  We report HETE-2 WXM/FREGATE observations of the X-ray flash, XRF 020903.
This event was extremely soft: the ratio log(S_X/S_gamma) = 0.7, where S_X and
S_gamma are the fluences in the 2-30 and 30-400 keV energy bands, is the most
extreme value observed so far by HETE-2. In addition, the spectrum has an
observed peak energy E^{obs}_{peak} < 5.0 keV (99.7 % probability upper limit)
and no photons were detected above ~10 keV. The burst is shorter at higher
energies, which is similar to the behavior of long GRBs. We consider the
possibility that the burst lies at very high redshift and that the low value of
E^{obs}_{peak} is due to the cosmological redshift, and show that this is very
unlikely. We find that the properties of XRF 020903 are consistent with the
relation between the fluences S(7-30 keV) and S(30-400 keV) found by Barraud et
al. for GRBs and X-ray-rich GRBs, and are consistent with the extension by a
decade of the hardness-intensity correlation (Mallozzi et al. 1995) found by
the same authors. Assuming that XRF 020903 lies at a redshift z = 0.25 as
implied by the host galaxy of the candidate optical and radio afterglows of
this burst, we find that the properties of XRF 020903 are consistent with an
extension by a factor ~300 of the relation between the isotropic-equivalent
energy E_iso and the peak E_peak of the nu F_nu spectrum (in the source frame
of the burst) found by Amati et al. for GRBs. The results presented in this
paper therefore provide evidence that XRFs, X-ray-rich GRBs, and GRBs form a
continuum and are a single phenomenon. The results also impose strong
constraints on models of XRFs and X-ray-rich GRBs.
