A Possible Intrinsic Fluence-Duration Power-Law Relation in Gamma-ray Bursts
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We argue that the distributions of both the intrinsic fluence and the intrinsic duration of the gamma-ray emission in gamma-ray bursts from the BATSE sample are well represented by log-normal distributions, in which the intrinsic dispersion is much larger than the cosmological time dilatation and redshift effects. We perform separate bivariate log-normal distribution fits to the BATSE short and long burst samples. The bivariate log-normal behavior results in an ellipsoidal distribution, whose major axis determines an overall statistical relation between the fluence and the duration. We show that this fit provides evidence for a power-law dependence between the fluence and the duration, with a statistically significant different index for the long and short groups. We discuss possible biases which might affect this result, and argue that the effect is probably real. This may provide a potentially useful constraint for models of long and short bursts.
revised version, ApJ subm 3/15/01; includes substantial additional calculations and discussion of biases, title change, additional figure
revised version, ApJ subm 3/15/01; includes substantial additional calculations and discussion of biases, title change, additional figure