The Hardness Distribution of Gamma‐Ray Bursts

It is often stated that gamma-ray bursts (GRBs) have typical energies ofseveral hundreds $\keV$, where the typical energy may be characterized by thehardness H, the photon energy corresponding to the peak of $\nu F_{\nu}$. Amongthe 54 BATSE bursts analyzed by Band et al. (1993), and 136 analyzed by us,more then 60% have 50 keV < H < 300 keV. Is the narrow range of H a realfeature of GRBs or is it due to an observational difficulty to detect harderbursts? We consider a population of standard candle bursts with a hardnessdistribution: rho(H) d log H \propto H^gamma d log H and no luminosity -hardness correlation. We model the detection algorithm of BATSE as a functionof H, including cosmological effects, detector characteristics and triggeringprocedure, and we calculate the expected distribution of H in the observedsample 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 samplesare consistent with a distribution above H=120 keV with gamma \sim -0.5 (aslowly decreasing numbers of GRBs per decade of hardness). Thus, we suggestthat a large population of unobserved hard gamma-ray bursts may exist.Comment: 15 Latex pages including five eps figures and a table; dicussions and two figures added, accepted for publication in the Astrophysical Journa