3 Discussion

A remarkable step forward has been achieved recently with the discovery of the GRB afterglow emission (Costa et al. 1997; Van Paradijs et al. 1997) which made it possible to measure the redshifts of some GRB hosts. In Fig. 2 we show, on top of the ULYSSES peak flux distribution, the peak fluxes of 8 GRBs with known host redshifts. It is interesting to note that the "Euclidean'' region of the peak flux distribution contains at least one, and possibly two, very distant sources (GB 971214 and GB 980329). If future observations confirm that a significant fraction of bright GRBs come from sources with redshifts > 1, this might be an indication that GRBs undergo significant luminosity evolution.

Our observations raise the issue of the interpretation of the -3/2 slope measured for bright bursts. Until the beginning of the $\rm 90's$ it was generally thought that this slope reflected the spatial homogeneity of nearby bursters in our local Euclidean universe. With the few redshifts now available, it appears that this explanation is no longer tenable. It is clear now that GRBs have a broad luminosity function, that they undergo significant density evolution (if they are the result of stellar evolution the burst rate must follow the stellar formation rate) and possibly luminosity evolution. In such a complex situation the interpretation of the peak flux distribution requires at least some knowledge of these effects. Understanding the influence of the luminosity function and of the density and luminosity evolution will probably require the measure of a few tens of redshifts. Until then the interpretation of the slope at the bright end of the peak flux distribution will remain speculative.

On the other hand, when we understand the role of the various parameters that impact the shape of the peak flux distribution, it will become increasingly important to have homogeneous datasets containing hundreds of GRBs like those of ULYSSES and BATSE. The long observing time of these two missions and the fact that they have hundreds of GRBs in common offer the opportunity to construct number-intensity curves with unprecedented accuracy over a broad range of intensities. In this respect it is especially important to continue to accumulate as much data as possible with these instruments.

  

Figure 2: The peak flux distribution of ULYSSES real time GRBs in physical units. Also indicated are the peak fluxes of 8 GRBs with measured redshifts (the value for GB 980613 is an upper limit as this burst is not seen in ULYSSES real time data)

Acknowledgements

We are grateful to the BATSE team for making the Current BATSE GRB Catalog available. KH is grateful for support under JPL Contract 958056 and NASA grant NAG5-1560.