The self-consistent keV to TeV spectra of gamma-ray bursts produced by the synchrotron-self-Compton emission in relativistic shocks

The spectra of Gamma-Ray Burst (GRB) emission have been investigated theoretically by a number of authors (e.g., [ 1, 2, 3]) for different versions of a general fireball-shock scenario [4, 5]. However, the existing models give rather coarse predictions and suffer from many uncertainties. Here we present a refined analytical model of synchrotron-self-Compton (SSC) emission. We take an arbitrary injection spectrum of relativistic particles and let them cool self-consistently, taking into account both synchrotron and inverse Compton (IC) losses and making corrections for the Klein-Nishina cut-off. When two-photon absorption is negligible, the problem is reduced to the single integral equation for the ratio of synchrotron to total losses as a function of particle's energy. The spectra of synchrotron and IC components, as well as the electron distribution, can be derived from this function in a regular way. The low-energy portion of the composite synchrotron spectrum in the fast cooling regime may have spectral index varying from 1/2 to 1, and the spectrum of the IC component is nearly flat around its maximum.