Determination of gamma-ray burst properties through integral moment self-consistency analysis

Abstract

Since April 1991, over 1000 GRBs have been observed with the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (GRO), providing unprecedented information on the brightnesses, spectra and celestial coordinates for these bursts. The authors address the application of inversion techniques to this data set (in particular the brightness distribution of observed bursts) in order to constrain the physical properties of these enigmatic objects. The central method used is based on the interdependence of normalized integral moments of non-negative functions. These techniques are applied to bursts distributed both in Euclidean space and in various cosmological (non-Euclidean) spaces. The authors derive surprisingly powerful constraints on the range of intrinsic luminosities of bursts and/or on their distribution in space. They also demonstrate the formal equivalence of their technique to one involving Mellin transforms. Finally, they point out the generality of their technique, which can be applied straightforwardly to any relation amongst three quantities A, B and C of the form A=B*C, where information about only the distribution of values of A is known or observed, and information about the distribution of values of B or C is desired.