Constraints on the Spatial Distribution and Luminosity function of GRBs

Abstract

The distance scale to gamma ray bursts has been a subject of scientific debate for almost thirty years. Up to the discovery of afterglows only indirect methods could be used to constrain the distance scale to this objects. I review some of these results, and show the current limits on the spatial distribution and luminosity function of GRBs. The results obtained with different methods indicate that gamma-ray bursts lie at the typical redshifts $z_{ave}$ between 1 and 2, however there can exist a long tail of the distribution stretching to higher redshifts. The width of the GRB luminosity function (the ratio of the intrinsic brightness of the brightest to the dimmest observed burst) estimated from Beppo SAX bursts with redshifts is almost $10^3$.