Statistical implications of the n = 1 observation of 1I/'Oumuamua

Abstract

ABSTRACT We obtain the exact statistical distribution of expected detection rates that may be obtained from the detection of ‘Oumuamua, which currently belongs to a class of objects that is only observed once in our Solar system. The derivation of the distribution of future detection rates starts from the assumption that the detection is a result of a Poisson process, and uses Bayes theorem along with information theory to get the result. We derive the probability for the next such observation along with the confidence limits of this prediction assuming that observations are done with the forthcoming Vera C. Rubin Observatory. This probability depends on the estimates of detection rates that existed prior to the ‘Oumuamua observation. However, unless the constraints given by these model-based estimates are within an order of magnitude of the actual detection rate, they have a negligible effect on the probability of making a second observation. The results are generalized to the expected future case where more than one observation exists.