**1. Introduction**

Gamma-ray bursts (GRBs) are observed as transient sources of radiation displaying a distinctive pattern that consists of two different phases. The first phase is dominated by emission in the keV-MeV energy range, lasting from fractions of a second to several minutes, and reaching isotropic equivalent peak luminosities in the range *<sup>L</sup>*∼1049–10<sup>53</sup> erg s−<sup>1</sup> . The bimodal distribution of the prompt emission duration reveals that there are two classes of GRBs, called short and long depending on whether the prompt emission lasts shorter or longer than 2 s [1,2]. The second emission phase, called the afterglow, follows the prompt with a delay of tens of seconds, and is detected on a very wide range of frequencies, from *γ*-rays to the radio band. The afterglow flux decays smoothly as a power-law in time for weeks or months, and the typical frequency of the radiation moves in time from the X-ray to the radio band. Since 2019, the detection of a few long GRBs between 0.3 and 3 TeV on time-scales from tens of seconds to a few days proved for the first time that GRBs can also be sources of radiation in the TeV band, where they can convey a sizable fraction (20–50%) of the total energy emitted during the afterglow phase [3–5].

All this prompt/afterglow emission is identified with radiation produced as a result of the launch of an ultra-relativistic (Γ∼100–1000) jet from a newly born compact object. The ejecta first undergoes internal dissipation (through mechanisms such as shocks between different parts of the outflow [6] or magnetic reconnection episodes [7,8]). In a second moment, the ejecta undergoes external dissipation [9], triggered by interactions with the

**Citation:** Miceli, D.; Nava, L. Gamma-Ray Bursts Afterglow Physics and the VHE Domain. *Galaxies* **2022**, *10*, 66. https:// doi.org/10.3390/galaxies10030066

Academic Editors: Elena Moretti, Francesco Longo and Yi-Zhong Fan

Received: 28 February 2022 Accepted: 29 April 2022 Published: 5 May 2022

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ambient medium (e.g., the interstellar medium or the wind of the progenitor's star [10]). The two different dissipation processes occur at different typical distances from the central engine (*R*∼1013−<sup>14</sup> cm and *<sup>R</sup>*∼1015−<sup>20</sup> cm) and generate two well distinguished emission phases, identified as the prompt and afterglow emission, respectively.

For long GRBs, it is widely believed that the involved energetics and time-scales and the successful launch of a relativistic jet can find justification in the collapsar model [11,12]. In this model, the core of a massive star collapses into a black hole and the accretion from the surrounding disk powers the launch of two opposite, collimated (*θjet*∼5–10◦ ) outflows. A similar scenario also applies to short GRBs, where the black hole originates from the merger of two neutron stars (as recently proven by the association of a short GRB with a gravitational wave signal [13]) or a neutron star and a black-hole. An alternative model [14–17] considers a millisecond magnetar (i.e., a rapidly rotating neutron star) as the progenitor of long GRBs (or at least a fraction of them). This model has the advantage of more naturally explaining the detections of late time activity (102–10<sup>3</sup> s after the prompt onset) in the form of X-ray flares and plateaus, observed in about one third of the population.

Beside the nature of the progenitor's star, another quite pressing open issue in GRB physics concerns the composition of the jet itself, i.e., the nature of the dominant energy stored in the outflow, which can be either magnetic (in the form of Poynting flux [7,14]) or kinetic (i.e., bulk motion of the matter). This uncertainty reflects an uncertainty on the mechanism extracting energy from the jet (i.e., the process converting part of the jet energy into random energy of the particles), which is identified with internal shocks in the latter case, and magnetic reconnection events in the case of a Poynting flux dominated outflows [14]. While internal shocks in a matter-dominated jet have been considered the mainstream model for a long time, tensions between some model predictions and observations have moved the attention in the last decade to a family of models based on magnetic jets [18–20]. In particular, internal shocks are not an efficient mechanism [21,22], and this is in contrast with the evidence that only a relatively small fraction (10–50%) of energy is still in the blast-wave during the afterglow phase, meaning that most of it must have been dissipated and radiated away during the prompt. It must be noted, however, that the estimate of the energy content of the blast during the afterglow is indirect, and contingent upon a proper modeling of the afterglow emission [23]. Investigations that took advantage of GeV emission detected by LAT (the Large Area Telescope onboard the Fermi satellite), reached the conclusion that the blast energy is usually underestimated by studies relying on X-ray emission, and inferred a prompt emission efficiency between 1–10% [24], which is still consistent with internal shocks. The nature and efficiency of the dissipation mechanism in the prompt phase are still matters of intense debate. In any case, the radiation is expected to be produced by the accelerated electrons, which efficiently lose energy via synchrotron cooling [6,25]. Inconsistencies between the expected synchrotron spectrum and the observed spectral shape of the prompt emission [25,26] have also called into question the nature of the radiative process. Recent works have performed major advances towards the comprehension of the radiative mechanism responsible for the prompt emission, supporting the synchrotron interpretation [27–31].

The nature of the afterglow emission is much better understood, at least on its general grounds. The interaction between the jet and the external medium triggers the formation of a forward shock running into the external medium and a reverse shock running into the ejecta [32–34]. These shocks are responsible for the acceleration of particles and for the deceleration of the outflow, eventually down to non-relativistic velocities [35–37]. The observed radiation is the result of synchrotron radiation from electrons accelerated at the forward shock [38]. A contribution from the reverse shock may also be relevant, typically in the radio and optical band [34,39]. Shock formation and particle acceleration in ultrarelativistic shocks are still not completely understood. Very important progresses have been achieved in the last decade on the theoretical side (see [40] for a recent review), especially thanks to numerical particle-in-cell (PIC) simulations [41,42]. Ultra-relativistic shocks in a

weakly magnetized medium are found to be efficient particle accelerators, with *ξ<sup>e</sup>* ∼ 1% of the electrons being accelerated into a power-law distribution with spectral index *p* ∼ 2.5, carrying about *e<sup>e</sup>* ∼ 10% of the shock-dissipated energy. A strong magnetic turbulence is self-generated by the accelerated particles counter-streaming in the upstream, ahead of the shock, at a level of magnetization *e<sup>B</sup>* =0.01–0.1 [42]. PIC simulations, however, are currently probing time-scales that are orders of magnitude smaller than the dynamical time-scale of the blast-wave. This implies that results from simulations can only be extrapolated to the relevant time-scales, introducing a certain degree of uncertainty and caution in using the results as inputs for the modeling of GRB afterglows. What is still poorly understood, even though dedicated simulations are starting to give important clues [43], is how the microturbulence generated in the shock vicinity evolves (decays) with time. This is particularly important for a proper interpretation of the observations, since it is likely that the particles produce synchrotron and synchrotron-self Compton (SSC) photons in a region of decayed micro-turbulence, and hence feel a magnetic field with *e<sup>B</sup>* << 0.01.

The afterglow emission, its spectral shape from radio to *γ*-rays, and its temporal evolution from seconds to months, contain a wealth of (convoluted) information on blast dynamics, particle acceleration, magnetic turbulence generation and decay, and external density in the progenitor's surroundings (up to a parsec scale). Nevertheless, since all these ingredients are poorly constrained from theoretical grounds, they enter the afterglow physics as free, unconstrained model parameters. The large degeneracy among different parameters and the small number of observables as compared to model variables are limiting our possibility to extract valuable and robust information from the modeling of the observed afterglow radiation. To go beyond the state-of-the-art, additional efforts are necessary both on the observational and theoretical sides.

An interesting opportunity has recently opened on the observational side, thanks to the discovery that GRBs can be sources of TeV radiation associated with the afterglow phase [3,4]. The characterization of the TeV spectra and light curves offers new observables to further constrain the unknown physics of the afterglow emission. These observations are expected to impact on our current understanding of the environment where GRBs explode (and hence on the nature of their progenitors), of the physics of ultra-relativistic shocks, and of the properties of the jet (e.g., bulk Lorentz factor and energy content). Constraining the jet properties is mandatory for a correct estimate of the prompt mechanism efficiency and then for determining its nature. It is then evident how the opening of this completely new energy window in GRBs is expected to boost the studies in a field that has many connections both with the general understanding of the GRB phenomenon and with topics of general interest, such as star formation and evolution, the last stages of massive stars and their environments and plasma physics under extreme conditions.

Given the impressive amount of new information that VHE observations are going to bring to the field, it is important to revise what is the state-of-the-art, what are the main issues and how we can benefit from the few existing and the upcoming observations in the TeV domain. This review revisits the present understanding of afterglow radiation, the discovery of very-high energy (VHE, > 100 GeV) emission from GRBs and future prospects for the detection of GRBs at VHE with the next generation of Cherenkov telescopes.

For recent and complete reviews on GRB's phenomenology and theoretical interpretation before the TeV era see [44,45]. An overview focused on high-energy emission (0.1–100 GeV) observations and interpretation can be found in [46].

This review is organized as follows. Section 2 presents an overview of the afterglow external shock model, revisiting our common understanding and phenomenological description of (i) the dynamics of the blast-wave, (ii) shock formation, particle acceleration and self-generation of turbulent magnetic field in the shock proximity, and (iii) the main processes shaping the radiative output, on the whole electromagnetic spectrum, from radio to very-high energy *γ*-rays. In Section 3, we propose a discussion of the main open issues of the afterglow model, outlining which observations are at odds with model predictions, which observed features are missing in the basic scenario and what are the present

limitations that prevent us from extracting valuable information from the modeling of multi-wavelength afterglow radiation. In Section 4, we describe the recent discovery that GRBs can be bright TeV emitters. Each GRB with a firm (or with a hint of) detection by MAGIC or H.E.S.S. is discussed in detail. We present multi-wavelength observations and review the proposed interpretations of the detected emission. In Section 5, we compare the general properties of the detected GRBs both among each other and with the general population. We discuss how the TeV emission can help to solve some of the most important issues of the afterglow model. Finally, in Section 6, we discuss the prospects for future studies of TeV emission from GRBs with the next generation of Cherenkov telescopes and their expected impact on GRB physics.
