AI 中文总结
本研究结合Sgr A*阴影与S2恒星轨道数据，用马尔可夫链蒙特卡洛方法约束Hernquist型环境黑洞时空参数，收紧了环境晕紧致度上限，发现特征尺度存在双峰简并，为探测黑洞周围物质分布提供了多尺度观测约束。
AI 中文摘要
位于银河系中心的超大质量黑洞Sgr A*为探测黑洞周围的环境物质分布提供了独特机会。本研究采用Hernquist型环境黑洞时空——一种爱因斯坦场方程的非真空精确解——作为引力模型，用以描述黑洞及其周围物质的联合引力场，其环境效应由无量纲紧致度$C$和特征尺度$α$表征。我们将黑洞阴影数据与Do等人及Gillessen等人提供的两组S2恒星数据相结合，使用马尔可夫链蒙特卡洛方法对模型参数进行约束。在95%置信上限下，仅使用阴影数据可约束$C < 1.498\times10^{-1}$，但无法对$α$给出有效约束。两组S2数据集分别得到$C<5.239\times10^{-5}$和$C<1.303\times10^{-4}$的结果，且两种情况下$α$均呈现双峰结构。结合阴影与S2恒星数据后，$C$的上限分别收紧至$C<3.760\times10^{-5}$和$C<1.073\times10^{-4}$。这些结果表明，当前观测排除了环境晕的高紧致度构型，且所得约束与物质晕的典型紧致度范围一致。然而，$α$仍存在显著的双峰简并性，说明当前观测不足以唯一确定环境晕的径向分布。未来对多颗恒星轨道的观测或许能为环境晕的径向结构提供更多认知。
英文摘要
The supermassive black hole Sgr A* at the Galactic center provides a unique opportunity to probe the distribution of environmental matter around black holes. In this work, we adopt the Hernquist-type environmental black hole spacetime, a non-vacuum exact solution of the Einstein field equations, as its gravitational model to describe the joint gravitational field of the black hole and its surrounding matter, with environmental effects characterized by the dimensionless compactness $C$ and the characteristic scale $α$. We combine black hole shadow data with two sets of S2 star data provided by Do et al. and Gillessen et al., and constrain the model parameters using the Markov chain Monte Carlo method. At the 95\% credible upper limit, the shadow-only data constrain $C < 1.498\times10^{-1}$.but provide no effective constraint on $α$. The two S2 datasets yield $C<5.239\times10^{-5}$ and $C<1.303\times10^{-4}$, respectively, with $α$ exhibiting a bimodal structure in both cases. After combining the shadow and S2 star data, the $C$ upper limits are tightened to $C<3.760\times10^{-5}$ and $C<1.073\times10^{-4}$, respectively. These results indicate that current observations rule out highly compact configurations of the environmental halo, while the obtained constraints are consistent with the typical compactness range of matter halos. However, $α$ still exhibits a significant bimodal degeneracy, indicating that current observations are insufficient to uniquely determine the radial distribution of the environmental halo. Future observations of multiple stellar orbits may provide further insights into the radial structure of the environmental halo.
