2013ApJ...779...28G

The shallow decay phase and flares in the afterglows of gamma-ray bursts (GRBs) are widely believed to be associated with the later activation of the central engine. Some models of energy injection involve a continuous energy flow since the GRB trigger time, such as the magnetic dipole radiation from a magnetar. However, in the scenario involving a black hole accretion system, the energy flow from the fall-back accretion may be delayed for a fall-back time ∼t_fb. Thus, we propose a delayed energy injection model. The delayed energy would cause a notable rise to the Lorentz factor of the external shock, which will "generate" a bump in the multiple band afterglows. If the delayed time is very short, our model degenerates to the previous models. Our model can explain the significant re-brightening in the optical and infrared light curves of GRB 081029 and GRB 100621A. A considerable fall-back mass is needed to provide the later energy; this indicates that GRBs accompanied with fall-back material may be associated with a low energy supernova so that the fraction of the envelope can survive during eruption. The fall-back time can give meaningful information on the properties of GRB progenitor stars.