AI 中文总结
本研究针对银心质量分布的球对称假设局限，解析推导幂律密度薄盘的引力加速度，发现其会引发半通径长期偏移与两类进动，可用于约束银心盘状不可见质量上限，对利用恒星轨道探测黑洞自旋具有重要意义。
AI 中文摘要
恒星轨道是探测银河系中心超大质量黑洞人马座A*（Sagittarius A*）周边环境的关键工具。此前，学界一直假设Sgr A*周围的质量呈球对称分布，但延展质量实际可能呈扁率形态，形成盘状结构。本文研究了薄盘结构对银心恒星的影响，重点关注恒星S2、S301以及顺时针恒星盘。我们通过解析方法推导了满足幂律密度分布Σ∝r^(-γ)的盘结构产生的加速度，利用该加速度计算吻切方程与轨道根数的变化，阐明了轨道根数变化与盘结构相对轨道平面取向的依赖关系。研究发现，盘结构会引发半通径的长期偏移、额外的轨道面内进动以及轨道面外进动。其中半通径长期偏移既不存在于我们用于描述黑洞的低阶后牛顿近似中，也不会在球对称质量分布假设下出现。轨道面外进动的强度可与Sgr A*自旋引发的S301轨道Lense-Thirring（参考系拖拽）进动相当，具体取决于盘的质量、径向延展范围与取向。由于Lense-Thirring进动对S2的运动影响可忽略，轨道面外进动可用于约束银心盘状结构的不可见质量上限，该上限可能与球对称分布下得到的结果存在显著差异，且依赖于盘的参数。这些结果凸显了利用恒星轨道探测中心黑洞（尤其是其自旋）时，约束盘状结构的重要性。一旦获得质量估计值，即可量化盘结构对S301运动的影响，以及其与未来Sgr A*自旋测量结果之间的简并性。
英文摘要
Stellar orbits are key for probing the environment of the supermassive black hole at the Galactic Center, Sagittarius A$^*$. So far, the mass around SgrA$^*$ has been assumed to be spherically distributed. However, the extended mass may instead be flattened, creating disk-like structures. We investigate the effects that a thin disk structure would have on stars at the Galactic Center, focusing on star S2 and S301 and the clockwise stellar disk. We derive analytically the acceleration exerted by a disk with power law density $Σ\propto r^{-γ}$. We use this acceleration to compute the osculating equations and the variations of the orbital elements, showing how the latter depend on the orientation of the disk with respect to the orbital plane. We find that the disk structure induces a secular shift in the semi-latus rectum, an extra in-plane precession and an out-of-plane precession. The former is neither present at the low-order post Newtonian description that we use for the black hole, nor when a spherical mass distribution is considered. The latter can be competitive with the Lense-Thirring precession induced by the spin of SgrA$^*$ on S301 motion, depending on the mass, the radial extent and the orientation of the disk. Since the Lense-Thirring precession is negligible in S2 motion, the out-of-plane precession can be used to place upper limits on the non luminous mass of disk-like structures at the Galactic Center. The limits might significantly differ from those obtained for spherical distributions and depend on the disk parameters. These results highlight the importance of constraining disk-like structures when using stellar orbits to probe the central black hole, in particular its spin. Once mass estimates are at hand, one can quantify the disk's effect on S301 motion and the resulting degeneracy with a future measurement of SgrA$^*$ spin.
CommentsSubmitted to A&A, 12 pages, 11 figures. Comments are welcome
