AI 中文总结
研究超大质量黑洞空损失锥中恒星双星演化，基于前人工作开发半解析模型，修正保持偏心率和角动量向量正交性，给出最终轨道参数概率分布解析拟合，揭示广义相对论进动和恒星潮汐对双星合并比例的影响。
AI 中文摘要
围绕超大质量黑洞运行的双星系统，通过与其他恒星、黑洞潮汐力以及双星内部动力学（包括广义相对论进动和潮汐）相互作用而演化。许多双星被驱动到高度偏心的内双星轨道，可能导致恒星合并；其他可能结果包括超高速恒星喷射或潮汐破坏事件。我们研究空损失锥区域中双星的演化，该区域中由于与其他恒星散射导致的外轨道每轨道角动量变化小于潮汐分离半径处的外角动量。我们在Hamers和Samsing的工作基础上，开发了一个计算效率高的半解析模型，该模型捕捉了在双星潮汐分离半径与围绕黑洞的近日点之比小于0.15的微扰区域中双星的长期演化。关键是，我们进行修正以保持双星偏心率和角动量向量之间的正交性，防止非物理的偏心率增长。从这些模拟中，我们找到了接近黑洞的双星最终轨道参数概率分布的解析拟合。我们发现广义相对论进动有效地抑制了类似冯·齐佩尔 - 利多维 - 科扎伊的偏心率振荡，并将合并双星的比例从仅牛顿物理时的84%降低到包括进动时的3%。恒星潮汐进一步将合并比例降低到0.4%。
英文摘要
Binary star systems orbiting close to a supermassive black hole (SMBH) evolve through encounters with other stars, the SMBH's tidal forces, and the binary's internal dynamics, including general relativistic precession and tides. Many are driven onto highly eccentric inner binary orbits, potentially leading to stellar mergers; other possible outcomes include hypervelocity star ejections or tidal disruption events. We study the evolution of binaries in the empty loss cone regime, where the outer orbit's angular momentum change per orbit due to scattering off other stars is smaller than the outer angular momentum at the tidal separation radius. We build on the work of Hamers \& Samsing to develop a computationally efficient semi-analytical model that captures the long term evolution of binaries in perturbative regimes where the ratio of the binary tidal separation radius to the pericenter around the SMBH is smaller than 0.15. Crucially, we apply corrections to preserve the orthogonality between the binary's eccentricity and angular momentum vectors, which prevents unphysical eccentricity growth. From these simulations, we find analytical fits for the probability distributions of the final orbital parameters of binaries approaching the SMBH. We find that general relativistic precession efficiently suppresses von-Zeipel-Lidov-Kozai-like eccentricity oscillations and reduces the fraction of merging binaries from $84\%$ with Newtonian physics only, to $3\%$ with precession included. Stellar tides further reduce the merger fraction to $0.4\%$.
