2.1. Ultra-fast variability: sparks from magnetic reconnection?
Vary rapid variations of the γ-ray flux, with inferred doubling time-scales down to few minutes, have been observed in several blazars (both BL Lacs and FSRQ), most notably PKS 2155-304 , Mkn 501 , BL Lac , PKS 1222+21 , IC 310 ( although the precise classification of this source is still matter of debate) and, last but not least, 3C 279 (at GeV energies by pointed observations with Fermi/LAT, ). Such small timescales directly imply, via the standard causality argument, very compact emission regions, with radii not exceeding r < c tvar δ ≈ 1014 (tvar / 1 min) (δ /10) cm, even smaller than the Schwarzschild radius of the black hole (Rs = 2GM / c2 = 2 × 1014 M9 cm) and incompatible with the expected size of a shock, encompassing a large fraction of the jet cross sectional area [49, 50]. For a recent compilation and discussions, see .
These observational evidences stimulated new theoretical approaches aimed at modeling the structure of the emission region(s) and trying to explain the required rapid acceleration of the relativistic particles. The very compact regions implied by the rapid variability have been identified either with turbulent cells [50, 52], with large plasmoids resulting from efficient magnetic reconnection in a relativistic regime [53, 54, 55] or with shocks formed in the jet around stars crossing the jet itself [56, 57]. In the first two cases (turbulence and reconnection), the compact regions could move relativistically in the jet reference frame (forming the so-called “mini-jets”). In this case the resulting relativistic beaming of the emitted radiation in the observer frame (dictated by the combination of the beaming factor of the compact region in the jet frame and that of the jet flow with respect to the observer) can be very large, with Doppler factors easily reaching δ ∼ 50.
The case of IC 310 is somewhat peculiar, since its jet is likely slightly misaligned with respect to the line of sight (θv ≃ 10°, to be compared to typical viewing angles for blazars θv ≲ 5°) and thus the Doppler factor cannot be larger than a few, thus making the interpretation of the rapid variability (with doubling times of few minutes as observed during an active state in november 2012) even more difficult. Moreover, also the observed VHE spectrum is quite peculiar, showing an unbroken hard (photon index close to 2) power law up to 10 TeV. An exciting possibility is that the fast variations flag the development of electromagnetic cascades triggered by pairs accelerated to the required TeV energies by unscreened electric fields in gaps of the black hole magnetosphere , a mechanism already proposed to work in other low-luminosity AGN, in particular the radiogalaxy M87 [58, 59, 60], and possibly related to the formation of the jet itself. Detailed calculations  show that the expected spectrum (originating from the IC scattering of the soft IR radiation from the radiatively inefficient accretion flow by the pairs in the cascade) can indeed be very hard and it is expected to cut-off around 10 TeV because of γγ absorption caused by the IR radiation field. A similar scenario involves the acceleration of narrow beams of electrons in the magnetosphere of the black hole through magnetocentrifugal effects [62, 63].
Coming back to blazars, the scenario mentioned above involving the formation of plasmoids during magnetic reconnection events (jets-in-the jet model) is being explored with quite some details and the results appear rather promising (see Sironi, these proceedings). From a fundamental perspective, magnetic reconnection-powered emission from jets is favored with respect to that associated to shocks since – as expected at the typical distance of the “blazar zone” – the flow is thought to be largely dominated by the Poynting (i.e. magnetic) flux . In these circumstances diffusive particle acceleration by shocks is expected to be quite inefficient [55, 65], while the large energy stored in the magnetic field can be efficiently extracted and channeled to particles. Recent dedicated particle-in-cell plasma simulations  demonstrate that the combined action of the acceleration by unscreened electric fields in the current sheets and the subsequent Fermi I-like acceleration caused by the bouncing of the particles off the magnetic islands, provides an efficient and rapid way to accelerate electrons (and ions). Simulations further robustly show that the post–reconnection regions – in which most of the radiation we receive is produced – should be characterized by a substantial equipartition between the relativistic particles and the magnetic field.
Some problems for the magnetic reconnection scenario arises when the general predictions sketched above are compared to the physical state of the jets (or, more precisely, of the emission regions of the jets) that we infer by modelling the SED. First of all it appears that, contrary to the assumptions of the model, the jets of VHE BL Lacs (which are the majority of the sources in which ultra-rapid variability events have been observed) are rather weakly magnetized, with the Poynting flux providing a negligible contribution to the total jet power (incidentally, this could be a major problem also for the general scenario for jet acceleration that foresees a substantial equality of magnetic and kinetic luminosities, their ratio decreasing only logarithmically with distance after the acceleration phase). Similarly, the regions probed through the emission are largely far from equipartition conditions, with derived magnetic over electronic energy density ratio of the order of UB / Ue ≃ 0.1 − 0.01 . These general conclusions are quite robust, at least in the framework of one-zone models, since, as already stressed, in this case all parameters are fixed by well sampled SED. Some works in the past already reached these conclusion on single sources, e.g. [67, 68]. In  we have extended the study to a large group of γ-ray emitting BL Lacs. The main results are shown in Fig. 1. In the left panel we report UB / Ue versus the energy of the high-energy SSC peak, assuming representative values for the other spectral parameters. Since most of the VHE BL Lac have the peak at energies EIC ≳ 100 GeV, the plot show that UB / Ue ≲ 0.01. I remark that the lines in the plot have been derived analitically. The right panel in Fig. 1 shows instead the derived UB / Ue applying the one-zone SSC model to a group of BL Lac with information on the high-energy peak. As expected, most of the sources lies in the region with UB ≪ Ue.
Figure 1. Left: ratio between the magnetic and the relativistic electron energy density for the one-zone leptonic model as a function of the peak energy of the SSC component, for three different values of the Doppler factor, δ = 10 (black), 20 (red), 30 (blue) and representative values of the other spectral parameters. Typical BL Lac detected at VHE have EIC ≳ 100 GeV, implying UB / Ue ≲ 10−2. Right: magnetic energy density, UB, versus relativistic electron energy density, Ue, derived for a group of γ-ray emitting BL Lac modelled with the one-zone leptonic model. Most of the sources lies in the region UB ≪ Ue. Adapted from .
The issue related to the low magnetization of the BL Lac jets shows up also when synthetic SED are derived in the framework of the reconnection model . Due to the large magnetic field, the derived SED systematically display a luminous synchrotron component, much more powerful (by almost one order of magnitude) than the SSC one. This has to be compared to the observed SED which generally show a substantial equality of the two peak luminosities. The reason for the discrepancy is clearly related to the large magnetic energy density predicted as a leftover of the reconnection process, which implies a large synchrotron emissivity.
A possible way out to these problems, advanced in , is to invoke the spine-layer structure for the jet. The idea at the base of this scenario can be simply grasped. In fact, as already remarked, with the spine-layer structure the luminosity of the IC bump produced by the spine can be increased because of the supplementary soft target radiation energy density provided by the boosted layer emission. Therefore, the required SSC luminosity can be produced by a smaller number of relativistic electrons, leading to reduce Ue. At the same time, to maintain the same synchrotron luminosity with a reduced number of electrons one has to increase the magnetic field, that is increase UB. The ratio between UB and Ue therefore increases. The equipartition can be reached assuming a reasonable level for the layer emission, see in Fig. 2 the case of Mkn 421. Besides solving the problem of the equipartition, the larger magnetic energy density and smaller particle density allowed by the spine-layer set-up, lead to increase the Poynting flux. In the benchmark case of Mkn 421 reported in Fig. 2, it comes out that the system reaches the condition LB ≈ Lkin, thus mitigating the problem represented by the small jet magnetization.
Figure 2. SED of Mkn 421 (gray, from ) reproduced with the spine-layer model (red solid line). The green long-dashed line displays the assumed emission from the layer. The blue dotted line shows the SSC emission alone. As explained in the text, the large radiation energy density available for the IC emission – provided by the layer – increases the IC luminosity and allows one to reproduce the SED in equipartition conditions. Adapted from .
2.2. Flat spectrum radio quasars at VHE
The great majority of blazars detected at TeV energies are BL Lacs (more precisely HBL – highly-peaked BL Lacs – defined as having the maximum of the synchrotron component in the UV-X-ray band, ). For a long time, FSRQ have not been considered good target for VHE observatories. There are several reasons supporting such theoretical prejudice: i) FSRQ are characterized by soft MeV-GeV γ-ray spectra (their SED peaks are generally located at E < 100 MeV); ii) the continuum, if produced through IC scattering, is expected to further soften above few GeV due to effects related to the Klein-Nishina cross section, ; iii) another important factor to consider is the anticipated huge “internal” absorption of γ-ray photons with energies exceeding few GeV interacting through the γγ → e± reaction with the various soft radiation fields in the FSRQ nucleus – most notably that associated to the BLR [72, 73]. In fact, γ rays produced well inside the BLR are characterized by optical depth τγγ ≫ 1 (i.e. absorption probabilities close to 1) for energies above 20 GeV – the energy threshold for the interaction with the abundant photons of the hydrogen Lyman α broad emission line.
Despite the pessimistic expectations, photons at several tens of GeV (source rest frame) from FSRQ are occasionally detected by Fermi-LAT, usually during high-states or flare [74, 48]. Generally, during these events the γ-ray spectra become quite hard, with photon index close to 2 (i.e. “flat” in the SED). These episodes are also commonly (but not always, e.g. ) accompanied by a shift of the entire SED toward higher frequencies, hence the name “blue flat spectrum radio quasars” [76, 77] sometimes used to describe FSRQ with these peculiar SED.
To avoid the huge opacity to high-energy γ rays, the emission during these events should occur outside the BLR. These more or less temporary states could thus be interpreted as (rare?) phases during which the emission region moves from within the BLR (where it is thought to permanently reside in classical “red” FSRQ) to the outer regions, where the external radiation field is dominated by the IR radiation field of the dusty torus [78, 77] (see Fig. 3). In , along the lines of , we remarked that the FSRQ most likely susceptible to change their SED from “red” to “blue” are those characterized by a relatively small size of the BLR, so that the blazar emission zone can easily go beyond it even in case of relatively small displacements. Since, as we discussed above, the BLR radius is set by the disk luminosity (as rBLR ∝ Ld1/2), the sources mostly prone to such transitions are expected to be FSRQ of low power.
Figure 3. Cartoon of the structure of a FSRQ (not to scale). Standard models assume that the bulk of the emission occurs within the BLR, at distances ≲ 0.1 pc (case A). To avoid huge absorption of γ rays the emission region must be located outside the BLR radiation field (case B), where the external radiation field is dominated by the IR thermal emission of the pc-scale dusty torus (pink).
The effect of the displacement of the emission region out of the BLR radiation field is twofold. On one hand the reduced optical depth permits the propagation of photons above 20-30 GeV, as observed during flares. On the other hand, a reduction of the external radiation energy density – which determines the cooling rate of the electrons, dominated by the IC process off the external photons, cool, IC ∝ Urad−1 – implies a reduced radiative cooling rate of the electrons and – in the view in which the maximum electron energy is fixed by the balance between losses and gains – a larger average energy of the accelerated electrons. The increased Lorentz factors of the electrons can then explain the shift of the SED peak at larger energies . Of course, in these circumstances the detection of FSRQ also at VHE becomes a possibility.
Until now, five FSRQ (3C 279, PKS 1510-089, 4C +21.35, PKS 1441+25, S3 0218+35) 3 have been detected at VHE, out of a total of 62 blazars 4. FSRQ and BL Lacs display a rather different cosmological evolution (for studies in the γ-ray band see [82, 83]) and this naturally reflects in the redshift distribution of the VHE detected sources (Fig. 4), with FSRQ showing redshifts significantly larger than those of BL Lacs: in particular, PKS1441+25 and S3 0218+35 are located at a redshift close to 1. The large distance exacerbates the effects of the absorption through the interaction with the extragalactic background light (EBL) through the pair production reaction γ + γEBL → e±. A consequence is that the recorded VHE spectra of FSRQ are quite soft and therefore instruments characterized by a low energy threshold are favored in their detection.
Figure 4. Redshift distribution of BL Lacs (blue) and FSRQ (black) detected at VHE. Sources without a firm redshift determination are not included.
As discussed above, the detection of photons with energies in the 100 GeV-1 TeV range allows us to locate the emission region beyond the BLR edge. A conservative possibility  is to assume that the emission occurs just beyond the BLR, where the radiation field is already dominated by the IR radiation field from the dusty torus . The lower energy of the IR photons (є < 1 eV) has two effects: i) the KN effects on the produced EC radiation starts at larger energies ; ii) the absorption threshold moves at larger energies, allowing the unattenuated propagation of γ-ray photons of hundreds of GeV. For typical temperatures of the dust (T ≈ 103 K), one expects huge absorption of the emitted γ-ray photons with E ≳ 1 TeV. This result can be derived though a simple back-on-the-envelope calculation. Close to threshold, the typical photon energy of the (black body-like) IR radiation field interacting with the γ-ray photons is ⟨є⟩ ≈ 2.82 kT ≃ 0.25 T3 eV, implying that absorption becomes relevant for photons of energy E = me2 c2 / ⟨є⟩ = 1 T3−1 TeV. The corresponding optical depth is expected to be very large. This can be well approximated as τγγ = σT / 5 nph rIR , where the nph is the number density of the target soft photons and rIR is the torus size. Using a scaling law for the torus radius as a function of the disk luminosity rIR = 1 Ld, 451/2 pc  one easily derives τγγ ≃ 300 ξ Ld, 451/2 T3−1, where ξ ≈ 0.5 is the fraction of the disk luminosity reprocessed into IR radiation. With such a large optical depth one naturally expects an abrupt cut-off of the high-energy spectrum at energies close to 1 TeV (source frame).
Unfortunately current detections do not reach such high energies. The most interesting case is that of the recently detected PKS 1441+25 (z = 0.940). The observed power-law spectrum  extends up to Emax ≈ 300 GeV, which, in the rest frame of the source corresponds to E′max = Emax (1 + z) ≈ 580 GeV, just at the edge expected cut-off. This is clearly visible in Fig. 5, reporting (red symbols) the nearly simultaneous multifrequency data recorded in the period 18-23 April 2015, during the highest γ-rat state. The blue line shows the result of the one-zone model assuming that the emission region lies just beyond the BLR radius. From the luminosity of the observed emission lines one can infer that the disk luminosity is Ld ≃ 2 × 1045 erg s−1 and from it, using the scaling law of  one can infer the radius of the BLR to be rBLR = 1.4 × 1017 cm. The emission region is located at rem = 5 × 1017 cm. At this distance the (de-beamed) radiation field from the BLR is negligible and the IC emission is dominated by the scattering of the IR radiation of the dusty torus. Clearly, the evidence for the expected absorption cut-off would be quite important, allowing to firmly locate the emission region within the IR torus. Of course, even the absence of the cut-off would be a quite precious information, demonstrating that, at least occasionally, the emission can occurs quite far out along the jet, as argued by several groups based on the observed behavior of the optical polarization, the ejection of new VLBI components apparently simultaneously with the flares or on the modelling of the SED [88, 89, 90, 91, 74].
Figure 5. SED of the FSRQ PKS 1441+25, detected at VHE by MAGIC and VERITAS. Red symbols (data taken from ) refer to an active phase on 2015 April 18-23. Gray symbols show historical data for the quiescent state. We report the results of a leptonic one-zone model, assuming that the emission occurs beyond the BLR edge (blue solid line). The green point-dashed line shows the inverse Compton component (produced through the scattering of the IR photons from the dusty torus), not including γγ absorption. The strong cut-off at around 1 TeV caused by absorption is clearly visible comparing the blue and the green lines. See  for details.
The scenario assuming that γ-ray production occurs beyond the BLR naturally foresees relatively long variability timescales (≈ days). In fact, in the standard cone geometry for the jet, at a distance rem the expected jet radius is rj = θ j rem, where θ j ≈ 0.1 rad is the jet semi-aperture angle. Using standard relations for the BLR radius one gets rem > rBLR ≈ 0.1 pc, implying rj ≳ 3 × 1016 cm, and thus variability timescales of the order of Δ tvar > rj / c δ ≃ 1 (δ / 10)−1 days. This line of reasoning was used to argue that the evidence of ≈ hour timescale variability implies that the emission occurs at small distances, well within the BLR . Indeed, the variability timescale inferred for most of the FSRQ detected at VHE, as PKS 1441+25 discussed above, show relatively smooth and slow variations in γ-rays. However there are some cases in which the condition is evidently violated. The first case was that of 4C +21.35, for which MAGIC detected a flare with a raising time of just 10 minutes , readily implying a quite compact emission region rem ≈ 1014 (δ / 10) cm located beyond the BLR . Similar is the recent case of the flare of 3C 279 detected by LAT , which reported variability with Δ tvar ≈ 5 minutes accompanied by the detection of photons with energies exceeding 50 GeV (likely flagging emission beyond the BLR).
The possible scenarios trying to reconcile minute-scale variability (hence requiring small emission regions, with rem≈ 1014 cm) with the absence of absorption (thus locating the emission region at large distances, outside the BLR) follow the lines of those already discussed above for the ultra-fast variability. For FSRQ, the physical conditions inferred for the emission regions are in better agreement with the magnetic reconnection scenario than those of BL Lac jets. In fact, equipartition between magnetic fields and relativistic particles (predicted for the magnetic reconnection model) generally holds for FSRQ . However, a still acute problem could remain, since the jets do not appear to be magnetically dominated at the distances assumed for the emission [26, 93], a conditio sine qua non for the model to work (magnetic reconnection models generally assume that the magnetic luminosity of the jet is >10 times larger than the kinetic one). However, this conclusion could be revised in case the jet composition includes at least 10-20 pairs every proton .
Further advances in the understanding of VHE emission from FSRQ requires more data and an enlarged sample of sources. For FSRQ, even more than BL Lac objects, the most effective way to understand the underlying physics is to put the VHE data in a broader context, including radio (especially VLBI monitoring, providing precious spatial information on the activity), optical (including polarization measurements), X-rays and GeV data (where most of the action takes place). Surely this will be a fruitful field in the upcoming CTA era.
3 I do not include in this list the blazar S4 0954+65, often considered a FSRQ, since it is likely a BL Lac of unknown redshift . Back.
4 Data from http://tevcat.uchicago.edu Back.