AI 中文总结
该研究利用S301 S星的自转作为宏观陀螺仪，通过分析其轨道参数和自转偏移的统计似然，为红外光谱仪提供目标以检验Sgr A*周围的施瓦西度规，拓展了广义相对论的测试范围。
AI 中文摘要
银心周围的恒星轨道为广义相对论提供了测试环境，这些恒星的本征自转在弯曲时空中的协变输运和经典牛顿四极矩力矩作用下演化。我们分析了最近观测到的S301 S星，以量化其自转轴的相对论进动。S301的轨道周期为8.7年，偏心率e=0.982，这使得测地岁差和牛顿四极矩力矩在近星点处呈现阶跃函数形式。我们将一阶后牛顿修正纳入轨道运动学中以计算空间轨道，在40年的时间内对初始取向和观测几何的各向同性分布进行采样，同时覆盖赤道速度和自转椭率的网格，计算投影自转线展宽的绝对偏移量|Δv sin i|的统计似然。相对论测地偏移与自转速度v_rot线性相关，而经典四极矩偏移与自转速度无关，与椭率q相关。对于扁球星，绝对最大速度偏移饱和于46.1 km/s；由测地岁差驱动的绝对中位偏移范围为3 km/s至6.3 km/s。我们计算了时域可观测的|Δv sin i|，为测试Sgr A*周围施瓦西度规的红外光谱仪提供目标。S301的自旋如同一个飞行陀螺仪，若能测量其漂移，便可在以往无法企及的 regime 中检验爱因斯坦的理论。
英文摘要
Stellar trajectories around the Galactic Center provide a testing environment for general relativity. The intrinsic rotation of these stars evolves under covariant transport in curved spacetime and classical Newtonian quadrupole torques. We analyze the recently observed S301 S-star to quantify the relativistic precession of its rotational axis. Its 8.7-year period and eccentricity of $e = 0.982$ localize geodetic precession and Newtonian quadrupole torques to a step function at periapsis. We incorporate first-order post-Newtonian corrections into the orbital kinematics to calculate the spatial trajectory. Sampling an isotropic distribution of initial orientations and viewing geometries over a 40-year period across a grid of equatorial velocities and rotational ellipticities, we calculate the statistical likelihood of an absolute shift in the projected rotational line broadening, $|Δv \sin i|$. The relativistic geodetic shift scales linearly with $v_{\rm rot}$ and the classical quadrupole shift is independent of rotation speed, scaling with $q$. The absolute maximum velocity shift saturates at $46.1\,\kms$ for oblate stars. The absolute median shifts, driven by geodetic precession, range from $3\,\kms$ to $6.3\,\kms$. We calculate the time-domain observable $|Δv \sin i|$ to provide a target for infrared spectrographs testing the Schwarzschild metric around Sgr~A$^\ast$. The spin of S301 acts as a flying gyroscope whose drift, if measured, can test Einstein's theory in a regime that has not previously been accessible.
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