THE DYNAMICS AND AFTERGLOW RADIATION OF GAMMA-RAY BURSTS. I. CONSTANT DENSITY MEDIUM

Direct multidimensional numerical simulation is the most reliable approach for calculating the fluid dynamics and observational signatures of relativistic jets in gamma-ray bursts (GRBs). We present a two-dimensional relativistic hydrodynamic simulation of a GRB outflow during the afterglow phase, which uses the fifth-order weighted essentially nonoscillatory scheme and adaptive mesh refinement. Initially, the jet has a Lorentz factor of 20. We have followed its evolution up to 150 years. Using the hydrodynamic data, we calculate synchrotron radiation based upon standard afterglow models and compare our results with previous analytic work. We find that the sideways expansion of a relativistic GRB jet is a very slow process and previous analytic works have overestimated its rate. In our computed light curves, a very sharp jet break is seen and the postbreak light curves are steeper than analytic predictions. We find that the jet break in GRB afterglow light curves is mainly caused by the missing flux when the edge of the jet is observed. The outflow becomes nonrelativistic at the end of the Blandford-McKee phase. But it is still highly nonspherical, and it takes a rather long time for it to become a spherical Sedov-von Neumann-Taylor blast wave. We find that the late-time afterglows become increasingly flatter over time. But we disagree with the common notion that there is a sudden flattening in light curves due to the transition into the Sedov-von Neumann-Taylor solution. We have also found that there is a bump in light curves at very late times (~1000 days) due to radiation from the counter jet. We speculate that such a counter jet bump might have already been observed in GRB 980703.