Gamma-Ray Bursts with Continuous Energy Injection and Their Afterglow Signature

TLDR: In this article, the authors considered the problem of 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.

Abstract: We consider generically the problem of 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. Generally, 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 light curves. When this criterion is met in the case of Poynting-flux-dominated injection, this leads to a gradual achromatic bump appearing in the otherwise power-law afterglow light curve. Alternatively, in the case when the injection is kinetic-energy-dominated, the results depend on whether the collision between the rear (injected) and the forward shell is mild or violent. If the relative velocity between the colliding shells does not exceed a critical value defined by their energy ratio, the collision is mild, and the injection may be analogous to the Poynting-flux injection case. Otherwise, the injection is violent, and an additional pair of strong 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 light curves. We describe the shell-merging process in detail, including collision and relaxation, by taking into account the dynamical evolution and the emission from the various shocks involved. Assuming synchrotron emission, we calculate afterglow light curves in the X-ray, optical, and radio bands for the various cases. The injection signatures due to violent matter-dominated collisions are abrupt and complicated, because of the emission from any of the three emitting regions and depending on the injection parameters and the observed energy bands. This differs from the gradual bump signature found in the Poynting-flux injection case. In both the Poynting-flux-dominated and the kinetic-energy-dominated cases, the energetics of the fireball as well as the absolute afterglow flux level after the injection are boosted with respect to the one without postburst 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.