Internal Luminosity Distribution of Bright Gamma‐Ray Bursts and Its Relation to Duration and Spectral Hardness

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Abstract
We present first results from a comprehensive investigation into the distribution of luminosity within the 50 brightest cosmic gamma-ray bursts detected by the Burst and Transient Source Experiment (BATSE). The internal luminosity function ψ(L) is defined such that the quantity ψ(L)dL represents the fraction of total emission time during which the burst possesses a luminosity between L and L + dL. For these brightest bursts, the ψ(L) functions are quasi-power-law-like and decrease in amplitude with increasing luminosity. Through investigation of both individual ψ(L) distributions and data from the ensemble of bursts, we demonstrate a high probability for correlation between the shape of the internal luminosity function as measured by the average logarithmic slope and the burst duration as measured by the T90 parameter and, with lower significance, between the shape of ψ(L) and the burst photon-fluence spectral index. We furthermore demonstrate a correlation between burst hardness ratio and duration in these brightest bursts which is opposite to that of the entire gamma-ray burst ensemble.

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