Reconciliation of the Disparate Gamma-Ray Burst Catalogs in the Context of a Cosmological Source Distribution

It is well known that Gamma-ray Burst spectra often display a break at energies $\text{simless}400$ keV, with some exceptions extending to several MeV.\
Modeling of a cosmological source population is thus non-trivial when comparing the catalogs from instruments with different energy windows since this spectral structure is redshifted across the trigger channels at varying levels of sensitivity. We here include this important effect in an attempt to reconcile all the available data sets and show that a model in which bursts have a ``standard’’ spectral break at $300$ keV and occur in a population uniformly distributed in a \qo $=1\mathrm{/}2$ universe with no evolution can account very well for the combined set of observations. We show that the source population cannot be truncated at a minimum redshift $z_{min}$ beyond $\sim 0.1$, and suggest that a simple follow-on instrument to BATSE, with the same trigger window, no directionality and 18 times better sensitivity might be able to distinguish between a \qo$=0.1$ and a \qo$=0.5$ universe in $3$ years of full sky coverage, provided the source population has no luminosity evolution.