Confirmation of the E-Eiso (Amati) Relation from the X-Ray Flash XRF 050416AObserved by the Swift Burst Alert Telescope

We report Swift Burst Alert Telescope (BAT) observations of the X-ray flash (XRF) XRF 050416A. The fluence ratio between the 15-25 and 25-50 keV energy bands of this event is 1.1, thus making it the softest gamma-ray burst (GRB) observed by BAT so far. The spectrum is well fitted by a Band function with E of 15.0 keV. Assuming the redshift of the host galaxy (z = 0.6535), the isotropic equivalent radiated energy Eiso and the peak energy at the GRB rest frame (E) of XRF 050416A are not only consistent with the correlation found by Amati et al. and extended to XRFs by Sakamoto et al. but also fill in the gap of this relation around the 30-80 keV range of E. This result tightens the validity of the E-Eiso relation from XRFs to GRBs. We also find that the jet break time estimated using the empirical relation between E and the collimation corrected energy Eγ is inconsistent with the afterglow observation by the Swift X-Ray Telescope. This could be due to the extra external shock emission overlaid around the jet break time or to the nonexistence of a jet break feature for XRFs, which might be a further challenge for GRB jet emission models and XRF/GRB unification scenarios.