Impulsive and Varying Injection in Gamma-Ray Burst Afterglows

The standard model of gamma-ray burst afterglows is based on synchrotron radiation from a blast wave produced when the relativistic ejecta encounters the surrounding medium. We reanalyze the refreshed shock scenario, in which slower material catches up with the decelerating ejecta and reenergizes it. This energization can be done either continuously or in discrete episodes. We show that such a scenario has two important implications. First, there is an additional component coming from the reverse shock that goes into the energizing ejecta. This persists for as long as the reenergization itself, which could extend for up to days or longer. We find that during this time the overall spectral peak is found at the characteristic frequency of the reverse shock. Second, if the injection is continuous, the dynamics will be different from that in constant energy evolution and will cause a slower decline of the observed fluxes. A simple test of the continuously refreshed scenario is that it predicts a spectral maximum in the far-infrared or millimeter range after a few days.