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

Title: 势场背景下的 N=4 混沌问题的数值研究

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量的$N=4$数值散射实验，实验对象是两个由相同点粒子组成的相同双星系统，在连续的背景势中相互作用。 出于研究目的，尽管这并不影响一般性，我们假设该势对应于均匀的（新生或恒星形成的）气体介质。 我们探索了一组恒定的气体密度范围，从$n=10~ {\rm cm}^{-3}$到$10^{5}~ {\rm cm}^{-3}$。 这些密度适用于各种天体物理环境，包括分子云（即恒星形成区域）以及这些云中的更密集且碎片化的核区。 我们的主要目标是表征背景势对随后恒星动力学的影响。 我们考虑了双星-双星相互作用过程中形成的所有双星系统的结局概率及其特性，例如双星结合能和偏心率的分布。 我们还展示了被抛射出的单星的最终速度分布。 背景势对恒星动力学有两个重要的影响：1）该势作用于重置整个系统的总能量零点，进而影响相遇产物的类型和特性；2）对于更高的$n$和弱束缚系统（即大半长轴），当恒星被困在势中并在系统质心附近振荡时，恒星的动力学受到显著影响。 这反过来增加了质心附近恒星（单星、双星或三合星）之间的散射事件数量，并使单星更难逃逸至无穷远处。 最终，这导致三合星和宽双星的优先电离以及紧凑双星的生存，同时单星以非常高的抛射速度逃离。