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 burs ts. We fit 41 pulses within 26 bursts with the trend reported by Liang & Ka rgatis, which found that E decays exponentially with respect to photon flue nce Phi(t). We also it these pulses with a slight modification of this tren d, where E,, decays linearly with energy fluence. In both cases, we found t he 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 constan t 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 r eported invariance in Phi(0) among different pulses in a single burst, we f ound probabilities of 0.49-0.84 (depending on the test used) that such inva riance would occur by coincidence, most likely because of the narrow distri bution of Phi(0) values among pulses.