AI 中文总结
该研究以S星团轨道为基础，建立超扩散分数阶输运模型，模拟共振弛豫过程，解释费米气泡能量需求，为空间引力波探测器提供轨道输运校准模型及星系核并合事件拓扑模型。
AI 中文摘要
追踪S星团围绕Sgr A*的轨道，可校准用于空间引力波探测器的轨道输运模型。标准动力学理论通过局域福克-普朗克方程对该星团建模，预测广义相对论岁差会在史瓦西屏障处终止角动量扩散。由于平方反比引力碰撞产生具有无限方差的霍尔茨马克力矩分布，共振弛豫表现为由非局域莱维飞行主导的空间分数阶过程。我们使用以实测S星轨道（包括新近观测到的S301）初始化的马尔可夫链，模拟这种超扩散连续时间随机游走。积分-微分分数阶算子使轨迹能穿过淬灭局域扩散区域，且不会在屏障处产生密度累积。非平衡态会产生即时线性通量增长，而近星点的长期潮汐加热会增大恒星半径，从而改变瓦解边界。分数阶输运方程的正则化反向积分，可将当前相空间构型回溯至初始沉积态，与费米气泡的能量需求匹配。相对论岁差不会抑制质量比并合率，这为目标星系核中的事件拓扑提供了模型。
英文摘要
Tracking S-star cluster orbits around Sgr A* calibrates orbital transport models for space-borne gravitational wave detectors. Standard kinetic theories model this cluster via local Fokker-Planck equations, which predict that general relativistic precession halts angular momentum diffusion at the Schwarzschild barrier. Because inverse-square gravitational encounters generate a Holtsmark torque distribution with infinite variance, resonant relaxation operates as a space-fractional process governed by non-local Lévy flights. We simulate this superdiffusive continuous-time random walk using a Markov chain initialized with empirical S-star orbits, including the recently observd S301. Integro-differential fractional operators allow trajectories to cross regions of quenched local diffusion without density buildup at the barrier. Non-equilibrium regimes yield immediate linear flux growth, while secular tidal heating at periastron inflates stellar radii to shift disruption boundaries. Regularized backward integration of the fractional transport equation traces current phase space configurations back to initial deposition states, matching the energy requirements of the \emph{Fermi} bubbles. Relativistic precession does not suppress mass-ratio inspiral rates, which provides a model for event topologies in target galactic nuclei.
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