Formation of runaway stars in a star-cluster potential
  We study the formation of runaway stars due to binary-binary (2+2)
interactions in young star-forming clusters and/or associations. This is done
using a combination of analytic methods and numerical simulations of 2+2
scattering interactions, both in isolation and in a homogeneous background
potential. We focus on interactions that produce two single stars and a binary,
and study the outcomes as a function of the depth of the background potential,
within a range typical of cluster cores. As reference parameters for the
observational properties, we use those observed for the system of runaway stars
AE Aur and $\mu$ Col and binary $\iota$ Ori. We find that the outcome fractions
have no appreciable dependence on the depth of the potential, and neither do
the velocities of the ejected single stars. However, as the potential gets
deeper and a larger fraction of binaries remain trapped, two binary populations
emerge, with the escaped component having higher speeds and shorter semi-major
axes than the trapped one. Additionally, we find that the relative angles
between the ejected products are generally large. In particular, the angle
between the ejected fastest star and the escaped binary is typically $\gtrsim
120-135^{\circ}$, with a peak at around $160^{\circ}$. However, as the
potential gets deeper, the angle distribution becomes broader. Finally, we
discuss the implications of our results for the interpretation of the
properties of the runaway stars AE Aur and $\mu$ Col.
