AI 中文总结
该研究通过层级三体系统的 N 体模拟，探究自由漂浮行星的抛射速度与质量函数，明确了巨行星质量、偏心率等参数对抛射的影响，为解释银河系自由漂浮行星的观测特征提供了动力学依据。
AI 中文摘要
自由漂浮行星（FFPs，又称 rogue 行星）是不受任何主恒星束缚、在银河系中运行的亚恒星天体。它们的速度分布携带了将它们从诞生系统中释放的动力学通道信息，而它们的质量函数则编码了可被抛射的行星的潜在丰度。我们开展了一系列层级三体系统的直接 N 体模拟，该系统包含一个太阳质量的主恒星、一个大质量巨行星摄动体，以及一个在限制性三体 regime 中处理的较轻行星。我们改变了被抛射行星的质量、巨行星摄动体的质量、轻行星的半长轴，以及两颗行星的偏心率，测量了渐近抛射速度 $v_\rm\infty$ 和首次被接受的抛射输出时的有限半径抛射速度 $v_\rm kick$。被抛射天体的质量在四个数量级范围内对结果几乎没有影响，证实了测试粒子极限。相比之下，巨行星质量设定了抛射的尺度和时间，遵循长期标度关系 $t_\rm ejec\propto M_J^{-1}$。偏心率主要影响高速尾部而非中位数：较高的轻行星偏心率将抛射上限延伸至约 23 km/s，而高度偏心率的巨行星可通过近心点增强的弹弓相遇产生罕见的接近 80 km/s 的抛射。我们基于希尔尺度散射、蒂斯朗参数以及弹弓能量交换的偏心率依赖上限包络，用半解析框架解释这些趋势，并讨论抛射速度如何映射到银河系 FFP 的速度弥散，以及质量函数如何设定与 Roman 和 Euclid 相关的微引力透镜时标分布。
英文摘要
Free-floating planets (FFPs), also known as rogue planets, are sub-stellar objects that travel through the Galaxy unbound to any host star. Their velocity distribution carries information about the dynamical channel that released them from their birth systems, while their mass distribution encodes the underlying abundance of planets available for ejection. We present a suite of direct $N$-body simulations of hierarchical three-body systems consisting of a Solar-mass host star, a massive giant perturber, and a lighter planet treated in the restricted three-body regime. We vary the mass of the ejected planet, the mass of the giant perturber, the light planet's semi-major axis, and the eccentricities of both planets, measuring the asymptotic ejection velocity $v_\infty$ and the finite-radius ejection speed $v_{\rm kick}$ at the first accepted ejection output. The ejected body's mass has little effect on the outcome over four orders of magnitude, confirming the test-particle limit. By contrast, the giant-planet mass sets the ejection scale and time, following the secular scaling $t_{\rm ejec}\propto M_J^{-1}$. The eccentricities mainly affect the high-velocity tail rather than the median: a higher light-planet eccentricity extends the kick ceiling to $\sim23$ km/s, while a highly eccentric giant can yield rare kicks near $80$ km/s via pericentre-enhanced slingshot encounters. We interpret these trends with a semi-analytic framework based on Hill-scale scattering, the Tisserand parameter, and an eccentricity-dependent upper envelope for slingshot energy exchange, and discuss how the ejection velocities map onto the Galactic FFP velocity dispersion and how the mass function sets the microlensing timescale distribution relevant for Roman and Euclid.
Comments39 pages, 9 figures, comments welcome
