The Prompt Energy Release of Gamma-Ray Bursts using a Cosmological [ITAL]k[/ITAL]-Correction

The fluences of gamma-ray bursts (GRBs) are measured with a variety ofinstruments in different detector energy ranges. A detailed comparison of theimplied energy releases of the GRB sample requires, then, an accurateaccounting of this diversity in fluence measurements which properly correctsfor 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-movingbandpass. This allows us to homogenize the prompt energy release of 17cosmological GRBs (using published redshifts, fluences, and spectra) to twocommon co-moving bandpasses: 20-2000 keV and 0.1 keV-10 MeV (``bolometric'').While the overall distribution of GRB energy releases does not changesignificantly by using a k-correction, we show that uncorrected energyestimates systematically undercounts the bolometric energy by ~5% to 600%,depending on the particular GRB. We find that the median bolometricisotropic-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-correctedenergy measurement is ~20%.Comment: Accepted to the Astronomical Journal. 21 pages (LaTeX) and 4 figure