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

The low velocity of interstellar asteroid 1I/'Oumuamua with respect to our galaxy's Local Standard of Rest implies it is young. Adopting the young age hypothesis, we assess possible origin systems for this interstellar asteroid and for 2I/Borisov, though the latter's higher speed means it is unlikely to be young. First, their past trajectories are modelled under gravitational scattering by galactic components ('disk heating') to assess how far back one can trace them. The stochastic nature of disk heating means that a back-integration can only expect to be accurate to within 15 pc and 2 kms$^{-1}$ at -10 Myr, dropping steeply to 400 pc and 10 kms$^{-1}$ at -100 Myr, sharply limiting our ability to determine a precise origin. Nevertheless, we show `Oumuamua's origin system is likely currently within 1 kpc of Earth, in the local Orion Arm. Second, we back-integrate 'Oumuamua's trajectory to assess source regions, emphasizing young systems and moving groups. Though disk heating allows for only a statistical link to source regions, `Oumuamua passed through a considerable subset of the Carina and Columba moving groups when those groups were forming. This makes them perhaps the most plausible source region, if 'Oumuamua was ejected during planet formation or via intra-cluster interactions. We find three stars in the Ursa Major group, one brown dwarf, and seven other stars to have plausible encounters with 2I/Borisov, within 2 pc and 30 kms$^{-1}$. These encounters' high relative speeds mean none are likely to be the home of 2I/Borisov.