A Numerical Gamma-Ray Burst Simulation Using Three-Dimensional Relativistic Hydrodynamics: The Transition from Spherical to Jet-like Expansion

We present the first unrestricted, three-dimensional relativistic hydrodynamical calculations of the blob of gas associated with the jet producing a gamma-ray burst. We investigate the deceleration phase of the blob corresponding to the time when afterglow radiation is produced, concentrating on the transition in which the relativistic beaming 1/gamma goes from being less than theta, where gamma is the bulk Lorentz factor and theta is the angular width of the jet, to 1/gamma > theta. We study the time dependent evolution of the physical parameters associated with the jet, both parallel to the direction of motion and perpendicular to it. We calculate light curves for observers at varying angles with respect to the velocity vector of the blob, assuming optically thin emission that scales with the local pressure. Our main findings are that (i) gas ahead of the advancing blob does not accrete onto and merge with the blob material but rather flows around the blob, (ii) the decay light curve steepens at a time corresponding roughly to 1/gamma equals theta (in accord with earlier studies), and (iii) the rate of decrease of the forward component of momentum in the blob is well-fit by a simple model in which the gas in front of the blob exerts a drag force on the blob, and the cross sectional area of the blob increases quadratically with laboratory time (or distance).