*3.2. On the Synchrotron Origin of GRB Prompt Emission*

The interpretation of the prompt emission spectrum as synchrotron from shockaccelerated electrons faced the contradicting evidence of the observed GRB spectra being harder, below the SED peak than the expected synchrotron spectral shape. Given the physical conditions of the emission region, in particular, a large magnetic field *<sup>B</sup>* <sup>∼</sup> <sup>10</sup>4−<sup>6</sup> Gauss, shock accelerated electrons should cool rapidly [177] producing a spectrum with photon index −1.5 below the synchrotron characteristic SED peak. One possible solution to this

issue [178–180] considered that electrons do not cool efficiently (so-called marginally fast cooling scenario) so that the separation between the characteristic synchrotron frequency (identified as the peak of the *νF<sup>ν</sup>* spectrum) and the cooling frequency is relatively small. As such, the hardest synchrotron spectral power law (i.e., the single electron spectrum with photon index −2/3) would become visible in the observer energy range. The tension with observations would be solved by admitting that the fitted empirical Band function captures an average spectral index between the two characteristic ones (i.e., −2/3 and −3/2 below and above the cooling break, respectively) [181]. This interpretation was recently proved valid by the discovery [182–185] in long *Swift* and *Fermi* GRBs of a spectral break distributed in the 1–100 keV range. Overall, these studies find that in a sizable fraction of bright GRBs (possibly limited by current detectors' performances - see [181]) there is a break, located at energies a factor ∼10 below the characteristic SED peak. Remarkably, the power-law indices below and above the break are consistent with the single electron synchrotron photon spectral index (−2/3) and cooling synchrotron photon index (−3/2), respectively. Further support for the synchrotron origin of the prompt emission was obtained by fitting a synchrotron model directly to the data [186,187].

While these results, after three decades of debate, represent a step forward to unveiling the synchrotron nature of the prompt emission, they present further challenges [188]. If the break is interpreted as the cooling synchrotron frequency, it implies a small magnetic field (*B* ∼ 10 G) in the emission region. If the latter is located relatively close to the central engine (as suggested by the observed small variability timescales) the Synchrotron Self Compton (SSC) emission would become relevant though its signature has not been clearly observed at GeV energies by *Fermi*/LAT. Possible solutions, consider emission in a downstream decaying magnetic field (e.g., [189]) or proton-synchrotron emission [188] (but see [190]).
