The Peak Energy Distribution of the νF_ν Spectra and the Implications for the Jet Structure Models of Gamma-Ray Bursts

We study the peak energy (E_p) distribution of the νF_ν spectra of gamma-ray bursts (GRBs) and X-ray flashes (XRFs) with a sample of 57 bursts observed by High Energy Transient Explorer (HETE-2) French Gamma Telescope and discuss its implications for the jet structure models. Combining the observed E_p distribution of HETE-2 GRBs/XRFs with that of BATSE GRBs, we find that the observed E_p distribution of GRBs/XRFs is a bimodal one with peaks of ≲30 keV and ~160-250 keV. According to the recently discovered equivalent-isotropic energy-E_p relationship, such a bimodal distribution implies a two-component structure of GRB/XRF jets. A simple simulation analysis shows that this structured jet model does roughly reproduce a bimodal distribution with peaks of ~15 and ~200 keV. We argue that future observations of the peak of ~15 keV in the E_p distribution would be evidence supporting this model. Swift, which covers an energy band of 0.2-150 keV, is expected to provide a key test for our results.