2001ApJ...561..171J

We determine the distribution of total energy emitted by gamma-ray bursts for bursts with fluence and distance information. Our core sample consists of eight bursts with BATSE spectra and spectroscopic redshifts. We extend this sample by adding four bursts with BATSE spectra and host galaxy R magnitudes. From these R magnitudes, we calculate a redshift probability distribution; this method requires a model of the host galaxy population. From a sample of 10 bursts with both spectroscopic redshifts and host galaxy R magnitudes (some do not have BATSE spectra), we find that the burst rate is proportional to the galaxy luminosity at the epoch of the burst. Assuming that the total energy emitted has a lognormal distribution, we find that the average emitted energy (assumed to be radiated isotropically) is <E_γiso≥1.3^+1.2_–0.7x10⁵³ ergs (for H₀=65 km.s^–1.Mpc^–1, Ω_m=0.3, and Ω_Λ=0.7); the distribution has a logarithmic width of σ_γ=1.7^+0.7_–0.3. The corresponding distribution of X-ray afterglow energy (for seven bursts) has <E_X,iso≥3.5^+2.1_–1.3x10⁵¹ ergs and σ_X=1.3^+0.4_–0.3. For completeness, we also provide spectral fits for all bursts with BATSE spectra for which there were afterglow searches.