Gamma-ray burst spectral parameters within the fireball model

Fireball model of the gamma-ray bursts (GRBs) predicts generation of numerous internal shocks, which then efficiently accelerate charged particles and generate magnetic and electric fields. These fields are produced in the form of relatively small-scale stochastic ensembles of waves, thus, the accelerated particles diffuse in space due to interaction with the random waves and so emit so-called diffusive synchrotron radiation (DSR) in contrast to standard synchrotron radiation they would produce in a large-scale regular magnetic fields. In this paper we present first results of comprehensive modelling of the GRB spectral parameters within the fireball/internal shock concept. We have found that the non-perturbative DSR emission mechanism in a strong random magnetic field is consistent with observed distributions of the Band parameters and also with cross-correlations between them; this analysis allowed to restrict GRB physical parameters from the requirement of consistency between the model and observed distributions.