The Jet Angular Profile and the Afterglow Light Curves

We investigate how the angular structure of GRB jets effects the afterglow light curves at different viewing angles, $\theta_{v}$, from the jet symmetry axis. A numerical hydrodynamical modeling for the evolution of a relativistic collimated outflow, as it interacts with the surrounding medium, is carried out, and compared to two simple models that make opposite and extreme assumptions for the degree of lateral energy transfer. The Lorentz factor, $\Gamma$, and kinetic energy per unit solid angle, $\epsilon$, are initially taken to be power laws of the angle $\theta$ from the jet axis. We find that the lateral velocity in the comoving frame, $v'_\theta$, is typically much smaller than the sound speed, $c_s$, as long as $\Gamma\gg 1$, and the dynamics of relativistic structured jets may be reasonably described by a simple analytic model where $\epsilon$ is independent of time, as long as $\Gamma(\theta=0)\ga$ a few. We perform a qualitative comparison between the resulting light curves and afterglow observations. This constrains the jet structure, and poses problems for a `universal' jet model, where all GRB jets are assumed to be intrinsically identical, and differ only by our viewing angle, $\theta_{v}$.