*2.1. Spectral Properties: Sub-MeV Emission*

Currently, the wealth of observations on prompt gamma-ray burst emission in the keV/GeV energy range comes from the *Fermi*, *Swift*, *INTEGRAL*, and Konus–*Wind* satellites. The spectrum in sub-MeV energy range is commonly fitted by the so-called Band function [11], which is an empirical function consisting of low- and high-energy power laws, smoothly connected around the peak energy at which most of the energy is emitted. The observed photon spectra indices, *α* and *β* of the low- and high-energy power-laws, respectively, may serve to distinguish different radiative mechanisms and properties of the electron distribution (that emit synchrotron radiation, if it is the dominant radiative process, see below). The most recent *Fermi* GBM (Gamma-ray Burst Monitor [18]; covering ∼8 keV to 40 MeV) gamma-ray burst spectral catalogue [19] provided *α* values for time-integrated ("fluence") spectra. When selecting only the models with spectral curvature, the lowenergy index values are distributed around *α* ∼ −1.1, which is in agreement with previous findings [20,21]. Somewhat steeper low energy spectra *α* ∼ −0.7 have been reported for a *Fermi* GBM time-resolved spectral analysis of brightest bursts [22] (excluding the values obtained for simple power-law fits).

Recent works (e.g., [23,24]) provided fits to the gamma-ray burst prompt emission spectra below the spectral peak with not a single, but rather two power laws, connecting at a characteristic low energy spectral break. The break energy below which the spectrum hardened was found to be at (80–280 keV) for a sample of *Fermi* bright long GRBs [24], while it was at lower energies (3–22 keV) for a sample of GRBs contemporaneously observed by *Swift* BAT+XRT [23] (in the latter sample also *Fermi* GBM data were included when available). The importance of these fits lies in the obtained slopes, −0.6 and −1.5 below and above the break, respectively, that are consistent with the prediction of the synchrotron emission theory. A low-energy spectrum having two breaks thus may be a general property of GRB prompt emission though possibly not easily observable with present instruments. On the other hand, studies of the proposed measure of the spectral sharpness, namely the width of the spectral peak [25], showed that a large fraction of the observed GRB prompt spectra is not consistent with the theoretically expected synchrotron model under various assumptions (e.g., delta-function distribution of electrons, and Maxwellian or power-law electron distribution). This result therefore suggests emission mechanisms other than the optically thin synchrotron radiation [26].

A viable alternative is that of a thermal emission, predicted as the first signal arriving from the relativistically expanding fireball, e.g., [27,28]. The thermal spectral component was fitted in the early time-resolved spectra [29,30], or the entire time-integrated spectrum was fitted with a blackbody spectrum [31]. Several authors proposed the fit of a blackbody superimposed on the power-law component in order to fully describe the low energy portion of the spectrum [32–35]. The thermal component exhibited temporal evolution, with a characteristic rise and subsequent decay of the thermal flux. Recent works stress the importance of considering the temporal evolution of the photospheric emission: At

earlier times, ∼50% of the analyzed pulses were preferably fit with the photospheric emission [36,37].
