Kinematic distinction of the two subpopulations of X-ray pulsars
  The population of Be/X-ray binaries shows strong evidence of bimodality,
especially in the spin period of neutron stars. Several physical mechanisms may
produce this bimodality. The most favored candidate mechanisms are two distinct
supernova channels or different accretion modes of the neutron stars in
Be/X-ray binaries. Investigating the kinematics of these systems may provide
some additional insight into the physics of this bimodality. If the two
Be/X-ray binary subpopulations arise from two distinct supernova types, then
the two subpopulations should have different peculiar (systemic) velocities.
This can be tested either directly, by measuring the velocity of the system, or
indirectly, by measuring the position of the system with respect to its
birthplace. Using the most recent Gaia dataset and the newest catalogs of Small
Magellanic Cloud (SMC) star clusters, we analyzed the tangential peculiar
velocities of Be/X-ray binaries in the Galaxy and the positions of Be/X-ray
binaries in the SMC. We used the distance of the system from the nearest young
star cluster as a proxy to the tangential velocity of the system. We applied
statistical testing to investigate whether the two subpopulations that are
divided by the spin of the neutron star are also kinematically distinct. There
is evidence that the two subpopulations are indeed kinematically distinct.
However, the tangential peculiar velocities of the two subpopulations are the
reverse from what is expected from the distinct supernova channel hypothesis.
We find some marginal evidence ($p \approx$~0.005) that the Galactic Be/X-ray
binaries from the short-spin subpopulation have systematically higher peculiar
velocities than the systems from the long-spin subpopulation. The same effect,
but weaker, is also recovered for the SMC Be/X-ray binaries for all considered
cluster catalogs.
