论文标题
用银河中心恒星轨道测试黑洞无发的定理
Testing the Black Hole No-hair Theorem with Galactic Center Stellar Orbits
论文作者
论文摘要
理论研究提供了原理证明的计算，表明在银河中心附近的恒星或脉冲星轨道测量可能会严重限制银河系中心黑洞，局部物质，甚至重力理论本身的特性。在这项工作中，我们既开发了马尔可夫链蒙特卡洛，也开发了一个分析模型（Fisher矩阵），以了解哪些特性受到良好的约束以及原因。我们得出的结论是，现有的天文测量不能限制银河中心黑洞的自旋。推断未来实验的精度和节奏，我们预计可以用已知的Star S2测量黑洞自旋。我们的计算表明，使用重力望远镜在银河系中心的最佳分辨率，每周测量S2的轨道40年，我们可以测量无量纲的黑洞旋转$ \ sim $ 0.1的精度。在观察策略，恒星的轨道参数和仪器分辨率方面，使用Fisher矩阵得出了黑洞旋转的测量不确定性的分析表达。从中，我们得出的结论是，高度偏心的轨道可以在旋转上提供更好的约束，并且即使轨道周期更长，具有较高偏心的轨道也更有利。我们还将其应用于S62，S4711和S4714，并显示它们是否可以比S2更快地限制黑洞旋转。此外，如果未来的测量结果包括发现新的，更紧密的恒星轨道，那么未来的数据可以通过直接测量黑洞四极矩来实现强场重力测试。我们的模拟表明，具有与S2相似的恒星轨道，但在与银河中心的距离和重力分辨率限制的距离的五分之遥，我们可以开始以20年的每周轨道测量测试无发品定理。
Theoretical investigations have provided proof-of-principle calculations suggesting measurements of stellar or pulsar orbits near the Galactic Center could strongly constrain the properties of the Galactic Center black hole, local matter, and even the theory of gravity itself. In this work, we develop both a Markov chain Monte Carlo and an analytic model (Fisher matrix) to understand what properties are well-constrained and why. We conclude that existing astrometric measurements cannot constrain the spin of the Galactic Center black hole. Extrapolating to the precision and cadence of future experiments, we anticipate that the black hole spin can be measured with the known star S2. Our calculations show that we can measure the dimensionless black hole spin to a precision of $\sim$0.1 with weekly measurements of the orbit of S2 for 40 years using the GRAVITY telescope's best resolution at the Galactic Center. An analytic expression is derived for the measurement uncertainty of the black hole spin using the Fisher matrix in terms of observation strategy, star's orbital parameters, and instrument resolution. From it, we conclude that highly eccentric orbits can provide better constraints on the spin and that an orbit with a higher eccentricity is more favorable even when the orbital period is longer. We also apply it to S62, S4711, and S4714 and show whether they can constrain the black hole spin sooner than S2. If in addition, future measurements include the discovery of a new, tighter stellar orbit, then future data could conceivably enable tests of strong field gravity, by directly measuring the black hole quadrupole moment. Our simulations show that with a stellar orbit similar to that of S2 but at one-fifth the distance to the Galactic Center and GRAVITY's resolution limits, we can start to test the no-hair theorem with 20 years of weekly orbital measurements.
