THE BRIGHTNESS DISTRIBUTION OF BURSTING SOURCES IN RELATIVISTIC COSMOLOGIES

We present analytical solutions for the integral distribution of arbit rary bursting or steady source counts as a function of peak photon cou nt rate within Friedmann cosmological models. We discuss both the stan dard candle and truncated power-law luminosity function cases with a p ower-law density evolution. While the analysis is quite general, the s pecific example discussed here is that of a cosmological gamma-ray bur st distribution. These solutions show quantitatively the degree of dep endence of the counts on the density and luminosity function parameter s, as well as the weak dependence on the closure parameter and the max imum redshift. An approximate comparison with the publicly available C ompton Gamma Ray Observatory data gives an estimate of the maximum sou rce luminosity and an upper limit to the minimum luminosity. We discus s possible ways of further constraining the various parameters.