Abstract
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 (i) identify which predictions are robust against model uncertainties and assess their implications, (ii) investigate which physical processes leave a clear imprint and may therefore be constrained observationally, and (iii) provide a suite of publicly available model predictions to allow for the use of kinematic constraints from the Gaia mission. 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 produces runaway stars (observationally defined as stars with velocities above 30 km s(-1)). 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. For stars more massive than 15 M-circle dot, we estimate that 10(-8)(+5)% are walkaways and only 0.5(-0.4)(+1.0)% are 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 of about 10%. Thus, astrometric data on presently single massive stars can potentially constrain the physics of massive binary evolution. Finally, we show that the high end of the mass distributions of runaway stars is very sensitive to the assumed black hole natal kicks, and we propose this as a potentially stringent test for the explosion mechanism. We also discuss companions remaining bound that can evolve into X-ray and gravitational wave sources.