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Constraints on the Gamma-ray Burst Luminosity Function from PVO and BATSE

We examine the width of the gamma-ray burst luminosity function through the distribution of GRB peak fluxes as detected by the Pioneer Venus Orbiter (PVO) and the Burst and Transient Source Experiment (BATSE). The strength of the analysis is greatly enhanced by using a merged catalog of peak fluxes from both instruments with good cross-calibration of their sensitivities. The range of peak fluxes is increased by approximately a factor of 20 relative to the BATSE catalog. Thus, more sensitive investigations of the $\log N-\log P$ distribution are possible. We place constraints on the width of the luminosity function of gamma-ray bursts brighter than the BATSE completeness limit by comparing the intensity distribution in the merged catalog with those produced by a variety of spatial density and luminosity functions. For the models examined, $90\%$ of the {\em detectable\/} bursts have peak luminosities within a range of 10, indicating that the peak luminosities of gamma-ray bursts span a markedly less wide range of values than many other of their measurable properties. We also discuss for which slopes of a power-law luminosity function the observed width is at the upper end of the constrained range. This is important in determining the power-law slopes for which luminosity-duration correlations could be important.