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

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 that 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 comoving bandpass. This allows us to homogenize the prompt energy release of 17 cosmological GRBs (using published redshifts, fluences, and spectra) to two common comoving 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 undercount the bolometric energy by ∼ 5% to 600%, depending on the particular GRB. We find that the median bolometric isotropic equivalent prompt energy release is 2.19 × 10⁵³ ergs, with an rms scatter of 0.80 dex. The typical estimated uncertainty on a given k-corrected energy measurement is ∼20%.