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

We study the peak energy ($E_{\rm{p}}$) distribution of the $\nu F_{\nu}$ spectra of gamma-ray bursts (GRBs) and X-ray flashes (XRFs) with a sample of 57 bursts observed by {\em High Energy Transient Explorer 2} ({\em HETE-2}) French Gamma Telescope and discuss its implications for the jet structure models. Combining the observed $E_{\rm{p}}$ distribution of {\em HETE--2} GRBs/XRFs with that of BATSE GRBs, we find that the observed $E_{\rm{p}}$ distribution of GRBs/XRFs is a bimodal one with peaks of $\lesssim 30$ keV and $\sim 160-250$ keV. According to the recently-discovered equivalent-isotropic energy-$E_{\rm{p}}$ 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 $\sim 15$ and $\sim 200$ keV. We argue that future observations of the peak of $\sim 15$ keV in the $E_{\rm{p}}$ distribution would be evidence supporting this model. {\em Swift}, which covers an energy band of 0.2--150 keV, is expected to provide a key test for our results.