A SIGNIFICANT PROBLEM WITH USING THE AMATI RELATION FOR COSMOLOGICAL PURPOSES

We consider the distribution of many samples of gamma-ray bursts when plotted in a diagram with their bolometric fluence (S-bolo) versus the observed photon energy of peak spectral flux (E-peak,E-obs). In this diagram, all bursts that obey the Amati relation (a luminosity relation where the total burst energy has a power-law relation to E-peak,E-obs) 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 Amati limit. But we find that the bursts from BATSE, Swift, Suzaku, and Konus are all greatly in violation of the Amati limit, and this is true whether or not the bursts have measured spectroscopic redshifts. That is, the Amati relation has definitely failed. In the S-bolo-E-peak,E-obs diagram, we find that every satellite has a greatly different distribution. This requires that selection effects are dominating these distributions, which we quantitatively identify. For detector selections, the trigger threshold and the threshold for the burst to obtain a measured E-peak,E-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 E-peak,E-obs makes bursts with low and high values rare, while the fluence distribution makes bright bursts relatively uncommon. For a detector with a high threshold, the combination of these selection effects serves to allow only bursts within a region along the Amati limit line to be measured, and 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. As such, the Amati relation should not be used for cosmological tasks. This failure of the Amati relation is in no way prejudicial against the other luminosity relations.