We present multi-wavelength observations and modeling of Gamma-ray Bursts (GRBs) that exhibit a simultaneous re-brightening in their X-ray and optical light curves, and are also detected at radio wavelengths. We show that the re-brightening episodes can be modeled by injection of energy into the blastwave and that in all cases the energy injection rate falls within the theoretical bounds expected for a distribution of energy with ejecta Lorentz factor. Our measured values of the circumburst density, jet opening angle, and beaming corrected kinetic energy are consistent with the distribution of these parameters for long-duration GRBs at both z ∼ 1 and z & 6, suggesting that the jet launching mechanism and environment of these events are similar to that of GRBs that do not have bumps in their light curves. However, events exhibiting re-brightening episodes have lower radiative efficiencies than average, suggesting that a majority of the kinetic energy of the outflow is carried by slow-moving ejecta, which is further supported by steep measured distributions of the ejecta energy as a function of Lorentz factor. We do not find evidence for reverse shocks over the energy injection period, implying that the onset of energy injection is a gentle process. We further show that GRBs exhibiting simultaneous X-ray and optical re-brightenings are likely the tail of a distribution of events with varying rates of energy injection, forming the most extreme events in their class. Future X-ray observations of GRB afterglows with Swift and its successors will thus likely discover several more such events, while radio follow-up and multi-wavelength modeling of similar events will unveil the role of energy injection in GRB afterglows.Astronom
