Spectral hardness decay with respect to fluence in BATSE gamma-ray bursts

We have analyzed the evolution of the spectral hardness parameter E-pk (the maximum of the vF(v), spectrum) as a function of fluence in gamma-ray bursts. We fit 41 pulses within 26 bursts with the trend reported by Liang & Kargatis, which found that E decays exponentially with respect to photon fluence Phi(t). We also it these pulses with a slight modification of this trend, where E,, decays linearly with energy fluence. In both cases, we found the set of 41 pulses to be consistent with the trend. For the latter trend, which we believe to be more physical, the distribution of the decay constant Phi(0) is roughly lognormal, where the mean of log(10) Phi(0) is 1.75 +/- 0.07 and the FWHM of log(10) Phi(0) is 1.0 +/- 0.1. Regarding an earlier reported invariance in Phi(0) among different pulses in a single burst, we found probabilities of 0.49-0.84 (depending on the test used) that such invariance would occur by coincidence, most likely because of the narrow distribution of Phi(0) values among pulses.