It is often stated that gamma-ray bursts (GRBs) have typical energies of several hundred keV, where the typical energy may be characterized by the hardness H, the photon energy corresponding to the peak of νFν. Among the 54 BATSE bursts analyzed by Band et al. in 1993 and the 136 analyzed by us, more than 60% have 50 keV H 300 keV. Is the narrow range of H a real feature of GRBs, or is it due to an observational difficulty in detecting harder bursts? We consider a population of standard candle bursts with a hardness distribution ρ(H)d log H ∝ Hγ d log H and no luminosity-hardness correlation. We model the detection algorithm of BATSE as a function of H, including cosmological effects, detector characteristics, and triggering procedure, and we calculate the expected distribution of H in the observed sample for various values of γ. Both samples show a paucity of soft (X-ray) bursts, which may be real. However, we find that the observed samples are consistent with a distribution above H = 120 keV with γ ~ -0.5 (a slowly decreasing number of GRBs per decade of hardness). Thus, we suggest that a large population of unobserved hard gamma-ray bursts may exist.
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