CONSTRAINTS ON THE LUMINOSITY FUNCTION OF GAMMA-RAY BURSTS DETECTED BY BATSE

We have utilized the integral moment analysis technique of Horack & Em slie to extract information on the allowable form of the luminosity fu nction for gamma-ray bursts observed by BATSE. Using the general prope rties of moments, we are able to derive constraints on-the range of lu minosity from which the gamma-ray bursts must be sampled. These constr aints are independent of the form of the radial distribution of the ga mma-ray bursts, and depend only on the assumptions that space is Eucli dean and that the luminosity function phi(L) is distance independent. For power-law luminosity functions of the form phi(L) = A(o)L(-alpha), we find that the range of luminosity from which 80% of the gamma-ray bursts must be sampled cannot exceed -6.5, with a 3 sigma upper limit of 12-15, regardless of the value of alpha.