DEGREE-SCALE GeV "JETS" FROM ACTIVE AND DEAD TeV BLAZARS

Significant progress in understanding the activity of blazars, i.e., active galaxies with relativistic jets aligned with the line of sight (LOS), was achieved with the start of operation of the Fermi telescope. The combination of data from Fermi in the 0.1–10 GeV energy band and from ground-based γ-ray telescopes such as HESS, MAGIC, and VERITAS in the 100 GeV–10 TeV band provides detailed simultaneous spectral and timing information for the most extreme representatives of the blazar population (Abdo et al. 2009).

The TeV γ-ray flux from distant blazars is significantly attenuated by pair production on the infrared/optical extragalactic background light (EBL; Kneiske et al. 2004; Stecker et al. 2006; Franceschini et al. 2008; Primack et al. 2008). TeV γ-rays that are absorbed on the way from the primary γ-ray source initiate electromagnetic cascades in the intergalactic space. The charged component of the electromagnetic cascade is deflected by the extragalactic magnetic field (EGMF). Potentially observable effects of such electromagnetic cascades in the EGMF include the "echoes" of multi-TeV γ-ray flares (Plaga 1995; Murase et al. 2008) and the appearance of extended emission around initially point-like γ-ray sources (Aharonian et al. 1994; Neronov & Semikoz 2007; Dolag et al. 2009; Elyiv et al. 2009).

TeV γ-ray emission from blazars is believed to be relativistically beamed into a narrow cone (jet) with an opening angle Θ_jet ∼ Γ⁻¹ ∼ 5°[Γ/10], where Γ is the bulk Lorentz factor of the γ-ray emitting plasma. Blazars are a special type of γ-ray emitting active galactic nuclei (AGNs) for which the angle between the LOS and the jet axis, θ_obs, is θ_obs ≲ Θ_jet; see Figure 1 (Urry et al. 1991).

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In general, the number of blazars with a given jet-LOS misalignment angle is expected to scale as dN/dθ_obs ∼ θ_obs in the range 0 < θ_obs ⩽ Θ_jet. Thus most observed TeV blazars should have θ_obs ∼ Θ_jet, rather than θ_obs ≃ 0. Consequently, the TeV γ-ray emission pattern is not symmetric with respect to the axis source observer. In sources with θ_obs ∼ Θ_jet, most multi-TeV γ-rays are preferentially emitted on one side of the LOS, as is shown in Figure 1. As a result, the extended emission from the cascade initiated by the absorption of TeV γ-rays in interactions with EBL photons should appear as a one- or two-sided jet-like extension next to the primary point source (Aharonian 2004), rather than as a previously discussed extended axially symmetric halo (Aharonian et al. 1994; Neronov & Semikoz 2007, 2009; Dolag et al. 2009; Elyiv et al. 2009).

In what follows, we discuss the spectral and timing properties of such jet-like cascade extensions in the 0.1–1 GeV images of TeV blazars. Our study is based on two independent Monte Carlo codes for γ-ray induced electromagnetic cascades in the intergalactic space, introduced by Dolag et al. (2009) and Elyiv et al. (2009).

Before presenting our numerical results, we discuss the basic physics of the phenomenon in a simplified picture. In particular, we assume that the electromagnetic cascade consists of two steps only and replace probability distributions by their means. Then the mean free path of very high energy γ-rays through the EBL can be approximated by $D_\gamma (E_{\gamma _0}) = \kappa [E_{\gamma _0}/1\mbox{ TeV}]^{-1}\mbox{ Gpc}$, where the numerical factor $\kappa =\kappa (E_{\gamma _0},z)\sim {\cal O}(1)$ includes the uncertainties of the EBL modeling. Pair production on EBL reduces the flux of γ-rays from the source by a factor $\exp [-\tau (E_{\gamma _0})]$, where τ ≃ D/D_γ is the optical depth with respect to pair production and D is the distance to the source.

Electron–positron pairs created in interactions of multi-TeV γ-rays with EBL photons produce secondary γ-rays via inverse Compton (IC) scattering on cosmic microwave background (CMB) photons. Typical energies of the IC photons reaching the Earth are $E_{\gamma } = (4/3)\epsilon _{\rm CMB}E_e^2/m_e^2\simeq 0.8 [E_{\gamma _0}/1 \mbox{ TeV}]^2\mbox{ GeV}$, where _CMB = 6 ×  10⁻⁴ eV is the typical energy of CMB photons.

Deflections of e⁺e⁻ pairs produced by the γ-rays, which were initially emitted away from the observer, can redirect secondary photons toward the observer. This effect leads to the appearance of extended emission around an initially point source of γ-rays (Neronov & Semikoz 2007; Dolag et al. 2009; Elyiv et al. 2009).

In the absence of perfect alignment of the jet axis with the LOS, the extended cascade emission might be strongly asymmetric. It might appear as a jet-like feature next to the primary γ-ray source. The maximal angular size of this jet-like feature can be estimated as the size of the projected γ-ray mean free path as Θ_ext,max ≃ D_γθ_obs/(D − D_γ), if D_γ < D (i.e., τ>1). If $\tau (E_{\gamma _0})<1$, the cascade emission from the TeV γ-ray beam can extend to very large angles Θ_ext,max ∼ π/2.

The jet-like extended emission can be observed only if deflections of the cascade e⁺e⁻ pairs are sufficiently large to redirect the cascade emission toward the observer. If the correlation length of the EGMF is larger than the electron cooling distance D_e = 3m²_ec³/(4σ_TU_CMBE_e) ≃ 0.7[E_e/0.5TeV]⁻¹Mpc, where σ_T denotes the Thomson cross section and U_CMB the energy density of the CMB photons, then the deflection angle can be estimated as (Neronov & Semikoz 2009) δ = D_e/R_L ≃ 3°[B/10⁻¹⁷G][E_e/0.5TeV]⁻² with R_L being the Larmor radius of electrons and positrons.

If the correlation length λ_B of the EGMF is much smaller than the electron cooling distance D_e, the deflection angle can be estimated using the diffusion approximation as $\delta =\sqrt{D_e\lambda _B}/R_L\simeq 3^\circ [E_e/0.5\mbox{ TeV}]^{-3/2}[B/10^{-17}\mbox{ G}][\lambda _B/0.7\mbox{ Mpc}]^{1/2}$. If the EGMF is weak, electron/positron trajectories are not strongly deflected during one cooling time, and thus secondary cascade γ-rays are emitted within a cone with an opening angle of order ${\cal O}(\delta)$. In this case, only a part of the cascade emission could be observed. If the mean free path of the primary γ-rays is much shorter than the distance to the source, the angular extension could be estimated from the simple geometrical consideration of Figure 1 as sin(Θ_ext(B)) = (D_γ/D)sin δ. Otherwise, the angular size of the source is found from the sum of the angles of triangle with vertices at the source, at the pair production point and at the position of the observer (see Figure 1) as Θ_ext(B) = δ − θ_obs.

Most of the known TeV blazars have moderate distances so that $\tau (E_{\gamma _0}=1\mbox{ TeV})\le 1$. In this case, Θ_ext,max ∼ π/2 and Θ_ext(B) = δ − θ_obs. A measurement of Θ_ext ≪ Θ_ext,max thus provides a measurement of δ and, in this way, gives a constraint on the parameters of the EGMF, i.e., B and λ_B.

The difference in the path length between the direct and cascade γ-rays leads to a significant time delay of the cascade emission signal. For a given jet misalignment angle θ_obs, the time delay of emission coming from the direction θ away from the source is $T_{\rm delay}\sim \frac{D}{c}\big(\frac{\sin \theta +\sin (\theta _{\rm obs}+\Theta _{\rm jet})}{\sin (\theta +\theta _{\rm obs}+\Theta _{\rm jet})}-1\big)\simeq \frac{D\theta (\theta _{\rm obs}+\Theta _{\rm jet})}{2c}\simeq 3\;\times \; 10^6\big[\frac{(\theta _{\rm obs}+\Theta _{\rm jet})}{5^\circ }\big]\big[\frac{\theta }{5^\circ }\big] \mbox{ yr }$. Comparing this time scale with the typical time scale of AGN activity, T_AGN ∼ 10⁷ yr, one sees that degree-scale extended emission in the GeV energy range depends on the TeV γ-ray luminosity of the blazar integrated over its lifetime.

To model the asymmetric extended emission from the γ-ray-initiated electromagnetic cascade in intergalactic space, we have extended our two Monte Carlo codes such that they now follow the three-dimensional trajectories of individual cascade particles moving through the EGMF. The turbulent component of the EGMF has been calculated following the algorithm of Giacalone & Jokipii (1994).

To produce an image of the γ-ray-induced electromagnetic cascade, as it would be detected by a γ-ray telescope, we use the algorithm described by Elyiv et al. (2009). We have verified that the results obtained using the two different codes are compatible with each other.

We record positions and directions of all secondary γ-rays that cross a sphere of the radius R = D around the source. We choose the directions of primary γ-rays to be distributed within a cone with an opening angle Θ_jet. We consider a primary γ-ray beam with a Gaussian profile, so that the probability for a primary γ-ray to have a direction misaligned by an angle Θ with respect to the jet axis is p(Θ) ∼ exp(−Θ²/Θ²_jet).

For simplicity, we consider a monochromatic primary γ-ray beam with all the primary γ-rays having the same energy $E_{\gamma _0}=1$ TeV. This is sufficient to demonstrate the existence of the effect discussed here for the first time, namely, degree-scale jet-like extensions in Fermi images of TeV blazars. The EBL background is taken from the calculations of Kneiske et al. (2004). We fix the distance to the source as D = 400 Mpc, so that $\tau (E_{\gamma _0})\sim 1$. The EGMF is chosen to have a correlation length of the order of several Mpc, with its power spectrum sharply peaked at the wavenumber k ≃ 1 Mpc⁻¹. Our results could be generalized in a straightforward way to the case of an arbitrary primary γ-ray spectrum, arbitrary distance to the source and different EBL models, when considering extended emission from particular TeV blazars with known TeV band spectra and known redshift.

Figure 2 shows the effect of the misalignment of the primary γ-ray beam with the LOS on the morphology of the extended emission. The left panel of the figure corresponds to the situation θ_obs = 0, which is equivalent to the axially symmetric case considered by Dolag et al. (2009) and Elyiv et al. (2009). An axially symmetric extended "halo" around the primary point source is clearly visible. The other panels of the figure show the cases of a jet with an opening angle Θ_jet = 3° misaligned by angles θ_obs = 3°, 6°, and 9°, respectively. It is clear that the misalignment of the jet axis with the LOS leads to the appearance of an extended jet-like feature on one side of the source. The ratio of the point source flux to the flux of the extension grows with the increase of the misalignment angle θ_obs.

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The angular extension of the cascade emission depends on the strength of the EGMF as long as the trajectories of e⁺e⁻ pairs are not completely randomized. The morphological properties of the jet-like emission are practically independent from the properties of the EGMF, when the EGMF strength is such that the deflection angle δ ⩾ 2π. Figure 3 shows the growth of the source extension with the increase of the EGMF strength. For magnetic fields stronger than B ∼ 10⁻¹⁵ G, the size of the extended source reaches ten(s) of degrees. In this case, the extended source could significantly contribute to the diffuse γ-ray background.

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Cascade emission coming from regions with angular distance θ ⩾ 1° to the primary source is delayed by T_delay ∼ 10⁵–10⁷ yr compared to the direct emission from the source. This means that "echoes" from periods of enhanced activity of the source (e.g., an enhanced accretion rate following major merger episodes), which happened all along the lifetime of an AGN some time T ago, could enhance the flux at the distance θ ≃ 17[T/10⁶yr][(θ_obs + Θ_jet)/5°] from the source.

Figure 4 shows a time sequence of E > 1 GeV band images of the sky region around a TeV source at different times after a short episode of TeV γ-ray emission. One can clearly see that the emission at large angular distances is delayed by up to 10⁷ yr.

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The flux coming from the region at an angular distance θ from the point source is proportional to the source flux averaged over the period T_delay. Therefore, it is possible that GeV γ-rays are detectable today from an AGN which was active some 10⁷ yr ago, but at present it is no longer active. In this case, a GeV source would be classified as "unidentified": the parent AGN (1) could not be identified as an AGN in the optical, X-ray, and TeV γ-ray bands or (2) the GeV source is displaced from the position of the parent AGN. The characteristic feature of such an unidentified "AGN remnant" is the absence of counterparts at lower energies: If the GeV γ-rays are produced by e⁺e⁻ pairs deposited in the intergalactic medium by primary TeV γ-rays, the only energy loss mechanism for the pairs is IC scattering on CMB photons.

The presence of extended jet-like emission at degree scales should be a generic feature of GeV band images of TeV blazars. The total flux of the jet-like extended source is proportional to the source luminosity in the TeV energy band. Taking into account the fact that TeV blazars have hard γ-ray spectra, the primary source luminosity in the TeV band could be much larger than its GeV luminosity, so that the overall extended source luminosity could be higher than the primary source luminosity in the GeV band. This means that the best candidates for the search of extended emission are TeV blazars with hard intrinsic spectra.

This does not automatically mean that the extended emission should be readily detectable in Fermi images of TeV blazars. In spite of the larger luminosity, the extended source flux might be suppressed if the EGMF is strong enough to randomize the trajectories of e⁺e⁻ pairs before they lose their energy to the GeV band via IC emission. The maximal possible suppression of the extended source flux is by a factor of Θ⁻²_jet ∼ 100.

Another potential problem for the detection of jet-like extended emission next to TeV blazars is that the extended source has to be identified on top of the diffuse γ-ray background. The minimal detectable flux for extended sources increases roughly as θ^1/2, where θ is the angular length of the jet-like extended source. Thus, sources at larger distances, for which the jet-like extensions appear more compact, are better candidates for the search of extended emission in the Fermi energy band.

Finally, the detectability of extended emission close to TeV blazars strongly depends on the angular resolution of the Large Area Telescope (LAT). At low energies, E_γ ∼ 0.1 GeV, the LAT angular resolution is relatively poor, θ_PSF ≃ 10°. It is clear that only very large angular size jet-like extensions with an angular diameter θ ∼ θ_PSF could be detected. However, the detectability of such large extended sources would be complicated by the high level of diffuse sky background within the ∼10° region around the source. At the same time, the size of the point-spread function (PSF) decreases to θ_PSF ⩽ 1° above GeV energies. This dramatically improves the sensitivity of the telescope for the search of extended emission: extensions of much smaller angular size could be detected on top of a strongly reduced background. This favors the search of extended emission at energies above ∼1 GeV.

As an example, we consider a blazar with the TeV band luminosity $L_0 (E_{\gamma _0})\sim 10^{43}$ erg s⁻¹ beamed in a cone with an opening angle Θ_jet = 3°, so that the equivalent isotropic luminosity of the source is L_iso ≃ 10⁴⁵ erg s⁻¹. In the absence of absorption, the source would give a flux F_iso,0 ≃ 10⁻¹⁰[D/300Mpc]⁻² erg (cm² s)⁻¹. At energies E_γ such that $\tau (E_{\gamma _0})\ge 1$ the overall luminosity of the cascade emission is comparable to the primary source luminosity at energy $E_{\gamma _0}$, so that in the case of small EGMFs (δ ⩽ Θ_jet), i.e., at the level of the lower bounds B ∼ 10⁻¹⁷–10⁻¹⁶ G derived from Fermi observations (Neronov & Vovk 2010; Tavecchio et al. 2010), the flux in the cascade is F_cascade ∼ F_iso,0. In this case, the cascade emission is readily detectable in the GeV band by Fermi. In the opposite case, the cascade emission is completely isotropized and the cascade flux is suppressed by a factor of 1/Θ²_jet ∼ 4 ×  10², so that it is marginally below the minimal detectable flux for extragalactic Fermi point sources in the GeV band, F_min ∼ 10⁻¹² erg (cm²s)⁻¹.

Thus, in the most pessimistic case jet-like extensions are detectable only for the brightest blazars with the observed steady-state flux at the level of F_iso ≃ exp(−τ)F_iso,0 ∼ 3 ×  10⁻¹¹ erg (cm² s)⁻¹ (assuming τ ≃ 1). Only several extragalactic sources with sufficient steady-state flux are detected by Fermi above 100 GeV (Neronov et al. 2010a). Among these sources, 3C 66A, 1ES 0502+675, PG 1553+113, and, possibly, PKS 2155–304 are at sufficiently large redshifts for strong cascade emission in the GeV energy range. These sources should be considered as primary candidates for the search of the jet-like extended emission. By contrast, all sources with sufficiently high flux at few  ×  100 GeV (Neronov et al. 2010b) are viable candidates for the detection of the extended jet-like emission, if the EGMF is weak.

The number of detectable "blazar remnants" also strongly depends on the EGMF. If the EGMF is so weak that T_delay ≪ T_AGN, blazar remnants would not exist, since cascade and direct emission would be observed together. If typical deflection angles of electrons emitting in the GeV band are several degrees (B ∼ 10⁻¹⁷ G for large λ_B), the number of blazar remnants observable in the GeV band should be comparable to the number of active TeV blazars, since T_delay ∼ T_AGN. If the EGMF is much stronger, the number of potentially observable blazar remnants grows because the cascade emission is emitted in a wider cone than emission from the parent blazar. However, the typical flux of the blazar remnants decreases because of the same effect. Thus, for strong EGMFs, the number of blazar remnants above the Fermi sensitivity limit might be very small. The strong dependence of the observability of blazar remnants on the EGMF strength implies that constraints on the EGMF could be deduced from their source statistics.

To summarize, we have shown that GeV band images of TeV blazars should possess degree-scale jet-like extended features. These features trace the direction of the TeV γ-ray beam emitted by the blazar. They are produced as results of electromagnetic cascades initiated by TeV γ-rays interacting with EBL photons. We have performed Monte Carlo simulations of three-dimensional electromagnetic cascades developing in the EGMF. Using these Monte Carlo simulations, we have derived the properties of the GeV jet-like extended emission near TeV blazars. We have investigated the dependence of the characteristics of the jet-like extended sources (the angular size, the brightness profile) on the strength of the EGMFs and on the opening angle and orientation of the primary TeV γ-ray beam from the blazar. We have also demonstrated that the γ-ray signal in the jet-like extended emission is delayed up to 10⁷ yr compared to the direct γ-ray signal from the primary point source. The very long time delay of the cascade emission means that the extended GeV source could be detected next to a blazar that is no longer active as a blazar.

A.E. is supported by a fellowship from the Belgium Federal Science Policy Office, A.N. by the Swiss National Science Foundation project PP00P2_123426/1, and S.O. by a Marie Curie IEF fellowship from the European Community and by the Romforskning program of Nork Forskningsradet.