**5. Advances in GRBs Studies and Open Issues at VHE**

The detection of a VHE signal from GRB by MAGIC and H.E.S.S. (particularly GRB 190829A) provided a puzzling and unexpected complexity of scenarios, mainly due to the differences between the phenomenology of the observed events. GRB 190114C and GRB 190829A are events that stand on the opposite edges of the GRB energy distribution being on the <sup>∼</sup>30% sub-sample of more energetic burst for GRB 190114C (*E*iso <sup>=</sup> <sup>3</sup> <sup>×</sup> <sup>10</sup><sup>53</sup> erg) and more than three orders of magnitude lower for GRB 190829A (*E*iso <sup>=</sup> <sup>2</sup> <sup>×</sup> <sup>10</sup><sup>50</sup> erg). The two events also significantly differ in their temporal profile at VHE, with an extremely bright VHE emission lasting ∼15 min for GRB 190114C and a dimmer but much longer-lasting emission for GRB 190829A (up to few days after GRB onset). On the other hand, GRB 180720B, which is more similar to GRB 190114C, was detected several hours after the event's onset. In order to exemplify these differences, we reported in Figure 12 (left panel) the value of the bulk Lorentz factor (Γ0) at the beginning of the afterglow phase, evaluated for a large sample of GRBs [91] once known their isotropic equivalent energy. The positions of the VHE-detected GRBs are overplotted, from which a different nature of GRB 190829A might be pointed out, although both events lie on the so-called Amati relation (Figure 12 right panel). This is an indication that the observed differences in luminosity and energy are not related to a different geometry of the emission (i.e., GRB 190829A is not an off-axis event). On the other hand, gamma rays of such high energies largely exceed the synchrotron burn-off limit, implying the coexistence of an extra emission component in the VHE band. However, the attempt of broadband modeling of the two events led to a different physical interpretation of the VHE emission. While GRB 190114C has been satisfyingly modeled within a synchrotron + SSC emission scenario, the H.E.S.S.S. collaboration reported an alternative hypothesis for GRB 190829A. In particular, in [3], it was proposed the possibility to interpret the VHE radiation as a synchrotron extending well above the burn-off limit at the time of H.E.S.S. observations. Although intriguing, such an interpretation has been challenged by other works, where, again, a synchrotron+SSC approach seems favorable in modeling the broadband spectrum without requiring peculiar and unconventional choices of the GRB microphysical parameters [86]. Whether an SSC component is at work in all GRBs and which is the maximum energy achievable by different emission mechanisms are still some of the open points that can be addressed with more observations of GRBs at VHE. The tension on the modeling side is also the result of the limited number of VHE GRBs detected up to now, and of the available multi-wavelength (MWL) data collected simultaneously. In particular, *Fermi*-LAT can be of great importance since it covers the energy range where the transition from the synchrotron radiation to the possible SSC component is expected, as exemplified by the case of GRB 190114C. However, such availability of MWL data might not be common, especially if GRBs are detected in the VHE range at late times, when the flux can be below the sensitivity of, e.g., *Fermi*-LAT. Such lack of MWL data can introduce difficulties in the modeling, or lead to degeneracy of the modeling parameters. From this perspective, early VHE follow-up seems to have an advantage, with a higher probability of having more simultaneous MWL data available for later modeling (e.g., the GRB is still bright enough to be detected by instruments such as *Fermi*-LAT). Furthermore, the prompt-to-early-afterglow phase, with the coexistence of forward and reverse shocks in the emitted outflow, could also lead to a large variety of different and interesting emitting scenarios in the VHE band. In this regard, while a deeper understanding of the afterglow phase at VHE is due, one of the next challenges is the detection of VHE emission in the prompt phase. The debate on the physical process at the origin of the prompt emission is still open, with different possibilities missing a clear observational proof. A detection of the prompt emission in the VHE range could resolve such a long-lasting issue, giving a new perspective on this poorly known phase of GRBs. The challenge for IACTs is the short duration of the prompt phase, compared to the delivery times of the alerts from triggering instruments and the time for their reaction. In particular, *T*<sup>90</sup> alone is not a good indicator of the duration of the prompt phase and of the nature of a GRB, as already debated within the GRB community (see, e.g., [92,93]). Therefore,

long-duration GRBs with *T*<sup>90</sup> of the order of hundreds of seconds (e.g., GRB 190114C) can also have prompt phases with a much shorter duration, as shown by the spectral and temporal analysis of the GRB light curves. For this reason, ground-based instruments such as HAWC https://www.hawc-observatory.org/ (that already reported results on GRB observations [94]), LHAASO (http://english.ihep.cas.cn/lhaaso/), and the future SWGO (https://www.swgo.org/SWGOWiki/doku.php) (all websites accessed on 10 April 2022) could be more suited, given their high-duty cycle and sky coverage, with the downside of a higher energy threshold.

**Figure 12. Left panel:** Correlation between the bulk Lorentz factor at the beginning of the afterglow phase (Γ0) and the isotropic equivalent energy Eiso for the sample of GRB reported in [91]. **Right panel:** the empirical correlation (Amati relation) between the isotropic equivalent energy Eiso and the peak energy of the GRB spectrum for the same sample in [91] and for the events detected in the VHE band. In both panels, GRBs followed-up by IACTs are denoted by green and red symbols, indicating those with and without detection, respectively. Reprinted with permission from Ref. [95].

An additional challenge for IACTs is the detection of short GRBs. While they are located (on average) at smaller redshift with respect to long GRBs, they are also less luminous, making a detection with IACTs difficult. Currently, the strongest evidence for a VHE emission component from short GRBs was reported by MAGIC for GRB 160821B [96]. The telescope's fast response played a major role, despite the adverse observational conditions (reduced atmospheric conditions, relatively high zenith of the observation, and increased night sky background due to the presence of the Moon). A signal at the level of <sup>3</sup>*<sup>σ</sup>* (post-trial) was found with a flux upper limit of 1.1 <sup>×</sup> <sup>10</sup>−<sup>11</sup> cm−<sup>2</sup> s −1 in the first half hour, giving the possibility to perform interesting studies on the expected energy flux at VHE in an MWL context [96]. The SSC model was found to be in tension with the data, nonetheless a firm detection and a higher statistics is needed to rule out this possibility. Such a discovery would be of utmost importance to understand if there are similarities at VHE between long and short GRBs. Moreover, short GRBs are intimately connected with searches of gravitational waves (GWs) from their progenitors. A coincident detection of a short GRB and GWs would allow a comprehensive picture of the system leading to the GRB itself, and of its following evolution.

Finally, the detection of other GRBs at VHE can open up the possibility of interesting studies on more fundamental topics. VHE signal from these events might be extremely valuable for probing external *γ* − *γ* absorption due to the EBL out to larger redshifts than the ones that can be typically reached with other extragalactic sources, such as blazars. Another possibility could involve the searches for Lorentz invariance violation (LIV), where distant GRBs with high-energy photons can considerably improve the sensitivity of the resulting lower limit (see, e.g., [97] for a LIV study using GRB 190114C data). VHE GRB data can also be used for the search of axion-like particles (ALPs), where we expect spectral signatures and a reduction of the optical depth, leading to a lower absorption with respect to the expectation from the EBL (see, e.g., [98]). The GRBs detected so far at VHE confirmed that a low–moderate redshift is still a necessary condition for the detection for current IACTs, especially if the luminosity is towards the low end of the distribution. GRB 201216C,

detected at *z* = 1.1, stands as an outsider and can represent an interesting case study for possible EBL or LIV studies. This is indeed a promising result for the next generation of Cherenkov telescopes that, thanks to improved sensitivity and energy threshold, might further extend the gamma-ray horizon of these observations.

#### **6. The Next Decades**

The Cherenkov Telescope Array Observatory (CTAO) represents the next-generation ground-based observatory for the study of VHE gamma rays. It will consist of two arrays, one for each hemisphere, made up of IACTs of different size and characteristics. The CTA array will routinely perform follow-up observations of GRB triggers and other transients objects also coming from other cosmic signal, such as neutrino and gravitational waves [99]. The estimation of the detection prospects for such observations are necessarily still preliminary and are dependent on the final array layout and performance. Nonetheless, even starting with simplified assumptions about the GRB emission, the CTA Consortium already reported the possibility of detecting ∼hundreds (or more) of photons from moderate to bright GRB, allowing for a significant improvement in the photon statistics and for the possibility to have good-quality time-resolved spectra [100]. The preliminary results reported in such a study show the possibility of detecting up to few GRB per year (considering both arrays) and allowing to move rapidly from the single-case GRB study, such as for current IACT, to a full GRB population study at VHE. In order to confirm these early results and achieve a step forward in the determination of CTA's prospects for GRB follow-ups, the CTA Consortium is currently working on a new study where the potential detection rate is estimated using a theoretical-based approach. Such an approach is based on the *POpulation Synthesis Theory Integrated code for Very high energy Emission* (POSyTIVE) model for GRBs [101]. The aim is to build a GRB population based on few intrinsic properties and assumptions such as Epeak and redshift distribution, Epeak-Eiso correlation (Amati relation) [102], and the bulk Lorentz factor distribution obtained by measured the time of the afterglow onset (providing the bulk Lorentz factor of the event's coasting phase). The population obtained (for both long and short GRBs) is calibrated against a wide dataset of multi-wavelength observations. In order to derive the final expected spectrum, both the prompt and the afterglow emission are simulated according to a standard leptonic synchrotron+SSC emission model [14]. The GRB spectra obtained are then used to simulate the detailed CTA response through the use of dedicated analysis pipelines based on gammapy (https://gammapy.org/) and ctools (http://cta.irap.omp.eu/ctools/) (accessed on 27 April 2022) and making use of the most recent instrument response functions (IRFs). The results of this study are expected by the end of 2022.

In the framework of the CTA, the earliest science operations have recently started thanks to the large-sized telescope prototype (LST-1). LSTs are the largest telescopes designed for CTA, having a 23 m diameter reflector. The first prototype, LST-1 (Figure 13 left panel), is located at the Roque de los Muchachos observatory (28.8◦ N, 17.8◦ W, 2200 m a.s.l.), on the Canary Island of La Palma [103], the designed site for the CTA north array. Thanks to the reflective surface of about 400 m<sup>2</sup> , the LST-1 will be able to achieve an energy threshold of ≈20 GeV, a value particularly suitable for transients and high-redshift source observations. Furthermore, LSTs are built with a light carbon-fiber structure in order to reduce the total weight of the telescope to about 103 tons and to make possible the fast repositioning (∼30 s for 180◦ azimuth displacement) to catch early emission phases of transient objects. LST-1 was inaugurated in October 2018 and is currently finalizing its commissioning phase. Starting from the first months of 2021, the time allocated for technical observations has been gradually reduced, allowing the first observations of targets of astrophysical interest. Transients follow-up, including GRBs, have the highest priority among LST-1 observed targets. Although a fully automatic procedure that will allow the telescope to react automatically to incoming alerts is still under development, the first observations of GRBs have been performed [95]. Preliminary analysis did not reveal VHE emission associated with any of the observed alerts; however, the continuous effort in improving the telescope's performance and robustness will soon place LST-1 in a key position for VHE observations of those peculiar events, making it a noticeable testbench for the forthcoming full-configured CTA array.

**Figure 13.** (**Left**) The LST prototype during night operation in La Palma. Picture credit: Tomohiro Inada. (**Right**) GRB detection rate for one of the CTA arrays as a function of the expected LST energy threshold. The curves represent two possible empirical assumptions for GRB spectrum at very high energy; one considering a simple extrapolation of the band emission up to VHE (solid black), the other considering an additional emission component (dashed blue). Reprinted with permission from Ref. [100].

The firm detection of a signal extending up to the multi-TeV band for GRB 190829A has opened new interesting possibilities for observations also with IACTs not specifically designed for transients follow-up, such as the small-sized telescopes (SST) foreseen for the CTA. An interesting example is the case of the ASTRI mini-array, composed of nine imaging atmospheric dual-mirror Cherenkov telescopes at the Teide Observatory site on the Canary Island of La Palma [104]. The telescopes will have a relatively small primary mirror of ∼4 m diameter, allowing to detect gamma rays in the 0.5–200 TeV range. Despite the corresponding limited gamma-ray horizon accessible, the authors in [105] proved the feasibility of the ASTRI mini-array to detect bright and nearby GRBs. This would guarantee to cover, with high sensitivity, the extreme edge of the VHE band, complementing the data collected at lower energies with instruments such as the LSTs.

#### **7. Conclusions**

VHE observations provide a new channel to study the physics of GRBs in an energy range particularly important for the discrimination of different emitting scenarios and for the constraint of the GRBs' physical parameters in space. The detection of GRBs at VHE represents one of the major breakthroughs for transient astrophysics in the last years. This result was finally achieved thanks to the relentless efforts and the continuous improvements on both the technical and the observational strategy side by current IACTs collaborations. The small sample of detected events shows a large variety of phenomenology that leaves some questions unanswered, creating difficulties in finding a possible common interpretative scenarios. In all detected events, VHE emission has been observed on timescales much longer than the corresponding prompt phase, confirming the results already observed in the GeV band. However, besides the detection of bright and powerful events, that for a long time were assumed to be the best candidates for VHE emission, relatively low-luminosity events also showed long-lasting emission up to the TeV band. This suggests that the detection of these GRBs is likely not unique and the VHE component might be a relatively common feature of many GRBs, although observable only under favorable conditions by IACTs. Whether *all* GRBs have a VHE emission component and whether the parameter space of a possible VHE-emitter GRB is larger than what was previously thought, this will be one of the key issues for the next generation of IACTs, namely, the CTAO. Short timescale transients (including GRBs) have been one of the key motivations when designing the different elements of the CTA, and in particular the LSTs, whose first prototype recently started its operation in the Canary Island of La Palma. Once fully configured, a detection rate of the order of a few bursts per year might be expected, allowing us to build and

characterize the GRB population at VHE. Furthermore, the achievable photon statistics would allow CTA to study the spectral and temporal properties of GRBs, shedding light into unresolved issues such as determining the jet formation dynamics and the mechanisms of particle acceleration.

**Author Contributions:** The authors contributed equally to this work. The authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors acknowledge the anonymous referees for their useful comments.

**Conflicts of Interest:** The authors declare no conflict of interest.
