Impact of Relativistic Fireballs on External Matter: Numerical Models of Cosmological Gamma‐Ray Bursts

We numerically model the interaction between an expanding fireball and astationary external medium whose density is either homogeneous or varies withdistance as a power-law. The evolution is followed until most of the fireballkinetic energy is converted into internal energy. The density, pressure andflow Lorentz factor profiles are shown at different stages, including shock andrarefaction wave reflections, for a fireball of initial bulk Lorentz factorGamma = 100, both in the adiabatic and non-adiabatic (radiative) regimes. Forcooling times shorter than the dynamic time, bolometric light-curves arecomputed for values of Gamma = 50, 100 and 200. We compare the numericallight-curves with analytic results, and find that for a homogeneous externalmedium there is a simple scaling relationship among light-curves obtained fordifferent parameters. The light-curves for power-law external densities aresimilar in shape to those in the homogeneous case. We discuss the implicationsof a comparison of the results with observed Gamma-Ray Burst time histories.Comment: submitted to ApJ, in press (vol. 482), latex, uses AAS macro aaspp4.sty and psfig.tex (version 1.9), 11 pages and 6 figures, revised version (more detailed comparison with the observational data