4.3.3. Interpretation

The properties of the VHE light curve and spectrum of GRB 190114C were studied by the MAGIC Collaboration in [3]. The PL behavior, the absence of variability, and the relatively long timescale of the emission support the evidence that the VHE component belongs to the afterglow phase. An estimate of the amount of radiated power in the TeV range can be derived, assuming that the afterglow onset is at ∼6 s [178]. In this case, the energy radiated in the TeV band is ∼10% of the isotropic-equivalent energy of the prompt emission *Eγ*,*iso* considering the temporal evolution estimated from the MAGIC light-curve.

The energy of the photons observed by the MAGIC telescopes was compared with the maximum energy of synchrotron photons assuming two possible scenarios for the radial profile of the external density, namely constant and wind-like (Figure 19). These estimates of the maximum energy are based on the widely adopted limit on the maximum electron Lorentz factor set by equating the acceleration at Bhom rate with the synchrotron cooling rate (see Equation (57)). Adopting this limit, synchrotron emission can not account for the TeV photons detected by MAGIC, and a different radiation mechanism must be invoked.

**Figure 19.** GRB 190114C: comparison between the distribution of the observed *γ*-ray events binned in time and energy (blue shaded areas) and the limiting curves for synchrotron maximum energy. Two different density radial profiles are considered for the derivation of the theoretical curves: constant (red-dotted curve) and wind-like (red-dashed curve). From [3].

An additional, model independent indication for the presence of a spectral component other than synchrotron is evident after multi-wavelength simultaneous SEDs are built. In [71], the VHE data were rebinned into five time intervals and XRT, BAT, GBM and LAT data were added when available, i.e., in the first two time intervals (Figure 20). The spectrum demonstrates a double-peaked behavior with a first peak in the X-ray band and the second one in the VHE band. The Fermi-LAT data play a particularly important role

in revealing the shape of the SED, as they show a dip in the flux, strongly supporting an interpretation of the whole SED as a superposition of two distinct components.

**Figure 20.** GRB 190114C SEDs from soft X-rays to 1 TeV in five different time intervals. The contour regions for flux uncertainties are also shown. For MAGIC and LAT the 1*σ* error of their best-fit power-law functions are displayed. For Swift data, the 90% confidence contours for the XRT-BAT joint fit is shown. MAGIC spectra are EBL-corrected assuming the model by [183]. From [71].

Following these considerations, in [71], the SSC mechanism is explored. The broadband emission is modeled with a numerical code reproducing the synchrotron and SSC radiation in the external forward shock scenario, including the proper KN cross section and the effects of *γ* − *γ* annihilation.

The predicted spectra and lightcurves are compared with the data in Figures 21 and 22. Acceptable modeling of the multi-wavelength afterglow spectra have been found for a constant medium with *<sup>E</sup><sup>k</sup>* & <sup>3</sup> <sup>×</sup> <sup>10</sup><sup>53</sup> erg, *<sup>ε</sup><sup>e</sup>* <sup>≈</sup> 0.05 <sup>−</sup> 0.15, *<sup>ε</sup><sup>B</sup>* <sup>≈</sup> (0.05 <sup>−</sup> <sup>1</sup>) <sup>×</sup> <sup>10</sup>−<sup>3</sup> , *<sup>n</sup>* <sup>≈</sup> 0.5 <sup>−</sup> <sup>5</sup> cm−<sup>3</sup> and *<sup>p</sup>* <sup>≈</sup> 2.4 <sup>−</sup> 2.6. It is found that, the peak of the SSC component being below 200 GeV, the KN suppression and the *γ* − *γ* internal absorption have a non-negligible role in shaping the peak of the VHE spectrum. The modeling reproduces the XRT, LAT and TeV emission very well (solid blue curve in Figure 21 and solid blue, green and red curves in Figure 22), while it overproduces both the optical and radio flux at late times (solid violet, yellow and cyan curves in Figure 22). According to [71], a similar fit is found, also assuming a wind-like profile for the external density. In this case, the parameters are *<sup>E</sup><sup>k</sup>* <sup>=</sup> <sup>4</sup> <sup>×</sup> <sup>10</sup><sup>53</sup> erg, *<sup>ε</sup><sup>e</sup>* <sup>=</sup> 0.6, *<sup>ε</sup><sup>B</sup>* <sup>=</sup> <sup>1</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> , *A*<sup>∗</sup> = 0.1 and *p* = 2.4. Very interestingly, the modeling shows that the late LAT observation (around 10<sup>4</sup> s) is completely dominated by SSC emission (red-dashed curve in Figure 22). A different type of modelization is also investigated by [71], under the requirement to model optical data. In this case (dotted curves in Figure 22), the fit is very good for optical, X-ray and LAT observations, but fails in reproducing the MAGIC light-curve.

The values inferred for the GRB afterglow parameters are similar to those used for past GRB afterglow studies at lower frequencies. This is an indication that the SSC component can be a relatively common process for GRB afterglows, since it does not require peculiar values of the parameters to be explained.

Several other successful modelings of GRB 190114C data within the synchrotron and SSC external forward shock scenario have been published in the literature [174,184–186]. A summary of the parameters inferred by different works can be found in Table 2.

**Figure 21.** GRB 190114C: modeling of two SEDs in consecutive time intervals. The different curves refer to: the observed spectrum (thin solid line), the EBL deabsorbed spectrum (thick blue line) and the SSC component neglecting the effects of internal *γ*-*γ* opacity (dashed line). From [71].

**Figure 22.** Modeling of broad band GRB 190114C light curves. Description of the different modelings used is given in Section 4.3.3. From [71].

In [174], the X-ray, optical and LAT data before 100 s are attributed to reverse shock emission or prompt contribution. A constant-density environment for the circumburst material is assumed. A time-averaged SED (50–150 s) is estimated, demonstrating that at GeV energies a transition between the synchrotron and SSC component can be identified. From the re-analysis of LAT data, a hard photon index (1.76 ± 0.21) is derived, in agreement with the hardening of the spectrum caused by the rising of the SSC component. Differently from what is observed by [71,184] *γ* − *γ*, the absorption does not contribute significantly in shaping the VHE spectrum.

A similar interpretation is given in [185], although the inferred value of *e<sup>B</sup>* is larger (*e<sup>B</sup>* <sup>∼</sup> <sup>10</sup>−<sup>3</sup> ). A consistent modeling of the multi-wavelength observations as synchrotron and SSC radiation is found in both the ISM and wind-like scenarios. The SED at 80 s (see Figures 2 and 5 in [185]) and the broad-band light curves (Figures 3 and 6 in [185]) are reproduced, despite at 10<sup>3</sup> s, the model predictions in the 0.3–1 TeV band and X-rays are slightly brighter than the observed data.

In [186], analytical approximations are adopted for the description of the synchrotron and SSC components. In addition, the KN cut-off energy and the *γ* − *γ* absorption contribution are calculated and compared with the data. A wind-like environment was used for the circumburst medium. The SEDs in the time intervals 68–110 s and 110–180 s are modeled, and the two values of the KN cut-off energies calculated at these times are

∼3.7 TeV and 2.1 TeV. This implies that the KN effect is relevant only at TeV levels and the VHE data can be modeled assuming that the SSC scattering is in the Thompson regime. The *γ* − *γ* absorption is also considered negligible since the estimated attenuation factor is way lower than the one due to EBL attenuation, and it reaches values around unity only for energies & 1 TeV.

In [184], the multi-wavelength data were fitted with a single-zone numerical code with an exact calculation of KN cross-sections as well as the attenuation due to the pair production mechanism. Smoothed analytical approximations for the electron injection function were used. A systematic scan over a 4-dimensional parameter space was performed to search for the best-fit solution at early and later times. The SED calculated at 90 s and 150 s (Figure 3 and Figure 9, respectively in [184]) are found to be well described by a fast cooling regime. The KN effect and the pair production mechanism shape the VHE spectrum significantly. It is estimated that '10% of the total emitted power, i.e., '25% of initially produced IC power, is absorbed.

**Table 2.** GRB 190114C: parameters inferred by different authors from the modeling of observations with a synchrotron-SSC scenario.


#### *4.4. GRB 190829A*

GRB 190829A is a nearby (*z* = 0.078) long GRB triggered by Swift-BAT [187] and Fermi-GBM [188]. The Fermi-GBM trigger time is *T*<sup>0</sup> = 19 : 55 : 53.13 UTC. H.E.S.S. detected this GRB over three consecutive nights, with a significance of 21.7*σ* during the first night (∼4 h after the GRB trigger).
