  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.
