Dynamical evolution of star-forming regions: III. Unbound stars and predictions for Gaia

We use $N$-body simulations to probe the early phases of the dynamical evolution of star-forming regions and focus on mass and velocity distributions of unbound stars. In this parameter space study, we vary the initial virial ratio and degree of spatial and kinematic substructure and analyse the fraction of stars that become unbound in two different mass classes (above and below 8 M$_{\odot}$). We find that the fraction of unbound stars differs depending on the initial conditions. After 10 Myr, in initially highly subvirial, substructured simulations, the high-mass and lower-mass unbound fractions are similar at $\sim$23 per cent. In initially virialised, substructured simulations, we find only $\sim$16 per cent of all high-mass stars are unbound, whereas $\sim$37 per cent of all lower-mass stars are. The velocity distributions of unbound stars only show differences for extremely different initial conditions. The distributions are dominated by large numbers of lower-mass stars becoming unbound just above the escape velocity of $\sim$3 km s$^{-1}$ with unbound high-mass stars moving faster on average than lower-mass unbound stars. We see no high-mass runaway stars (velocity > 30 km s$^{-1}$) from any of our initial conditions and only an occasional lower-mass runaway star from initially subvirial/substructured simulations. In our simulations, we find a small number of lower-mass walkaway stars (with velocity 5-30 km s$^{-1}$) from all of our initial conditions. These walkaway stars should be observable around many nearby star-forming regions with Gaia.