal emission and they show a bimodal feature (e.g., Sikora et al. 1994; Ghisellini et al. 2009; Zhang et al. 2010, 2013, 2014, 2018). High-energy radiation beyond the X-ray band of the core region should be dominated by the synchrotron self-Compton (SSC) scattering process (Sikora et al. 1994; Ghisellini et al. 2009; Zhang et al. 2013) and/or the inverse Compton (IC) scattering of photons in the broadline region (IC/BLR; Ghisellini et al. 2009; Zhang et al. 2014, 2015) or torus (IC/torus, Sikora et al. 2009; Kang et al. 2014). The high-energy (X-ray to γ-ray bands) radiation mechanisms of large-scale jets are still debated (Harris & Krawczynski 2006; Zhang et al. 2010; Meyer et al. 2015; Zargaryan et al. 2017).

4C +49.22 is a γ-ray flat-spectrum radio quasar (FSRQ) at redshift z = 0.334 (Burbidge 1968; Lynds & Wills 1968). It has a one-side, knotty, and wiggling jet, and its knots were resolved in the radio, optical, and X-ray bands (Owen & Puschell 1984; Akujor & Garrington 1991; Sambruna et al. 2004, 2006). This source was not detected by previous γ-ray detectors, such as EGRET (Hartman et al. 1999) and AGILE (Pittori et al. 2009), but a bright γ-ray outburst was detected with Fermi/Large Area Telescope (LAT; Reyes et al. 2011; Cutini et al. 2014). The outburst was also simultaneously observed from the microwave to the X-ray bands with Planck and Swift. The γ-ray flux is highly variable and correlated with the emission in the low-energy bands, indicating that the γ-ray outburst is from the compact core region (Cutini et al. 2014). In addition, a new component from the radio core around the time of the γ-ray outburst was caught with the Very Long Baseline Array (VLBA, Cutini et al. 2014). This robustly suggests that the outburst is in the vicinity of the core region and is related to the activity of the central black hole. Interestingly, a steady γ-ray emission component was detected with Fermi/LAT during the past eight years of operation. It is unclear whether the steady γ-ray emission component should be attributed to the radio core or to the knots of this source. So far, γ-ray emission outside the radio core has only been convincingly detected by Fermi/LAT for the radio lobes of Cen A (Abdo et al. 2010) and Fornax A (McKinley et al. 2015; Ackermann et al. 2016). If the steady γ-ray emission of 4C +49.22 is from the knots, it would constitute a valuable source with γ-ray emission from the large-scale jet structure.

This paper is dedicated to studying the emission mechanisms of the radio core and knots for 4C +49.22 to reveal the jet properties from the radio core to large-scale knots. We analyzed the observational data from Fermi/LAT for 4C +49.22 over the past eight years, and the derived γ-ray light curve is presented in Section 2. We model the broadband SEDs of the core region at different epochs with a single-zone leptonic model in the IC/BLR scenario (Section 3.1). We also model the SEDs in the radio–optical–X-ray band for the knots with the leptonic model in the scenario of IC scattering of the cosmic microwave background (CMB) and compare the γ-ray flux predicted by the model to the steady γ-ray component of the LAT observation (Section 3.2). The jet properties from the core region to the large-scale knots are presented in Section 4. Discussion and a summary are given in Sections 5 and 6, respectively. Throughout, H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_m = 0.27, and Ω_Λ = 0.73 are adopted.

We downloaded the Fermi/LAT data of 4C +49.22 covering from 2008 August 6 (Modified Julian Day, MJD 54684) to 2018 January 24 (MJD 58142) from the Fermi data archive (Pass 8 data). The reduction and analysis of Fermi/LAT data were performed with the standard analysis tool gtlike/pyLikelihood, which is part of the Fermi Science Tool software package (ver. v10r0p5). The P8R2-SOURCE-V6 set of instrument response functions was used. Photons with energies from 0.1 to 100 GeV are taken into account in our analysis. The significance of the γ-ray signal from the source is evaluated with the maximum-likelihood test statistic (TS). The events are selected from the region of interest (ROI) with a radius of 10° centered at the position of 4C +49.22. All point sources in the third Fermi/LAT source catalog located in the ROI and an additional surrounding 10° wide annulus were modeled in the fits. In the model file, the spectral parameters for sources lying within the ROI were kept free and those for sources lying within the annulus were fixed. The isotropic background, including the sum of residual instrumental background and extragalactic diffuse γ-ray background, was fitted with a model derived from the isotropic background at high Galactic latitude, i.e., "iso-P8R2-SOURCE-V6-v06.txt," and the Galactic diffuse GeV emission was modeled with "gll-iem-v06.fits." In order to eliminate contamination from the γ-ray-bright Earth limb, events with zenith angles >100° were excluded. The spectral analysis in the energy range 0.1–100 GeV was performed by using the unbinned likelihood analysis. A power-law (PL) function, i.e., ${dN}{(E)/{dE}={N}_{{\rm{p}}}(E/{E}_{{\rm{p}}})}^{-{{\rm{\Gamma }}}_{\gamma }}$, is used to fit the spectrum accumulated in each time-bin.

We do not use an even time-bin to make the Fermi/LAT light curve, but adopt an adaptive-binning method to generate it (Lott et al. 2012). The criterion for selecting the size of the time-bins is taken as TS ≥ 9, where TS = 9 corresponds to ∼3σ detection (Mattox et al. 1996). The derived light curve is shown in Figure 1. One can observe that the light curve is roughly composed of a long-term, steady γ-ray emission component and a bright outburst lasting about one year (from MJD 55573 to MJD 55978), which was reported by Hays & Dona (2011). The flux of steady γ-rays is at a low level, appearing almost constant. With the six-year LAT data (MJD 55978-58142) after the outburst, we get an average flux ${F}_{\gamma ,{\rm{c}}}=(2.3\pm 0.1)\times {10}^{-8}$ photons cm⁻² s⁻¹. The residuals defined as residual $\equiv ({F}_{\gamma }-{F}_{\gamma ,{\rm{c}}})/{F}_{\gamma ,{\rm{c}}}$ during the eight years of LAT observations, is also shown in the bottom panel of Figure 1, where the residuals of the outburst data are excluded to better illustrate the flux variation of the steady γ-ray component. One can observe that this steady γ-ray component has a temporal coverage from before the outburst to a late epoch after it, and flux variations with a residual greater than 3 are also seen in some time-bins.

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As reported by Cutini et al. (2014), the γ-ray outburst should occur in the core region. This is also confirmed by observations with the VLBA of a new component from the radio core around the time of the γ-ray outburst. The simultaneously observed SEDs of the core region during the flare (MJD 55695–55697) and post-flare (MJD 55698–55706) and the archival low-state data of the core region are taken from Cutini et al. (2014), as shown in Figure 2. On a large scale, eight knots of the 4C +49.22 jet are resolved in the radio and X-ray bands, but no optical data are available for knot-F, knot-G, or knot-H (Sambruna et al. 2006). The SED data of the eight knots are taken from Sambruna et al. (2006). The average spectra in the Fermi/LAT band during the steady γ-ray emission (MJD 55978–58142) and during compilation of the second Fermi/LAT source catalog (the same data as in Figure 2(c), approximately being the average spectrum before the outburst) are also shown in the SEDs of these knots. Although we cannot confirm that they are indeed from the knots, they place a constraint on our SED fits.

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The single-zone synchrotron+IC radiation models are used to reproduce the broadband SEDs of the core region and knots. The radiation region is assumed to be a sphere of radius R and magnetic field strength B. The bulk Lorentz factor of the emission region is Γ, and the beaming factor should be $\delta =1/{\rm{\Gamma }}(1-\beta \cos \theta )$, where θ is the viewing angle. The radiation electron distribution is taken to be a broken power law (Ghisellini et al. 2009; Chen et al. 2012; Zhang et al. 2014, 2015), and this distribution is characterized by an electron density parameter (N₀), a break energy (γ_b), and two slope indices (p₁ and p₂) below and above the break energy in the energy range ${\gamma }_{{\rm{e}}}\in [{\gamma }_{\min },{\gamma }_{\max }]$. The Klein–Nishina effect and the absorption of high-energy γ-ray photons by extragalactic background light (Franceschini et al. 2008) are also taken into account in our model calculations.

3.1. The Core Region

As illustrated in Figure 2, the blue bump of the thermal emission from the accretion disk is prominent when the source is in a low state of γ-ray radiation. Following our previous work (Sun et al. 2015; Zhang et al. 2015), the standard spectrum of the accretion disk (Davis & Laor 2011) is used to explain this thermal emission. The fitting parameters include the inner (R_in) and outer (R_out) radii of the accretion disk, black hole mass (M_BH), Eddington ratio, and inclination to the line of sight i. The inner radiative edge of the accretion disk may be at the marginally stable orbit radius and outside the Schwarzschild radius (R_s; e.g., Krolik & Hawley 2002). We take R_in = R_s, ${R}_{\mathrm{out}}=500{R}_{{\rm{s}}}$, $\cos i=1$, and ${M}_{\mathrm{BH}}=4.0\times {10}^{8}\,{M}_{\odot }$ (Shields et al. 2003) in this analysis. We vary the Eddington ratio to model the emission from the accretion disk in the ultraviolet band when the source is in a low state of γ-ray radiation, as shown in Figure 2(c). However, the thermal emission from the accretion disk is overwhelmed by the non-thermal emission of the jet when the source is in a high state of γ-ray radiation. The variability produced by the variations in the accretion rate is on a timescale of years (e.g., Zhang et al. 2013; Smith et al. 2018). Therefore, the thermal emission component of the accretion disk is fixed during the SED fitting of the source in the flare state (Figure 2(a)) and post-flare state (Figure 2(b)).

We assume that the radiation region is inside the BLR, which is also consistent with the short timescale of variability in the GeV band. The SSC and IC/BLR processes are taken into account in our modeling. This model is widely used and can represent well most observed SEDs of FSRQs (e.g., Sikora et al. 1994; Ghisellini et al. 2009; Chen et al. 2012; Zhang et al. 2014, 2015). The energy density of the BLR in the rest frame is estimated as ${U}_{\mathrm{BLR}}=\tfrac{{L}_{\mathrm{BLR}}}{4\pi {R}_{\mathrm{BLR}}^{2}c}=0.046$ erg cm⁻³, where R_BLR = 1.26 × 10¹⁷ cm (Decarli et al. 2008) is the radius of the BLR and its luminosity (L_BLR) is estimated using the fluxes of emission lines reported in Table 3 and Equation (1) in Celotti et al. (1997). In the comoving frame, the energy density of the BLR is boosted by a factor of Γ², and a correction factor of 17/12 (Ghisellini & Madau 1996) should be considered. Therefore, the energy density of the BLR photon fields in the comoving frame is ${U}_{\mathrm{BLR}}^{{\prime} }=\tfrac{17}{12}{{\rm{\Gamma }}}^{2}{U}_{\mathrm{BLR}}$. The spectrum of the BLR can be approximated by a blackbody with a peak in the comoving frame at 2 × 10¹⁵Γ Hz (Ghisellini & Tavecchio 2008).

The radiation region within the core region is assumed to be a sphere with $R=\delta c{\rm{\Delta }}t/(1+z)$, where Δt is taken as 0.33 day (the timescale of rapid variability in Cutini et al. 2014), 12 hr (the value for other FSRQs in Zhang et al. 2014, 2015), and 24 hr during SED fitting for flare, post-flare, and low states, respectively. We use the χ² minimization technique to evaluate the goodness of the SED fits; for the details of this technique please refer to Zhang et al. (2014, 2015). We first take δ = Γ in the calculation for modeling the SED of the γ-ray flare. This means that the viewing angle is equal to the beaming angle of a jet, i.e., 1/Γ. We obtain δ = Γ = 13.2, yielding a viewing angle of θ ∼ 43, which satisfies the constraint of θ < 11° derived from the measured apparent superluminal speed of 9.9c (Cutini et al. 2014). For consistency, we fix the viewing angle as θ ∼ 43 during SED modeling for post-flare and low states.

The results of our SED fits are shown in Figure 2 and the derived model parameters with 1σ confidence level are reported in Table 1. The radio emission cannot be fitted due to the synchrotron self-absorption, and thus it may be from the larger radiation regions. The radiation in the X-ray band is mostly contributed by the SSC process, while the γ-ray emission is represented by the IC/BLR process. It is found that the model fits appear appropriate to represent the observed SEDs of 4C +49.22 at different epochs.

Table 1.  SED Modeling Parameters for the Core Region and Knots

Componenta	γmin	$\mathrm{log}{\gamma }_{{\rm{b}}}$	γmax	log N0	p1	p2	Γ	B	R
				(cm−3)				(G)	(cm)
FB	59 ± 25	2.55 ± 0.14	5 × 104	4.61 ± 0.11	2	3.7	13.2 ± 0.8	6.7 ± 0.7	(8.46 ± 0.51) × 1015
PFB	2 ± 1	2.16 ± 0.10	1 × 104	4.67 ± 0.10	2	3.38	9.1 ± 1.0	4.3 ± 0.8	(1.21 ± 0.05) × 1016
LB	6 ± 4	2.29 ± 0.11	5 × 104	5.81 ± 0.12	2.4	3.8	3.9 ± 0.5	3.3 ± 0.7	(1.38 ± 0.15) × 1016
FT	1 ± 0	2.86 ± 0.10	2 × 105	2.85 ± 0.13	1.4	3.6	20.0 ± 1.5	1.05 ± 0.20	(1.28 ± 0.09) × 1016
PFT	1 ± 0	2.34 ± 0.10	2.3 × 104	2.55 ± 0.08	1.2	3.38	16.5 ± 1.2	0.96 ± 0.10	(1.89 ± 0.02) × 1016
LT	12 ± 6	2.35 ± 0.12	2 × 105	2.77 ± 0.14	1.2	3.68	7.0 ± 0.8	0.59 ± 0.18	(2.41 ± 0.22) × 1016
Knot-B	2.5 ± 0.5	4.35 ± 0.30	5 × 105	−5.43 ± 0.04	2.68	3.4b	13.0 ± 1.0	(7.1 ± 0.3) × 10–6	1.12 × 1022*
Knot-C	40 ± 20	5.44 ± 0.11	2 × 107	−5.67 ± 0.10	2.5	3.7	7.4 ± 1.0	(3.5 ± 0.6) × 10–6	1.34 × 1022*
Knot-D	3 ± 2	4.50 ± 0.50	6 × 105	−6.41 ± 0.10	2.4	3.4b	8.1 ± 1.0	(3.5 ± 0.5) × 10–6	1.34 × 1022*
Knot-E	35 ± 25	4.45 ± 0.13	5.6 × 106	−5.97 ± 0.11	2.36	3.3	7.7 ± 0.9	(4.0 ± 0.5) × 10–6	1.05 × 1022*
Knot-F	10–60	4.38 ± 0.35	5 × 105	−6.32 ± 0.16	2.3	3.4b	7.6 ± 1.2	(3.2 ± 0.7) × 10–6	1.05 × 1022*
Knot-G	15–70	4.35 ± 0.35	5 × 105	−5.70 ± 0.14	2.5	3.4b	6.4 ± 1.0	(3.4 ± 0.8) × 10–6	1.05 × 1022*
Knot-H	10–60	4.49 ± 0.37	5 × 105	−5.69 ± 0.18	2.42	3.4b	6.1 ± 1.0	(4.6 ± 1.1) × 10–6	1.05 × 1022*
Knot-IJ	45 ± 30	5.28 ± 0.11	4.2 × 106	−4.65 ± 0.20	2.56	4.36	3.9 ± 0.6	(8.9 ± 2.0) × 10–6	1.05 × 1022*

Notes. The superscript * in the column for R indicates that it is fixed.

^a"F," "PF," and "L" indicate the flare, post-flare, and archival low state of the γ-ray emission, respectively. The superscripts denote the different IC processes, i.e., "B" for IC/BLR and "T" for IC/torus. ^bIt is fixed and derived from the average spectral index of the γ-ray emission from the core region in different states as shown in Figure 2.

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As shown in Table 1, the derived values of B and Γ decrease with decreasing γ-ray emission flux. The jet may be launched with strong magnetic fields, and then the magnetic energy converts into kinetic energy with increasing bulk speed at the parsec scale (see Boccardi et al. 2017 for a review; Chen 2018). Hence, the decrease in B and Γ may indicate that the radiation region is away from the central engine following the decay of the γ-ray emission flux.

It is found that the peak frequencies of both synchrotron and external Compton (EC) bumps (ν_s and ν_c) decrease following the decay of the γ-ray flux, i.e., from 4.63 × 10¹³ Hz to 3.10 × 10¹² Hz for ν_s and from 9.62 × 10²² Hz to 4.17 × 10²¹ Hz for ν_c. This tendency has been reported by Cutini et al. (2014), and similar results have also been observed in other blazars (e.g., Zhang et al. 2013). As illustrated in Figure 2, the thermal emission of the accretion disk is overwhelmed by the non-thermal emission of the jet during the states of high γ-ray emission. This phenomenon is also present in other FSRQs, e.g., 3C 454.3 (Bonnoli et al. 2011). In addition, some sources are classified as BL Lac objects but show some properties similar to FSRQs (Sbarufatti et al. 2005; Raiteri et al. 2007; Ghisellini et al. 2011; Giommi et al. 2012), which may be due to their intrinsically weak broad lines being overwhelmed by the beamed non-thermal continuum. Therefore, 4C +49.22 was suggested to display some features more typical of BL Lac objects and to support a smooth transition between the division of blazars into BL Lac objects and FSRQs (Cutini et al. 2014).

3.2. The Knots

The radio emission of knots, sometimes including the optical radiation, should be of a synchrotron origin (e.g., Harris & Krawczynski 2006). As suggested by Sambruna et al. (2006), the X-ray fluxes of some knots in 4C +49.22 are well above the extrapolation from the radio-to-optical spectra and the X-ray spectra are hard, indicating that an IC component is necessary to explain the X-ray emission. We therefore model the SEDs of the knots in the radio, optical, and X-ray bands by considering both the synchrotron radiation and the IC process. As reported in Zhang et al. (2018), except for knot-IJ, if the X-ray emission is produced by the SSC process, the derived magnetic field strengths for the other four knots (knot-B, knot-C, knot-D, and knot-E) are smaller than 1 μG, i.e., smaller than the magnetic field strength of the interstellar medium. Hence, the IC/CMB process is suggested to produce the X-ray emission of knots (see also Tavecchio et al. 2000; Kataoka & Stawarz 2005; Harris & Krawczynski 2006; Sambruna et al. 2006; Zhang et al. 2009, 2010, 2018). The observed radio spectral indices are comparable to the X-ray slopes for the knots of 4C +49.22, which is also consistent with the model prediction if the same population of electrons contributes the radiation at the two energy bands by the synchrotron and IC/CMB processes, respectively. Although the IC/CMB scenario requires highly relativistic outflows (Γ ∼ 10), implying that the jet does not suffer severe deceleration between parsec and kiloparsec scales, it is also favored by some observations; the high ratio of X-ray to radio luminosity for the intermediate-redshift (z = 2.5) quasar B3 0727+490 appears consistent with the amplification being $\propto {(1+z)}^{4}$ (Simionescu et al. 2016) and the X-ray-to-radio flux ratios of the high-redshift jets being marginally inconsistent with those from lower redshifts (McKeough et al. 2016), which is expected from the IC/CMB model for the X-ray emission.

Although the contribution of the SSC process is negligible in comparison with the IC/CMB component, we still take the SSC process into account in our calculations. The single-zone synchrotron+SSC+IC/CMB model is used to fit the SEDs of knots. The CMB peak frequency at z = 0 is ν_CMB = 1.6 × 10¹¹ Hz and the CMB energy density in the comoving frame is ${U}_{\mathrm{CMB}}^{{\prime} }=\tfrac{4}{3}{{\rm{\Gamma }}}^{2}{U}_{\mathrm{CMB}}{(1+z)}^{4}$ (Dermer & Schlickeiser 1994), where U_CMB = 4.2 × 10⁻¹³ erg cm⁻³. For the SED fitting of these knots, we also take a viewing angle of θ ∼ 43 and adjust the value of Γ to get the value of δ during SED modeling, which is different from the assumption in Zhang et al. (2010, 2018).

The radius of the radiation region is derived from the angular radius at the X-ray band and this are taken from Sambruna et al. (2006). However, observational data are available for only three knots (knot-B, knot-C, knot-E), so we take the same value for knot-D and knot-C while the value of knot-E is used for the other four knots, as listed in Table 1. In order to constrain the model parameters, we assume that these knots satisfy the minimum energy condition, i.e., the energy densities of relativistic electrons and magnetic fields are in equipartition (see also Sambruna et al. 2006). Therefore, the magnetic field strength is estimated from $\tfrac{{B}^{2}}{8\pi }={U}_{{\rm{e}}}^{{\prime} }$, where ${U}_{{\rm{e}}}^{{\prime} }$ is the energy density of relativistic electrons in the comoving frame.

The slopes of the electron distribution, i.e., p₁ and p₂, can be constrained with the spectral indices observed in the radio and optical bands for knot-C, knot-E, and knot-IJ. For the other five knots, p₁ is also derived from their radio spectral indices, but their p₂ values are taken as p₂ = 3.4, which is derived from the average spectral index of the γ-ray emission from the core region in different states as shown in Figure 2. The values of γ_min can be constrained by comparing the predicted flux of the IC/CMB process with the observational data. Too small a value of γ_min would result in the predicted flux of the IC/CMB model in the low-energy band exceeding the observations, while too large a value could not explain the X-ray observations. γ_max is fixed at a large value. Similar to the SED fitting of the core region, we also use the χ² minimization technique to search for the best SED fits. Our results are shown in Figure 3 and the derived model parameters with 1σ confidence level are reported in Table 1.

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As shown in Figure 3, the γ-ray flux of each knot predicted by the IC/CMB process is lower than the observed steady γ-ray emission component. This indicates that a single knot may be insufficient to produce this emission component. Note that the low spatial resolution of Fermi/LAT makes it difficult to judge the location of the γ-ray emission. Therefore, we add up our SED fits of the eight knots to make a synthetic SED. This is also shown in Figure 3 in comparison with the spectra of the steady γ-ray emission component. It is found that the γ-ray flux of the synthetic SED is still lower than the observations of Fermi/LAT during the steady γ-ray emission (MJD 55978–58142) with an integral flux ratio of 0.21. However, the γ-ray fluxes of the synthetic SED at energies of several GeV are roughly consistent with the observations. The steady emission component may be contributed by both the radio core and large-scale knots, though the contribution from knots is the smaller. Thus the fluctuations of the core emission would be concealed if the flux levels of emission from the radio core and knots are comparable.

The fluxes of these knots at 4.9 GHz, 4.8 × 10¹⁴ Hz, and 1 keV, together with the values of Γ, B, and N₀ derived from the model, are plotted against their distances from the radio core in Figure 4. Except for the outermost knot-IJ, the fluxes in the optical and X-ray bands together with the values of Γ tend to decrease along the jet, but no similar trend is found for the radio flux, B, or N₀. This may be because the optical and X-ray radiation is produced by the IC/CMB process and the IC/CMB emission component is proportional to Γ², which makes Γ a more efficient probe of the IC/CMB process than the other parameters. As reported in Sambruna et al. (2006), the X-ray jet of 4C +49.22 has a "twisted" morphology, with a change in position angle of ΔP.A. ∼ 20°, which closely follows the radio morphology (Owen & Puschell 1984). The plasma from the core region may be decelerated beyond the region that corresponds to knot-B due to the environment of the medium, and may result in the "twisted" jet morphology, which is also consistent with the results of our analysis.

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As illustrated in Figure 4, the outermost knot-IJ does not follow the same tendency as other knots; it has the highest B and N₀ and the smallest Γ among the eight knots. These features make knot-IJ more like a hotspot than a knot (see also Sambruna et al. 2006). As suggested by Zhang et al. (2010, 2018), the observed luminosity ratio of radio waves to X-rays, i.e., ${L}_{5\mathrm{GHz}}/{L}_{1\mathrm{keV}}$, is a characteristic to distinguish hotspots and knots. In the ${L}_{5\mathrm{GHz}}\mbox{--}{L}_{1\mathrm{keV}}$ plane, knot-IJ is located almost at the division line of ${L}_{1\mathrm{keV}}={L}_{5\mathrm{GHz}}$. Therefore, at the jet terminal of 4C +49.22, i.e., knot-IJ, there is a significant increase in magnetic field and electron density and a decrease in bulk speed due to the interaction of the jet with the surrounding medium.

The derived γ_b values of electrons in the knots are ∼2 × 10⁴ to 3 × 10⁵, corresponding to the typical energy of these electrons of ${E}_{{\gamma }_{{\rm{b}}}}\sim (10\mbox{--}154)$ GeV. The maximum energy is ${E}_{{\gamma }_{\max }}\,\sim (0.26\mbox{--}10.2)$ TeV, indicating that the electrons are effectively accelerated. The cooling time of electrons can be estimated from ${t}_{\mathrm{cool}}=3{m}_{{\rm{e}}}{c}^{2}/4{\sigma }_{{\rm{T}}}c{\gamma }_{e}({U}_{B}^{{\prime} }+{U}_{\mathrm{CMB}}^{{\prime} }+{U}_{\mathrm{syn}}^{{\prime} })$, where m_e is the electron mass, σ_T is the Thomson cross section, ${U}_{\mathrm{syn}}^{{\prime} }$ is the synchrotron radiation energy density. B ranges from 3.2 to 8.9 μG among the knots, and thus the corresponding ${U}_{B}^{{\prime} }$ is ∼(0.4–3.2) × 10⁻¹² erg cm⁻³. In the comoving frame, ${U}_{\mathrm{CMB}}^{{\prime} }$ is much higher than ${U}_{B}^{{\prime} }$ and ${U}_{\mathrm{syn}}^{{\prime} }$. The IC/CMB process should dominate the cooling of electrons. We then obtain the light travel distance of c × t_cool ≃ 0.15–9.0 kpc, which is shorter than the distance from the radio core and even smaller than the size of knots. Therefore, the particles should be accelerated locally (see also in 3C 120; Zargaryan et al. 2017).

On the basis of the model parameters derived from our SED fits, we estimate the power of each jet component by assuming that the jet consists of electrons and cold protons in a ratio of one to one, magnetic fields, and radiation. The total jet power is the sum of the power carried by each component, i.e., ${P}_{\mathrm{jet}}=\pi {R}^{2}{{\rm{\Gamma }}}^{2}c({U}_{{\rm{e}}}^{{\prime} }+{U}_{{\rm{p}}}^{{\prime} }+{U}_{B}^{{\prime} }+{U}_{{\rm{r}}}^{{\prime} })$. The energy density of radiation is calculated from ${U}_{{\rm{r}}}^{{\prime} }={L}_{\mathrm{obs}}/4\pi {R}^{2}c{\delta }^{4}$. The derived jet powers together with the power carried by each component are reported in Table 2. The magnetization parameter (σ_B) and radiation efficiency (ε_r) of the jet are estimated from ${\sigma }_{B}={P}_{B}/({P}_{{\rm{r}}}+{P}_{{\rm{p}}}+{P}_{{\rm{e}}})$ and ${\varepsilon }_{{\rm{r}}}={P}_{{\rm{r}}}/{P}_{\mathrm{jet}}$, and the derived values of σ_B and ε_r for the core region and these knots are also given in Table 2.

Table 2.  Derived Jet Power and Power Carried by Each Component

Compa	$\mathrm{log}{P}_{{\rm{e}}}$	$\mathrm{log}{P}_{{\rm{p}}}$	$\mathrm{log}{P}_{B}$	$\mathrm{log}{P}_{{\rm{r}}}$	$\mathrm{log}{P}_{\mathrm{jet}}$	εr	σB
	(erg s−1)	(erg s−1)	(erg s−1)	(erg s−1)	(erg s−1)
FB	43.94 ± 0.18	44.96 ± 0.22	45.31 ± 0.13	44.99 ± 0.05	45.60 ± 0.08	0.25 ± 0.06	1.03 ± 0.32
PFB	44.30 ± 0.16	46.51 ± 0.21	44.91 ± 0.18	44.58 ± 0.10	46.53 ± 0.20	0.011 ± 0.006	0.025 ± 0.010
LB	44.08 ± 0.27	45.95 ± 0.38	44.03 ± 0.24	43.76 ± 0.11	45.96 ± 0.37	0.006 ± 0.005	0.012 ± 0.007
FT	44.59 ± 0.19	46.16 ± 0.18	44.40 ± 0.20	44.76 ± 0.07	46.20 ± 0.17	0.036 ± 0.015	0.016 ± 0.007
PFT	44.56 ± 0.14	46.21 ± 0.11	44.51 ± 0.12	44.40 ± 0.06	46.24 ± 0.10	0.015 ± 0.004	0.019 ± 0.005
LT	44.15 ± 0.26	45.48 ± 0.24	43.49 ± 0.33	43.42 ± 0.10	45.51 ± 0.23	0.008 ± 0.005	0.010 ± 0.007
Knot-B	45.68 ± 0.10	48.14 ± 0.16	45.60 ± 0.08	41.71 ± 0.07	48.15 ± 0.16	(3.6 ± 1.5) × 10–7	(2.9 ± 0.5) × 10–3
Knot-C	44.70 ± 0.19	45.85 ± 0.32	44.66 ± 0.18	41.83 ± 0.12	45.91 ± 0.28	(8.4 ± 5.9) × 10–5	0.06 ± 0.02
Knot-D	44.73 ± 0.17	46.91 ± 0.33	44.74 ± 0.15	41.27 ± 0.11	46.91 ± 0.33	(2.3 ± 1.8) × 10–6	0.007 ± 0.002
Knot-E	44.58 ± 0.19	45.67 ± 0.34	44.60 ± 0.15	41.52 ± 0.10	45.74 ± 0.30	(6.0 ± 4.3) × 10–5	0.08 ± 0.03
Knot-Fb	44.37 ± 0.24	45.30–46.23	44.39 ± 0.22	41.36 ± 0.14	45.39–46.24	(1.3–9.3) × 10–5	0.01–0.11
Knot-Gb	44.32 ± 0.24	45.21–46.10	44.30 ± 0.23	40.80 ± 0.14	45.31–46.11	(0.5–3.1) × 10–5	0.02–0.11
Knot-Hb	44.51 ± 0.26	45.45–46.44	44.51 ± 0.23	41.08 ± 0.14	45.54–46.45	(0.4–3.4) × 10–5	0.01–0.10
Knot-IJ	44.78 ± 0.28	45.87 ± 0.42	44.71 ± 0.23	41.05 ± 0.13	45.93 ± 0.37	(1.3 ± 1.2) × 10–5	0.06 ± 0.03

Notes.

^a"F," "PF," and "L" indicating the flare, post-flare, and archival low state of the γ-ray emission, respectively. The superscripts denote the different IC processes, i.e., "B" for IC/BLR and "T" for IC/torus. ^bTheir powers for protons are derived from the two sets of parameters with the smallest and largest γ_min values. Hence, the ranges of P_p, P_jet, ε_r, and σ_B are presented for the three knots.

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For the core region, the jet powers are from (4.0 ± 0.8) × 10⁴⁵ erg s⁻¹ to (3.4 ± 1.5) × 10⁴⁶ erg s⁻¹ by considering the IC/BLR process, which is lower than the Eddington luminosity of L_Edd = 5.0 × 10⁴⁶ erg s⁻¹ for ${M}_{\mathrm{BH}}=4.0\times {10}^{8}\,{M}_{\odot }$ (Shields et al. 2003) and ${L}_{\mathrm{Edd}}=2.0\times {10}^{47}$ erg s⁻¹ for ${M}_{\mathrm{BH}}=1.6\,\times {10}^{9}\,{M}_{\odot }$ (Decarli et al. 2008). The magnetization parameter of the jet changes from 0.012 ± 0.007 to 1.03 ± 0.32 while its radiation efficiency changes from 0.006 ± 0.005 to 0.25 ± 0.06 following the increase in the γ-ray flux. Therefore, the core jet is highly magnetized with a high radiation efficiency in the state with high γ-ray emission. However, the jet becomes particle-dominated in the state with low γ-ray emission. As described in Section 3.1, the γ-ray radiation region may be away from the central engine following the decrease in the γ-ray flux, and the Poynting flux-dominated jet changes into the particle-dominated jet at the same time.

The estimated powers of the knots are in the range from 2.0 × 10⁴⁵ to 1.4 × 10⁴⁸ erg s⁻¹. Calculations of the jet powers are sensitive to γ_min and most power is carried by the protons for a small γ_min value under the assumption of equal numbers of electrons and protons. Note that the γ_min values of knot-F, knot-G, and knot-H are constrained in a broad range because of their poor observational data. Therefore, we give a range of the proton powers for the three knots in Table 2. The powers of knot-B and knot-D are 1.4 × 10⁴⁸ erg s⁻¹ and 8.2 × 10⁴⁶ erg s⁻¹, which exceed the Eddington luminosity. This may be due to their γ_min values being close to 1, and may thus result in the so-called "super-Eddington" jet powers as suggested by some authors (e.g., Dermer & Atoyan 2004; Uchiyama et al. 2006; Meyer et al. 2015). As given in Table 2, both the magnetization parameters and radiation efficiencies are low for these knots, especially the radiation efficiencies, which are much lower than that of the core region, indicating that these knots are particle-dominated.

It is found that the jet powers estimated independently for parsec- and kiloparsec-scale jets of 4C +49.22 are roughly of the same order except for knot-B, and similar results have been reported for the γ-ray-emitting radio galaxy 3C 120 (Zargaryan et al. 2017). We plot the derived power carried by each component against the distance from the radio core in Figure 5. Unlike the core region, the jet powers of knots are dominated by the particle powers. As suggested in Zargaryan et al. (2017), the jet may not substantially dissipate its power until its end, but it becomes radiatively inefficient on a large scale compared with the core region. In addition, the Poynting flux-dominated jet on a parsec scale becomes a particle-dominated jet on a kiloparsec scale through some unknown mechanism, and the jet decelerates on a large scale by interacting with the surrounding medium (Boccardi et al. 2017; Chen 2018).

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The multiwavelength observations are useful for judging the origin of the γ-ray emission. 4C +49.22 was spectroscopically observed twice in the Sloan Digital Sky Survey (SDSS) during the Fermi/LAT observations; however, on both occasions the source was in the steady γ-ray state, i.e., at MJD 56385 and MJD 57134. After correcting for the Galactic extinction and transforming into the rest frame of the source, we analyze its SDSS spectra following the approach adopted in Yao et al. (2015).⁶ A broken power law is used to model the continuum emission and the Fe ii multiplets are modeled with the templates in Véron-Cetty et al. (2004). The results of spectroscopic analysis in the SDSS observations are given in Figure 6 and Table 3.

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An obvious bluer-when-brighter trend can be found for the two epochs of spectroscopic observation; however, the fluxes of the broad lines remain constant when the continuum flux increases. The continuum flux is estimated as the flux at 3000 Å and its ratio is ∼2.6 for the two epochs. With a radio-quiet AGN sample, Ai et al. (2010) reported that the continuum variation from the accretion disk is weaker for the brighter sources. The disk luminosity derived by fitting the blue bump when 4C +49.22 was in a low state is 6.4 × 10⁴⁵ erg s⁻¹, which likely indicates the smaller variability amplitude of the accretion disk. And no variation of broadline flux also indicates that the continuum variation may be due to the beamed contribution from the jet, not the unbeamed thermal disk radiation. This is also consistent with the results of the broadband SED fitting of the core region; the disk radiation component of 4C +49.22 remains constant in different γ-ray emission states.

As displayed in Figure 1, the γ-ray fluxes are very low at MJD 56385 and MJD 57134. The lack of a counterpart in the γ-ray emission to the flare in the low-energy bands may be caused by a variation of the magnetic field in the emitting region (Chatterjee et al. 2013). On the other hand, it likely demonstrates that the steady γ-ray emission component of 4C +49.22 is partly contributed by the large-scale knots. Note that there is a He ii λ4687 component in the spectrum at MJD 57134, which is not seen in the spectrum at MJD 56385. If the BLR has a radial stratification of ionization as reported by Poutanen & Stern (2010), this implies that the radiation regions at different epochs may be located at different distances from the black hole (see also 3C 273 in Patiño-Álvarez et al. 2018). We will not discuss this issue further since the derived He ii λ4687 component is not significant.

Although the increase in flux density and polarization degree in the radio core of 4C +49.22 after the γ-ray flare implies that the γ-ray emission is produced in or close to the radio core (Cutini et al. 2014), we cannot judge for certain whether the γ-ray radiation region is inside or outside the BLR. Hence, we also consider the IC/torus process to explain the γ-ray emission by assuming that the γ-ray radiation region is outside the BLR. In this scenario, the corresponding energy density of the photon field in the comoving frame is ${U}_{\mathrm{IR}}^{{\prime} }=3\times {10}^{-4}{{\rm{\Gamma }}}^{2}$ erg cm⁻³. The spectrum of the torus is assumed to be a blackbody with a peak frequency in the comoving frame at 3 × 10¹³Γ Hz (Ghisellini & Tavecchio 2008). Similar to the IC/BLR scenario, the assumption of δ = Γ is taken during the SED fitting for the γ-ray flare, and then a viewing angle of θ ∼ 29 is obtained and fixed during SED modeling for the post-flare and low states. The fitting results are given in Figure 7 and the derived parameters and jet powers are also listed in Tables 1 and 2.

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Compared with the IC/BLR scenario, Γ is larger and B is smaller in the IC/torus case, and the radio-core jet is likely dominated by the particle powers with low radiation efficiency. The single-zone synchrotron+SSC+IC/torus model can also represent the observed SEDs of the core region well. However, the electron spectrum is harder, which cannot be explained with first-order Fermi acceleration via relativistic shocks (e.g., Kirk et al. 2000; Achterberg et al. 2001; Virtanen & Vainio 2005). In this respect, we suggest that the synchrotron+SSC+IC/BLR model is the preferred model to explain the SEDs of the core region.

Note that the photon fields of accretion disk, torus, and BLR were taken into account together to calculate the EC process in Cutini et al. (2014). We used the different electron distribution spectrum and radiation models to explain the SEDs of the core region, and therefore we obtained the different fitting parameters from them. The values of B and δ reported in Cutini et al. (2014) are closer to the derived values in the IC/torus case of our work.

We dealt with and analyzed the long-term monitoring data of 4C +49.22 by Fermi/LAT. Besides a large outburst, a long-term, steady γ-ray emission component is observed in the γ-ray light curve, which can almost be fitted by a constant flux. The broadband SEDs of the core region at different γ-ray emission epochs (during the large flare, post-flare, and low state) can be well reproduced with the single-zone leptonic model, synchrotron+SSC+IC/BLR. The SEDs of the eight knots on a large scale can also be well explained with the single-zone leptonic model, synchrotron+SSC+IC/CMB, and the γ-ray fluxes predicted by the model are lower than that of the steady γ-ray emission observed with Fermi/LAT. The synthetic fluxes predicted by the model for the eight knots in the Fermi/LAT energy band are still lower than this steady γ-ray emission with an integral flux ratio of 0.21. This indicates that the steady γ-ray emission is still dominated by the core radiation, but it may be partially contributed by the large-scale knots, which may conceal a low-level flux variation of the γ-ray emission from the core region. The decreases in the flux in the X-ray and optical bands and the derived bulk Lorentz factors along the jet on a large scale may indicate that the jet decelerates on a large scale by interacting with the surrounding medium.

On the basis of the fitting parameters, we calculated the jet powers and the power carried by each component on the parsec scale and the kiloparsec scale. It was found that the jet powers independently estimated for parsec- and kiloparsec-scale jets of 4C +49.22 are of roughly the same order. The magnetization parameters and radiation efficiencies of the core region decrease with decreasing γ-ray emission flux, and the jet changes from Poynting flux-dominated to particle-dominated. Unlike the core region, the knots on a large scale are particle-dominated with very low radiation efficiencies. Therefore, the Poynting flux-dominated jet on a parsec scale becomes a particle-dominated jet on a kiloparsec scale through some unknown mechanism. The synchrotron+SSC+IC/CMB model indeed induces the "super-Eddington" jet powers for some sources as suggested by some authors (e.g., Dermer & Atoyan 2004; Uchiyama et al. 2006; Meyer et al. 2015).

We thank the anonymous referee for the valuable suggestions. We thank Dr. Sara Cutini for providing us with the observational data on the core region and we are also grateful for the helpful discussion with Dr. Yuan Liu. This work is supported by the National Natural Science Foundation of China (grants 11573034, 11533003, 11851304, and U1731239), the National Basic Research Program (973 Programme) of China (grant 2014CB845800). En-Wei Liang acknowledges support from the special funding from the Guangxi Science Foundation for Guangxi distinguished professors (grant 2017AD22006 for Bagui Yingcai & Bagui Xuezhe). Su Yao acknowledges the support by the KIAA-CAS Fellowship, which is jointly supported by Peking University and Chinese Academy of Sciences.