AI 中文总结
本文针对自旋黑洞周围的相对论捕获与潮汐瓦解问题，研究发现损失锥模型忽略倾角扩散的假设不成立，推导了含倾角扩散的克尔黑洞损失流量闭式解，揭示积分流量稳定时仍需考虑倾角分辨扩散的重要性。
AI 中文摘要
自旋黑洞周围的相对论捕获和潮汐瓦解取决于恒星角动量的大小和方向，但损失锥模型常假设轨道倾角固定，忽略相关扩散。本文证明该假设不成立：在小损失阈值附近的各向同性两体弛豫中，角动量大小$L$和倾角$x = L_{z}/L$的扩散时标相当，满足$t_{E} \gg t_{L} \sim t_{x}$。对于克尔（Kerr）黑洞捕获，保留倾角扩散会显著增大顺行-逆行对比，而总倾角积分流量几乎不变；几乎正确的积分流量可能掩盖严重错误的角分布。三维扩散问题仍保留足够角结构以进行解析处理，通过将近心点移除表示为连续汇，本文得到近线性克尔潮汐瓦解边界的闭式损失流量解，其与相位分辨计算结果吻合良好。因此，即使积分率看似稳定，依赖倾角的损失仍需考虑倾角分辨的扩散。
英文摘要
Relativistic capture and tidal disruption around a spinning black hole depend on both the magnitude and direction of the star's angular momentum, yet loss-cone models often assume fixed orbital inclinations by ignoring the associated diffusion. We show that this is not justified: for isotropic two-body relaxation near a small loss threshold, angular-momentum magnitude $L$ and inclination $x = L_{z}/L$ diffuse on comparable timescales, $t_{E} \gg t_{L} \sim t_{x}$. For Kerr capture, retaining inclination diffusion significantly amplifies the prograde--retrograde contrast while leaving the total inclination-integrated flux nearly unchanged. An almost correct integrated flux can hide a badly wrong angular distribution. The three-dimensional diffusion problem nevertheless retains enough angular structure to permit analytic treatment. By representing pericenter removal as a continuous sink, we obtain a closed-form loss flux solution for a nearly linear Kerr tidal-disruption boundary, finding close agreement with phase-resolved calculations. Inclination-dependent loss therefore requires inclination-resolved diffusion even when integrated rates appear robust.
Comments8 pages, 2 figures. Comments welcome
