The prompt energy release of gamma-ray bursts using a cosmological k-correction

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Abstract
The fluences of gamma-ray bursts (GRBs) are measured with a variety of instruments in different detector energy ranges. A detailed comparison of the implied energy releases of the GRB sample requires, then, an accurate accounting of this diversity in fluence measurements which properly corrects for the redshifting of GRB spectra. Here, we develop a methodology to ``k-correct'' the implied prompt energy release of a GRB to a fixed co-moving bandpass. This allows us to homogenize the prompt energy release of 17 cosmological GRBs (using published redshifts, fluences, and spectra) to two common co-moving bandpasses: 20-2000 keV and 0.1 keV-10 MeV (``bolometric''). While the overall distribution of GRB energy releases does not change significantly by using a k-correction, we show that uncorrected energy estimates systematically undercounts the bolometric energy by ~5% to 600%, depending on the particular GRB. We find that the median bolometric isotropic-equivalent prompt energy release is 2.2 x 10^{53} erg with an r.m.s. scatter of 0.80 dex. The typical estimated uncertainty on a given k-corrected energy measurement is ~20%.

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