PROTON SYNCHROTRON RADIATION FROM EXTENDED JETS OF PKS 0637–752 AND 3C 273

Quasars are a class of active galaxies that are highly energetic and powered by the accretion of mass around central supermassive black holes. Jets of FRII radio galaxies and quasars often exhibit regions of extreme brightness or knots, as have been observed by radio telescopes for a long time. However, more recently, images from the Hubble Space Telescope (HST) and the Chandra X-Ray Observatory have shown that the significant amount of high-energy radiation is also produced from the bright knots present in these jets. The first discovery of high-energy X-ray emission from the kiloparsec-scale relativistic jet of quasar PKS 0637–752 by the Chandra Observatory (Chartas et al. 2000) has led to many similar significant discoveries (Harris & Krawczynski 2006).

PKS 0637–752, located at redshift z = 0.651 (Savage et al. 1976), was the first X-ray target of the Chandra Observatory (Chartas et al. 2000; Schwartz et al. 2000; Weisskopf et al. 2000), which accidentally discovered a 100 kpc one-sided jet from the source coincident with the radio jet reported by Tingay et al. (1998). The strong X-ray flux observed from this jet is difficult to explain via standard mechanisms such as Synchrotron Self Compton (SSC) or thermal Bremsstrahlung (Schwartz et al. 2000). Since the launch of Chandra in 1999, many tens of such quasar jets luminous in X-rays have been detected. The periodic structure of knots in the megaparsec-scale jet of PKS 0637–752 has been observed by the Australian Telescope (Godfrey et al. 2012).

3C 273, located at redshift z = 0.158 (Strauss et al. 1992), is the brightest and most studied active galactic nucleus (AGN) and is accompanied by a large-scale jet with a projected length of 57 kpc (Harris & Krawczynski 2006). An analysis has been performed on its broadband energy spectrum by various authors (Jester et al. 2001, 2005; Uchiyama et al. 2006; Meyer & Georganopoulos 2014). Soldi et al. (2008) have analyzed long-term multiwavelength data to study its temporal variability properties. Sambruna et al. (2001) and Uchiyama et al. (2006) have found two distinct components in the jet emission of 3C 273. The radio emission from the kiloparsec-scale jet has been explained with synchrotron radiation from shock-accelerated relativistic electrons by Marscher & Gear (1985) and Türler et al. (2000).

The radio to optical spectral energy distribution from jets of both 3C 273 and PKS 0637–752 can be well explained by the synchrotron radiation of relativistic electrons present in the jets (Sambruna et al. 2001). However, in several jets, the X-ray emission from the knots is much higher and/or harder than expected from the radio-optical synchrotron spectrum as explained by Schwartz et al. (2000) for quasar PKS 0637–752. The SSC mechanism could not explain the observed X-radiation in both of the sources, as explained by Chartas et al. (2000) for PKS 0637–752 and Sambruna et al. (2001) for 3C 273. Hence, it was suggested by Tavecchio et al. (2000) and Celotti et al. (2001) that the X-ray emission from PKS 0637–752 can arise due to inverse Compton scattering of the cosmic microwave background photons by shock-accelerated relativistic electrons in the jet (IC/CMB). The IC/CMB model has also been applied to explain X-ray radiation from Knot A of 3C 273 (Sambruna et al. 2004). The IC/CMB mechanism has been the most popular explanation for X-radiation in quasar jets, by far. Sambruna et al. (2004) explained the X-ray emission from most of the radio jets included in their survey, by IC/CMB. IC/CMB model predictions were verified for the source PKS 1150+49 with follow-up observations by Sambruna et al. (2006).

However, a number of problems have been noticed with the IC/CMB X-ray model. It requires the jet to remain highly relativistic (i.e., high Lorentz factor ∼10–20) even up to kiloparsec scales and pointed at a very small angle to our line of sight. However, it was predicted by Arshakian & Longair (2004) that the jets decelerate and can only remain mildly relativistic when they reach kiloparsec scales, though this lacks direct experimental support. Moreover, the small angle subtended by the jet to our line of sight sometimes gives rise to deprojected jet length of megaparsec size. Also IC/CMB models require huge jet kinetic power, sometimes exceeding the Eddington limit for the source (Uchiyama et al. 2006). As an alternative to IC/CMB, it was proposed that X-radiation from large-scale quasar jets can also be explained by synchrotron radiation from a second shock-accelerated electron population, different from the one giving rise to the radio-optical spectra (Jester et al. 2006; Uchiyama et al. 2006). Although this second synchrotron model overcomes the problem of super-Eddington power requirements, high Lotentz factor, and megaparsec-scale jet length of the IC/CMB to explain the observed X-Ray data, the problem lies in its unexplained co-spatial existence with the first high-energy electron population (Schwartz et al. 2000).

Recently, it has been shown by Meyer & Georganopulos (2014) and Meyer et al. (2015), using observational results from Fermi-LAT, that IC/CMB incorrectly predicts the gamma-ray flux at GeV energies. They have shown, using long-term Fermi monitoring data, that the hard and steady gamma-ray emission implied by the IC/CMB X-ray models, overproduces the GeV flux, thus violating observational results from Fermi for both quasar jets PKS 0637–752 and 3C 273. Thus IC/CMB is ruled out as a possible X-ray emission mechanism in both of our target sources. The implication of explaining X-ray emission from the knots with electron synchrotron has also been discussed by Meyer et al. (2015). The shock-accelerated electrons emitting X-rays in synchrotron emission would also give GeV–TeV gamma-rays by inverse Compton scattering of the CMB photons. The luminosity expected in TeV gamma-rays is very high in this case.

Aharonian (2002) proposed synchrotron radiation by a shock-accelerated proton population, which explained the radio to X-ray spectrum from knot A of 3C 273. Also, the jet emission from PKS 0637–752 in the optical to X-ray spectrum was well explained by the proton synchrotron model in this paper. A broken power-law spectrum of accelerated protons having energy up to 10²⁰ eV was used, where the spectral indices were determined by three important timescales: the synchrotron loss and escape timescales of the protons and the age of the jet. The protons lose energy very slowly in the magnetic field of the order of milliGauss in the jet, and as a result they can diffuse through the length of the kiloparsec-scale jet.

We have used this proton synchrotron model (Aharonian 2002) to propose the possible common origin of the high-energy photons in kiloparsec-scale jets of quasars PKS 0637–752 and 3C 273. For the source PKS 0637–752, we have modeled the X-ray–gamma-ray flux by proton synchrotron. Kundu & Gupta (2014) demonstrated the possible proton synchrotron origin of X-ray and gamma-ray emission from the large-scale jet of 3C 273. In the recent work of Meyer et al. (2015), the optical HST data near 10¹⁵ Hz for the source 3C 273 has not been included in the radio-optical synchrotron fit, which we have included in our updated proton synchrotron model proposing a common origin of optical, X-ray, and gamma-ray photons.

We have also discussed the possibility of TeV photon emission from large-scale quasar jets within the proton synchrotron model. For the knot wk8.9 of PKS 0637–752, we have shown that the proton synchrotron mechanism can, in principle, give rise to a TeV flux within a reasonable budget in luminosity if protons are accelerated to an energy close to 10²¹ eV.

2.1. High Energy Spectral Energy Distribution

We describe the formalism used in our work (earlier discussed in Aharonian 2002; Kundu & Gupta 2014). The shock-accelerated protons are diffusing through the large-scale jets of the quasars and losing energy due to synchrotron emission and diffusion. We have calculated the Doppler factors (δ_D) of the jets assuming their Lorentz factor to be Γ = 3 to fit the observational data. Within a spherical blob of size R and magnetic field B, the relativistic protons are trapped. Their escape timescale is

$$\begin{eqnarray}&&{t}_{{\rm{esc}}}\simeq 4.2\times {10}^{5}{\eta }^{-1}{B}_{{\rm{mG}}}{R}_{{\rm{kpc}}}^{2}{(E/{10}^{19}\mathrm{eV})}^{-1}\;{\rm{year}}.\end{eqnarray} \tag{ 1 }$$

In the Bohm diffusion limit, the gyrofactor η = 1. Another expression for the escape time, which is energy dependent, reduces the energy budget (Aharonian 2002)

$$\begin{eqnarray}&&{t}_{{\rm{esc}}}=\displaystyle \frac{1.4\times {10}^{7}}{{(E/{10}^{14}{\rm{eV}})}^{0.5}}\;{\rm{year}}.\end{eqnarray} \tag{ 2 }$$

The synchrotron energy loss timescale of the relativistic protons in the jet is

$$\begin{eqnarray}&&{t}_{{\rm{synch}}}\simeq 1.4\times {10}^{7}{B}_{{\rm{mG}}}^{-2}{(E/{10}^{19}\mathrm{eV})}^{-1}\;{\rm{year}}.\end{eqnarray} \tag{ 3 }$$

We have considered the broken power-law spectrum of the shock-accelerated relativistic protons

$$\begin{eqnarray}\displaystyle \frac{{{dN}}_{p}({E}_{p})}{{{dE}}_{p}}=A\left\{\begin{array}{ll}{{E}_{p}}^{-{p}_{1}} & {E}_{p}\lt {E}_{p,\mathrm{br}}\\ {{E}_{p,\mathrm{br}}}^{({p}_{2}-{p}_{1})}{{E}_{p}}^{-{p}_{2}} & {E}_{p}\gt {E}_{p,\mathrm{br}}.\end{array}\right.\end{eqnarray} \tag{ 4 }$$

We compare the synchrotron loss and escape timescales of the protons in the jet whose age is assumed to be 3 × 10⁸ years. When the synchrotron loss timescale is shorter than the escape or diffusion timescale, given in Equation (1), and the age of the jet, synchrotron loss becomes important. As a result, the spectrum of high-energy protons steepens by ${E}_{p}^{-1}$ above the break energy E_p,br (our model 1). For knot wk8.9 of PKS 0637–752 at ${{\boldsymbol{E}}}_{p,\mathrm{br}}$ = 10¹⁶ eV, the synchrotron loss timescale is t_sync = 1.4 × 10⁸ years, which is smaller than the age of the jet and the escape time (t_esc = 7.56 × 10⁹ years); the case in the combined knot scenerio is similar, thus increasing the spectral index by one. For knot A and knots A+B1 combined of 3C 273, at E_p,br = 10¹⁶ eV (and 5.62 × 10¹⁵ eV), t_sync = 1.4 × 10⁸ years (and 2.49 × 10⁸ years), whereas t_esc = 1.52 × 10¹⁰ years and 8.14 × 10¹⁰ years respectively.

We have also considered another scenario where the escape timescale given in Equation (2) becomes shorter than the synchrotron timescale and the age of the jet for very high-energy protons. This results in a steeper spectrum by a factor of ${E}_{p}^{-0.5}$ above the break energy E_p,br (our model 2). For PKS 0637–752, both for the single knot and combined knot scenarios, at E_p,br = 10¹² eV, the escape time is 1.4 × 10⁸ years which thus becomes dominant over the synchrotron loss (t_sync ∼ 10¹² years) and the age of the jet. Similar are the cases for knot A and the combined knots of 3C 273, where, according to our model 2, the escape loss also becomes more important compared to other timescales.

The high-energy photon spectrum from knots of PKS 063–752 and 3C 273 are compared with the theoretical predictions of our models 1 and 2 (see Figures 1–4). The values of the parameters used in our flux calculations are given in Tables 1 and 2.

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Table 1.  Model Parameters for PKS 0637–752

Knot	Parameter	Notation	Model 1	Model 2
wk8.9	Size of knot (m)	R	2.2 × 1019	3.6 × 1019
	Lorentz factor	Γ	3	3
	Viewing angle	θ	35°	30°
	Doppler factor	δD	1.46	1.79
	Magnetic field (mG)	B	8	5
	Minimum proton energy (eV)	Ep,min	1014	1010
	Maximum proton energy (eV)	Ep,max	7.2 × 1019	5.2 × 1019
	Break proton energy (eV)	Ep,br	1016	1012
	Low energy proton spectral index	p1	1.35	1.63
	High energy proton spectral index	p2	2.35	2.13
	Luminosity in magnetic field (erg s−1)	LB	1.19 × 1043	2.06 × 1043
	Luminosity in proton (erg s−1)	Lp	7.07 × 1042	2.06 × 1043
wk7.8+	Size of knot (m)	R	2.1 × 1019	4.6 × 1019
wk8.9+	Lorentz factor	Γ	3	3
wk9.7+	Viewing angle	θ	35°	23°
wk10.6	Doppler factor	δD	1.46	2.47
	Magnetic field (mG)	B	9	7
	Minimum proton energy (eV)	Ep,min	1014	1010
	Maximum proton energy (eV)	Ep,max	5.62 × 1019	5.2 × 1019
	Break proton energy (eV)	Ep,br	1.58 × 1016	1012
	Low energy proton spectral index	p1	1.35	1.9
	High energy proton spectral index	p2	2.35	2.4
	Luminosity in magnetic field (erg s−1)	LB	1.3 × 1043	8.4 × 1043
	Luminosity in protons (erg s−1)	Lp	1.3 × 1043	8.4 × 1043

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Table 2.  Model Parameters for 3C 273

Knot	Parameter	Notation	Model 1	Model 2
A	Size of knot (m)	R	1.9 × 1019	3.15 × 1019
	Lorentz factor	Γ	3	3
	Viewing angle	θ	45°	23°
	Doppler factor	δD	1	2.47
	Magnetic field (mG)	B	10	9
	Minimum proton energy (eV)	Ep,min	1014	1010
	Maximum proton energy (eV)	Ep,max	1.9 × 1020	8.9 × 1019
	Break proton energy (eV)	Ep,br	1016	1012
	Low energy proton spectral index	p1	1.62	2.02
	High energy proton spectral index	p2	2.62	2.52
	Luminosity in magnetic field (erg s−1)	LB	1.2 × 1043	4.45 × 1043
	Luminosity in protons (erg s−1)	Lp	7.59 × 1042	4.45 × 1043
A+	Size of knot (m)	R	3.3 × 1019	3.6 × 1019
B1	Lorentz factor	Γ	3	3
	Viewing angle	θ	45°	22°
	Doppler factor	δD	1	2.59
	Magnetic field (mG)	B	10	9
	Minimum proton energy (eV)	Emin	1014	1010
	Maximum proton energy (eV)	Emax	1.25 × 1020	7.24 × 1019
	Break proton energy (eV)	Eb	5.62 × 1015	1012
	Low energy proton spectral index	p1	1.57	2.03
	High energy proton spectral index	p2	2.57	2.53
	Luminosity in magnetic field (erg s−1)	LB	6.3 × 1043	6.65 × 1043
	Luminosity in protons (erg s−1)	Lp	1.38 × 1043	6.65 × 1043

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2.2. Proton Synchrotron Origin of TeV Gamma-rays

In this section, we show that proton synchrotron radiation can, in principle, give rise to TeV gamma-rays from extended quasar jets within a reasonable budget in photon luminosity. TeV blazars can exhibit luminosity beyond 10⁴² erg s⁻¹ (Abramowski et al. 2014). We discuss the implications of our proton synchrotron model in the context of TeV emission, for knot wk8.9 of PKS 0637–752. The expressions for escape and synchrotron timescales used in our models are given in Equations (2) and (3). For the range of parameters considered, the synchrotron loss becomes shorter than escape loss and jet age resulting in a steeper proton spectrum by ${E}_{p}^{-1}$ above the break energy. We propose that proton synchrotron radiation can give rise to TeV emission from knot wk8.9, if proton acceleration to energies near 10²¹ eV is possible. Ebisuzaki & Tajima (2013) have discussed that protons/nuclei in AGN jets can be accelerated to beyond 10²¹ eV by the plasma wakefield field formed by the intense electromagnetic field. Our parameter estimates are listed in Table 3 and the model fits can be found in Figure 5. The models have been constructed under the assumption of equipartition in energy density of the particles and magnetic field. In our calculations, we have shown the intrinsic source spectrum, not the observed spectrum. However, due to the severe absorption of the TeV gamma-rays by the extragalactic background light (EBL), direct observation of the TeV spectra would be difficult. Our photon luminosity budget near 1 TeV, for the four models considered ∼10⁴¹–10⁴³ erg s⁻¹, which is reasonable for TeV blazars, thus implying the validity of our proposition.

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Table 3.  TeV Emission from Knot wk8.9 of PKS 0637–752 at a Distance of 3.8 Gpc

Parameter	Notation	Model 1	Model 2	Model 3	Model 4
Size of knot (m)	R	1.53 × 1019	1.53 × 1019	1.75 × 1019	3.2 × 1019
Lorentz factor	Γ	3	3	3	3
Viewing angle	θ	28°	23°	23°	23°
Doppler factor	δD	1.9	2.47	2.47	2.47
Magnetic field (mG)	B	10	8	7	5
Min proton energy (eV)	Emin	1014	1014	1014	1014
Max proton energy (eV)	Emax	3.16 × 1021	3.16 × 1021	5.6 × 1021	5.6 × 1021
Break proton energy (eV)	Eb	7.08 × 1015	1016	1.99 × 1016	3.98 × 1016
Low energy proton spec. index	p1	1.8	1.9	2	2.25
High energy proton spec. index	p2	2.8	2.9	3	3.25
Luminosity in magnetic field (erg s−1)	LB	6.29 × 1042	4.06 × 1042	4.63 × 1042	1.44 × 1043
Luminosity in protons (erg s−1)	Lp	6.29 × 1042	4.06 × 1042	4.63 × 1042	1.44 × 1043
Photon luminosity in jet (erg s−1)	Lj,ph	1.81 × 1043	6.74 × 1042	2.75 × 1042	2.28 × 1041

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The radio to optical data from the single knot wk8.9 and the knots wk7.8, wk8.9, wk9.7, and wk10.6 of PKS 0637–752, the single knot A, and the combined knots A, B1 of 3C 273 are fitted by the synchrotron emission of shock-accelerated electrons by Meyer et al. (2015). We have fitted the higher energy photon data (X-ray data and Fermi-LAT upper limits) from these knots with a proton synchrotron mechanism. Moreover, in the case of 3C 273, the optical data at 10¹⁵ Hz, which cannot be fitted by electron synchrotron emission (Meyer et al. 2015), has been included within our updated proton synchrotron models. The existence of very high-energy protons (∼10²⁰ eV) in the kiloparsec-scale knots, is the basic assumption of this model.

In the work of Aharonian (2002), it was proposed that proton synchrotron can give rise to radio to X-ray flux from extended quasar jets. In this work, it was assumed that during the jet lifetime, protons with a time independent energy spectrum are injected (quasi) continuously into a spherically symmetric blob. Aharonian considered three models to explain the observed spectral energy distribution, each of which reduces the energy budget compared to the previous one. For Knot A of 3C 273 with jet lifetime 3 × 10⁷ years, the first model uses a broken power-law spectrum of protons with spectral indices 2.4 and 3.4 below and above the break and a magnetic field B = 5 mG. This model fits the radio to X-ray data with luminosity in magnetic field L_B = 1.33 × 10⁴⁴ erg s⁻¹ and that in protons L_p = 1.2 × 10⁴⁷ erg s⁻¹, implying a large deviation from equipartition. To reduce the energy budget Aharonian's second model considers magnetic field B = 10 mG, initial proton spectral index p1 = 2, an energy-dependent escape timescale which becomes dominant over synchrotron losses, thus resulting in spectral index p2 = 2.5 after break. This model also explains the radio to X-ray spectrum of 3C 273, but for reduced energy requirements (L_B = 1.1 × 10⁴⁵ erg s⁻¹; L_p = 1.1 × 10⁴⁴ erg s⁻¹). To further reduce the luminosity, in his third model, Aharonian adopted a power-law spectrum with an exponential cut-off at E = 10¹⁸ eV, which fits only the X-ray data for a magnetic field value of 3 mG and a spectral index of 2. The luminosities in cosmic-ray protons and magnetic field are L_p = 10⁴⁵ erg s⁻¹ and L_B = 3.7 × 10⁴⁴ erg s⁻¹ respectively, which is less compared to the other two models.

For PKS 0637–752, instead of taking the individual knots, Aharonian considered that the overall X-ray emission is coming from a single source. The first model considers a broken power law with exponential cut-off at E = 10²⁰ eV and spectral indices 1.75 and 2.75 below and above the break. It was assumed that particles propagate in the relaxed-Bohm diffusion limit with a magnetic field of 1.5 mG and an emitting region of 5 kpc, where escape losses dominate over synchrotron losses. This model fits the optical to X-ray spectrum of PKS 0637–752 with a large proton acceleration power of L_p = 3 × 10⁴⁶ erg s⁻¹. The second model adopted a higher value of magnetic field (B = 3 mG), the size was reduced to 3 kpc, and it was assumed that particle propagation takes place in the Bohm regime, which results in dominance of the synchrotron loss timescale over escape timescale. In order to reduce the proton acceleration power by another order of magnitude, in his third model, Aharonian uses an early exponential cut-off at E = 2 × 10¹⁸ eV, which requires a proton power of 2.9 × 10⁴⁵ erg s⁻¹.

In our work, we revisit the proton synchrotron models to explain the higher energy observations from knots of PKS 0637–752 and 3C 273, under the assumption that particles diffuse in the Bohm limit (η = 1). We fit the X-ray to gamma-ray observational data from Knot wk8.9 and combined knots wk7.8, wk8.9, wk9.7, and wk10.6 of PKS 0637–752 with parameter estimates according to Table 1. The spectral index of protons has been varied in the range of 1.35–1.9 below the break in models 1 and 2 and luminosities required to explain the observed X-ray to gamma-ray spectral energy distribution from the knots of PKS 0637–752 are ∼6 × 10⁴³ erg s⁻¹, which is about 0.6% of the Eddington luminosity of the source (see Table 1). Our models also explain the optical to gamma-ray energy spectrum from Knots A and A+B1 of 3C 273 with luminosity ∼5 × 10⁴³ erg s⁻¹ in models 1 and 2 (0.5% of the Eddington luminosity; see Table 2). For this source, in order to match the experimental observations, we consider an initial proton spectra in the range p1 = 1.57–2.03 which changes by 1 or 0.5 (according to model 1 or model 2) after break. In all cases, our model 2 fits the observed photon data with equipartition of energy between the magnetic field and the relativistic cosmic-ray protons. Thus our model 2 remains more favorable.

We also discuss the possible proton synchrotron origin of the TeV component from extended quasar jets, in the context of knot wk8.9 of PKS 0637–752 and show that TeV emission is, in principle, possible with a photon luminosity of 10⁴¹–10⁴³ erg s⁻¹ at the peak near 1 TeV in the energy spectrum, if protons in the kiloparsec-scale jets are accelerated up to 5.6 × 10²¹ eV. However, direct observations of such TeV spectrum would be difficult due to severe EBL absorption.