2.4.1. The LGRB-Supernova Connection

The possible connection between LGRB and massive progenitor stars has been speculated long before the first afterglow detection [23,36]. The first observational evidence came with the association between the broad line Type Ic (Ic-BL) SN 1998bw and the low-luminous LGRB 980425 at *z* = 0.0085 and with lack of an optical afterglow [37]. Later on, this association was also confirmed between the Type Ic-BL SN 2003dh, temporally and spatially coincident with the standard more luminous long GRB 030329 at *z* = 0.1685, with an optical afterglow light curve comparable with other cosmological GRBs [38].

The launch of *Swift* has increased the sample of GRB-SN pairs, both spectroscopic, at *z* . 0.5 and most of them with isotropic-equivalent *γ*-ray energies *E*iso < 10<sup>49</sup> erg, and photometric, in the form of SN bumps appearing in the optical afterglows 10–30 days<sup>6</sup> after the GRB, at *<sup>z</sup>* & 0.5 and *<sup>E</sup>*iso <sup>≈</sup> <sup>10</sup><sup>51</sup> <sup>−</sup> <sup>10</sup><sup>52</sup> erg [36]. Most of the GRB-SN pairs belong to this second kind, very likely at the hand of a selection effect: the more common lowluminosity LGRBs per unit volume are not detectable at high redshift, whereas luminous LGRBs, with higher detectability at high redshift, are observed from a larger volumetric area [39].

SNe Ic associated with some long GRBs are characterized by no hydrogen (H) and no weak helium (He) lines [36]. Their occurrence close to star-forming regions offers very strong evidence that long GRBs could be associated with massive star death [36]. In this regard, the best progenitor candidates are the Wolf–Rayet stars, very massive stars with a hydrogen envelope largely depleted, endowed with a fast rotation [23,40]. Within the collapsar model, very massive stars are able to fuse material in their centers all the way to iron (Fe). At this point, they cannot continue to generate energy through fusion and collapse mechanisms forming a BH. Matter from the star around the core rains down towards the center and swirls into a high-density accretion disk. In this picture, the core carries high angular momentum to form a pair of relativistic jetsout along the rotational axis where the matter density is much lower than in the accretion disk. Jets propagate through the stellar envelope at velocities approaching the speed of light, creating a relativistic shock wave at the front [15,41]. If the star is not surrounded by a thick, diffuse H envelope, the leading shock accelerates as the stellar matter density decreases. Thus, by the time it reaches the star surface, Γ ≥ 100 is attained and the energy is released in the form of *γ*-ray photons [15,41].

The collapsar model attempts to explain the time structure of GRBs' prompt emission, through the modulation of the jets by their interaction with the surrounding medium, which could produce the variable Lorentz factor needful for internal shock occurrence [23]. As the relativistic jet propagation through the stellar envelope of a collapsing star proceeds, its collimation was shown to occur analytically and numerically [15]. Another prediction of this model is the prolonged activity of the central engine which can potentially contribute to the GRB afterglow [23,40,41]. This occurs because the jet and the disk are inefficient at ejecting all the matter in the equatorial plane of the pre-collapse star and some continues to fall back and accrete [23,40,41].

The SNe associated with LGRBs appear to belong to the bright tail of type Ic SNe and can be considered as a "subclass" of SNe Ic, alternatively addressed as *hypernovae*, in order to emphasize the extremely high energy involved in these explosions. Remarkably, the SNe associated with both low- and high-luminous (XRFs and normal LGRBs, respectively) share very similar spectra and their peak luminosities span only two orders of magnitude, whereas the associated GRBs isotropic luminosities span six orders of magnitude [36]. Another distinctive feature of the GRB-SN pairs is the high photospheric expansion velocity, up to 0.1*c* [36]. In this scenario, one has to also fit the class of ULGRBs. The spectroscopic detection of the SN 2011kl coincident with the ULGRB 111209A [42] favors a common core-collapse origin for LGRBs and ULGRBs. This SN exhibited a peculiar, very blue and featureless spectral shape, which was unlike other SNe Ic associated with LGRBs, but more like the newly discovered class of superluminous SNe [43]. Other ULGRBs have either been too far or too dust-extinct to secure any detection of an underlying SN, whereas other

cases proved the indicative flattening from a rising SN in their optical and NIR light curves at 10–20 days after the GRB trigger [36].

In this picture, however, exceptions to the LGRB-SN association have been found from deep optical observations in two nearby bursts, GRB 060505 and GRB 060614, for which the hypothetical accompanying SN would have been a hundred times fainter than SN 1998bw [44–46].

To conclude, ULGRBs and SNless LGRBs give proof for the existence of further progenitor channels for LGRBs.

#### 2.4.2. SGRBs, Macronovae, and Gravitational Waves

The *Swift* satellite has enabled rapid and precise localizations and an increase in the number of X-ray and optical afterglow detection of both LGRBs and SGRBs. However, SGRBs have less luminous afterglows than those of LGRBs and this fact makes difficult to obtain optical spectra and a precise burst location to plan optical follow-up to search for host galaxy associations. The lack of any associated core-collapse SNe, the typically large offsets of the GRB position with respect to galaxy center, and the frequent association with galaxies with no ongoing star formation, provide evidence in support of a compact binary merger progenitor scenario [47].

The proposed progenitors for SGRBs are NS–NS and/or NS–BH binary mergers [24,48–50]. These mergers take place as binary orbits decay due to gravitational radiation emission [51]. A merger releases <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>53</sup> erg, but most of this energy is due to low energy neutrinos and gravitational waves. Thus, there is enough energy available to produce a GRB, notwithstanding how a merger generates the relativistic wind required to power a burst is still the object of speculations and not well understood. It has been argued that about one out of thousand of these neutrinos annihilates and produces pairs that in turn produces *γ*-rays via *νν*¯ → *e* +*e* <sup>−</sup> → *γγ*, but it has been pointed out that a large fraction of the neutrinos would be swallowed by the newly-born BH [15].

A further confirmation to the binary merger scenario consists of the detection of the so-called *macronova* (MN). The MN emission originates in NS-BH or NS-NS mergers from a fast-moving, rapidly-cooling ejected debris of neutron-rich radioactive species that decay to form transient emission and create atomic nuclei heavier than iron through neutron capture process, named the *r-process* [52]. The opacities of these produced heavy elements lead to a dim MN emission, requiring deep follow-up observations down to NIR bands. The first indication of a MN, in the form of a re-brightening, detected approximately nine days after the GRB trigger, has been obtained by extensive follow-up of the SGRB 130603B, one of the nearest and brightest SGRBs ever detected [53]. An MN emission accompanies also the nearest SGRB ever detected, SGRB 160821B [54,55], and the recently detected SGRB 200522A [56]. For a list of other MN emissions, see Ref. [57].

In the binary merger scenario, SGRBs are expected to be significant sources of gravitational waves (GWs). The smoking gun occurred on 17 August 2017, when the Advanced LIGO and Virgo detectors observed the event GW 170817, unambiguously detected in spatial and temporal coincident with the SGRB 170817A independently measured by the *Fermi* Gamma-ray Burst Monitor, and the Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory [58] 7 .

As a further confirmation on the nature of the progenitor system of SGRB 170817A, an intense observing campaign from radio to X-ray wavelengths over the following days and weeks after the trigger led to the spectroscopic identification of a MN emission, dubbed AT 2017gfo [59].

The observation of SGRB, GW, and MN emission has improved our understanding of the physical properties related to the binary merger, such as the mass of the compact object, the ejected mass, and the details of the CBM surrounding the merger site.

#### *2.5. Observable Quantities from GRBs*

Understanding GRB physics passes through the experimental evidence of the energy that can be collected from detectors. In particular, we can start discussing about GRB prompt emission. It is typically observed in the hard-X (above ∼ 5 keV) and *γ*-ray energy domain.

The operative duration of the prompt emission is due to the previously defined *t*90. Within this time interval, and also within any sub-interval with enough photons to perform a significant analysis<sup>8</sup> , the observed spectral energy distribution (SED) of GRBs is nonthermal, and it is best fitted by a phenomenological model composed of a smoothly joined broken power-law called *Band* model [60] (see Figure 2). Its functional form is

$$N\_{\rm E}(E) = K \begin{cases} \left(\frac{E}{100}\right)^{\alpha} \exp\left[\frac{(2+\alpha)E}{E\_{\rm P}^{\rm obs}}\right] & \text{, } E \le \left(\frac{\alpha-\beta}{2+\alpha}\right) E\_{\rm P}^{\rm obs} \\\\ \left(\frac{E}{100}\right)^{\beta} \exp(\beta-\alpha) \left[\frac{(\alpha-\beta)E\_{\rm P}^{\rm obs}}{(2+\alpha)}\right]^{\alpha-\beta} & \text{, } E > \left(\frac{\alpha-\beta}{2+\alpha}\right) E\_{\rm P}^{\rm obs} \end{cases} \tag{1}$$

where typical power-law index values are −1.5 . *α* . 0 (with an average h*α*i ' −1) and −2.5 ≤ *β* ≤ −1.5 (with an average h*β*i ' −2), while the peak energy at the maximum of the of the *E* <sup>2</sup>*N*<sup>E</sup> (or *EF*E) spectrum lies within <sup>100</sup> keV <sup>≤</sup> *<sup>E</sup>* obs <sup>p</sup> . few MeV (with an average of h*E* obs p i ' 200 keV). Finally, *K* is the normalization constant with units of photons cm−<sup>2</sup> s <sup>−</sup>1keV−<sup>1</sup> . In some cases, the SED is also best fitted by a power-law model<sup>9</sup> composed of a power-law plus an exponential cutoff. However, these models are purely mathematical, i.e., not yet physically linked to GRB intrinsic properties. Hence, fitting data with them do not provide any insight about the emission physical origin but may be useful for the classification scheme of GRBs and for comparing the fitted results with the predictions of different theoretical models.

**Figure 2.** Band spectral model applied to the data of GRB 990123. In the upper panel, the photon spectrum is shown; in the lower panel, the *E* <sup>2</sup>*N*<sup>E</sup> (or *EF*E) spectrum is shown. Courtesy from Ref. [60].

In the recent years, with a much broader spectral coverage enabled by detectors such as Fermi, evidence for more complicated broad band spectra fitted by a combined Band+thermal model has been found in an increasing number of bursts [61–64], where the peak of the thermal component is always observed below *E* obs p .

However, the search of the best-fit model in describing GRB prompt emission spectra depends on the analysis method. Typically, a significant spectral analysis is performed when enough photons are collected. For weak bursts, only time-integrated spectral analyses can be done, and this implies that important time-dependent features may be lost or averaged, leading to a wrong theoretical interpretation. Another issue is that the chosen spectral model is convolved with the detector response and, because of the nonlinearity of the detector response matrix, this procedure cannot be inverted. Therefore, two different models can equally provide a similar minimal difference between the model and the detected counts' spectrum and lead to different theoretical interpretations.

From the fit of the time-integrated prompt emission spectrum, one can get the flux *F* (in units of erg cm−<sup>2</sup> s −1 ) on a detector energy bandpass *E*min–*E*max as

$$F = \kappa \int\_{E\_{\rm min}}^{E\_{\rm max}} EN\_{\rm E}(E) dE \, \text{ \,\tag{2}$$

where *κ* is a constant, commonly used to convert the energy, expressed in keV, to erg.

To compute the total energy emitted by a GRB in all wavelengths, a bolometric spectrum is needed. However, the GRB prompt emission triggers *γ*-rays detectors in a given energy bandpass; therefore, a limited part of the spectrum is available, instead of a bolometric one. Moreover, GRBs are cosmological sources spread over a wide redshift range, so, for GRBs observed by the same detector, the measured energy range corresponds to different energy bands in the cosmological rest frame of the sources.

To standardize all GRBs, fluxes are computed in the fixed rest-frame band 1–10<sup>4</sup> keV, which is a range larger than that of most of the *γ*-ray detectors. The "bolometric" timeintegrated flux is then given by

$$F\_{\rm bolo} = F \times \frac{\int\_{1/(1+z)}^{10^4/(1+z)} EN\_{\rm E}(E) dE}{\int\_{E\_{\rm min}}^{E\_{\rm max}} EN\_{\rm E}(E) dE} \; , \tag{3}$$

and the total isotropically-emitted energy and luminosity are, respectively,

$$E\_{\rm iso} = -4\pi d\_L^2 F\_{\rm bolo} t\_{90} (1+z)^{-1} \tag{4}$$

$$L\_{\rm iso} = \, 4\pi d\_L^2 \mathcal{F}\_{\rm bolo} \tag{5}$$

where the factor (1 + *z*) −1 corrects the *t*<sup>90</sup> duration from the observer frame to the GRB cosmological rest-frame. In a similar way, the peak luminosity *L*p, computed from the observed peak flux *F*<sup>p</sup> within the time interval of 1 s around the most intense peak of the burst light curve and in the rest frame 30–10<sup>4</sup> keV energy band10, is given by

$$L\_\mathbf{P} = 4\pi d\_\mathbf{L}^2 \mathbf{F}\_\mathbf{P}.\tag{6}$$

The luminosity distance *d*<sup>L</sup> depends upon the cosmological models adopted as backgrounds and can be related to the continuity equation recast as

$$\frac{d\rho}{dz} = \Im\left(\frac{P+\rho}{1+z}\right),\tag{7}$$

which relates the total energy density *ρ* and pressure *P* to the barotropic factor *ω*(*z*) ≡ *P*/*ρ* of a given cosmological model. For a two component flat background cosmology composed

of standard pressure-less matter with *ω* = 0 and a generic DE component with *ω*(*z*) (dubbed generically *ω*CDM), the luminosity distance is then given by<sup>11</sup>

$$d\_{\mathcal{L}}(z) = (1+z)\frac{c}{H\_0} \int\_0^z \frac{dz'}{\sqrt{\Omega\_{\mathcal{m}}(1+z')^3 + \Omega\_{\mathcal{k}} f\_{\mathcal{k}}(z')}} \,\,\,\tag{8}$$

where *H*<sup>0</sup> is the Hubble constant, Ω<sup>m</sup> and Ω<sup>x</sup> are the cosmological density parameters of matter and DE, respectively, and *f*x(*z*) is given by

$$f\_{\mathbf{X}}(z') = \exp\left[\mathfrak{Z} \int\_0^{z'} \frac{\mathbf{1} + w(\mathbf{z})}{\mathbf{1} + \mathfrak{Z}} \mathbf{d}\mathbf{z}\right]. \tag{9}$$

For the concordance paradigm, namely the ΛCDM model, the DE equation of state is *w*(*z*) ≡ −1 corresponding to a cosmological constant Λ. Thus, *f*<sup>x</sup> ≡ 1 and Ω<sup>x</sup> ≡ ΩΛ. In the following, the choice *w*(*z*) ≡ −1 is adopted, unless otherwise specified.

The above isotropic energy output can be corrected for the beaming (see Section 3), once the jet opening angle *θ* is known, leading to beam corrected energy

$$E\_{\gamma} = (1 - \cos \theta) E\_{\text{iso}} \,. \tag{10}$$

It is important to stress that the prompt emission is not limited to the *γ*-rays and that, differently from the afterglow emission starting ∼ 100 s after the GRB trigger, current information in other energy bands is extremely difficult to observe without fast triggering. Observations at lower energies (optical and X-rays) have been enabled only for GRBs with a precursor or a very long prompt emission duration, which gave the possibility of performing fast pointing to the source during the prompt phase [66].

Regarding the GeV energy domain, a delayed (with respect to the trigger), long lived emission (& 10<sup>2</sup> s), and separate lightcurve [67] with a decaying luminosity as a power law in time, *L*GeV ∝ *t* <sup>−</sup>1.2 has been observed [67]. These distinctive features point towards a separate origin of the GeV with respect to the lower energy photons.

After ∼ 100 s since the trigger, the prompt emission starts to decay in flux and, in many cases, this feature is caught by X-ray detectors *Swift*-XRT within the 0.3–10 keV energy band. In general, X-ray afterglow light curves show complex behaviors [15] consisting of (see Figure 3):


**Figure 3.** The X-ray afterglow of GRB 060729 with all the three power-law segments and an initial flare clearly shown.

The X-ray afterglow is also characterized by the presence of a flaring activity [15]. The observed behavior of these flares, the rapid rise, and exponential decay together with a fluence comparable in some cases to the prompt emission, points out that the same mechanism for the prompt emission is responsible for the flaring activity [15]. Concluding, as already stressed above, these X-ray afterglow features are important to understand the nature of GRB progenitors.
