Simulation of High Lorentz Factor Flows from Gamma-Ray Bursts

Introduction: The plan of this work is as follow. In the first part I briefly review what is currently known about Gamma-Ray Bursts. Observations (Chapter 1) are followed by an overview on the most likely models and inner-engines (Chapter 2). One of the most relevant aspects in the Gamma-Ray Burst physics concerns relativistic hydrodynamics. Emission caused by dissipation of the kinetic energy of massive shells via shocks is commonly invoked in a large family of astrophysical phenomena, such as supernova remnants, active galactic nuclei, micro-quasars, galaxy clusters and – as I describe in Chapter 2 – Gamma-Ray Bursts. As a result, since Bell proposed the first order Fermi mechanism for non-thermal particle acceleration, there has been a strong surge of interest in blast waves dynamics, in general, and, as for Gamma-Ray Bursts, in the highly and mildly relativistic regime, in particular. However, in Chapter 3 I show how the hydro codes hitherto developed prove inadequate to properly follow the evolution of high Lorentz factor shock waves (Γ [is approx. greater than] 10). The second part of this work is dedicated to the results of the last three years of research. In Chapter 4 I deal with the corrugation stability analysis in the linear regime for accelerating hyper-relativistic shock waves which propagate in a decreasing atmosphere (Palma & Vietri, 2006). Chapter 5 contains the numerical results we obtained with regard to the non-linear counterpart of the stability analysis described in Chapter 4 (Palma et al., 2008). In Chapter 6 I present in detail a quite general numerical method I devised to follow with great accuracy the evolution of highly relativistic shock waves. Such a scheme, presented in its planar version in Chapter 5, is here generalized to cylindrical and spherical explosions (Palma et al., 2009). What I think may be the feature developments of the research hitherto