Limits to the burster repetition rate as deduced from the 2nd catalog of the interplanetary network

The burster repetition rate is an important parameter in many gamma ray burst models. The localizations of the interplanetary network, which have a relatively small combined surface area, may be used to estimate the average repetition rate. The method consists of (1) estimating the number of random overlaps between error boxes expected in the catalog and comparing this number to that actually observed; (2) modeling the response of the detectors in the network, so that the probability of detecting a burst can be estimated; and (3) simulating the arrival of bursts at the network assuming that burster repetition is governed by a Poisson process. The application of this method for many different burster luminosity functions shows that (1) the lower limit to the burster repetition rate depends strongly upon the assumed luminosity function; (2) the best lower limit to the repetition period obtainable from the data of the network is about 100 months; and (3) that a luminosity function for all bursters similar to that of the 1979 Mar 5 burster is inconsistent with the data.