Abstract Similar to the case of pulsars the magnetic axis and the spin axis of gamma-ray burst sources may not lie on the same line. This may cause the formation of a ring-like jet due to collimation of the precessing magnetic axis. We analyze the tail emission from such a jet, and find that it has a shallow decay phase with a temporal index of -1/2 if the Lorentz factor of the ejecta is not very high, which is consistent with the shallow decay phase of some early X-ray afterglow detected by Swift. The ring-like jet has a tail cusp with sharp rising and very sharp decay. This effect can provide an explanation for the re-brightening and sharp decay of the X-ray afterglow of GRB 050709.
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