Measuring the beaming angle of GRB 030329 by fitting the rebrightenings in its multiband afterglow

Multiple rebrightenings have been observed in the multiband afterglow of GRB 030329. In particular, a marked and quick rebrightening occurred at about t 1.2 × 10^5 s. Energy injection from late and slow shells seems to be the best interpretation for these rebrightenings. Usually it is assumed that the energy is injected into the whole external shock. However, in the case of GRB 030329, the rebrightenings are so quick that the usual consideration fails to give a satisfactory fit to the observed light curves. Actually, since these late/slow shells freely coast in the wake of the external shock, they should be cold and may not expand laterally. The energy injection then should only occur at the central region of the external shock. Considering this effect, we numerically re-fit the quick rebrightenings observed in GRB 030329. By doing this, we were able to derive the beaming angle of the energy injection process. Our result, with a relative residual of only 5% - 10% during the major rebrightening, is bet- ter than any previous modeling. The derived energy injection angle is about 0.035. We assume that these late shells are ejected by the central engine via the same mechanism as those early shells that produce the prompt gamma-ray burst. The main difference is that their velocities are much slower, so that they catch up with the external shock relatively late and are manifested as the observed quick rebrightenings. If this were true, then the derived energy injection angle can give a good measure of the beaming angle of the prompt γ-ray emission. Our study may hopefully provide a novel method to measure the beaming angle of gamma-ray bursts.

X-ray Flashes from Off-axis Nonuniform Jets

It has been widely believed that the outflows in gamma-ray bursts are jetted and some jets may have structures like ∈(θ)∝θ-k. We check the possibility that X-ray flashes come from such jets. Both qualitative and quantitative analyses have shown that this model can reproduce most of the observational features of both X-ray flashes and gamma-ray bursts. Using the usual parameters of gamma-ray bursts, we have carried out numerical calculations for both uniform and nonuniform jets, of their fluxes, spectra and peak energies. It seems that nonuniform jets are more appropriate to these observational properties than uniform jets. We have also shown that in our model the observational ratio of gamma-ray bursts to X-ray flashes is about a few units.

Testing Lorentz violation using propagating UHECRs

Lorentz invariant violation （LIV） test is important for studying modem physics. All the known astrophysical constraints either have a very small examinable parameter space or are only suitable for some special theoretical models. Here, we suggest that it is possible to directly detect the time-delay of ultra-high-energy cosmic-rays （UHECRs）. We discuss some difficulties in our method, including the intergalactic magnetic fields. It seems that none of them are crucial, hence this method could give a larger examinable parameter space and a stronger constraint on LIV.