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.
