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 follow the Yonetoku relation, i.e., E_p^rest \propto (L_p)^1/2, 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_p^rest \propto (E_iso)^0.4 for large viewing angle. For the multiple subjet model under the universal structured jet model, we obtained the Amati relation (E_p^rest \propto (E_iso)^1/2) over three orders of magnitude in E_p^rest 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 redshifs and the BATSE GRBs with the pseudo redshifts from the lag-luminosity relation