Global Characteristics of X-Ray Flashes and X-Ray-Rich GRBs Observed by HETE-2

We describe and discuss the global properties of 45 gamma-ray bursts (GRBs) observed by HETE-2 during the first three years of its mission, focusing on the properties of X-Ray Flashes (XRFs) and X-ray-rich GRBs (XRRs). We find that the numbers of XRFs, XRRs, and GRBs are comparable. We find that the durations and the sky distributions of XRFs and XRRs are similar to those of GRBs. We also find that the spectral properties of XRFs and XRRs are similar to those of GRBs, except that the values of the peak energy $E^{\\rm obs}_{\\rm peak}$ of the burst spectrum in $\\nu F_\\nu$, the peak energy flux $\\Fp$, and the energy fluence $S_E$ of XRFs are much smaller -- and those of XRRs are smaller -- than those of GRBs. Finally, we find that the distributions of all three kinds of bursts form a continuum in the [$S_E$(2-30 keV),$S_E$(30-400) keV]-plane, the [$S_E$(2-400 keV), $E_{\\rm peak}$]-plane, and the [$F_{\\rm peak}$(50-300 keV), $E_{\\rm peak}$]-plane. These results provide strong evidence that all three kinds of bursts arise from the same phenomenon.