**3. Theory of GRB Progenitors**

GRBs require progenitor systems able to guarantee enough energy for their powerful explosions to occur and emission mechanisms that can explain the above discussed spectral features. Although it is essential to better understand the physics of GRBs, neither clear evidence for consolidated classes of suitable progenitors nor a definitive GRB model have been yet established, as stressed above. However, observations, in the form of GRB spectra and light curves (see Section 2.5) and correlations between observable quantities (see Sections 6.1 and 7), enhanced our comprehension of these phenomena and led to a general agreement on a few aspects listed below [69]:



The observed spectra have a considerable amount of *γ*-ray photons. Photons with high energy *E*<sup>1</sup> annihilate with those at a low energy *E*<sup>2</sup> and produce *e* +*e* <sup>−</sup> pairs if √ *E*1*E*<sup>2</sup> & *mec* 2 (up to an angular factor), where *m<sup>e</sup>* is the electron mass. If GRBs were not relativistic sources, the observed light curve variability time scale of *δt* ≈ 10 ms would imply that their emission would originate from a very compact region not larger than *R* = *cδt* ≈ 3000 km. For typical values of the luminosity distance *<sup>d</sup><sup>L</sup>* <sup>≈</sup> 3Gpc <sup>≈</sup> <sup>10</sup><sup>22</sup> cm and fluence *<sup>S</sup>* <sup>≈</sup> <sup>10</sup>−<sup>7</sup> erg cm−<sup>2</sup> (energy at the detector per unit area) of GRBs, the opacity for pair creation is enormous, and it is given by [69]

$$\pi\_{\gamma\gamma} = f\_{\varepsilon^{\pm}} \frac{\sigma\_T d\_l^2 S}{m\_\varepsilon c^2 (c\delta t)^2} \approx 10^{14} f\_{\varepsilon^{\pm}} \tag{12}$$

where *f <sup>e</sup>*<sup>±</sup> is the fraction of photons with energies sufficient to produce pairs and *σ<sup>T</sup>* is the Thomson cross-section. Such a large optical depth would imply that that the source must be optically thick leading to a thermal spectrum. On the contrary, observations indicate that GRB spectra are typically non-thermal, pointing to the opposite conclusion that their source must be optically thin. This issue is called the *compactness problem* [69].

However, the problem is only apparent, once relativistic effects are taken into account. In fact, the causality limit of a source moving relativistically with bulk Lorentz factor Γ 1 towards the observer is *R* ≤ Γ 2 *cδt*. Consequently, the observed photons are blue-shifted and their energy at the source is lower by a factor ≈ 1/Γ, which may be insufficient for pair production. This leads to a decrease in the opacity, by a factor Γ −2(*β*+1) , where the *β* is the high-energy power-law index of a photon spectrum of the burst. For Γ & 100, one obtains the optically thin condition of the source. Ultra-relativistic expansion of GRBs is unprecedented in astrophysics. There are indications that relativistic jets in active galactic nuclei have Γ ∼ 2–10, but some GRBs have Γ & 100. These large expansion velocities in GRB outflows find confirmations from the radio scintillation observed in their afterglows, and also from the apparent observation of self-absorption in the radio spectrum of the afterglow, where it is possible to obtain independent estimates of the dimensions of the afterglow relic [15].
