*5.5. The TeV Contribution to the Multi-Wavelength Modeling*

Modeling of multi-wavelength afterglow data provide important insights concerning the GRB afterglow physics. In particular, the VHE data were crucial to investigate (i) the radiation mechanisms responsible for the production of photons between 10–100 GeV already detected by LAT; (ii) the environmental conditions at the GRB site; (iii) the free parameters which describe the shock micro-physics, and in particular, the self-generated magnetic field.

The modelings proposed so far in literature to explain the VHE component have considered two different radiation processes at the origin of the TeV emission: SSC and synchrotron. In the first case, the VHE emission is interpreted as a distinct spectral component from the synchrotron radiation dominating from radio to ∼ GeV energies, which provides the seed photons that are upscattered at higher energies by the same electron population. In the second scenario, the VHE emission is observed as the extension of the synchrotron spectrum up to TeV energies.

In principle, a simultaneous SED covering the X-ray, HE and VHE range should be sufficient to discriminate among these two different possibilities. A hardening of the spectrum from GeV to TeV energies should be the smoking gun for the presence of a distinct component. In reality, the uncertainties in the spectral slope at VHE (caused by the uncertainty on the EBL and on the narrow energy range of TeV detection) can make the distinction hard to perform. In this case, LAT observations are of paramount importance to reveal the presence of a dip in the SED, which would also prove the need to invoke a different origin for the VHE emission. This seems to be the case for GRB 190114C, for which, at least in one SED, the LAT flux strongly suggests a dip in the GeV flux and hence the presence of the characteristic double bump observed for a synchrotron-SSC emission (Figure 20). For GRB 190829A, LAT provides only an upper limit, which is not constraining for modeling the shape of the SED (Figure 25). In this GRB, an interpretation of the whole SED in terms of synchrotron radiation cannot be excluded, although a modeling as SSC radiation has been proven to be successful [72] (Figure 23). For the other events detected at VHE, either the data do not allow for building a proper SED with simultaneous multi-wavelength observations, or they are not yet public. Despite this, the SSC emission seems to be the most viable mechanism able to explain the TeV data. A firm conclusion on the responsible radiation mechanism has not been reached yet and future detections will be crucial for deeper investigations.

Assuming one of the two scenarios, TeV data coupled with broad band observations at lower energies can be exploited to give additional information on the details of the afterglow external forward shock scenario.

Concerning the shock micro-physics, several modelings have suggested the possibility that the fraction of electrons accelerated in non-thermal distribution, *ξ<sup>e</sup>* , is different from the standard value of one, which is usually assumed. In a few GRBs' modelings, namely for GRB 190114C [185] and GRB 190829A [72,198], the introduction of a *ξ<sup>e</sup>* < 1 was essential in order to consistently fit the observational data. In particular in [72], the requirement for a low value of *<sup>ξ</sup><sup>e</sup>* . 6.5 <sup>×</sup> <sup>10</sup>−<sup>2</sup> was required to provide an acceptable fit of the data. The other modelings assume a greater value of *ξ<sup>e</sup>* , around ∼0.3. Further detections will be exploited in order to verify if such an indication could be present also in other events.

Some considerations can also be drawn for the equipartition parameters *e<sup>e</sup>* and *eB*. These values, especially the former one, are usually well unconstrained and can span several orders of magnitudes. The TeV modeling described so far suggest that around <sup>∼</sup>10% of the energy is given to the electrons, while a lower value (from <sup>10</sup>−<sup>5</sup> to 10−<sup>3</sup> ) is given to the magnetic field. larger values of *e<sup>B</sup>* such as 0.1–0.01, which are considered in an external shock scenario, are excluded. Moreover, some results can also be interpreted as an indication of an evolution in time of these parameters. In Figure 22, the modeling of the broad band light curves of GRB 190114C is shown. Two different modeling are presented: one optimized for the early time X-ray, HE and VHE observations (solid line) and one optimized for the late time lower energy bands (dotted line). This is due to the fact that the model that reproduces the early time data over-predicts the late time optical and radio observations. This result points towards the possibility that some of the fixed parameters of the afterglow theory (e.g., the electron and magnetic field equipartition parameters) may evolve in time. A further clue of the presence of time-dependent shock micro-physics parameters is derived from the low frequency multi wavelength modeling of GRB 190114C presented in [121]. In order to model the optical and the radio data, it is required that the micro-physical parameters evolve with time as *e<sup>e</sup>* ∝ *t* <sup>−</sup>0.4 and *e<sup>B</sup>* ∝ *t* 0.1 in the ISM case and *e<sup>B</sup>* ∝ *t* 0.76 for the stellar wind scenario.

An issue that still is not solved by TeV observations is the discrimination between constant and wind-like profile for the ambient density. It is expected that long GRBs occur in wind-like environments. Nevertheless, at the current stage there seems to be no preference between such an environment and a constant ISM one, which is able to well reproduce the observational data. Therefore conclusive answers on the topic cannot be drawn yet.

In conclusion, the current population of GRBs at VHE already demonstrate quite broad properties, spanning more than three orders of magnitude in *Eγ*,*iso* and more than two orders of magnitude in terms of afterglow luminosity and ranging in redshift between 0.079–1.1. The afterglow X-ray and VHE emission have comparable fluxes and decay slopes. The afterglow emitted power in the VHE band seems to constitute from 15% up to 60% of the X-ray one. Data modeling suggest that the responsible VHE radiation mechanism is the SSC emission, although different mechanisms (e.g., synchrotron radiation, EIC) cannot be completely excluded and a conclusive answer cannot be given yet. Multi-wavelength modeling show no preferences concerning the GRB environments between an ISM or wind-like scenario and indicate that shock micro-physics parameters, which seem to be able to reproduce VHE emission, are *<sup>ε</sup><sup>e</sup>* <sup>∼</sup> 0.1 and *<sup>ε</sup><sup>B</sup>* <sup>∼</sup> <sup>10</sup>−5–10−<sup>3</sup> . Such features can be an indication of the universality of TeV emission in GRBs. It is then expected that a larger sample of GRBs than the current one will be detected in the VHE band, including also short GRBs for which, at the current stage, there are no confirmed detections except for the hint of excesses observed for GRB 160821B.
