Perspective on Afterglows: Numerically Computed Views, Lightcurves and the Analysis of Homogeneous and Structured Jets with Lateral Expansion

Abstract

Herein I present numerical calculations of lightcurves of homogeneous and structured afterglows with various lateral expansion rates as seen from any vantage point. Such calculations allow for direct simulation of observable quantities for complex afterglows with arbitrary energy distributions and lateral expansion paradigms. A simple, causal model is suggested for lateral expansion of the jet as it evolves; namely, that the lateral expansion kinetic energy derives from the forward kinetic energy. As such the homogeneous jet model shows that lateral expansion is important at all times in the afterglow evolution and that analytical scaling laws do a poor job at describing the afterglow decay before and after the break. In particular, I find that lateral expansion does not cause a break in the lightcurve as had been predicted. A primary purpose of this paper is to study structured afterglows, which do a good job of reproducing global relationships and correlations in the data and thus suggest the possibility of a universal afterglow model. Simulations of structured jets show a general trend in which jet breaks become more pronounced with increasing viewing angle with respect to the jet axis. In fact, under certain conditions a bump can occur in the lightcurve at the jet break time. I derive scaling relations for this bump and suggest that it may be a source of some bumps in observed lightcurves such as that of GRB 000301C. A couple of lateral expansion models are tested over a range of efficiencies and viewing angles and it is found that lateral expansion can, in some cases, substantially sharpen the jet break. I show flux surface contour maps and simulated images of the afterglows which give insight into how they evolve and determine their lightcurves.