**1. Introduction**

The recent observation of Gamma-Ray Bursts (GRB) in the Very High-Energy domain (VHE, *E* > 100 GeV) [1,2] marked an extraordinary milestone in our understanding of these outstandingly powerful transients. From the moment of their first identification as cosmological sources [3–5], it was immediately clear that their luminosity ranged up to

**Citation:** La Mura, G.; Barres de Almeida, U.; Conceição, R.; de Angelis, A.; Pimenta, M.; Tomé, B.; Miceli, D. Probing Gamma-Ray Burst VHE Emission with the Southern Wide-Field-of-View Gamma-Ray Observatory. *Galaxies* **2021**, *9*, 98. https://doi.org/10.3390/ galaxies9040098

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Academic Editor: Yi-Zhong Fan

Received: 29 September 2021 Accepted: 5 November 2021 Published: 8 November 2021

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values as high as *<sup>L</sup>* <sup>∼</sup> <sup>10</sup><sup>52</sup> erg s−<sup>1</sup> , making them the brightest sources of electromagnetic radiation known in the Universe and requiring an extremely efficient energy production mechanism. At present it is thought that GRBs arise as the consequence of ultra-relativistic shocks in magnetized plasma jets, which are launched in the fast accretion process that follows the collapse of very massive stars (*M* > 20 M) or the merger of compact stellar remnants, such as neutron stars (NS) and black holes (BH), to form a *magnetar* or a new BH [6,7]. The conversion of the huge amount of gravitational binding energy and thermal energy into kinetic and radiative power, within fractions of a second, triggers the emission of intense radiation, through mechanisms that naturally lead to the production of highenergy photons.

In general, a GRB is characterized by two emission regimes: an initial pulse of radiation, named *prompt* emission, most frequently observed in the energy range between 100 keV and 1 MeV and characterized by fast and strong variability [8], followed by a smoothly decaying *afterglow* phase, which can be detected from the radio and optical frequencies all the way up to energetic *γ* rays. The prompt phase lasts only a few seconds and it can be used to distinguish between a class of short GRBs, where the prompt emission takes place for less than 2 s, and one of long GRBs, whose prompt radiation is emitted for longer times [9–11]. These two classes can be fairly well interpreted by different types of source, with the long GRBs being more likely associated with a massive star core-collapse event [12,13], while the short ones can be better reproduced in the compact binary merger scenario [7,14], as confirmed by the Multi-Messenger observation of GRB 170817A in connection with GW170817 [15–17].

Apart from the generally well-understood picture, the nature of GRBs and of their radiation mechanisms still poses many difficult questions. On one side, there are solid theoretical arguments that predict energetic radiation from relativistic magnetized plasmas. On the other hand, the explanation of the spectral and temporal properties is not totally consistent with simple leptonic scenarios. It is very likely that synchrotron emission should be the dominant radiation mechanism for GRBs, as argued, e.g., in [18–20]. However, the variability that is observed down to millisecond timescales in the prompt stage [21] implies compact emission regions, where the magnetic and radiative energy densities are so high that the radiative cooling should consequently be very fast and produce soft spectra [22]. This is inconsistent with the observational evidence [23,24]. Many different possibilities, invoking thermal components, re-acceleration mechanisms or non-leptonic scenarios e.g., [25–27], have been proposed to address this problem.

The observation of VHE photons has a crucial role in the identification of the radiation mechanisms at work. These photons can be produced as a consequence of shocks between relativistic blobs in the jet (internal shocks, probably dominant during the prompt stage), as well as between the jet and the external environment (external shocks, expected to occur in the afterglow). In addition, they require compact sources in relativistic motion, to escape the production site. VHE radiation can be observed at the ground, using either Imaging Atmospheric Cherenkov Telescopes (IACT), such as MAGIC [28] and H.E.S.S. [29], or Extensive Air Shower (EAS) particle detector arrays, such as HAWC [30] and LHAASO [31]. At present, IACTs have been able to firmly detect VHE emission in the afterglow of some powerful GRBs. It is very likely that the next-generation Cherenkov Telescope Array (CTA) [32] will further improve our ability to investigate the VHE signal of GRBs. However, due to their small field of view (FoV) and to the consequent requirement to be alerted and pointed towards the source, these instruments can only track GRBs with a certain delay after their actual onset.

Here we describe the scientific opportunities that can be explored by means of EAS arrays. Thanks to their large FoV, which grants a continuous sky coverage of more than 1 sr, these instruments have a higher chance to probe the early phases of GRB emission, without the necessity of an external trigger. We discuss the issue taking into account the characteristics of an array concept based on Water Cherenkov Detectors (WCD) and investigated by the Southern Wide-field-of-view Gamma-ray Observatory collaboration

(SWGO) [33]. Our work is structured as follows: in §2 we present the theoretical framework of GRB emission; in §3 we describe the known and the expected VHE properties of GRBs; in §4 we discuss the detection opportunities of an instrument such as SWGO; finally, in §5 we summarize our conclusions.

#### **2. Theoretical Framework**

Despite several decades of investigation, we do not yet have a complete theory for GRBs. What we know for sure is that the presence of high-energy *γ* rays with a nonthermal spectrum implies emission from a highly relativistic source. This result stems from the well-known *compactness problem* [34,35]. A relatively simple argument can be used to illustrate the concept. A bright GRB has a time integrated energy flux, or *fluence*, of the order of *<sup>F</sup>* <sup>∼</sup> <sup>10</sup>−<sup>7</sup> erg cm−<sup>2</sup> , which is approximately related to the total emitted energy *E* by:

$$E = 4\pi D\_L^2 F \approx 10^{50} \text{erg} \left(\frac{D\_L}{3000 \,\text{Mpc}}\right)^2 \left(\frac{F}{10^{-7} \,\text{erg} \,\text{cm}^{-2}}\right) \tag{1}$$

where *<sup>D</sup><sup>L</sup>* is the luminosity distance. The typical variability timescale is *<sup>δ</sup><sup>T</sup>* <sup>≈</sup> <sup>10</sup>−<sup>2</sup> s, implying an emitting region size limit *R* 6 *cδT* ≈ 3000 km. As a result, the source would be characterized by an extremely high radiation density. High-energy photons can produce electron-positron pairs whenever the condition √ *E*1*E*<sup>2</sup> > 2*mec* 2 is met. Introducing a probability factor *f<sup>p</sup>* that accounts for the likelihood of the pair production mechanism, we obtain a pair production opacity of:

$$\tau\_{\gamma\gamma} = \frac{f\_p \sigma\_T \text{FD}\_L^2}{\text{R}^2 m\_c c^2 (1+z)} \approx \frac{10^{13} f\_p}{1+z} \left(\frac{\text{F}}{10^{-7} \text{erg} \,\text{cm}^{-2}}\right) \left(\frac{D\_L}{3000 \,\text{Mpc}}\right)^2 \left(\frac{\delta T}{10^{-2} \text{s}}\right)^{-2}, \tag{2}$$

where *σ<sup>T</sup>* denotes the Thomson scattering cross-section. For typical GRB characteristics, the opacity predicted in Equation (2) is very large and should result in a thermal spectrum, in clear contradiction with observational evidence. If we allow the source to be a blob of plasma, approaching in a relativistic motion with bulk Lorentz factor Γ, at small angles with respect to the line of sight, and characterized by a power-law energy spectrum *N*(*γ*) ∝ *γ* −*α* , the energy and the rate of arrival of the observed photons are both a factor Γ higher than the corresponding values in the emission frame. Due to the Doppler effect on frequency, this implies that the photons that we observe at a given frequency are a factor of Γ <sup>2</sup>*<sup>α</sup>* denser than what would be seen in the emitting frame. The size of the emitting region is also affected by relativistic contraction, implying that *Rem* 6 Γ 2 *cδT*. Thus, Equation (2) should be corrected to:

$$\pi\_{\gamma\gamma} \approx \frac{10^{13} f\_p}{(1+z)\Gamma^{(4+2a)}} \left(\frac{F}{10^{-7} \text{erg} \, \text{cm}^{-2}}\right) \left(\frac{D\_L}{3000 \, \text{Mpc}}\right)^2 \left(\frac{\delta T}{10^{-2} \, \text{s}}\right)^{-2} \tag{3}$$

that since 1 < *α* < 3 and *f<sup>p</sup>* < 1, predicts an optically thin regime when the condition <sup>Γ</sup> <sup>&</sup>gt; <sup>10</sup>13/(4+2*α*) <sup>≈</sup> <sup>10</sup><sup>2</sup> is satisfied.

Similar order of magnitude considerations could be drawn to estimate the predicted spectrum. When reproducing GRB spectra starting from theoretical considerations, it is common use to introduce a set of free parameters containing some assumptions due to unknown properties of the detailed structure of the jet, the ongoing acceleration process and the shock micro-physics. In particular, an unknown fraction of the energy dissipated through the shock will go to the particle distribution and to the magnetic field. To account for this effect, two normalization parameters *e<sup>e</sup>* and *eB*, expressing, respectively, the fractions of total energy carried by the particles and the magnetic field, are then introduced. When particles are accelerated in shock waves through the Fermi mechanism, we expect a resulting power-law energy distribution in the form of *N*(*γ*) ∝ *γ* <sup>−</sup>*<sup>p</sup>* and magnetic fields that can be as large as *<sup>B</sup>* <sup>≈</sup> <sup>10</sup><sup>4</sup> G [36]. If the radiating species are electrons and positrons,

the energy is quickly converted into radiation, through the emission of fast pulses of synchrotron and Compton scattered photons, with a spectral form similar to the one illustrated in Figure 1 [37,38]. As a result, we expect that GRBs should in principle be powerful sources of transient VHE emission, although the most energetic part of the spectrum is prone to pair production opacity on the Extragalactic Background Light (EBL) photons, which implies suppression of the most energetic radiation from sources located at large cosmological distances [39–41].

**Figure 1.** Spectral energy distribution expected for a relativistic blob of plasma, with bulk Lorentz factor Γ = 300, moving with an inclination of *ϑ* = 1 o from the line of sight and carrying a magnetic field *B* = 10<sup>4</sup> G. The radiating particles are assumed to be electron-positron pairs in a power-law distribution *N*(*γ*) ∝ *γ* <sup>−</sup>2.5, with 10 6 *γ* 6 10<sup>6</sup> . The red line represents synchrotron emission, while the blue line shows the inverse Compton scattering contribution. The resulting spectrum is represented as a continuous black line. The dashed curves illustrate the effects of *γγ*-opacity on the Universe background radiation for redshifts 0.25 6 *z* 6 1, in steps of 0.25.

Although the scenario depicted above can in principle justify the energies and the spectra that we see in GRBs, it is nonetheless prone to many important problems. The pulselike appearance of the prompt stage light curve is consistent with the presence of particle acceleration processes, followed by a rapid cooling. The typical burst duration, however, requires many acceleration events or an effective supply of energetic particles, to match the data. A critical aspect is the onset and the duration of the production of the most energetic photons [42]. If they are emitted as a continuation of the synchrotron spectrum, they should be highly correlated with the low energy radiation. On the contrary, the interaction of several emitting regions, or the presence of non-leptonic contributions, can lead to the prediction of delayed high-energy emission [43]. Although the currently available observations tend to favor a delayed detection of energetic photons, the existence of earlier VHE contributions is not ruled out and it represents a critical factor to discriminate between different possible scenarios. More accurate spectral models would need to take into account the evolution of the system and the probably important effects of non-homogeneity and orientation. We also must consider the possibility that the existence of very energetic photons (up to the TeV scale) in a presumably dense environment can lead to important

photo-hadronic interactions and, therefore, to potentially much more elaborated spectral forms. This type of processes is actually expected to occur when the jet plasma collides with the external environment, therefore taking a major role in the afterglow emission. The true nature of GRBs in their initial stages, however, will only be clarified when precise spectral and temporal information on their most energetic emission at early times are obtained.
