Likelihood Methods and Classical Burster Repetition

Abstract

We develop a likelihood methodology which can be used to search for evidence of burst repetition in the BATSE catalog, and to study the properties of the repetition signal. We use a simplified model of burst repetition in which a number $N_{\rm r}$ of sources which repeat a fixed number of times $N_{\rm rep}$ are superposed upon a number $N_{\rm nr}$ of non-repeating sources. The instrument exposure is explicitly taken into account. By computing the likelihood for the data, we construct a probability distribution in parameter space that may be used to infer the probability that a repetition signal is present, and to estimate the values of the repetition parameters. The likelihood function contains contributions from all the bursts, irrespective of the size of their positional errors --- the more uncertain a burst's position is, the less constraining is its contribution. Thus this approach makes maximal use of the data, and avoids the ambiguities of sample selection associated with data cuts on error circle size. We present the results of tests of the technique using synthetic data sets.