2004MNRAS.348..153L

The distribution of the duration of gamma-ray bursts (GRBs), and the relations of the jet opening angles (θ) to prompt gamma-ray emissions and X-ray afterglow emissions have been investigated within the framework of a relativistic beaming model for a sample including 10 GRBs. The redshifts, the temporal breaks of the optical afterglow light curves and the X-ray afterglows of these GRBs have been well measured. The results show that: (I) the distribution of the intrinsic burst durations extend over only approximately one order of magnitude, suggesting that these bursts tend to have a similar burst duration; (II) the gamma-ray fluence in the comoving frame (S_γ) as a function of θ is roughly fitted by a broken power law with indices of -0.4 and -3.79 before and after a break at θ= 0.1 rad, respectively, while the X-ray fluxes decay with θ following a single power law with an index of -1.8; (III) the relation between the ratio of F_x/S_γand θ follows a turnover power law with indices of -3.2 and 2.9 before and after the break at θ= 0.1, respectively; and (iv) the temporal indices of X-ray afterglows are significantly anticorrelated with θ with a Spearman rank linear correlation coefficient of r =-0.84 and a probability of chance occurrence of p = 0.004. These results are consistent with the expectations of the beaming model. They have been interpreted using both the areas of emission regions that instruments can observe and the number of baryons contained in the jets.