Proper motions of OB stars in the far Carina Arm
  In large scale maps of the Galactic disc, the Carina Arm stands out as a
clear spiral feature, hosting prominent star clusters and associations rich in
massive stars. We study the proper motions of 4199 O and early B most likely in
the far Carina Arm, at distances mainly in excess of 4 kpc from the Sun, within
the sky region, $282^{\circ} < \ell < 294^{\circ}$ and $-3^{\circ} < b <
+1^{\circ}$ (Galactic coordinates). The sample is constructed by extending an
existing blue-selected catalogue, and cross-matching with Gaia EDR3 astrometry.
The observed pattern of proper motions is modulated into a saw-tooth pattern,
with full amplitude approaching 1 mas yr$^{-1}$, recurring roughly every 2--3
degrees of longitude (200--300 pc at the median OB-star distance of 5.8 kpc).
Kinematic perturbation of underlying circular rotation is most likely present.
The data also reveal a moving group containing $>50$ OB stars at $\ell \sim
286^{\circ}$, $b \sim -1^{\circ}.4$ behind the main run of the far arm. An
analysis of relative proper motions is performed that yields an incidence of
runaway O stars of at least 10\% (potentially $>20$\% when full space motions
become available). To map where runaways have run away from, we set up
simulations for the region that assume linear trajectories and test for
trajectory impact parameter in order to identify likely ejection hot spots. We
find the method currently gives good results for times of flight of up to
$\sim$4 Myr. It shows convincingly that only NGC 3603 and Westerlund 2 have
ejected OB stars in significant numbers. Indeed, both clusters have experienced
intense spells of ejection between 0.6--0.9 and 0.5--0.8 Myr ago, respectively.
