3 Small IPN boxes

This conclusion is actually an old one (e.g. Schaefer 1992; Schaefer et al. 1997) and can be substantially improved

upon. The improvement comes with using the smallest error boxes produced by the Interplanetary Network (IPN), since these bursts are greatly brighter than those with OT boxes. For the 16 IPN boxes with a size less than 25 square arc-minutes and more than $10^{\circ}$ from the galactic equator, the maximum and median and minimum P₂₅₆ values are 73 and 44 and 15 photon s^-1 cm^-2. In contrast, the eight GRBs with OT boxes have maximum and median and minimum P₂₅₆ values of 13.3 and 2.4 and 0.6 photon s^-1 cm^-2. Thus, the IPN bursts are $\sim 16$ times brighter than the OT bursts. Approximately, the IPN bursts will be four times closer. This is important since these all-time bright bursts will be sufficiently close such that all of the problems that plague the faint and distant OT bursts will be small. From detailed calculations for the SFR case, the IPN bursts have median red shifts of 0.6 while the OT bursts have median red shifts of 2.2. Thus, the bright IPN bursts can be used with minimal uncertainties related to K corrections, luminosity functions, anomalous dust extinction, and cosmology.

Schaefer (1999) analyses the limits on host galaxy brightnesses from the compilation of Schaefer et al. (1998) with the same method as reported in this paper. The result is that $<F_{\min}\gt\ =0.14 \pm 0.05$ for the no-evolution case, $<F_{\min}\gt\ = 0.29 \pm 0.12$ for the SFR case, the minimum peak luminosity acceptable at the one-sigma level is $6\ 10^{58}$ photon s^-1, while the best estimate of $<F_{\min}\gt$ is acceptable only for peak luminosities $\geq 1\ 10^{59}$ photon s^-1. These limits are more restrictive than those from the OT bursts, and the uncertainties associated with high red shift are minimal.

From either the IPN or OT bursts, I conclude that the average peak luminosity of GRBs must be $\geq 6\ 10^{58}$ photon s^-1 if the bursters reside in normal galaxies. This corresponds to the faint BATSE bursts typically at red shifts of 5.9. Alternatively, GRBs might reside in systematically and greatly subluminous galaxies or perhaps even outside galaxies.