The Effect of Angular Structure of Gamma-Ray Burst Outflows on the Afterglow Emission

Abstract

We investigate analytically the effect of an anisotropic distribution of the kinetic energy within a relativistic fireball on the decay of the afterglow emission, focusing on axially symmetric fireballs with a uniform core and a power-law decrease with angle outside the core. The afterglow fall-off steepens after the core becomes fully visible. For observer directions within the core, simple formulae are derived for the afterglow decay after the break, while for off-core observers results are shown graphically. Some criteria for assessing from observations the necessity of an angular structure and/or collimation are given. Applying them to several afterglows with light-curve breaks, we find that jets endowed with structure are required only if the circumburst medium has a wind-like (r^{-2}) stratification. Numerical fits to the multiwavelength emission of the afterglows 990510 and 000301c show that, for the former, the angular distribution of the ejecta kinetic energy is not far from uniformity, and that, with a standard power-law electron distribution, the sharp steepening of the R-band light-curve of the latter is better accommodated by a structured jet than an uniform outflow. Structured outflows may accommodate the shallower light-curve breaks observed in other afterglows.