We propose a model for the spectral formation of Gamma Ray Burst (GRB) prompt emission, where the phenomenological Bands function is usually applied to describe the GRB prompt emission. We suggest that the GRB prompt emission is mainly a result of two upscattering processes. The first process is the Comptonization of relatively cold soft photons of the star off electrons of a hot shell of plasma of temperature T_e of the order of 10^{9} K (or kT_e~100 keV) that moves sub-relativistically with the bulk velocity V_b substantially less than the speed of light c. In this phase, the Comptonization parameter Y is high and the interaction between a blackbody-like soft seed photon population and hot electrons leads to formation of a saturated Comptonization spectrum modified by the sub-relativistic bulk outflow. The second process is an upscattering of the previously Comptonized spectrum by the plasma outflow once it becomes relativistic. This process gives rise to the high-energy power-law component above the peak in the EF(E)-diagram where F(E) is the energy flux. The latter process can be described by a convolution of the Comptonized spectrum with a broken-power-law Green function. Possible physical scenarios for this second upscattering process are discussed. In the framework of our model, we give an interpretation of the Amati relation between the intrinsic spectral peak photon energy and radiated energy or luminosity, and we propose a possible explanation of the GRB temporal variability.
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