Testing the Gamma-Ray Burst Energy Relationships

Building on Nakar & Piran's analysis of the Amati relation relating gamma-ray burst peak energies E(sub p) and isotropic energies E(sub iso ) we test the consistency of a large sample of BATSE bursts with the Amati and Ghirlanda (which relates peak energies and actual gamma-ray energies E(sub gamma)) relations. Each of these relations can be exp ressed as a ratio of the different energies that is a function of red shift (for both the Amati and Ghirlanda relations) and beaming fraction f(sub B) (for the Ghirlanda relation). The most rigorous test, whic h allows bursts to be at any redshift, corroborates Nakar & Piran's r esult - 88% of the BATSE bursts are inconsistent with the Amati relat ion - while only l.6% of the bursts are inconsistent with the Ghirlan da relation if f(sub B) = 1. Modelling the redshift distribution resu lts in an energy ratio distribution for the Amati relation that is sh ifted by an order of magnitude relative to the observed distributions; any sub-population satisfying the Amati relation can comprise at mos t approx. 18% of our burst sample. A similar analysis of the Ghirland a relation depends sensitively on the beaming fraction distribution f or small values of f(sub B); for reasonable estimates of this distrib ution about a third of the burst sample is inconsistent with the Ghir landa relation. Our results indicate that these relations are an artifact of the selection effects of the burst sample in which they were f ound; these selection effects may favor sub-populations for which the se relations are valid.