Numerical study of the chaotic N=4 problem in a background potential
  We perform a large suite of $N=4$ numerical scattering experiments between two identical binaries consisting of identical point particles in a (continuous) background potential. For investigative purposes, albeit without loss of generality, we assume that the potential corresponds to a uniform (natal or star-forming) gas medium. We explore a range of constant gas densities, from $n=10~ {\rm cm}^{-3}$ to $10^{5}~ {\rm cm}^{-3}$. These densities are relevant for various astrophysical environments, including molecular clouds (i.e., star-forming regions) and denser, fragmented cores within these clouds. Our primary goal is to characterize the effects of the background potential on the subsequent stellar dynamics. We consider the outcome probabilities as well as the properties of any binaries formed during the binary-binary encounters, such as the distributions of binary binding energies and eccentricities. We also present the final velocity distributions of the ejected single stars. The background potential has two important effects on the stellar dynamics: 1) The potential acts to reset the zero-point of the total system energy, which in turn affects the types and properties of the products of the encounter; 2) For higher $n$ and weakly bound systems (i.e., large semimajor axes), the stellar dynamics are significantly affected when stars become trapped in the potential, oscillating around the system centre of mass (CM). This, in turn, increases the number of scattering events between stars (single, binary or triple) near the CM and makes it harder for single stars to escape to infinity. This ultimately leads to the preferential ionization of triples and wide binaries and the survival of compact binaries, with the single stars escaping at very high ejection velocities. 
Taeho Ryu, Nathan W. C. Leigh, Rosalba Perna
astro-ph.SR astro-ph.GA