Late internal shock model for bright X-ray flares in Gamma-ray Burst afterglows and GRB 011121

We explore two possible models which might give rise to bright X-ray flares in GRBs afterglows. One is an external forward-reverse shock model, in which the shock parameters of forward/reverse shocks are taken to be quite different. The other is a so called "late internal shock model", which requires a refreshed unsteady relativistic outflow generated after the prompt $\gamma-$ray emission. In the forward-reverse shock model, after the time $t_\times$ at which the RS crosses the ejecta, the flux declines more slowly than $(t_\oplus/t_\times)^{-(2+\beta)}$, where $t_\oplus$ denotes the observer's time and $\beta$ is the spectral index of the X-ray emission. In the ``late internal shock model", decaying slopes much steeper than $(t_\oplus/t_{\rm e, \oplus})^{-(2+\beta)}$ are possible if the central engine shuts down after $t_{\rm e, \oplus}$ and the observed variability timescale of the X-ray flare is much shorter than $t_{\rm e, \oplus}$. The sharp decline of the X-ray flares detected in GRB 011121, XRF 050406, GRB 050502b, and GRB 050730 rules out the external forward-reverse shock model directly and favors the "late internal shock model". These X-ray flares could thus hint that the central engine operates again and a new unsteady relativistic outflow is generated just a few minutes after the intrinsic hard burst.