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The low velocity of interstellar asteroid 1I/'Oumuamua with respect to ourgalaxy's Local Standard of Rest implies it is young. Adopting the young agehypothesis, we assess possible origin systems for this interstellar asteroidand for 2I/Borisov, though the latter's higher speed means it is unlikely to beyoung. First, their past trajectories are modelled under gravitationalscattering by galactic components ('disk heating') to assess how far back onecan trace them. The stochastic nature of disk heating means that aback-integration can only expect to be accurate to within 15 pc and 2kms$^{-1}$ at -10 Myr, dropping steeply to 400 pc and 10 kms$^{-1}$ at -100Myr, sharply limiting our ability to determine a precise origin. Nevertheless,we show `Oumuamua's origin system is likely currently within 1 kpc of Earth, inthe local Orion Arm. Second, we back-integrate 'Oumuamua's trajectory to assesssource regions, emphasizing young systems and moving groups. Though diskheating allows for only a statistical link to source regions, `Oumuamua passedthrough a considerable subset of the Carina and Columba moving groups whenthose groups were forming. This makes them perhaps the most plausible sourceregion, if 'Oumuamua was ejected during planet formation or via intra-clusterinteractions. We find three stars in the Ursa Major group, one brown dwarf, andseven other stars to have plausible encounters with 2I/Borisov, within 2 pc and30 kms$^{-1}$. These encounters' high relative speeds mean none are likely tobe the home of 2I/Borisov.

The Dynamics of Interstellar Asteroids and Comets within the Galaxy: an Assessment of Local Candidate Source Regions for 1I/`Oumuamua and 2I/Borisov