AI 中文总结
研究气态星团中绕轨道运行的恒星黑洞周围吸积盘形成，通过分析黑洞影响球平流及速度剪切等，用模拟验证，得出盘形成时间尺度和半径公式，并给出特定质量黑洞在原恒星团核心内的相关数值。
AI 中文摘要
我们考虑在非旋转气态星团核心中沿规则轨道运动的低质量黑洞，其代表原恒星团或原星系中心。我们认为，随着黑洞的影响球（邦迪球）沿黑洞轨迹平流，内外半球之间的横向速度剪切注入角动量，驱动吸积盘形成。科里奥利力阻碍角动量注入，延迟但不阻止盘的形成。盘位于黑洞轨道平面内且相对于轨道上的黑洞运动反向旋转。我们在绕轨道运行的黑洞的非惯性系中用二维和三维流体动力学模拟验证了这一图景。我们发现，破坏事件后的盘形成时间尺度约为邦迪穿越时间尺度，\(\tau_{\rm d} \sim R_{\rm B}/V_{\bullet}\)，且盘半径约为\(R_{\rm d} \sim \omega_{\bullet}^2 R_{\rm B}^4/ G m_{\bullet} \)，由邦迪球中捕获气体的圆化半径设定。对于质量为\(m_{\bullet} = 50\,{\rm M}_\odot\)的黑洞，在典型致密原恒星团核心内，这些值为\(\tau_{\rm d} \sim 0.1 P_{\rm orbit}\)和\(R_{\rm d} \sim 10^{-3} R_{\rm B}\)。
英文摘要
We consider low-mass black holes (BHs) moving in regular orbits in the cores of non-rotating gaseous star clusters, representative of proto-stellar clusters or the centers of protogalaxies. We argue that as the BH's sphere of influence -- the Bondi sphere -- is advected along the BH trajectory, the transverse velocity shear between the inner and outer hemispheres injects angular momentum, driving the formation of an accretion disk. Coriolis forces oppose angular momentum injection, delaying disk formation but not preventing it. The disk lies in the BH orbital plane and is counter-rotating with respect to the orbital BH motion. We verify this picture with 2D and 3D hydrodynamic simulations in the non-inertial frame of the orbiting BH. We find that the disk-formation timescale following a disruption event is of order the Bondi crossing timescale, $τ_{\rm d} \sim R_{\rm B}/V_{\bullet}$, and that the disk radius is of order $R_{\rm d} \sim ω_{\bullet}^2 R_{\rm B}^4/ G m_{\bullet} $, set by the circularization radius of gas captured in the Bondi sphere. For the case of a BH with $m_{\bullet} = 50\,{\rm M}_\odot$, inside the core of a typical compact proto-stellar cluster, these values read $τ_{\rm d} \sim 0.1 P_{\rm orbit}$ and $R_{\rm d} \sim 10^{-3} R_{\rm B}$.
