2018ApJ...859..160W

Gamma-ray Burst (GRB) collimation has been inferred with the observations of achromatic steepening in GRB light curves, known as jet breaks. Identifying a jet break from a GRB afterglow light curve allows a measurement of the jet opening angle and true energetics of GRBs. In this paper, we re-investigate this problem using a large sample of GRBs that have an optical jet break that is consistent with being achromatic in the X-ray band. Our sample includes 99 GRBs from 1997 February to 2015 March that have optical and, for Swift GRBs, X-ray light curves that are consistent with the jet break interpretation. Out of the 99 GRBs we have studied, 55 GRBs are found to have temporal and spectral behaviors both before and after the break, consistent with the theoretical predictions of the jet break models, respectively. These include 53 long/soft (Type II) and 2 short/hard (Type I) GRBs. Only 1 GRB is classified as the candidate of a jet break with energy injection. Another 41 and 3 GRBs are classified as the candidates with the lower and upper limits of the jet break time, respectively. Most jet breaks occur at 90 ks, with a typical opening angle θ_j = (2.5 ± 1.0)°. This gives a typical beaming correction factor f_b^–1∼1000 for Type II GRBs, suggesting an even higher total GRB event rate density in the universe. Both isotropic and jet-corrected energies have a wide span in their distributions: log(E_γ,iso/erg) = 53.11 with σ = 0.84; log(E_K,iso/erg) = 54.82 with σ = 0.56; log(E_γ/erg) = 49.54 with σ = 1.29; and log(E_K/erg) = 51.33 with σ = 0.58. We also investigate several empirical correlations (Amati, Frail, Ghirlanda, and Liang-Zhang) previously discussed in the literature. We find that in general most of these relations are less tight than before. The existence of early jet breaks and hence small opening angle jets, which were detected in the Swfit era, is most likely the source of scatter. If one limits the sample to jet breaks later than 10⁴ s, the Liang-Zhang relation remains tight and the Ghirlanda relation still exists. These relations are derived from Type II GRBs, and Type I GRBs usually deviate from them.