MAXIMUM-LIKELIHOOD ANALYSIS OF CLUSTERS OF ULTRAHIGH-ENERGY COSMIC-RAYS

We present a numerical code designed to conduct a likelihood analysis for clusters of nucleons above 10(19) eV originating from discrete ast rophysical sources such as powerful radio galaxies, gamma-ray bursts o r topological defects. The code simulates the propagation of nucleons in a large-scale magnetic field and constructs the likelihood of a giv en observed event cluster as a function of the average time delay due to deflection in the magnetic field, the source activity time scale, t he total fluence of the source, and the power-law index of the particl e injection spectrum. Its dependence on coherence length and the power spectrum of the magnetic field are found to be negligible within thei r usually considered ranges. We apply our code to the three pairs of e vents above 4 X 10(19) eV recently reported by the Akeno Giant Air Sho wer Array (AGASA) experiment, assuming that these pairs were caused by nucleon primaries which originated from a common source. Although cur rent data are too sparse to constrain fully each of the parameters con sidered, and/or to discriminate models of the origin of ultrahigh ener gy cosmic rays, several tendencies are indicated. If the clustering su ggested by AGASA is real, next generation experiments with their incre ased exposure should detect more than similar to 10 particles per sour ce over a few years and our method will put strong constraints on both the large-scale magnetic field parameters and the nature of these sou rces. [S0556-2821(97)03720-X].