Peak Energy-Isotropic Energy Relation in the Off-Axis Gamma-Ray Burst   Model
  Using a simple uniform jet model of prompt emissions of gamma-ray bursts (GRBs), we reproduce the observed peak energy--isotropic energy relation. A Monte Carlo simulation shows that the low-isotropic energy part of the relation is dominated by events viewed from off-axis directions, and the number of the off-axis events is about one-third of the on-axis emissions. We also compute the observed event rates of the GRBs, the X-ray-rich GRBs, and the X-ray flashes detected by HETE-2, and we find that they are similar. 
Ryo Yamazaki (1,2), Kunihito Ioka (2), Takashi Nakamura (1) ((1)Kyoto   University, (2)Osaka University)