A Numerical Gamma‐Ray Burst Simulation Using Three‐Dimensional Relativistic Hydrodynamics: The Transition from Spherical to Jetlike Expansion

We present the first unrestricted, three-dimensional relativistichydrodynamical calculations of the blob of gas associated with the jetproducing a gamma-ray burst. We investigate the deceleration phase of the blobcorresponding to the time when afterglow radiation is produced, concentratingon the transition in which the relativistic beaming 1/gamma goes from beingless than theta, where gamma is the bulk Lorentz factor and theta is theangular width of the jet, to 1/gamma > theta. We study the time dependentevolution of the physical parameters associated with the jet, both parallel tothe direction of motion and perpendicular to it. We calculate light curves forobservers at varying angles with respect to the velocity vector of the blob,assuming optically thin emission that scales with the local pressure. Our mainfindings are that (i) gas ahead of the advancing blob does not accrete onto andmerge with the blob material but rather flows around the blob, (ii) the decaylight 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 forwardcomponent of momentum in the blob is well-fit by a simple model in which thegas in front of the blob exerts a drag force on the blob, and the crosssectional area of the blob increases quadratically with laboratory time (ordistance).Comment: 30 pages, 10 Postscript figures, uses aasms4.st