类S62恒星轨道推断中的PPN参数与自旋简并性
PPN--spin degeneracies in mock S62-like stellar-orbit inference
- A.I. Alikhanian National Science Laboratory（A.I. 阿里哈尼扬国家科学实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对类S62恒星轨道推断，发现PPN参数与黑洞自旋存在强简并，提出联合多恒星推断可拆解该简并以提升约束精度。
AI中文摘要：
我们研究了环绕人马座A*的类S2和类S62恒星的相对论轨道动力学中，黑洞（BH）自旋效应与参数化后牛顿（PPN）参数之间的简并性。采用1阶后牛顿加自旋-轨道耦合（1PN+SO）哈密顿框架和合成天体测量与视向速度数据集，我们开展了贝叶斯参数推断。对于当前基线观测精度，主导相对论可观测量——史瓦西近星点进动，可恢复有效进动参数Υ，但使单个PPN参数γ和β简并。假设达到微角秒级天体测量精度，自旋诱导的冷泽-提尔苓（Lense-Thirring）信号可部分被探测；将PPN sector固定为广义相对论时，黑洞自旋幅度可被约束至约10⁻²的不确定度。然而，同时改变PPN和自旋参数时，Υ与无量纲自旋参数χ间呈现强近似线性协方差。为克服该局限，我们证明联合多恒星推断可通过结合宽轨道恒星（约束主导1PN sector）与紧凑相对论轨道（对冷泽-提尔苓框架拖曳敏感）来拆解此简并性。
英文摘要：
We investigate the degeneracies between black hole (BH) spin effects and parametrized post-Newtonian (PPN) parameters in the relativistic orbital dynamics of S2-like and S62-like stars orbiting Sagittarius A$^{\ast}$. Using a 1PN+SO Hamiltonian framework and synthetic astrometric and radial velocity datasets, we perform Bayesian parameter inference. For current baseline observational precisions, the dominant relativistic observable--the Schwarzschild periapsis advance--allows the recovery of the effective precession parameter $Υ$, while leaving the individual PPN parameters $γ$ and $β$ degenerate. Assuming microarcsecond-level astrometric precision, the spin-induced Lense-Thirring signal becomes partially detectable; fixing the PPN sector to General Relativity allows the BH spin magnitude to be constrained to an uncertainty of $\sim10^{-2}$. However, simultaneously varying PPN and spin parameters reveals a strong, approximately linear covariance between $Υ$ and the dimensionless spin parameter $χ$. To overcome this limitation, we demonstrate that joint multi-star inference can disentangle the degeneracy by combining a wider-orbit star, which constrains the dominant 1PN sector, with a compact relativistic orbit that is sensitive to Lense-Thirring frame dragging.
