Previous
abstract 
Next abstract
\noindent The distribution of gamma-ray burst sources detected with BATSE is iso\-tro\-pic yet non-uniform. There is a deficit of weak events which is commonly expressed by a \vvm less than the 0.5 expected for a uniform Eu\-clid\-ean distribution. It has been argued (e.g., Mao and Paczynski 1992) that this may be a signature of a Cosmological expansion in a FRW universe with a uniform, co-moving distribution of sources. However, a comparison of the \vvm and burst detection rates of several experiments presents an apparent paradox: e.g., Konus detected the bursts more frequently than SMM, implying a better sensitivity and larger sampling volume, yet its measured \vvm was $\sim 0.45$ compared to SMM's value of $\sim 0.40$, suggesting instead a lesser deviation from Eu\-clid\-ean space. We point out that this apparent conflict stems from the assumption that all bursts have a standard spectrum with a single power law. But realistic spectra often exhibit broken power laws, with a break energy $100\;\hbox{keV} \simless\epsilon_b\simless 3$ MeV.\ \ Thus, the flux measured by a particular instrument depends on both the redshift of the source and the energy window of the detector. In other words, for a given energy window, the flux of a more distant burst will be further decreased below the value expected from the Cosmological model due to the red-shifting of $\epsilon_b$ across the window. We show that the inclusion of an intrinsic $\epsilon_b$ ($\sim 500$ keV) and a consideration of the different detector energy responses and sensitivities can self-consistently account for the rates and \vvm of the Konus, PVO, SMM, and BATSE datasets. Because of the dependence of the observed characteristics on the energy window, a subset of the BATSE catalog, based solely on the burst fluence in the higher energy (i.e., 4${th}$) channel, provides an additional ``data'' point in the \vvm versus rate plane. In particular, Konus's higher rate for a larger value of \vvm is due to its better sensitivity, but smaller and lower energy window than SMM.\ \ In the context of this improved model, BATSE is apparently sampling a source distribution out to a redshift $z_{max} \sim 1.3$, whereas Konus was limited to $z_{max} \approx 0.5$, SMM to $\approx 0.3$, and PVO to $\approx 0.2$.
