Multi-wavelength Afterglows in Gamma-ray Bursts: Refreshed Shock and Jet Effects

We present an analytical approach to calculate the hydrodynamics of the interaction between a relativistic ejecta and a surrounding medium, whose evolution serves as a model for Gamma-Ray Burst afterglows. We investigate the effect of the relevant model parameters on the X-ray, optical and radio fluxes, and the effect of a refreshed shock energy input and anisotropy in the ejecta on the shape of the light-curves. We compare our numerical results to observed afterglows and give a quantitative description of the conditions (geometry and physical parameters) in the ejecta that are compatible with the light-curves of the 970508 afterglow, for which a large number of accurate flux measurements are available. We find that the radio, optical and X-ray light-curves of this afterglow can be explained satisfactorily within the spherically symmetric fireball model, assuming a delayed energy injection, or by an axially symmetric jet surrounded by a less energetic outflow. Subject headings: gamma-rays: bursts methods: numerical radiation mechanisms: non-thermal