Gamma-ray bursts with continuous energy injection and their afterglow signature

(Abridged) We discuss a Gamma-ray burst (GRB) fireball with an additional energy injection, either in the form of a Poynting-flux-dominated outflow or a kinetic-energy-dominated matter shell injected after the burst. A total injection energy comparable to that of the impulsive energy in the initial fireball is required to make a detectable signature in the afterglow lightcurves. For the case of a Poynting-flux-dominated injection, this leads to a gradual achromatic bump feature. For the case when the injection is kinetic-energy-dominated, the collision between the rear (injected) and the forward shell mild if the relative velocity between the colliding shells does not exceed a critical value defined by their energy ratio. Otherwise, the injection is violent, and an additional pair of shocks will form at the discontinuity between two colliding shells, so that there are altogether three shock-heated regions from which the emission contributes to the final lightcurves. We describe the shell-merging process in detail and present broadband lightcurves with the injection signatures. A violent collision results in very complicated features, which differs from the gradual bump signature found in the Poynting-flux or mild matter injection cases. In all the cases, the energetics of the fireball as well as the absolute afterglow flux level after the injection are boosted after the injection. Identifying the different injection signatures from future early afterglow observations may provide diagnostics about the nature of the fireball and of the central engine.