Massive runaways and walkaway stars
  Anticipating the kinematic constraints from the Gaia mission, we perform an
extensive numerical study of the evolution of massive binary systems to predict
the peculiar velocities that stars obtain when their companion collapses and
disrupts the system. Our aim is to (1) identify which predictions are robust
against model uncertainties and assess their implications, (2) investigate
which physical processes leave a clear imprint and may therefore be constrained
observationally and (3) provide a suite of publicly available model
predictions. We find that $22_{-8}^{+26}$% of all massive binary systems merge
prior to the first core collapse in the system. Of the remainder,
$86_{-9}^{+11}$% become unbound because of the core-collapse. Remarkably, this
rarely produce runaway stars (i.e., stars with velocities above 30 km/s). These
are outnumbered by more than an order of magnitude by slower unbound
companions, or "walkaway stars". This is a robust outcome of our simulations
and is due to the reversal of the mass ratio prior to the explosion and
widening of the orbit, as we show analytically and numerically. We estimate a
$10^{+5}_{-8}$% of massive stars to be walkaways and only $0.5^{+1.0}_{-0.4}$%
to be runaways, nearly all of which have accreted mass from their companion.
Our findings are consistent with earlier studies, however the low runaway
fraction we find is in tension with observed fractions 10%. If Gaia confirms
these high fractions of massive runaway stars resulting from binaries, it would
imply that we are currently missing physics in the binary models. Finally, we
show that high end of the mass distributions of runaway stars is very sensitive
to the assumed black hole natal kicks and propose this as a potentially
stringent test for the explosion mechanism. We discuss companions remaining
bound which can evolve into X-ray and gravitational wave sources.
