1 Introduction

What is the average peak luminosity of Gamma-Ray Bursts (GRBs)? We now know that they are indeed cosmological in distance, yet there is still a wide range of possible luminosities. If the number density does not evolve, then fits to the ${\rm Log}N-{\rm Log}P$ curve suggest that the peak luminosity is $1 \ 10^{57}$ photon s^-1 or roughly $6\ 10^{50}$ erg s^-1. (Peak luminosities in photon units are all for 50-300 keV with 256 ms time bins, while those in ergs are for 30-2000 keV.) If the number density traces the star formation rate (SFR) of our Universe, then fits to the ${\rm Log}N-{\rm Log}P$ curve suggest that the peak luminosity is $2 \ 10^{58}$ photon s^-1 or roughly $1\ 10^{52}$ erg s^-1. At this meeting, there were several suggestions that the peak luminosity might be substantially larger than even the SFR value.

The average luminosity of GRBs still has large uncertainties. The GRB optical transients (OTs) with a reported red shift yield luminosity values which range over roughly five orders of magnitude. GRB 971214 has a galaxy with red shift z=3.42 and a luminosity of $1\ 10^{59}$ photon s^-1. GRB 980703 has an optical transient with a red shift of z = 0.966 which corresponds to a luminosity of $1 \ 10^{58}$ photon s^-1. GRB 970508 has an optical transient with a red shift of z = 0.83 and a luminosity of $2\ 10^{57}$ photon s^-1. GRB 970425 has an associated unusual supernova at a red shift of z = 0.0085 for a luminosity of $1\ 10^{54}$ photon s^-1. Although the optical red shift measures provides promise of definitive answers within a few years, the current situation has no clear conclusion.

In the mean time, other measured quantities give information on the distance and luminosity distribution of bursters. In particular, the limits on apparent magnitudes of possible host galaxies inside the small GRB optical transient boxes carries information on the GRB distance scale. The idea is that nearby (low luminosity) events should have their hosts appear relatively bright while distant (high luminosity) events should have their hosts appear systematically faint. This paper gives the result from an analysis on the limits to possible host galaxies inside the error boxes for eight GRBs with optical transients.