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 gamma-ray burst (GRB) 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(x) at which the reverse shock crosses the ejecta, the flux declines more slowly than (t(+)/t(x))(-(2+beta)), where t(+) 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(+)/t(e,+))(-(2+beta)) are possible if the central engine shuts down after t(e,+) and the observed variability time-scale of the X-ray flare is much shorter than tau(e,circle plus). 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 favours the 'late internal-shock model'. These X-ray flares could thus hint that the central engine has begun to operate again and a new unsteady relativistic outflow is generated just a few minutes after the intrinsic hard burst.