*5.2. Redshift and the Impact of EBL*

The redshift of the detected GRBs covers a broad range, from *z* = 0.079 (GRB 190829A) to *z* = 1.1 (GRB 201216C). The impact of the EBL attenuation on the spectrum is severely changing, depending on the redshift value and on the photon energy. For redshift z ∼ 0.4, the impact becomes relevant for energies & 0.2 TeV with a flux attenuation of ∼50% for 0.2 TeV and almost ∼99.5% for 1 TeV [183]. For nearby events (*z* . 0.1–0.2), the effect of EBL is less severe and becomes relevant only for energies & 0.3 TeV, reaching an attenuation factor of an order of magnitude only for energies & 2 TeV. As a result, the GRB observed photon indices and the energy range of detected TeV photons differs significantly between the events. GRBs with redshift *z* > 0.4 such as GRB 190114C or GRB 180720B have very steep photon indices and they are detected in the lower energy range up to 0.44 TeV for GRB 180720B and 1.0 TeV for GRB 190114C. Spectral analysis from GRB 201216C are not yet public but preliminary results indicate that the emission is concentrated in the lower energy band between 0.1–0.2 TeV. Nearby GRBs with redshift *z* . 0.1–0.2 such as GRB 160821B or GRB 190829A show a less steep photon spectrum (around −2.5) and the TeV detection range extends above 1 TeV. The detection of several GRBs with significant value of redshift (*z* > 0.4) is robust proof that IACTs can overcome the limitations due to the EBL absorption and can expand the VHE detection horizon at the current stage up to *z* = 1.1. On the other hand, it is evident that detection of nearby GRBs is fundamental in order to more robustly explore the spectral shape, unbiased by the EBL effect, which is a non-negligible source of uncertainty for higher redshifts.

## *5.3. Energetics*

In terms of *Eγ*,*iso*, the VHE GRB sample spans more than three orders of magnitude from <sup>∼</sup>10<sup>49</sup> erg up to <sup>∼</sup><sup>6</sup> <sup>×</sup>10<sup>53</sup> erg. The five long GRBs detected follows the Amati correlation, as shown in Figure 28. GRB 160821B, the only short GRB of the sample, is consistent with the existence of a possible Amati-like correlation for short GRBs, with this event falling in the weak-soft part of the correlation. The detections of GRB 190829A and GRB 201015A show that an event does not need to be extremely energetic in terms of isotropic-equivalent prompt energy in order to produce a TeV emission with (intrinsic) luminosity comparable to the X-ray luminosity. As a result, sources with *<sup>E</sup>γ*,*iso* <sup>∼</sup> <sup>10</sup>50−<sup>51</sup> erg are not excluded as possible TeV emitters, even though their detection is possible only for relatively low redshift. This reduces the available volume, and hence the detection rate of similar events. In any case, this is relevant also for short GRBs which are less energetic than long ones, with typical isotropic energies falling within the <sup>∼</sup>1049−<sup>52</sup> erg range [144].

**Figure 28.** The Amati (*Epeak*–*Eiso*) correlation for a sample of 136 long GRBs (grey dots, from [230]) and a sample of 11 short GRBs (empty blue squares) detected by Swift. The corresponding power-law fit for the sample of long GRBs and the 3*σ* scatter of the distribution of points around the best fits are shown. The six GRBs detected in VHE are also added in the plot. Adapted from [231].
