3.6.1. Synchrotron Emission and Inverse Compton Scatterings

Among the non-thermal radiative processes, synchrotron emission from relativistic electrons has been considered an important mechanism in the context of the prompt emission of GRBs [79,135,174–176]. Several authors have taken a general approach and determined the source properties (e.g., jet bulk Lorentz factor, electrons' Lorentz factor, distance from the central engine to location where gamma-ray are produced) by assuming that the peak of the gamma-ray emission spectrum is produced by the synchrotron process (e.g., [31,130,132,177]; for the case of a magnetic jet, see, e.g., [178]). The major challenge for the synchrotron model is posed by the observed hard low energy spectrum that is in apparent contradiction with the predictions of the simple synchrotron model (e.g., [99,138,179]). The flux *f<sup>ν</sup>* ∝ *ν* <sup>−</sup>1/2 below the peak of the spectrum is expected when electron's radiative time scales are much shorter than the dynamical times ('fast-cooling regime') [99]. We define *γ<sup>c</sup>* as the Lorentz factor of electrons whose synchrotron loss timescale is equal to the adiabatic cooling timescale *t*ex, *γ<sup>c</sup>* = 6*πmec*/(*σTB* 2 *t*ex), where *m<sup>e</sup>* is the electron's mass, *c* is the speed of light, and *σ<sup>T</sup>* is the Thomson cross-section. The synchrotron fast-cooling regime is then characterized by *γ<sup>c</sup>* < *γm*. This regime is favorable for prompt gamma-ray emission as it has a high radiative efficiency. There have been several studies reconciling the observed spectrum with the synchrotron emission, and proposing solutions for harder spectral slope: The pitch-angle distribution [138], the small scale structure of the magnetic field [180,181], or processes that involve the appearance of a quasi-thermal component in addition to non-thermal synchrotron [27,182].

It is also possible to have the synchrotron mechanism responsible for the GRB prompt phase, however modified by including an additional source of cooling due to inverse Compton scatterings [183–186]. The soft low-energy spectral slope of the photon spectrum *α* = −1.5, resulting from the assumption of fast cooling synchrotron spectrum, could be hardened if a sub-dominant radiative process (like inverse Compton scatterings) transferred around 20–40% of the energy from the synchrotron component to higher energies [185]. There are two parameters that control the importance of inverse Compton scatterings:

*w<sup>m</sup>* = *γmem*, where *e<sup>m</sup>* = *hνm*/*mec* <sup>2</sup> and *ν<sup>m</sup>* = *ν*(*γm*), determine whether the scatterings occur in the Thomson regime (*w<sup>m</sup>* 1) or if Klein–Nishina effects need to be taken into account; another parameter is YTh, which determines the intensity of the inverse Compton component peaking at high energies. When Klein–Nishina corrections are important (*w<sup>m</sup>* & 1), the cross section and the energy boost are reduced so that the ratio of the total energy in the inverse Compton component over the total energy in the synchrotron component becomes Eic/Esyn YTh [131]. It has been shown that the physical conditions in the emitting region allow for a synchrotron component peak at ∼ a few 100 keV, and a moderately efficient inverse Compton scatterings in the Klein–Nishina regime. In particular, in the internal shock scenario [185], a large fraction of the dissipated energy *e<sup>e</sup>* ∼ 0.1–1/3 should be injected in a small fraction of electrons *ζ* . 0.01 and the fraction of the energy injected in the magnetic field should remain low, *e<sup>B</sup>* . 10−<sup>3</sup> . Additionally, the 'marginally fast cooling regime' was proposed by [185], considering that electrons are in the fast cooling regime but not deeply in this regime (i.e., *γ<sup>c</sup>* . *γ<sup>m</sup>* rather than *γ<sup>c</sup> γm*). When the cooling frequency becomes close to the frequency *νm*, the observed photon index can become very close to the value −2/3 below the cooling frequency, even in the fast cooling regime. This solution requires collisions at small radii and/or low magnetic fields. However, in this context, and focusing on conditions where synchrotron cooling is balanced by a continuous source of heating, one naturally finds solutions consistent with those of the minijets model in the magnetically dominated jet described above [187], where dissipation occurs far from the central engine.

High energy gamma-rays in the prompt GRB phase could be also produced by inverse Compton scattering of synchrotron photons: "synchrotron-self-Compton" SSC emission. However, in its simplest form, this mechanism either produces a more energetic component in very high energy gamma-rays or would require a more energetic component as a lowenergy synchrotron seed, which is inconsistent with observations [143,188]. On the other hand, the SSC it is defined in the beginning of the paragraph origin of GRB prompt emission seems to work well in the context of the relativistic turbulence model [142].
