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The properties of dynamically ejected runaway and hyper-runaway stars

Runaway stars are stars observed to have large peculiar velocities. Two mechanisms are thought to contribute to the ejection of runaway stars, both involve binarity (or higher multiplicity). In the binary supernova scenario a runaway star receives its velocity when its binary massive companion explodes as a supernova (SN). In the alternative dynamical ejection scenario, runaway stars are formed through gravitational interactions between stars and binaries in dense, compact clusters or cluster cores. Here we study the ejection scenario. We make use of extensive N-body simulations of massive clusters, as well as analytic arguments, in order to to characterize the expected ejection velocity distribution of runaways stars. We find the ejection velocity distribution of the fastest runaways (>~80 km s^-1) depends on the binary distribution in the cluster, consistent with our analytic toy model, whereas the distribution of lower velocity runaways appears independent of the binaries properties. For a realistic log constant distribution of binary separations, we find the velocity distribution to follow a simple power law; Gamma(v) goes like v^(-8/3) for the high velocity runaways and v^(-3/2) for the low velocity ones. We calculate the total expected ejection rates of runaway stars from our simulated massive clusters and explore their mass function and their binarity. The mass function of runaway stars is biased towards high masses, and depends strongly on their velocity. The binarity of runaways is a decreasing function of their ejection velocity, with no binaries expected to be ejected with v>150 km s^-1. We also find that hyper-runaways with velocities of hundreds of km s^-1 can be dynamically ejected from stellar clusters, but only at very low rates, which cannot account for a significant fraction of the observed population of hyper-velocity stars in the Galactic halo.