*5.4. X-ray Lightcurves*

The comparison between TeV and X-ray light-curves suggests an intimate connection between the emission in these two bands, both in terms of emitted energy and luminosity decay rate. In Figure 29, the XRT afterglow light-curves (luminosity versus rest-frame time) in the 0.3–10 keV energy range are compared with the VHE light-curves (integrated over different energy ranges, depending on the detection window, see Table 4). Different colors refer to the six different GRBs. The VHE luminosity is shown with empty circles.

Considering the X-ray luminosity, the GRB sample can be divided into two groups: GRB 190114C, GRB 180720B and GRB 201216C display large and clustered X-ray luminosity (at *<sup>t</sup>* <sup>∼</sup> <sup>10</sup><sup>4</sup> s their luminosity is around 1–5 <sup>∼</sup> <sup>10</sup><sup>47</sup> erg s−<sup>1</sup> ) and their light curves almost overlap for the entire afterglow phase. The other three GRBs (GRB 190829A, GRB 201015A and GRB 160821B) are much fainter in terms of X-ray luminosity (at least two orders of magnitude at *<sup>t</sup>* <sup>∼</sup> <sup>10</sup><sup>4</sup> s). This is consistent with the fact that they also have a smaller *Eγ*,*iso*. The correlation between X-ray afterglow luminosity and prompt *Eγ*,*iso* is found in the bulk of the long GRB population, and these GRBs make no exception.

Observations in the VHE band (empty circles in Figure 29) reveal that the VHE luminosities observed in the afterglow phase are in general smaller but comparable to the simultaneous X-ray luminosity, implying that almost an equal amount of energy is emitted in the two energy bands. Any theory aimed at explaining the origin of the TeV radiation should explain the origin of these similarities. Concerning the decay rate, observations are still not conclusive. The decay rate of the TeV emission is available only for two events. For GRB 190829A, the temporal indices in X-ray and VHE are very similar, while for GRB 190114C, the VHE clearly decays faster than the X-ray emission.

For GRB 190114C at *<sup>t</sup>* <sup>∼</sup> <sup>380</sup> s, the VHE luminosity *<sup>L</sup>VHE* is <sup>∼</sup>1.5–2.5 <sup>×</sup>10<sup>48</sup> erg s−<sup>1</sup> and the X-ray one *<sup>L</sup><sup>X</sup>* is <sup>∼</sup>0.6–1.0 <sup>×</sup>10<sup>49</sup> erg s−<sup>1</sup> . As a result, the power radiated in the VHE band is about ∼25% of the X-ray one. Similarly for GRB 190829A at *t* ∼ 4.5 h the VHE luminosity *<sup>L</sup>VHE* is <sup>∼</sup>4.0–8.5 <sup>×</sup>10<sup>44</sup> erg s−<sup>1</sup> , which is around ∼15–20% of the corresponding X-ray one (*L<sup>X</sup>* <sup>∼</sup> 2.0–5.0 <sup>×</sup>10<sup>45</sup> erg s−<sup>1</sup> ). For GRB 180720B at *<sup>t</sup>* <sup>∼</sup> <sup>2</sup> <sup>×</sup> <sup>10</sup><sup>4</sup> s the VHE luminosity *LVHE* is <sup>∼</sup><sup>9</sup> <sup>×</sup>10<sup>47</sup> erg s−<sup>1</sup> and the X-ray one *<sup>L</sup><sup>X</sup>* is <sup>∼</sup>1.5–2.5 <sup>×</sup>10<sup>49</sup> erg s−<sup>1</sup> . In this case, the power radiated in the VHE band is around ∼35–60% of the X-ray one.

**Figure 29.** X-ray and VHE luminosity versus rest-frame time for the six GRBs detected in the TeV domain. The X-ray light-curve in the 0.3–10 keV energy range is taken from the Swift Burst Analyzer webpage <sup>8</sup> .
