A Significant Problem With Using the Amati Relation for Cosmological   Purposes
  We consider the distribution of many samples of Gamma-Ray Bursts (GRBs) when plotted in a diagram with their bolometric fluence (Sbolo) versus the observed photon energy of peak spectral flux (Epeak,obs). In this diagram, bursts that obey the Amati relation must lie above some limiting line, although observational scatter is expected to be substantial. We confirm that early bursts with spectroscopic redshifts are consistent with this limit. But, we find that the bursts from BATSE, Swift, Suzaku, and Konus are all greatly in violation of the limit. In the Sbolo-Epeak,obs diagram, we find that every satellite has a greatly different distribution. This requires that selection effects are dominating these distributions, which we identify. For detector selections, the trigger threshold and the threshold to measure Epeak,obs combine to make a diagonal cutoff with the position of this cutoff varying greatly detector to detector. For selection effects due to the intrinsic properties of the burst population, the distribution of Epeak,obs makes for bursts with low and high values to be rare, while the fluence distribution makes bright bursts uncommon. For a poor threshold, the combination of selection effects serves to allow only bursts within a region along the limit to be measured; these bursts will then appear to follow an Amati relation. Therefore, the Amati relation is an artifact of selection effects within the burst population and the detector. Therefore, the Amati relation should not be used for cosmological tasks. This failure is in no way prejudicial against the other luminosity relations. 
Andrew C. Collazzi, Bradley E. Schaefer, Adam Goldstein, Robert D.   Preece
astro-ph.HE