标题： 星系中心颗粒质量分布对S2轨道的影响 显示英文标题

标题： Impact of a granular mass distribution on the orbit of S2 in the Galactic center

摘要： S2恒星围绕人马座A*的轨道为测试广义相对论和研究超大质量黑洞附近的动态过程提供了独特的机会。 观测结果表明，在10$\sigma$置信水平下，S2的轨道与施瓦茨希尔德轨道一致，假设质量分布是平滑且球对称的，其轨道内的扩展质量小于1200 M$_\odot$。 在本工作中，我们研究了质量分布的不均匀性对S2轨道的影响，假设其由围绕人马座A*的等质量物体集群组成。 使用一种通过完整N体模拟验证的快速动力学方法，我们进行了大量模拟，研究S2在不同集群物体分布情况下的运动。 我们发现，不均匀性可以在平滑势场中引起轨道的显著偏离，导致轨道平面的进动以及平面内进动的变化。 与集群物体的相互作用还会导致人马座A*出现一种“布朗运动”。 模拟数据分析表明，这些效应可能在S2轨迹上产生可观测的偏离，特别是在远心点附近。 在S2于2026年再次经过远心点时，赤纬方向的天体测量残差可能超过GRAVITY的天体测量精度阈值约30$\mu as$，这在20到100 M$_\odot$的黑洞模拟中，有35%到60%的情况会发生。 这提供了一个独特的机会，首次探测由恒星级黑洞引起的S2轨道上的散射效应，这得益于GRAVITY所能达到的卓越精度。 我们还证明，任何试图限制S2轨道内扩展质量的努力都必须明确考虑恒星级黑洞种群中的不均匀性。 显示英文摘要

摘要： The orbit of the S2 star around Sagittarius A* provides a unique opportunity to test general relativity and study dynamical processes near a supermassive black hole. Observations have shown that the orbit of S2 is consistent with a Schwarzschild orbit at a 10$\sigma$ confidence level, constraining the amount of extended mass within its orbit to less than 1200 M$_\odot$, under the assumption of a smooth, spherically symmetric mass distribution. In this work we investigate the effects on the S2 orbit of granularity in the mass distribution, assuming it consists of a cluster of equal-mass objects surrounding Sagittarius A*. Using a fast dynamical approach validated by full N-body simulations, we perform a large set of simulations of the motion of S2 with different realizations of the cluster objects distribution. We find that granularity can induce significant deviations from the orbit in case of a smooth potential, causing precession of the orbital plane and a variation of the in-plane precession. Interactions with the cluster objects also induce a sort of "Brownian motion" of Sagittarius A*. Mock data analysis reveals that these effects could produce observable deviations in the trajectory of S2 from a Schwarzschild orbit, especially near apocenter. During the next apocenter passage of S2 in 2026, astrometric residuals in Declination may exceed the astrometric accuracy threshold of GRAVITY of about 30 $\mu as$, as it happens in 35 to 60% of simulations for black holes of 20 to 100 M$_\odot$. This presents a unique opportunity to detect, for the first time, scattering effects on the orbit of S2 caused by stellar-mass black holes, thanks to the remarkable precision achievable with GRAVITY. We also demonstrate that any attempt to constrain the extended mass enclosed within the orbit of S2 must explicitly account for granularity in the stellar-mass black hole population.