For GRB 140629A, our analysis suggests that the optical and X-ray afterglows are from a narrow jet (





 rad) with a low B 





 in a dense medium (n = 60 cm−3). In addition, the radiation efficiency of GRB 140629A is extremely low. We test whether or not it satisfies various empirical relations reported in the literature derived from observations of the prompt gamma-ray phase and the multi-wavelength afterglows. By estimating the jet opening angle with a jet-like break time tj in late multi-wavelength light curves, Ghirlanda et al. (2004a) derived a tight correlation between geometrically corrected jet energy 





 and the peak energy 





 of 





 spectrum in the burst frame, i.e., 





. The 





 value inferred from the Ghirlanda relation is 46 keV for GRB 140629A, which is definitely inconsistent with the data, i.e., 





. Liang & Zhang (2005) derived an empirical relation between 





, 





, and the jet break time (





) in the burst frame, i.e., 





/





/





/





Based on this relation, an isotropic energy 





 erg is obtained, which is larger than that observed by more than one order of magnitude. These results suggest that GRB 140629A does not follow these two relations (Ghirlanda et al. 2004a; Liang & Zhang 2005), although both tight correlations have been used for measuring the cosmological parameters with GRBs (e.g., Dai et al. 2004; Ghirlanda et al. 2004b; Liang & Zhang 2005; Wang et al. 2015a). Note that the observed jet break time of GRB 140629A is much earlier, hence the inferred θj is much lower than those of the GRBs used to derive these relations (e.g., Frail et al. 2001; Bloom et al. 2003). It is unclear whether the violation of GRB 140629A is due to the selection effect or other physical reasons. For example, two-component jet models composed of a narrow and a wide component have been proposed to explain the data of some GRBs (e.g., Huang et al. 2004; Racusin et al. 2008). In these cases, the high-energy emission was proposed to be emitted by the narrow jet. However, one cannot exclude the possibility that the observed gamma-ray energy would be dominated by the wide jet component under certain conditions. Meanwhile, the early break time for GRB 140629A is likely due to the effect of the narrow jet component but not the wide one. If this is the case, the inconsistency between the jet energy and the opening angle would result in this violation of GRB 140629A. Liang et al. (2015) discovered a tight empirical correlation between Liso, 





, and Γ0 to reveal the direct connection between the gamma-ray and afterglows,
7





Based on the equation above, we get 





 for GRB 140629A, where the error is calculated from the uncertainties in 





 and Γ0 only. The derived 





 is well consistent with the observed one, 





 erg s−1, as shown in Figure 6. Note that the initial Lorentz factor of the ejecta Γ0 is sensitive to the deceleration time (the peak time of the onset bump), but not strongly related to the jet break time. The onset of the afterglow bump is usually bright (Liang et al. 2010, 2013; Li et al. 2012; Wang et al. 2013), and it is easier to identify than the jet break time from an observed light curve.10

10
The jet break is usually detected in late optical afterglow light curves. It is dim and also contaminated by emission from the host galaxy and/or associated supernovae (e.g., Li et al. 2012). This is also an issue in identifying an observed jet break as the narrow or the wide component in the case of a two-component jet.
 The consistency of GRB 140629A with 





 suggests that this relation is more robust than the Ghirlanda or Liang–Zhang relations, since it is not sensitive to the jet opening angle θj.
Citation: Liang & Zhang (2005)
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Citation: Liang & Zhang 2005
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Citation: Ghirlanda et al. 2004a
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Citation: Ghirlanda et al. (2004a)
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