利用黑洞探测器进行自旋推断。I. 费舍尔信息矩阵预测
Spin inference with the Black Hole Explorer. I. Fisher information matrix forecast
AI总结：
本研究针对黑洞探测器（BHEX），利用费舍尔信息矩阵（FIM）结合双锥半解析发射模型，预测其可将M87*和Sgr A*的无量纲自旋约束到σ_a* ≪ 0.1的精度，验证了其探测光子环并精确约束黑洞自旋的能力。
AI中文摘要：
广义相对论预测，黑洞图像上会叠加一层薄而明亮的光环（即“光子环”），其几何形状对黑洞的自旋敏感。在核超大质量黑洞的观测中探测到该光子环，将为强场引力以及黑洞的增长历史提供新的认识。黑洞探测器（BHEX）是为首次探测光子环而开发的任务，由此产生了一个问题：我们能从其观测中多精确地约束黑洞自旋？我们采用费舍尔信息矩阵（FIM）方法，结合简单的双锥半解析发射模型，针对主要科学目标（M87*和Sgr A*）的多种配置，预测BHEX的自旋后验宽度。研究发现，即使存在显著的系统误差，BHEX在30个轨道周期后，仍能将目标的无量纲自旋约束到精度σ_a* ≪ 0.1。我们通过数值稳定性和鲁棒性检查，以及合成数据交叉验证来评估FIM对协方差和先验信息的处理能力，并与完整后验探索结果进行对比以验证结论。
英文摘要：
General relativity predicts the presence of a thin, bright ring of light superimposed on the image of a black hole (the ``photon ring''), whose geometry is sensitive to the spin of the black hole. Detecting this photon ring in observations of nuclear supermassive black holes would yield insight into gravity in the strong-field regime as well as their growth histories. The Black Hole Explorer (BHEX) is a mission being developed to detect the photon ring for the first time, raising the question of how precisely we can constrain spin from its observations. We use the method of Fisher information matrices (FIMs) along with a simple dual-cone semi-analytic emission model to forecast BHEX spin posterior widths for the primary science targets (M87* and Sgr~A*) in a variety of configurations. We find that BHEX can constrain the dimensionless spin of its targets to a precision of $σ_{a_*} \ll 0.1$ after 30 orbits, even in the presence of significant systematic errors. We validate our results via numerical checks for stability and robustness, as well as synthetic data cross-validation to assess handling of covariances and prior information in the FIM against a full posterior exploration.
