4.1.3. Interpretation

A modeling of the multi-wavelength observations, including MAGIC data, has been presented by the MAGIC Collaboration in [145]. The emission is interpreted as the sum of several components, dominating at different times and in different energy bands:


• an X-ray extended emission component, widely attributed to long-lasting activity of the central engine, here dominating the X-ray band for *t* < 10<sup>3</sup> s.

In performing this multi-component modeling, the synchrotron and SSC forward shock emission have been calculated with a one-zone numerical code (see [71] for details), while the reverse shock and kilonova emission contributions have been taken from [148]. Only X-ray data at *t* > 10<sup>3</sup> s have been included in the modeling, to exclude the extended emission component. The broad-band modeling is shown over-plotted to the light-curves in Figure 11 (solid lines) and to the SED between 1.7 and 4 h in Figure 12.

**Figure 11.** GRB 160821B: multi-wavelength light curves (from radio to TeV) and their modeling according to [145]. ©AAS. Reproduced with permission. The different contributions from the forward shock (FS), reverse shock (RS) and kilonova are shown (see legend).

**Figure 12.** GRB 160821B: modeling of the simultaneous multi-wavelength SED at approximately ∼3 h according to [145] (©AAS. Reproduced with permission.), for the same parameters used to model the lightcurves in Figure 11. The shaded areas show the sensitivity energy range of the different instruments. The MAGIC error box on the reconstructed flux is also shown. Synchrotron (solid black line), intrinsic SSC (before EBL absorption, dashed black line) and SSC emission with EBL attenuation (solid red line) estimated from the numerical modeling are shown.

A very good agreement between data and modeling is found in radio (green lines and points), optical (yellow and pink lines and points) and X-rays (blue lines and points). A large degeneracy is present in the parameters, and the data modeling only allows us to identify the ranges for the permitted values of each parameter. These are reported in Table 1 and we note that they are very similar to those estimated in [148] and in a later work by [157]. In the allowed parameter space defined by radio, optical and X-ray observations, different combinations of the parameters predicts different SSC fluxes at 1 TeV are found, reaching at most *F* (1*TeV*) *SSC* <sup>∼</sup> <sup>2</sup> <sup>×</sup> <sup>10</sup>−<sup>13</sup> erg cm−<sup>2</sup> s −1 . This value, when attenuated by EBL, is at least one order of magnitude fainter than the one inferred from the data analysis of the MAGIC observations. In other words, the parameter space constrained by the observations

at lower frequencies is unable to account for such energetic TeV emission, and the SSC forward shock scenario fails to reproduce the observations, provided that the hint of excess found by MAGIC is a real signal from the source.

An alternative scenario that has been explored is the external inverse Compton (EIC) scenario, investigated by [157]. These authors first consider a one-zone SSC model, and reach similar conclusions to those presented by the MAGIC Collaboration [145]: the SSC mechanism predicts a TeV flux around 1–2 orders of magnitude lower than the MAGIC observations (see Figure 13, orange curves). The alternative EIC scenario is then considered by the authors, where the seed photons are provided by the extended X-ray emission and the X-ray plateau. The extended emission and the plateau are fitted using two phenomenological functions. The energy spectrum of the late-prompt emission is described by a broken power-law (see Figure 13, top and bottom panels). For the EIC model, the VHE spectrum is inferred for three different observed times (*t* = 1.1, 1.8, 2 h) and compared to the MAGIC flux averaged between 1.7 and 4 h. As can be observed in Figure 13 (bottom panel), the model flux at 2 h under-predicts the MAGIC flux (the MAGIC observed flux, green shaded area, should be compared with the EBL-absorbed model flux). We conclude that the EIC model is also unable to explain the large TeV flux suggested by MAGIC observations.

1 2 3 4 5 6 7 8 9 log10( <sup>e</sup>) 3 2 1 0 1 2 3 lo g 1 0(YS S C/EIC) YSSC/EIC at tobs = 10 3 , 10 4 , 10 <sup>5</sup> s (from thick to thin lines) YSSC, Th = ( <sup>e</sup>/ <sup>B</sup>)1/2 YSSC YEIC **Figure 13.** GRB 160821B: modeling of multi-wavelength light curves (top panel) and simultaneous SED (bottom panel) in radio, optical, X-ray and VHE band presented by [157]. ©AAS. Reproduced with permission. Two scenarios are considered: SSC (dashed orange lines) and EIC (dash-dotted green lines). In the top panel, the flux contribution in the different energy bands due to the forward shock (FS) both in the SSC and in the EIC scenario, the extended X-ray emission (EE) and the X-ray plateau emission (PL) are shown. In the bottom panel for the VHE band, both the intrinsic (thin lines) and the absorbed (thick lines) VHE curves are shown for the SSC and EIC scenarios for three different observed times. For the lower energies, the broken power-law of the late prompt emission (dashed violet line) and the expected synchrotron SEDs (solid red line) are displayed. The MAGIC observations (green symbols and green shaded area) are absorbed by EBL.


**Table 1.** GRB 160821B. List of the best fit parameters inferred from multi-wavelength modeling of the afterglow radiation by different authors.
