The hardness distribution of gamma-ray bursts

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 nu F-nu. 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 rho(H)d log H proportional to H(gamma)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 gamma. 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 gamma similar to -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.