AI 中文总结
研究核星团中恒星碰撞、双星破裂等对恒星分布及紧密束缚轨道恒星丰度的影响，通过模型得出不同质量超大质量黑洞周围恒星的情况，突出碰撞对极端质量比吸积盘形成的挑战，应用于银河系中心与观测相符并做了相关估计和预测。
AI 中文摘要
围绕超大质量黑洞的核星团包含数百万颗恒星和恒星残骸。我们研究恒星碰撞、双星破裂、双体散射和引力波发射如何塑造恒星分布并调节紧密束缚轨道上的恒星丰度。结果表明：星团内部区域恒星遵循稳态密度分布，由碰撞损耗和双星补充平衡设定；对于质量较小的超大质量黑洞，约一半由希尔斯机制注入的恒星最终碰撞，其余在数月至数年周期轨道上被潮汐破坏；对于更大质量的超大质量黑洞，短轨道周期潮汐破坏事件受抑制，多数注入恒星最终被碰撞摧毁；恒星极端质量比吸积盘在质量较大的超大质量黑洞周围可形成，但通常在圆化前被碰撞终止。我们的模型突出了恒星碰撞对极端质量比吸积盘形成的动力学挑战。应用于银河系中心，碰撞调节的密度分布与观测到的恒星分布斜率一致，并据此进行了一系列估计和预测。
英文摘要
The nuclear stellar clusters surrounding supermassive black holes (SMBHs) host millions of stars and stellar remnants. We study how stellar collisions and binary disruptions, alongside two-body scattering and gravitational-wave (GW) emission, shape the stellar distribution and regulate the abundance of stars on tightly bound orbits. We show the following. (a) Stars in the inner region of the cluster follow a steady-state density profile scaling as $n(r)\propto r^{-5/4}$, set by the balance between collisional depletion and binary replenishment. This profile is largely independent of whether two-body scattering or GW emission drives the orbital evolution prior to the collisions. (b) For SMBHs with $M\lesssim2 \times 10^7 M_\odot$, roughly half of the stars injected by the Hills mechanism eventually collide. The rest are tidally disrupted while on orbits with periods of order months to years. (c) For more massive SMBHs, these short-orbital-period tidal disruption events are suppressed, and most injected stars are ultimately destroyed by collisions. (d) Stellar extreme-mass-ratio inspirals (sEMRIs) can form around SMBHs with $M\gtrsim2\times10^6 M_\odot$, but are typically terminated by collisions before circularizing. Our model highlights the dynamical challenge stellar collisions pose for the formation of sEMRIs and, consequently, for stellar models of quasiperiodic eruptions. Applied to the Galactic Center, the collision-regulated density profile is consistent with the observed stellar distribution slope. Based on this profile, we estimate the stellar mass within the orbit of S2, finding it consistent with the observational upper limit, account for the recently discovered star S301, predict that most stars near Sgr$~{\rm A}^*$ follow eccentric orbits, and determine their typical eccentricities.
Comments16 pages, 5 figures. Accepted for publication in ApJL
