Intense flares that occur at late times relative to the prompt phase have been observed by the $Swift$ satellite in the X-ray afterglows of gamma-ray bursts (GRBs). Here, we present a detailed analysis on the fall back accretion process to explain th
e intense flare phase in the very early X-ray afterglow light curves. To reproduce the afterglow at late times, we resort to the external shock by engaging energy injections. By applying our model to GRBs 080810, 081028 and 091029, we show that their X-ray afterglow light curves can be reproduced well. We then apply our model to the ultra-long $Swift$ GRB 111209A, which is the longest burst ever observed. The very early X-ray afterglow of GRB 111209A showed many interesting features, such as a significant bump observed at around 2000 s after the $Swift$/BAT trigger. We assume two constant energy injection processes in our model. These can explain the observed plateau at X-ray wavelength in the relatively early stage ($8.0times10^{3}$ s) and a second X-ray plateau and optical rebrightening at about $10^{5}$ s. Our analysis supports the scenario that a significant amount of material may fall back toward the central engine after the prompt phase, causing an enhanced and long lived mass accretion rate powering a Poynting-flux-dominated outflow.
The combination of a long duration and the absence of any accompanying supernova clearly shows that GRB 060614 can not be grouped into the two conventional classes of gamma-ray bursts, i.e. the long/soft bursts deemed to be collapsars and the short/h
ard bursts deemed to be merging binary compact stars. A new progenitor model is required for this anomalous gamma-ray burst. We propose that GRB 060614 might be produced through the tidal disruption of a star by an intermediate mass black hole. In this scenario, the long duration and the lack of any associated supernova are naturally expected. The theoretical energy output is also consistent with observations. The observed 9-s periodicity in the $gamma$-ray light curve of GRB 060614 can also be satisfactorily explained.
The discovery of multiband afterglows definitely shows that most $gamma$-ray bursts are of cosmological origin. $gamma$-ray bursts are found to be one of the most violent explosive phenomena in the Universe, in which astonishing ultra-relativistic mo
tions are involved. In this article, the multiband observational characteristics of $gamma$-ray bursts and their afterglows are briefly reviewed. The standard model of $gamma$-ray bursts, i.e. the fireball model, is described. Emphasis is then put on the importance of the nonrelativistic phase of afterglows. The concept of deep Newtonian phase is elaborated. A generic dynamical model that is applicable in both the relativistic and nonrelativistic phases is introduced. Based on these elaborations, the overall afterglow behaviors, from the very early stages to the very late stages, can be conveniently calculated.
