Multi-Wavelength Afterglows in Gamma-Ray Bursts: Refreshed Shock and Jet Effects

Abstract

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.

14 pages, 3 figures, to appear in ApJ, vol. 503; revised version, errors in some equations corrected, Figure 1 altered (includes a new parameter: the electron injection fraction), the discussion of the inhomogeneous external medium case (section [4]) was extended, references up-dated