Ep–eiso Relation in a Multiple Subjet Model of Gamma-ray Bursts under the Universal Structured Jet Model and the Yonetoku Relation

Assuming that each subjet follows the Yonetoku relation, i.e., E rest p ∝ L 1/2 p , we performed Monte Carlo simulations in the context of a multiple subjet model (or inhomogeneous jet model) for gamma-ray bursts (GRBs), X-ray–rich GRBs (XRRs), and X-ray flashes (XRFs). For a single subjet, we found that E rest p ∝ Eiso 0.4 for large viewing angle. For the multiple subjet model under the universal structured jet model, we obtained the Amati relation (E rest p ∝ Eiso ) over three orders of magnitude in E rest p for 5000 random viewing angles. Although the scatter around the Amati relation is large in the simulation, the results are consistent with the observed GRBs with known redshifts and the BASTE GRBs with the pseudo redshifts from the lag-luminosity relation. Subject headings: gamma rays: bursts — gamma rays: theory