5 Conclusions

Our observations have two interesting consequences: they confirm that the ${E_{\rm p}}$ distribution is broader than previously thought (Mallozzi et al. 1995; Preece et al. 2000; Brainerd et al. 2000) and they show that we do not see yet the faint end of the GRB distribution. If we assume that the correlation found by Amati et al. (2002) extends down to ${E_{\rm p}}$ as low as 20 keV, it would imply that the isotropic-equivalent energy radiated by a GRB with ${E_{\rm p}}$ = 20 keV is about 80 times smaller than the isotropic-equivalent energy radiated by a "typical'' GRB with ${E_{\rm p}}$ = 200 keV. Combined with the conclusion of Frail et al. (2000) that the total energy of GRBs is roughly constant, it implies that the jet opening angle of X-ray rich GRBs are substantially larger than the jet opening angle of "typical'' GRBs.

Future work with HETE-2 will bring several advances in this field and should contribute to our understanding of the population of soft/faint GRBs. The continuously growing GRB sample of FREGATE should provide better statistical evidence for the effects discussed in this paper and additional clues about the possible differences between bright and faint GRBs and about the nature of X-ray rich GRBs. Joint spectral analysis with the WXM will allow more precise determinations of ${\alpha }$ and ${E_{\rm0}}$ for X-ray rich GRBs. Finally, measuring the redshifts of a greater number of GRBs detected by HETE-2 will allow us to test the extent of the correlation between the spectral hardness of GRBs and their radiated energy in gamma-rays. X-ray rich GRBs also present an interesting challenge for future GRB missions and for observers on the ground. Future GRB missions will have to detect events which are much softer and fainter than the typical GRB population sampled by BATSE. Observers on the ground are faced with events which have fainter afterglows than the classical gamma-ray bursts.

To conclude we note that the joint detection of GRB 010213 (with ${E_{\rm p}}$ = 2.5 keV, Kawai et al. 2003; Sakamoto et al. 2003) by WXM and FREGATE and of GRB 020903 (with ${E_{\rm p}}$ = 3 keV, Kawai et al. 2003) by WXM only demonstrate the existence of events which are even softer than the bulk of the X-ray rich GRBs discussed in this paper.

Acknowledgements

The HETE-2 mission is supported in the US by NASA contract NASW-4690; in France by CNES contract 793-01-8479; and in Japan in part by the Minisitry of Education, Culture, Sports, Science and Technology Grant-in-Aid 13440063. KH is grateful for support under MIT contract SC-R-293291. GP aknowledges support by the Italian Space Agency (ASI) The authors acknowledge the support of the HETE-2 operation team. The authors acknowledge the use of J. Greiner GRB page at http://www.mpe.mpg.de/~jcg/grbgen.html.