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. Especially, 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 coast freely 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 better 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 very lately and manifest 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 gamma-ray emission. Our study may hopefully provide a novel method to measure the beaming angle of gamma-ray bursts.