A general method for assessing the origin of interstellar small bodies: the case of 1I/2017 U1 ('Oumuamua)

With the advent of more and deeper sky surveys, the discovery of interstellar small objects entering into the Solar System has been finally possible. In October 19, 2017, using observations of the Pan-STARRS survey, a fast moving object, now officially named 1I/2017 U1 ('Oumuamua), was discovered in a heliocentric unbound trajectory suggesting an interstellar origin. Assessing the provenance of interstellar small objects is key for understanding their distribution, spatial density and the processes responsible for their ejection from planetary systems. However, their peculiar trajectories place a limit on the number of observations available to determine a precise orbit. As a result, when its position is propagated $\sim 10^5-10^6$ years backward in time, small errors in orbital elements become large uncertainties in position in the interstellar space. In this paper we present a general method for assigning probabilities to nearby stars of being the parent system of an observed interstellar object. We describe the method in detail and apply it for assessing the origin of 'Oumuamua. A preliminary list of potential progenitors and their corresponding probabilities is provided. In the future, when further information about the object and/or the nearby stars be refined, the probabilities computed with our method can be updated. We provide all the data and codes we developed for this purpose in the form of an open source {\tt C/C++/Python package}, {\bf\tt iWander} which is publicly available at http://github.com/seap-udea/iWander.