(a)
(b)
Figure 9: (a) relation for GRBs with known redshift. The filled circles represent for the events where a jet break was detected. Grey symbols indicate lower/upper limits. The solid line represents the best fit, that is, . Open circles denote for the GRBs. The dashed line represents the best fit to these points and the dash-dotted line is the relation shown by Amati et al. [111]. (Figure after Ghirlanda et al. [188]; see Figure therein. @ AAS. Reproduced with permission.) (b) Rest frame plane of GRB energy. The large black dot indicates that all simulated GRBs were assigned and . Since but less than 8000, regions (I) are forbidden. Since for all the simulated GRBs , they cannot stay in region (II). When is small, the beaming cone turns out to be larger than the jet. Therefore, the isotropic-equivalent energy is given by , lower than the energy computed by . This brings in a constraint, , and GRBs cannot lie to the right of this constraint. Hence, region (III) is not allowed. The black dots indicate the actual GRBs of the Swift sample. The fit to the Swift sample is displayed as the dot-dashed line. (Figure after Ghirlanda et al. [209]; see Figure therein.)