| The origin of Gamma-Ray Bursts, one of the long-standing mysteries of modern Astrophysics, has been recently established observationally by the discovery of the afterglows that follow them. The correlations between the temporal and spectral features manifested by these afterglows are in accord with the predictions of the relativistic fireball model, giving it a very strong support. Here we model the dynamics and radiation emission of fireballs interacting with an external medium and compare some of the results with the observations.; First we present a one-dimensional code to solve ultra-relativistic hydrodynamic problems, using an exact Riemann solver for the treatment of discontinuities. The accuracy of the code is investigated in tests involving strong shocks and Lorentz factors of up to 2000. With the aid of the hydrodynamic code we model the fireball-external medium interaction and calculate burst spectra and light-curves arising from synchrotron radiation and inverse Compton scatterings by non-thermal electrons accelerated at shocks. We investigate the effect of varying the most important model parameters on the resulting burst spectra, and we present a set of correlations among the spectral and temporal features of the bursts. Multi-pulse structures are simulated using a variable magnetic field and the most important properties of these pulses are compared with observations. The fireball dynamics is further followed to study the afterglow spectral evolution.; We analyze the shape of the equal photon arrival time surfaces for different dynamic and radiative regimes, and tabulate the most relevant parameters describing the source brightness distribution over these surfaces, which are useful for more accurate analytic estimates of the afterglow evolution.; We also present an analytical approach to calculate the dynamics of decelerated fireballs. It is a flexible approach, that can be easily extended to include more complex situations, such as a continuous injection of energy at the reverse shock, and the sideways expansion in non-spherical ejecta, and is computationally much less expensive than hydrodynamic simulations. We investigate the effects of the model parameters on the X-ray, optical and radio fluxes, as well as those of a refreshed shock energy input, anisotropy in the ejecta, and jet sideways expansion. |
