Swift BAT has detected $200 long-duration GRBs, with redshift measurements for $50 of them. We derive the luminosity function (È HL ) and the local event rate ( HL 0 ) of the conventional high-luminosity (HL) GRBs by using the z-known Swift GRBs. Our results are generally consistent with that derived from the CGRO BATSE data. However, the fact that Swift detected a low-luminosity (LL) GRB, GRB 060218, at z ¼ 0:033 within $2 years of operation, together with the previous detection of the nearby GRB 980425, suggests a much higher local rate for these LL-GRBs. We explore the possibility that LL-GRBs are a distinct GRB population from the HL-GRBs. We find that LL 0 is $325 þ352 À177 Gpc À3 yr À1 , which is much higher than HL 0 (1:12 þ0:43 À0:20 Gpc À3 yr À1 ). This rate is $0.7% of the local Type Ib/c SNe. Our results, together with the finding that less than 10% of Type Ib/c SNe are associated with off-beam GRBs, suggest that LL-GRBs have a beaming factor typically less than 14, or a jet angle typically wider than 31 . The high local GRB rate, small beaming factor, and low-luminosity make the LL-GRBs distinct from the HL-GRBs. Although the current data could not fully rule out the possibility that both HL-and LL-GRBs are the same population, our results suggest that LL-GRBs are likely a unique GRB population and that the observed low-redshift GRB sample is dominated by the LL-GRBs.

We analyze in detail the hydrodynamics and afterglow emission of an ultrarelativistic blast wave when it expands in a density-jump medium. Such a medium is likely to appear in the vicinity of gamma-ray bursts (GRBs) associated with massive stars. The interaction of the blast wave with this medium is described through a reverse shock and a forward shock. We show that the reverse shock is initially relativistic if the factor of a density jump (α) is much larger than 21, and Newtonian if 1 < α ≪ 21. We also calculate light curves of the afterglow emission during the interaction if the reverse shock is relativistic, and find that the optical flux density initially decays abruptly, then rises rapidly, and finally fades based on a power-law, which could be followed by an abrupt decay when the reverse shock has just crossed the originally swept-up matter. Therefore, one property of an afterglow occurring in a large-density-jump medium is an abrupt drop followed by a bump in the light curve and thus provides a probe of circumburst environments. In addition, this property could not only account for the optical afterglows of GRB 970508 and GRB 000301C but also explain the X-ray afterglow of GRB 981226.

Recent observations support the suggestion that short-duration gamma-ray bursts are produced by compact star mergers. The x-ray flares discovered in two short gamma-ray bursts last much longer than the previously proposed postmerger energy-release time scales. Here, we show that they can be produced by differentially rotating, millisecond pulsars after the mergers of binary neutron stars. The differential rotation leads to windup of interior poloidal magnetic fields and the resulting toroidal fields are strong enough to float up and break through the stellar surface. Magnetic reconnection-driven explosive events then occur, leading to multiple x-ray flares minutes after the original gamma-ray burst.