Title: Numerical study of the chaotic N=4 problem in a background potential Show Chinese title

Title: N=4问题在背景势场中的混沌数值研究

Abstract: 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. Show Chinese abstract

Abstract: 我们进行了一系列大规模的$N=4$数值散射实验，涉及两个由相同点粒子组成的双星系统，在(连续)背景势场中进行相互作用。 出于研究目的，尽管不失去一般性，我们假设该势场对应于均匀的(natal或恒星形成)气体介质。 我们探索了从$n=10~ {\rm cm}^{-3}$到$10^{5}~ {\rm cm}^{-3}$的一系列恒定气体密度。 这些密度与多种天体物理环境相关，包括分子云（即恒星形成区域）以及这些云中的更密集、碎片化的核心。 我们的主要目标是表征背景势场对后续恒星动力学的影响。 我们考虑了结果的概率以及在双星-双星相遇过程中形成的任何双星的特性，例如双星结合能和偏心率的分布。 我们还展示了被抛出的单星的最终速度分布。 背景势场对恒星动力学有两个重要影响：1) 该势场会重置整个系统能量的零点，从而影响碰撞产物的类型和特性；2) 对于较高的$n$和弱束缚系统（即较大的半长轴），当恒星被困在势场中并在系统质心（CM）周围振荡时，恒星动力学会受到显著影响。 这反过来增加了在CM附近恒星（单星、双星或三体）之间的散射事件数量，并使单星更难逃逸到无限远。 最终导致三体和宽双星的优先电离以及致密双星的存活，而单星则以非常高的抛射速度逃逸。