Ep-Eiso Correlation in a Multiple Subjet Model of Gamma-Ray Bursts
  We perform Monte Carlo simulations to study Ep-Eiso correlation 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 find that Ep prop. Eiso^0.4 for large viewing angles. For the multiple subjet model in which all the subjets have the same intrinsic properties, off-axis events show Ep prop. Eiso^a with 0.4<a<0.5. If the intrinsic properties of the subjets are distributed so that on-axis emission of each subjet follows a correlation Ep prop. Liso^1/2, we obtain the Amati correlation (Ep prop. Eiso^1/2) over three orders of magnitude in Ep. Although the scatter around the Amati correlation is large in the simulation, the results are consistent with the observed properties of GRBs with known redshifts and the BASTE GRBs with pseudo redshifts derived from the lag-luminosity correlation. We also calculate the event rates, the redshift distributions, and the T90 duration distributions of GRBs, XRRs, and XRFs which can be detected by HETE-2, assuming that the source redshift distribution is in proportion to the cosmic star formation rate. It is found that the event rates of three classes are comparable, that the average redshift of the XRRs is a little larger than those of the GRBs and the XRFs, and that short XRRs arise when a single subjet is viewed off-axis or viewed on-axis with slightly high redshift. 
Kenji Toma, Ryo Yamazaki, Takashi Nakamura