POWERFUL HIGH-ENERGY EMISSION OF THE REMARKABLE BL Lac OBJECT S5 0716+714

Blazars constitute a class of active galactic nuclei (AGNs) that often show very strong and rapid flux variability over the electromagnetic spectrum. They are widely held to contain a black hole (BH) with mass in the range 10⁷–10⁹ M_☉, that launches relativistic jets emitting highly non-thermal radiation.

The jet transports energy in electromagnetic form and bulk plus random kinetic energy of charged particles. The source radiation may also show a contribution by the accretion disk (including the big blue bump (BBB)), the broad-line region (BLR), and a dusty torus (see Urry & Padovani 1995); lack or weakness of such contributions mark out the class of BL Lac objects. The primary energy of the jet may be supplied by power extracted from the central rotating BH via interaction with its accretion disk (Blandford & Znajek 1977; Blandford & Payne 1982; see also discussions in Cavaliere & D'Elia 2002 and McKinney 2005).

The blazar 0716+714 is a distant BL Lac at z = 0.31 ± 0.08 (Nilsson et al. 2008); its optical–UV continuum is so featureless (Biermann et al. 1981; Stickel et al. 1993) that a redshift estimate has been possible only resolving and using the host galaxy as a standard candle (Nilsson et al. 2008). This BL Lac is of the IBL type, displaying a first broad peak in the optical–UV bands and showing another broad peak near 1 GeV; the crossover between the two components falls in X-ray range (Massaro et al. 2008; Ferrero et al. 2006). Recently, 0716+714 has been detected by AGILE above 100 MeV several times during the period 2007 September–October when the source was quite active in optical band with variations on 1-day timescale (Villata et al. 2008). Two bright γ-ray flares were detected. The first one reached a flux of ≃(200 ± 40) × 10⁻⁸ photons cm⁻² s⁻¹ on 2007 September 11 with a photon index of ≃ 1.6 and duration ⩽1 day. In 2007 October, following another prominent optical activity detected by the WEBT consortium, AGILE and Swift satellites pointed again at the source. On 2007 October 23, another 1 day bright flare was observed with a γ-ray flux comparable to that detected in September (Chen et al. 2008). Around this date a bright 1 day flare and strong day variability were observed in the optical band (Villata et al. 2008); UV and soft X-rays also showed strong and fast variability, whereas modest or none variability appeared in the band 4–10 keV (Giommi et al. 2008). Meanwhile, the radio flux showed a slow coherent increase that remarkably begins around the day of the first γ-ray flare and culminates around the date of the second γ-ray flare (Villata et al. 2008). Thereafter, 0716+714 was detected going back to its ground state in all bands, with the γ-ray photon index that softened toward 1.9 (Chen et al. 2008) as previously observed by EGRET (Lin et al. 1995).

In this paper, we present a physical model for the 0716+714 flaring states, and study their extreme energetics with implications on energy extraction from a rotating BH.

2.1. One Simple Model, Synchrotron Self-Compton

The simplest homogeneous synchrotron self-Compton (SSC) model assumes the blazar emissions to be produced in a "blob" of radius R, containing relativistic electrons in a combination of tangled and uniform magnetic fields. The emitters move toward the observer with bulk Lorentz factor Γ (see, e.g., Tavecchio et al. 1998). We assume the emitters to emerge from the injection/acceleration phase with a jet-frame distribution of the random energies γmc² in the form of a standard broken power law

$$\begin{equation} n_{\rm e}(\gamma)=\frac{K\,\gamma _{\rm b}^{-1}}{ (\gamma /\gamma _{\rm b})^{\zeta _{1}}+(\gamma /\gamma _{\rm b})^{\zeta _{{\rm 2}}}}, \end{equation} \tag{ 1 }$$

where ζ₁ and ζ₂ are the spectral indices for γ < γ_b and γ>γ_b, respectively, γ_b is the Lorentz factor at the break. These electrons emit a primary synchrotron spectrum; a second contribution is then produced by inverse Compton (IC) as the primary synchrotron photons scatter off the same electron population. The spectral energy distribution (SED) behaves as F() ∝ ^1−α, where is the energy of the received photons, and α = (ζ − 1)/2.

For electrons in a magnetic field B, the synchrotron SED peaks around

$$\begin{equation} \epsilon _s=h\,\frac{3.7\times 10^6B\,\gamma _{\rm b}^2\,\delta }{1+z}, \end{equation} \tag{ 2 }$$

where h is Planck's constant, z is the redshift of the source, and δ = [Γ(1 − βcos θ)]⁻¹ is the bulk Doppler factor due to the flow of emitters toward the observer at an angle θ relative to his/her line of sight; the SED at the synchrotron peak is

$$\begin{equation} \epsilon _s\,F(\epsilon _s)\propto \delta ^4R^3B^2K\,\gamma _{\rm b}^2. \end{equation} \tag{ 3 }$$

As to the IC component, its SED contribution peaks at

$$\begin{equation} \epsilon _c=\frac{4\gamma _{\rm b}^2\epsilon _s}{3} \end{equation} \tag{ 4 }$$

with a peak value of

$$\begin{equation} \epsilon _c\,F(\epsilon _c)\propto \delta ^4R^4B^2K^2\gamma _{\rm b}^4 \end{equation} \tag{ 5 }$$

if the scattering takes place in the Thomson regime with the density of target photons scaling as n_ph ∝ F_sR/c. The relativistic motion toward the observer amplifies the emitted power by the factor δ⁴, and allows it to vary on a timescale

$$\begin{equation} t_{\rm var}\gtrsim \frac{t_{\rm cr}(1+z)}{\delta } \end{equation} \tag{ 6 }$$

close to or shorter than the crossing time t_cr = R/c.

Due to the synchrotron and IC losses, the electrons cool with timescale

$$\begin{equation*} \tau _{\rm cool}(\gamma)=\frac{3mc}{4\beta ^2\sigma _T\gamma (U_{\rm B}+U_{\rm r})}, \end{equation*}$$

where σ_T is the Thomson cross section, U_B = B²/8π, and U_r is the energy density of radiation before scattering. This sets a typical cooling break at γ_cool = 3mc²/4σ_T R β²(U_B +  U_r) beyond which the electrons cool rapidly. In the following, we take into account this constraint on the particle distributions.

Simultaneous multi-frequency observations can provide the five quantities R,   δ,   B,   K_e, and γ_b with the five Equations (2)–(6).

For BL Lacs with high-frequency peaks (HBLs) requiring electrons of higher energies (γ_b > 10⁴), the scattering approaches the Klein–Nishina (KN) regime with a blob-frame photon energy >m_ec²/γ_b. In the extreme KN regime the IC SED peaks at _c ∼ γ_bm_ec²δ/(1 + z); the dependence on B and γ_b progressively weakens as the two latter parameters grow.

2.2. An Addition to the Model, External Seed Photons

Additional target photon can be provided by a source external to the jet (see Dermer et al. 2009). In this case, the high-energy component of the spectra is due to the electrons that Compton-scatter the external photons (EC); the SED now peaks at energies

$$\begin{equation} \epsilon _c=\frac{4\gamma _b^2\epsilon _{\rm ext}^{\prime }\delta }{3(1+z)}\,, \end{equation} \tag{ 7 }$$

and the corresponding SED value is

$$\begin{equation} \epsilon _c\,F(\epsilon _c)\propto \delta ^4R^3K\,\gamma _b^2N_{\rm ext}^{\prime }\epsilon _{\rm ext}^{\prime }\,. \end{equation} \tag{ 8 }$$

In this EC process two new ingredients enter: '_ext and N'_ext, respectively, the energy and the density at peak of the EC as seen by the moving blob. This has two main consequences.

• 1.  
  The model contains two further degrees of freedom and the parameter evaluation may be degenerate.
• 2.  
  These news quantities are related to N_ext and _ext in the observer frame by means of the bulk Lorentz factor Γ in a manner that depends on the geometry of the system (Dermer & Schlickeiser 2002), causing an additional dependence on Γ in the external photon spectra. Dermer & Schlickeiser (1993) discuss SED dependences on Γ varying from ∝Γ³ to ∝Γ⁶, for photons entering into the blob from behind or head-on, respectively.

2.3. Flux Variation Patterns

Equations (2)–(8) show that, in the synchrotron–IC framework, variabilities of the first and second peaks are correlated, possibly with a lag t_del ∼ t_cr(1 + z)/δ.

When the energy fluxes around these peaks ϕ ∝ F() are simultaneously monitored, we can compare the corresponding light curves ϕ(t) in the respective band energy _s and _c, possibly with a time lag t_del. Then given two times t₁ and t₂, the ratio r_c ≡ ϕ_c(t₂ + t_del)/ϕ_c(t₁ + t_del) shows a dependence on r_s ≡ ϕ_s(t₂)/ϕ_s(t₁) that is related to the emission mechanism. Here, we consider some relevant cases.

If the variability is mainly due to electron injection/acceleration, K and/or γ_b changes; then, r_c = r²_s results if SSC dominates the IC emission. If instead EC dominates then r_c = r_s applies (compare Equation (3) with Equations (5) and (8)). If variations are mainly due to changes in B, then r_c = r_s holds for SSC, and r_c = 1 applies for EC. If instead Γ varies, we have r_c = r_s in the SSC; in the EC framework we have different behaviors depending on the geometric of the jet relative to the external radiation: r_c = r^x_s with x ranging from 3/4 for seed photons entering from behind, to 3/2 for photons entering head-on the flow.

In Table 1, we report the relations for the Thomson and the extreme KN regimes (see also Paggi et al. 2009). The cooling of electrons acts as a variation of K and γ_b. Hence, in a flare due to electron injection/acceleration, the trajectories r_c versus r_s remain unchanged by pure radiative cooling.

Table 1. Variability Patterns

Model	$\bGamma$ Changes	B Changes	K Changes	γb Changes
SSC Th.	rc = rs	rc = rs	rc = rs2	rc = rs2
EC Th.	rc = rsx	rc = 1	rc = rs	rc = rs
SSC KN	rc = rs	rc → rs0.5	rc = rs2	rc → 1
EC KN	rc = rsx	rc = 1	rc = rs	rc → 1

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2.4. Modeling the γ-ray Flaring States

A 1 day time lag between the emission in optical and γ-ray bands during the two flares is apparent form Figures 1 and 3 of Chen et al. (2008). This constrains the emitting region radius and the Doppler factor to R ⩽ 5 × 10¹⁶(δ/20)  cm; the duration of both flares is 1 day or less, which argues for cooling times τ_cool(γ_b) ∼ R/c.

Moreover, optical and gamma light curves around the two flare dates show evidence that r_c = r²_s applies (see Figure 2 and its caption): this argues for a SSC process in the Thomson regime, and concurs with the lack of sign of external gas to rule out EC process (see also Table 1).

Previous radio monitoring by the Very Long Baseline Array (VLBA) telescope of 0716+714 showed the presence of more superluminal components relative to the active state of 2003–2004 (Rastorgueva et al. 2009). Moreover, the absence of the signatures of IC catastrophe provided a lower limit δ ⩾ 14 for the Doppler factor (Ostorero et al. 2006; Fuhrmann et al. 2008; see also Wagner et al. 1996); Bach et al. (2005) also argue for high Doppler factors in these fast variable components and for a viewing angle θ ⩽ 49.

We note that modeling the SED of 0716+714 with a standard one-zone SSC model would fail to reproduce the simultaneous radio, optical, X-ray, and γ-ray data for the October flare. In particular, the crossover in the X-ray band would not be well reproduced, and the hard X-ray flux would be overestimated by a factor ∼3; furthermore, it would be difficult to model the hardness of the γ-ray spectrum during the September flare (Figure 1, red dashed lines). A one-component model also hardly explain together the slow trends of the radio, optical, and hard X-ray bands and the faster variability observed in the optical, soft X-ray, and γ-ray bands (see Villata et al. 2008; Giommi et al. 2008; Chen et al. 2008). Hence, we adopt a two-component model: the first produces the slowly variable radio and hard X-ray bands, whereas the second is responsible for the faster variability in optical-UV, soft X-, and γ-ray bands. Despite these problems, the possibility to fully constrain by observations the parameters stimulate us to also show for comparison a one-component model.

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The SEDs of all these models are shown in Figure 1 and the parameters are listed in Table 2; a viewing angle θ ≈ 2° is adopted according to Bach et al. (2005).

Table 2. Model Parameters for the 2007 γ-ray Flares of 0716+714

Date	Comp.	Γ	B (G)	R (cm)	K(cm−3)	γb	γmin	ζ1	ζ2	τcool(γb)/tcr
Sept 11	c I	10	0.4	3 × 1016	3.5	3800	100	2	4.5	1.3
	c II	15	0.3	3.5 × 1016	1.4	7000	3500	2	5	1.0
	Single	15	0.3	3.5 × 1016	1.8	7000	60	1.8	5	1.0
Oct 23	c I	10	0.4	3 × 1016	2.5	4000	40	2	4.5	1.2
	c II	15	0.3	3.5 × 1016	1.5	6500	1300	2	5	1.1
	Single	15	0.3	3.5 × 1016	1.8	6500	30	1.8	5	1.1

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Under the assumption of isotropic emission, the observed power radiated from a source with luminosity distance D_L(z) is

$$\begin{equation*} L_{\rm obs}=4\pi D_L(z)^2\int d\epsilon F(\epsilon). \end{equation*}$$

The jet transports a total power P_tot,flare = L_r +  L_kin +  L_B contributed by intrinsic radiated power, kinetic energy flow of the electrons and of the cold protons (with one proton per emitting electron), and Poynting flux, respectively:

$$\begin{eqnarray} &L_{{\rm r}}&=L_{\rm obs}\Gamma ^2/\delta ^4=2\times 10^{-3}(\delta /15)^{-4}{\Gamma _1}^2\,L_{\rm obs}, \end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray} &L_{\rm e}&=0.8\times 10^{43}R_{16}^2\,{\Gamma _1}^2\,{\langle {n_e\gamma }\rangle }_{4}\,\rm erg\,s^{-1}, \end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray} &L_{\rm p}&=1.4\times 10^{43}R_{16}^2\,{\Gamma _1}^2\,{\langle {n_p}\rangle }_{1}\,\rm erg\,s^{-1}, \end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray} &L_{\rm B}&=3.8\times 10^{43}R_{16}^2\,{\Gamma _1}^2B^2\,\rm erg\,s^{-1}, \end{eqnarray} \tag{ 12 }$$

see also Celotti & Ghisellini (2008). The latter authors show that in BL Lacs L_r tends to match the sum of the other contributions. In fact, for the two flares of 0716+714 at redshift z = 0.31 we find L_r ≃ 2 × 10⁴⁵ erg s⁻¹, and from our two-component SSC model (with the parameters listed in Table 2) we obtain a total jet power

$$\begin{equation*} P_{\rm tot, flare}= (3.5\pm 1)\times 10^{45}\,\rm erg\,s^{-1} \end{equation*}$$

with L_r ≳ (L_e + L_p + L_B). Under this condition, the total jet power is minimized and the details of cooling does not affect materially the global energetics, being the radiated luminosity L_r mainly contributed by peaks emission. Moreover, the uncertainty in P_tot,flare is mainly due to the observed γ-ray flux error.

For the one-component model, we obtain P_tot,flare = (1 ± 0.5) × 10⁴⁶ erg  s⁻¹ and L_r ≲ (L_e + L_p + L_B) holds. In this case, the total jet power is not dominated by the radiated one, but the parameters now are well constrained by the observation and the uncertainty is still due to the flux error.

3.1. Testing the Blandford–Znajek Mechanism

Here, we compare the jet powers provided by our models with the BZ mechanism; this set a limit on the power extractable from a rotating BH

$$\begin{equation} P_{BZ}\simeq 2\times 10^{45}M_9\,\rm erg\,s^{-1} \end{equation} \tag{ 13 }$$

under conservative values of B, as discussed in Cavaliere & D'Elia (2002, and references therein; see also our discussion).

Estimating the redshift and the BH mass of 0716+714 is not trivial because of the lack of emission lines. Recently, however, Nilsson et al. (2008) pinpointed the host galaxy of this source and reported a determination of its redshift at z = 0.31 ± 0.08. Then, for this host, a BH of mass M ∼ 5 × 10⁸ M_☉ should accord with the fundamental plane of BL Lacs (Falomo et al. 2003).

On the other hand, some authors using micro-variability of the optical flux estimate the mass of the central BH for 0716+714 by

$$\begin{equation} M<\frac{c^3\tau \,\delta }{6G(1+z)}\approx 3\times 10^8\,M_{\odot } \bigg[\frac{\delta }{20}\,\frac{\tau }{600}\bigg]. \end{equation} \tag{ 14 }$$

Considering τ ≃ 450 s as the shortest variability time found by Sasada et al. (2008) one obtains M < 2 × 10⁸(δ/20) M_☉. Gupta et al. (2009) obtain the more stringent constraint M < 5 × 10⁷ M_☉ for the case of a Kerr BH. However, these authors discuss that the micro-variability in 0716+714 may be due to a small region in the jet or due to internal disk modes, so that the BH mass would be higher.

We note that a BH of mass M < 10⁸ M_☉ in 0716+714 would imply in Equation (13) a power limit P_BZ ≪ L_r inconsistent with the power L_r emitted during the flares.

We modeled the 0716+714 flares of 2007 September 11 and October 23 with a two-component SSC model, similarly to Tavecchio & Ghisellini (2009). Despite the larger number of model parameters, we believe that our two-component modeling reproduces the complex variability and the hard γ-ray spectra of 0716+714 better than a one-component model.

Our Figure 2 indicates a quadratic dependence between the synchrotron and IC fluxes. This concurs with the lack of emission lines and BBB to rule out models involving external sources of seed photons that produce a linear dependence, and to strongly support electrons radiating in the Thomson regime within the SSC framework as the most likely radiation process. We refer to our Figures 2 and 1 in Chen et al. (2008) to show that the 2007 September data lie around the maximum; in time, the trajectory starts from the lower r_c value, attains a maximum and then falls down. In 2007 October, the trajectory describes the decline of a flare starting from the higher r_c value. Rises and falls both occur on one-day timescale, and the trajectories are quadratic. This suggests the electron acceleration and cooling to occur on similar timescales.

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The crossover between the synchrotron and IC branches of the SED is located in X-rays (see also Foschini et al. 2006; Ferrero et al. 2006), and is contributed by both the slowly variable component (I) and the faster component (II).

As to the faster components (II) adopted for the two flares, they are marked by high electron energies γ_b ∼ 7 × 10³ with a sharp low energy cutoff γ_min ∼ 2 10³ (see also Tsang & Kirk 2007). Moreover, high bulk Lorentz factor Γ = 15 (that is δ ≃ 23) is used in accord with Wagner et al. (1996). In Table 2, it is shown that our choice of parameters implies τ_cool(γ_b) ≃ t_cr for the fast components II: those quench very rapidly causing strong variability in the optical–UV, soft X- and γ-ray bands. Little or no variability results in radio and hard-X ray bands produced by the rising part of the slow components I. This behavior is in agreement with the complex multi-band variability reported by Chen et al. (2008), Giommi et al. (2008), and Villata et al. (2008).

Considering the redshift z = 0.31 of 0716+714, we find that its intrinsic radiative luminosity is of order L_r ≈ 2 × 10⁴⁵ erg s⁻¹. On adding the other jet components in Equations (10)–(12), the total power becomes P_tot,flare ≈ 4 × 10⁴⁵ erg s⁻¹ for the two-component model, and P_tot,flare ≈ 2 × 10⁴⁶ erg s⁻¹ for the one-component model: the source exceeds the BZ limit P_BZ ≈ 2 × 10⁴⁵M_BH/M₉ erg s⁻¹ (see Figure 3). This obtains for a maximally rotating BH of 10⁹ M_☉ (spun by past accretion) via interaction with a disk magnetic field B ∼ 10⁴ G sustained by gas or radiation pressure, in the absence of ongoing accretion (see discussion by Cavaliere & D'Elia 2002). The simultaneous nature of our multi-frequency data during the 2007 γ-ray flares of 0716+714 is a crucial ingredient of our result. Other BL Lacs with weak or negligible accretion disk or BLR contributions have been reported to attain (model dependent) high total luminosities, e.g., 2032+107 with an inferred P ∼ 10⁴⁶ erg s⁻¹ (see Celotti & Ghisellini 2008). Corbel & Reyes (2008, ATel 1744) report the high γ-ray peak flux recently attained by 0235+164 at z ≃ 0.94 for which, however, EC contributions cannot be ruled out. However, to our knowledge, only the simultaneous data obtained by our group for 0716+714 provide a model-independent evaluation of the total jet power from a BL Lac being close or just above the BZ limit.

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We also show in Figure 3 the intrinsic radiated power for other BL Lacs with intense γ-ray and TeV emissions, as for the 1997 flare of BL Lacertae with peak flux around 500 × 10⁻⁸ photonscm^-2s⁻¹ but with lower redshift z = 0.069 (Bloom et al. 1997; see also Ravasio et al. 2002) and intermittent evidence of lines and thermal emissions. We also report W Comae with redshift z = 0.102 but γ-ray flux at levels of 50 × 10⁻⁸ photonscm^-2s⁻¹ (Böttcher et al. 2002).

The increasing trend of L_r with z is likely to arise from the Malmquist bias, while the decrease at low z may result from sampling a limited cosmological volume. Nevertheless, we stress that up to now no BL Lac source has sharply exceeded the BZ limiting power. It will be worthwhile to keep under close watch the most distant BL Lacs (despite the obvious monitoring difficulties) to catch powerful emissions. If violations will be found, these may be possibly discussed in terms of the Blandford–Payne mechanism (Blandford & Payne 1982) that, however, requires ongoing accretion not supported in the case of 0716+714. Alternatively, higher powers may be attained with higher magnetic fields up to B²/4π ≲ ρc² related to the plunging orbits (see Meier 1999), which however imply short source lifetimes in the absence of accretion.

In conclusion, we find the total power transported in the jet of 0716+714 to be P_tot,flare ∼ 4 × 10⁴⁵ erg s⁻¹, and so to approach the limit of the BZ mechanism for a BH up to 10⁹ M_☉ with conservative values of B. Such high powers in 0716+714 constitute an unescapable consequence of two observed facts.

• 1.  
  The γ-ray flux attains high levels in the SED during the two flares, with an emitted power comparable with the optical one as shown by simultaneous observations (see Figure 1).
• 2.  
  The lack of external sources of seed photons related to emission lines or BBB concurs with the observed quadratic dependence r_c = r²_s to rule out EC contributions to the high energy hump (see Figure 2) and considerable ongoing accretion.

This investigation was carried out with partial support under ASI contract No. I/089/06/2.