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Abstract: Firmani et al. proposed a new Gamma Ray Burst GRB luminosity relation thatshowed a significant improvement over the L iso-E peak relation. The newproposed relation simply modifies the E peak value by multiplying it by a powerof T 0.45, where T 0.45 is a particular measure of the GRB duration. We beginby reproducing the results of Firmani for his 19 bursts. We then test theFirmani relation for the same 19 bursts except that we use independentlymeasured values for L iso, T 0.45, and E peak, and we find that the relationdeteriorates substantially. We further test the relation by using 60 GRBs withmeasured spectroscopic redshifts, and find a relation that has a comparablescatter as the original L iso-E peak relation. That is, a much larger sample ofbursts does not reproduce the small scatter as reported by Firmani et al.Finally, we investigate whether the Firmani relation is improved by the use ofany of 32 measures of duration in place of T 0.45. The quality of eachalternative duration measure is evaluated with the root mean square of thescatter between the observed and fitted logarithmic Liso values. Although wefind some durations yield slightly better results than T 0.45, the differencesbetween the duration measures are minimal. We find that the addition of aduration does not add any significant improvement to the L iso-E peak relation.We also present a simple and direct derivation of the Firmani relation fromboth the L iso-E peak and Amati relations. In all we conclude that the Firmanirelation neither has an independent existence nor does it provide anysignificant improvement on previously known relations that are simpler.

Autor: Andrew C. Collazzi, Bradley E. Schaefer


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