On the kinematics of a runaway Be star population
  We explore the hypothesis that B type emission-line stars (Be stars) have
their origin in mass-transfer binaries by measuring the fraction of runaway Be
stars. We assemble the largest-to-date catalogue of 632 Be stars with 6D
kinematics, exploiting the precise astrometry of the Tycho-Gaia Astrometric
Solution (TGAS) from the first Gaia Data Release. Using binary stellar
evolution simulations, we make predictions for the runaway and equatorial
rotation velocities of a runaway Be star population. Accounting for
observational biases, we calculate that if all classical Be stars originated
through mass transfer in binaries, then $17.5\%$ of the Be stars in our
catalogue should be runaways. The remaining $82.5\%$ should be in binaries with
subdwarfs, white dwarfs or neutron stars, because those systems either remained
bound post-supernova or avoided the supernova entirely. Using a Bayesian
methodology, we compare the hypothesis that each Be star in our catalogue is a
runaway to the null hypothesis that it is a member of the Milky Way disc. We
find that $13.1^{+2.6}_{-2.4}\%$ of the Be stars in our catalogue are runaways,
and identify a subset of 40 high-probability runaways. We argue that
deficiencies in our understanding of binary stellar evolution, as well as the
degeneracy between velocity dispersion and number of runaway stars, can explain
the slightly lower runaway fraction. We thus conclude that all Be stars could
be explained by an origin in mass-transfer binaries. This conclusion is
testable with the second Gaia data release (DR2).
