Impact of relativistic fireballs on external matter: Numerical models of cosmological gamma-ray bursts

We numerically model the interaction between an expanding fireball and a stationary external medium whose density is either homogeneous or varies with distance as a power law. The evolution is followed until most of the fireball kinetic energy is converted into internal energy. The density, pressure, and flow Lorentz factor profiles are shown at different stages, including shock and rarefaction wave reflections, for a fireball of initial bulk Lorentz factor Γ = 100 in both the adiabatic and the nonadiabatic (radiative) regimes. For cooling times shorter than the dynamic time, bolometric light curves are computed for values of Γ = 50, 100, and 200. We compare the numerical light curves with analytic results and find that for a homogeneous external medium there is a simple scaling relationship between light curves obtained for different parameters. The light curves for power-law external densities are similar in shape to those in the homogeneous case. We discuss the implications of a comparison of the results with observed gamma-ray burst time histories.