The Hardness Distribution of Gamma-Ray Bursts

It is often stated that gamma-ray bursts (GRBs) have typical energies of several hundreds 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. (1993), and 156 analyzed by us, more then 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 to detect harder bursts? We consider a population of bursts with standard luminosity, and a distribution of hardness: $\rho(H) d log H \propto H^{\gamma} d log H$. We model the detection efficiency of BATSE as a function of H, including cosmological effects and detector characteristics, and calculate the expected distribution of H in the observed sample for various values of $\gamma$. Both samples shows 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 $\gamma \sim -0.5$ (a slowly decreasing numbers of GRBs per decade of hardness). Thus, we suggest that a large population of unobserved hard gamma-ray bursts may exist.