Solo dwarfs III: Exploring the orbital origins of isolated Local Group
  galaxies with Gaia Data Release 2
  We measure systemic proper motions for distant dwarf galaxies in the Local
Group and investigate if these isolated galaxies have ever had an interaction
with the Milky Way or M31. We cross-match photometry of isolated, star forming,
dwarf galaxies in the Local Group, taken as part of the {\it Solo} survey, with
astrometric measurements from Gaia Data Release 2. We find that NGC 6822, Leo
A, IC 1613 and WLM have sufficient supergiants with reliable astrometry to
derive proper motions. An additional three galaxies (Leo T, Eridanus 2 and
Phoenix) are close enough that their proper motions have already been derived
using red giant branch stars. Systematic errors in Gaia DR2 are significant for
NGC 6822, IC 1613 and WLM. We explore the orbits for these galaxies, and
conclude that Phoenix, Leo A and WLM are unlikely to have interacted with the
Milky Way or M31, unless these large galaxies are very massive ($\gtrsim 1.6
\times 10^{12}\,M_\odot$). We rule out a past interaction of NGC 6822 with M31
at $\sim 99.99\%$ confidence, and find there is a $<10$\% chance that NGC 6822
has had an interaction with the Milky Way. We examine the likely origins of NGC
6822 in the periphery of the young Local Group, and note that a future
interaction of NGC 6822 with the Milky Way or M31 in the next 4\,Gyrs is
essentially ruled out. Our measurements indicate that future Gaia data releases
will provide good constraints on the interaction history for the majority of
these galaxies.
