AI 中文总结
研究克尔黑洞周围偏心轨道的拉普拉斯面，分析黑洞相对论效应及对利杜夫-科萨伊循环的影响，解释银心S星族的取向。
AI 中文摘要
我们研究了带有伴星的克尔黑洞周围偏心轨道的拉普拉斯面。两个相对论效应（近心点进动和冷泽-提尔进动）与伴星的潮汐效应相平衡。通过求解长期方程，我们发现平衡解的两个分支仅存在于测试粒子轨道倾角的窄范围内，且当伴星的倾角接近90度时解是稳定的。随后我们研究了黑洞对利杜夫-科萨伊循环的影响。除了黑洞对循环振幅的抑制作用外，我们还发现循环频率相对于到黑洞的距离呈非单调变化，并在广义相对论近心点进动与伴星潮汐进动的过渡区间达到最小值。最后我们利用该机制很好地解释了银心S星族近乎各向同性的取向。
英文摘要
We study the Laplace surface of eccentric orbits around a Kerr black hole with a companion star. The two relativistic effects (periapsis apsidal precession and Lense-Thirring precession) balance companion's tidal effect. By solving the secular equations, we find that the two branches of equilibrium solutions exist only in a narrow range of orbital inclinations of test particle, and that the stability exists when companion's obliquity approaches 90 degree. We then study the black-hole effects on Lidov-Kozai cycles. In addition to the black-hole suppression on cycle amplitude, we find that the cycle frequency is non-monotonic about distance from black hole and reaches its minimum in the transition between GR apsidal precession and companions's tidal precession. Finally we use this mechanism to well interpret the nearly isotropic orientation of S-cluster in the Galactic center.
