VERY HIGH ENERGY GAMMA-RAY-INDUCED PAIR CASCADES IN THE RADIATION FIELDS OF DUST TORI OF ACTIVE GALACTIC NUCLEI: APPLICATION TO Cen A

Blazars are a class of radio-loud active galactic nuclei (AGNs) comprised of flat-spectrum radio quasars (FSRQs) and BL Lac objects. Their spectral energy distributions (SEDs) are characterized by non-thermal continuum spectra with a broad low-frequency component in the radio–UV or X-ray frequency range and a high-frequency component from X-rays to γ-rays, and they often exhibit substantial variability across the electromagnetic spectrum. In the very high energy (VHE) γ-ray regime, the timescale of this variability has been observed to be as short as just a few minutes (Albert et al. 2007; Aharonian et al. 2007). While previous generations of ground-based Atmospheric Cerenkov Telescope (ACT) facilities detected almost exclusively high-frequency-peaked BL Lac objects (HBLs) as extragalactic sources of VHE γ-rays (with the notable exception of the radio galaxy M87), in recent years, a number of non-HBL blazars and even non-blazar radio-loud AGNs have been detected by the current generation of ACTs. This suggests that most blazars might be intrinsically emitters of VHE γ-rays. According to AGN unification schemes (Urry & Padovani 1995), radio galaxies are the misaligned parent population of blazars with the less powerful FR I radio galaxies corresponding to BL Lac objects and FR II radio galaxies being the parent population of radio-loud quasars. Blazars are those objects which are viewed at a small angle with respect to the jet axis. If this unification scheme holds, then, by inference, radio galaxies may also be expected to be intrinsically emitters of VHE γ-rays within a narrow cone around the jet axis.

While there is little evidence for dense radiation environments in the nuclear regions of BL Lac objects—in particular, HBLs—strong line emission in FSRQs as well as the occasional detection of emission lines in the spectra of some BL Lac objects (e.g., Vermeulen et al. 1995) indicates dense nuclear radiation fields in those objects. This is supported by spectral modeling of the SEDs of blazars using leptonic models which prefer scenarios based on external radiation fields as sources for Compton scattering to produce the high-energy (HE) radiation in FSRQs, low-frequency peaked BL Lac objects (LBLs), and also in some intermediate BL Lac objects (IBLs) (e.g., Ghisellini et al. 1998; Madejski et al. 1999; Böttcher & Bloom 2000; Acciari et al. 2008). If the VHE γ-ray emission is indeed produced in the high-radiation-density environment of the broad-line region (BLR) and/or the dust torus of an AGN, it is expected to be strongly attenuated by γγ pair production (e.g., Protheroe & Biermann 1997; Donea & Protheroe 2003; Reimer 2007; Liu et al. 2008; Sitarek & Bednarek 2008). Aharonian et al. (2008) have suggested that such intrinsic γγ absorption may be responsible for producing the unexpectedly hard intrinsic (i.e., after correction for γγ absorption by the extragalactic background light) VHE γ-ray spectra of some blazars at relatively high redshift. A similar effect has been invoked by Poutanen & Stern (2010) to explain the spectral breaks in the Fermi spectra of γ-ray blazars. This absorption process will lead to the development of Compton-supported pair cascades in the circumnuclear environment (e.g., Bednarek & Kirk 1995; Sitarek & Bednarek 2010; Roustazadeh & Böttcher 2010).

In Roustazadeh & Böttcher (2010), we considered the full three-dimensional development of a Compton-supported VHE γ-ray-induced cascade in a monochromatic radiation field. This was considered as an approximation to BLR emission dominated by a single (e.g., Lyα) emission line. In that work, we showed that for typical radio-loud AGN parameters rather small (∼μG) magnetic fields in the central ∼1 pc of the AGN may lead to efficient isotropization of the cascade emission in the Fermi energy range. We applied this idea to fit the Fermi γ-ray emission of the radio galaxy NGC 1275 (Abdo et al. 2009a) under the plausible assumption that this radio galaxy would appear as a γ-ray bright blazar when viewed along the jet axis.

In this paper, we present a generalization of the Monte Carlo cascade code developed in Roustazadeh & Böttcher (2010) to arbitrary radiation fields. In particular, we will focus on thermal blackbody radiation fields, representative of the emission from a circumnuclear dust torus. In Section 2, we will outline the general model setup and assumptions and describe the modified Monte Carlo code that treats the full three-dimensional cascade development. Numerical results for generic parameters will be presented in Section 3. In Section 4, we will demonstrate that the broadband SED of the radio galaxy Cen A, including the recent Fermi γ-ray data (Abdo et al. 2009c), can be modeled with plausible parameters expected for a misaligned blazar, allowing for a contribution from VHE γ-ray-induced cascades in the Fermi energy range. We summarize in Section 5.

Figure 1 illustrates the geometrical setup of our model system. We represent the primary VHE γ-ray emission as a mono-directional beam of γ-rays propagating along the X-axis, described by a power law with photon spectrum index α and an HE cutoff at E_γ,max. For the following study, we assume that the primary γ-rays interact via γγ absorption and pair production with an isotropic thermal blackbody radiation field within a fixed boundary, given by a radius R_ext, i.e.,

$$\begin{equation} u_{\rm ext} (\nu, r, \Omega) = 2 h \nu ^3 / c^3 \frac{A}{\exp (\frac{h\nu }{k T})-1} \, H(R_{\rm ext} - r), \end{equation} \tag{ 1 }$$

where A is a normalization factor chosen to obtain a total radiation energy density u_ext (see Equation (2) below) and H is the Heaviside function, H(x) = 1 if x > 0 and H(x) = 0 otherwise. A magnetic field of order ∼mG is present. Without loss of generality, we choose the y and z axes of our coordinate system such that the magnetic field lies in the (x,  y) plane.

Zoom In Zoom Out Reset image size

The input parameters to our model simulation describing the external radiation field are the integral of u_ext(ν, r, Ω) over all frequencies:

$$\begin{equation} u_{\rm ext}=4\pi \int _0 ^\infty u_{\rm ext} (\nu, r, \Omega) d\nu, \end{equation} \tag{ 2 }$$

the blackbody temperature T, and the radial extent R_ext.

We have used the Monte Carlo code developed by Roustazadeh & Böttcher (2010). This code evaluates γγ absorption and pair production using the full analytical solution to the pair production spectrum of Böttcher & Schlickeiser (1997) under the assumption that the produced electron and positron travel along the direction of propagation of the incoming γ-ray. The trajectories of the particles are followed in full three-dimensional geometry. Compton scattering is evaluated using the head-on approximation, assuming that the scattered photon travels along the direction of motion of the electron/positron at the time of scattering. While the Compton energy loss to the electron is properly accounted for, we neglect the recoil effect on the travel direction of the electron. In order to improve the statistics of the otherwise very few highest-energy photons, we introduce a statistical weight, w, inversely proportional to the square of the photon energy, w = 1/², where $\epsilon = \frac{E_{\gamma }}{m_e c^2}$.

To save CPU time, we precalculate tables for the absorption opacity κ_γγ, Compton scattering length λ_IC, and Compton cross section for each photon energy, electron energy, and interaction angle before the start of the actual simulation.

The simulation produces a photon event file, logging the energy, statistical weight, and travel direction of every photon that escapes the region bounded by R_ext. A separate post-processing routine is then used to extract angle-dependent photon spectra with arbitrary angular and energy binning from the log files.

For comparison with our previous study on mono-energetic radiation fields, we conduct a similar parameter study as presented in Roustazadeh & Böttcher (2010), investigating the effects of parameter variations on the resulting angle-dependent photon spectra. Standard parameters for most simulations in our parameter study are a magnetic field of B = 1 mG, oriented at an angle of θ_B = 5° with respect to the X-axis (B_x = 1 mG, B_y = 0.1 mG); an external radiation energy density of u_ext = 10⁻⁵ erg cm⁻³, extended over a region of radius R_ext = 10¹⁸ cm; a blackbody temperature of T = 10³ K (corresponding to a peak of the blackbody spectrum at a photon energy of E^pk_s = 0.25 eV). The incident γ-ray spectrum has a photon index of α = 2.5 and extends out to E_γ,max = 5 TeV. The emanating photon spectra for all directions have been normalized with the same normalization factor, corresponding to a characteristic flux level of a γ-ray bright (Fermi) blazar in the forward direction.

Figure 2 illustrates the viewing angle dependence of the cascade emission. The γγ absorption cutoff at an energy E_c = (m_ec²)²/E_s ∼ 1 TeV is very smooth in this simulation because of the broad thermal blackbody spectrum of the external radiation filed. In contrast, the δ-function approximation for the external radiation field adopted in Roustazadeh & Böttcher (2010) resulted in an artificially sharp cutoff in that work.

Zoom In Zoom Out Reset image size

At off-axis viewing angles, the observed spectrum is exclusively the result of the cascade. In the limit of low photon energies (far below the γγ absorption threshold) and neglecting particle escape from the cascade zone, one expects a low-frequency shape close to νF_ν ∝ ν^1/2 due to efficient radiative cooling of secondary particles injected at high energies (Roustazadeh & Böttcher 2010). However, with the typical parameters used for this parameter study, the assumption of negligible particle escape is not always justified. In order to estimate the possible suppression of the low-frequency cascade emission due to particle escape, we calculate the critical electron energy for which the Compton cooling timescale τ_IC(γ) equals the escape timescale, τ_esc = R_ext/(c cos θ_B). Using a characteristic thermal photon energy of _Th = 2.8 kT/(m_ec²), the resulting Compton-scattered photon energy, _esc, below which we expect to see the effects of particle escape and, hence, inefficient radiative cooling is

$$\begin{equation} \epsilon _{\rm esc} = {9 \times 2.8 \, k T \, m_e c^2 \, \cos ^2\theta _B \over 16 \, \sigma _T^2 \, u_{\rm ext}^2 \, R_{\rm ext}^2} \end{equation} \tag{ 3 }$$

corresponding to an actual energy (in GeV) of

$$\begin{equation} E_{\rm esc} \approx 2 \; T_3 \, u_{-5}^{-2} \, R_{18}^{-2} \, \cos ^2\theta _B \; {\rm GeV}, \end{equation} \tag{ 4 }$$

where T = 10³ T₃ K, u_ext = 10⁻⁵ u₋₅ erg cm⁻³, and R = 10¹⁸ R₁₈ cm. Therefore, for our standard parameters, we expect the low frequency (E≲ a few GeV) to be significantly affected by particle escape. This explains why the low-energy photon spectra shown in Figure 2 are harder than ν^1/2. The cascade emission is progressively suppressed at high energies with increasing viewing angle due to incomplete isotropization of the highest-energy secondary particles. This effect becomes important beyond the energy E_IC,br of Compton-scattered photons by secondary electrons/positrons for which the Compton scattering length λ_IC equals the distance traveled along the gyrational motion over an angle θ, λ_IC(γ) = θr_gyr(γ), which is given by

$$\begin{equation} E_{\rm IC, br} = {3 \, e \, B \over 4 \, \sigma _T \, u_{\rm ext} \, \theta } \, E_s \; \sim \; 1.3 \; B_{-3} \, u_{-5}^{-1} \, T_3 \, \theta ^{-1} \; {\rm GeV}, \end{equation} \tag{ 5 }$$

where B = 10⁻³ mG (Roustazadeh & Böttcher 2010).

Figure 3 shows the cascade spectra for different values of the external radiation field energy density u_ext. For large energy densities u_ext ≳ 10⁻⁴ erg cm⁻³, τ_γγ ≫ 1 for photons above the pair production threshold γγ so that essentially all VHE photons will be absorbed and the photon flux from the cascade becomes independent of u_ext.

Zoom In Zoom Out Reset image size

The figure confirms our discussion concerning escape and hence inefficient radiative cooling of low-energy particles above (see Equation (4)). For large values of u_ext, the Compton loss timescale for all relativistic electrons producing γ-rays in the considered range is much shorter than the escape timescale. Hence, the expected νF_ν ∝ ν^1/2 shape results. In the low-u_ext case, escape affects even ultrarelativistic electrons, resulting in a substantial hardening of the low-energy photon spectrum.

Figure 4 illustrates the effect of a varying temperature of the external blackbody radiation field. As the temperature increases up to 1000 K, the cascade flux increases because the γγ absorption threshold energy decreases so that an increasing fraction of γ-rays can be absorbed. The isotropization turnover is almost independent of T. For temperatures T > 1000 K, the cascade flux decreases with increasing T because u_ext remains fixed, leading to a decreasing photon number density and absorption opacity κ_γγ with increasing T (and, hence, increasing E_s). The figure also confirms our expectation (Equation (4)) that an increasing blackbody temperature leads to an increasing suppression of the low-frequency portion of the cascade emission due to particle escape.

Zoom In Zoom Out Reset image size

Figures 5 and 6 illustrate the effects of varying magnetic-field parameters (strength and orientation). As expected, the results are essentially the same as for cascades in monoenergetic radiation fields investigated in Roustazadeh & Böttcher (2010). The cascade development is extremely sensitive to the transverse magnetic field B_y. The limit in which even the highest-energy secondary particles are effectively isotropized before undergoing the first Compton scattering interaction is easily reached for typical magnetic fields expected in the circumnuclear environment of AGNs.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The standard AGN unification scheme (Urry & Padovani 1995) proposes that blazars and radio galaxies are intrinsically identical objects viewed at different angles with respect to the jet axis. According to this scheme, FR I and FR II radio galaxies are believed to be the parent population of BL Lac objects and FSRQs, respectively. Hence, if most blazars, including LBLs and FSRQs, are intrinsically VHE γ-ray emitters potentially producing pair cascades in their immediate environments, the radiative signatures of these cascades might be observable in many radio galaxies. In fact, EGRET provided evidence for >100 MeV γ-ray emission from three radio galaxies (Cen A: Sreekumar et al. 1999, 3C 111: Hartman et al. 2008, and NGC 6251: Mukherjee et al. 2002). These sources have been confirmed as HE γ-ray sources by Fermi (Abdo et al. 2009c, 2010b), along with the detection of five more radio galaxies (NGC 1275: Abdo et al. 2009a, M 87: Abdo et al. 2009b, 3C 120, 3C 207, and 3C 380: Abdo et al. 2010b). In this paper, we focus on the radio galaxy Cen A (Abdo et al. 2009c).

The FR I Cen A is the nearest radio-loud active galaxy to Earth. It has a redshift of z = 0.00183 at the distance of D = 3.7 Mpc. Recently, the Auger collaboration reported that the arrival directions of the highest-energy cosmic rays (E ≳ 6 × 10¹⁹ eV) observed by the Auger observatory are correlated with nearby AGN, including Cen A (Abraham et al. 2007, 2008). This suggests that Cen A may be the dominant source of observed UHECR nuclei above the Greizen-Zatsepin-Kuzmin cutoff.

Cen A has an interesting radio structure on several size scales. The most prominent features are its giant radio lobes, which subtend ∼10° on the sky, oriented primarily in the north–south direction. They have been imaged at 4.8 GHz by the Parkes telescope (Junkes et al. 1993) and studied at up to ∼60 GHz by Hardcastle et al. (2009). The radio lobes are the only extragalactic source structure that has so far been spatially resolved in GeV γ-rays by Fermi (Abdo et al. 2010c). The innermost region of Cen A has been resolved with very long baseline interferometry (VLBI) and shown to have a size of ∼3 × 10¹⁶ cm (Kellerman et al. 1997; Horiuchi et al. 2006). Observations at shorter wavelengths also reveal a small core. Very Large Telescope (VLT) infrared interferometry resolves the core size to ∼6 × 10¹⁷ cm (Meisenheimer et al. 2007). The angle of the sub-parsec jet of Cen A to our line of sight is ∼50°–80° (Tingay et al. 1998) with a preferred value of ∼70° (Steinle 2010).

The K-band nuclear flux with starlight subtracted is F(K) ∼ 38 mJy, corresponding to νL_ν ∼ 7 × 10⁴⁰ erg s⁻¹ for a distance of 3.5 Mpc (Marconi et al. 2000). The mid-IR flux of ∼1.6 Jy at 11.7 μm corresponds to νL_ν ∼ 6 × 10⁴¹ erg s⁻¹. The broadband SED from radio to γ-rays has been fitted with a synchrotron self-Compton model by Abdo et al. (2010a). In their model (see Table 2 of Abdo et al. 2010a), a maximum electron Lorentz factor of γ_max = 1 × 10⁸ was required in order to produce the observed γ-ray emission. However, given the assumed magnetic field of B = 6.2 G, this does not seem possible since for γ = 10⁸ electrons, the synchrotron loss timescale is shorter than their gyro-timescale, which sets the shortest plausible acceleration timescale. Here, we therefore present an alternative interpretation of the SED, based on the plausible assumption that Cen A would appear as a VHE γ-ray emitting blazar in the jet direction, and cascading of VHE γ-rays on the nuclear infrared radiation field produces an observable off-axis γ-ray signature in the Fermi energy range.

Figure 7 illustrates a broadband fit to the SED of Cen A (data from Abdo et al. 2010a), using the equilibrium version of the blazar radiation transfer code of Böttcher & Chiang (2002), as described in more detail in Acciari et al. (2009). For this fit, standard blazar jet parameters were adopted, but the viewing angle was chosen in accord with the observationally inferred range. Specifically, we chose θ_obs = 70°. Other model parameters include a bulk Lorentz factor of Γ = 5, a radius of the emission region of R = 1 × 10¹⁶ cm, a kinetic luminosity in relativistic electrons, L_e = 9.4 × 10⁴³ erg s⁻¹, a comoving magnetic field of B = 11 G, corresponding to a luminosity in the magnetic field (Poynting flux) of L_B = 1.1 × 10⁴⁵ erg s⁻¹, and a magnetic-field equipartition fraction _B ≡ L_B/L_e = 12, corresponding to a Poynting-flux-dominated jet. Electrons are injected into the emission region at a steady rate, with a distribution characterized by low- and high-energy cutoffs at γ₁ = 1.2 × 10³ and γ₂ = 1.0 × 10⁶, respectively, and a spectral index of q = 3.5. The code finds a self-consistent equilibrium between particle injection, radiative cooling, and escape, from which the final photon spectrum is calculated. The resulting broadband SED fit is illustrated by the solid green curve in Figure 7. The flux emanating in the forward direction (θ_obs = 0°, i.e., the blazar direction) has been chosen as an input to our cascade simulation to evaluate the cascade emission in the nuclear infrared radiation field of Cen A observed at the given angle of θ_obs = 70°.

Zoom In Zoom Out Reset image size

For the cascade simulation, we assumed a blackbody temperature of 2300 K resulting in a peak frequency in the K band. The external radiation field is parameterized through u_ext = 1.5 × 10⁻³ erg cm⁻³ and R_ext = 3 × 10¹⁶ cm. These parameters combine to an IR luminosity of L_BLR = 4πR²_ext c u_ext = 5 × 10⁴¹ erg s⁻¹, in agreement with mid-IR flux observed for Cen A (Marconi et al. 2000). The magnetic field is B = 1 mG, oriented at an angle of θ_B = 4°. The cascade spectrum shown in Figure 7 pertains to the angular bin 0.28 < μ < 0.38 (corresponding to 67° ≲ θ ≲ 73°), appropriate for the known orientation of Cen A and consistent with our broadband SED fit parameters. The cascade spectrum is shown by the maroon curve in Figure 7, while the total observed spectrum is the solid red curve. The figure illustrates that the cascade contribution in the Fermi range substantially improves the fit, while still allowing physically reasonable parameters for the broadband SED fit.

We investigated the signatures of Compton-supported pair cascades initiated by the interaction of nuclear VHE γ-rays with the thermal infrared radiation field of a circumnuclear dust torus in AGNs. We follow the spatial development of the cascade in full three-dimensional geometry and study the dependence of the radiative output on various parameters pertaining to the infrared radiation field and the magnetic field in the cascade region.

We confirm the results of our previous study of cascades in monoenergetic radiation fields that small (≳μG) perpendicular (to the primary VHE γ-ray beam) magnetic field components lead to efficient isotropization of the cascade emission out to HE γ-ray energies. The cascade intensity as well as the location of an HE turnover due to inefficient isotropization also depend sensitively on the energy density and temperature of the soft blackbody radiation field, as long as the cascade is not saturated in the sense that not all VHE γ-rays are absorbed.

The shape of the low-frequency tail of the cascade emission is a result of the interplay between radiative cooling and escape. For environments characterized by efficient radiative cooling, the canonical νF_ν ∝ ν^1/2 spectrum results. If radiative cooling is inefficient compared to escape, the low-frequency cascade spectra are harder than ν^1/2.

We provide a model fit to the broadband SED of the dust-rich, γ-ray-loud radio galaxy Cen A. We show that typical blazar-like jet parameters may be used to model the broadband SED, if one allows for an additional cascade contribution to the Fermi γ-ray emission due to γγ absorption and cascading in the thermal infrared radiation field of the prominent dust emission known to be present in Cen A.

We thank J. Finke for providing the SED data points of Cen A. This work was supported by NASA through Fermi Guest Investigator Grants NNX09AT81G and NNX10AO49G.