# Formation of runaway stars in a star-cluster potential

## TL;DR

This study investigates how binary interactions in star clusters lead to runaway stars, analyzing the effects of cluster potential depth on outcomes and velocities through simulations and analytic methods.

## Contribution

It provides new insights into the formation of runaway stars, showing that potential depth does not affect outcome fractions but influences binary populations and ejection angles.

## Key findings

- Outcome fractions are unaffected by potential depth.
- Escaped binaries have higher speeds and shorter semi-major axes.
- Ejection angles are generally large, peaking around 160 degrees.

## Abstract

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.