Hydrodynamical Simulations of Gamma Ray-Bursts from Internal Shocks in Relativistic Fireballs

Abstract

We simulate the dynamics of the interaction between relativistically expanding spherically symmetric shells using a 1-dimensional hydrodynamic code and calculate spectra and light-curves arising from such collisions by integrating the synchrotron and inverse Compton emission of the shocked gas. The numerical results reflect the most important features observed in Gamma-Ray Bursts: the spectrum exhibits a progressive softening (its break energy decaying exponentially with the 50--300 keV photon fluence), and the pulses that form the burst appear narrower in higher energy bands. Analytical results for the most important physical parameters of the burst are obtained by solving the shock jump conditions for a pair of interacting shells, in the case when both the forward and reverse shocks are relativistic.