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A Simultaneous Spectral Invariant Analysis of the GRB Count Distribution and Time Dilation

Ehud Cohen·Tsvi Piran
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Abstract

The analysis of the BATSE's count distribution within cosmological models suffers from observational uncertainties due to the variability of the bursts' spectra: when BATSE observes bursts from different redshifts at a fixed energy band it detects photons from different energy bands at the source. This adds a spectral dependence to the count distribution $N(C)$. Similarly variation of the duration as a function of energy at the source complicates the time dilation analysis. We describe here a new statistical formalism that performs the required ``blue shifting" of the count number and the burst duration in a statistical manner. This formalism allows us to perform a combined best fit (maximal likelihood) to the count distribution, $N(C)$, and the duration distribution simultaneously. The outcome of this analysis is a single best fit value for the redshift of the observed bursts.

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Ehud Cohen, Tsvi Piran. 1995-12-19. A Simultaneous Spectral Invariant Analysis of the GRB Count Distribution and Time Dilation. https://doi.org/10.1063/1.51560

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