AI 中文总结
研究克尔时空中热亚开普勒吸积流，开发半解析运动学模型，通过插值构建，不含磁场等项，用过渡函数连接速度分量。经MAD模拟校准验证，能捕获吸积流参数特性，误差低，可用于多种应用。
AI 中文摘要
我们为热的、厚的吸积流开发了一个简单的半解析运动学模型，通过在克尔度规中的开普勒和自由落体测地线解之间进行插值构建。与自洽的广义相对论磁流体动力学（GRMHD）框架不同，我们的模型不包含明确的磁场或应力项，而是使用一个平滑的、径向变化的过渡函数T(r)来连接大距离处近开普勒旋转的速度分量到事件视界附近的自由落体状态。虽然系数α和β保持不变，但过渡函数是半径的真实函数，使流动特性随半径平滑变化。我们根据跨越广泛黑洞自旋（a = -0.9到+0.9）的长时间磁捕获盘（MAD）模拟的时间和方位平均剖面校准并验证了该模型。该模型成功捕获了顺行和逆行配置下吸积流参数的特性。定量地说，预测的径向速度、角速度和密度剖面分别与模拟数据在平均因子约1.8、1.6和1.6以内匹配，而比角动量表现出最接近的一致性，保持在约1.2以内。这种快速的半解析方法比以前的常系数模型具有显著更低的误差，并且是用于各种应用（如光线追踪、吸积参数探索和光谱建模）的计算上可承受的工具。
英文摘要
We develop a simple, semi-analytical, kinematic model for hot, thick accretion flows, constructed by interpolating between Keplerian and free-fall geodesic solutions in the Kerr metric. Unlike self-consistent general relativistic magnetohydrodynamics (GRMHD) frameworks, our model contains no explicit magnetic fields or stress terms; instead, it uses a smooth, radially varying transition function T(r) to connect the velocity components from near-Keplerian rotation at large distances to a free-fall state near the event horizon. While the coefficients $α$ and $β$ remain constant, the transition function is a true function of radius, allowing the flow properties to vary smoothly with radius. We calibrate and validate this model against time- and azimuthally averaged profiles from long-duration magnetically arrested disk (MAD) simulations spanning a wide range of black hole spins ($a=-0.9$ to $+0.9$). The model successfully captures the properties of accretion flow parameters across both prograde and retrograde configurations. Quantitatively, the predicted radial velocity, angular velocity, and density profiles match the simulation data to within an average factor of approximately 1.8, 1.6, and 1.6, respectively, while the specific angular momentum exhibits the closest agreement, remaining within a factor of approximately 1.2. This fast semi-analytical prescription gives significantly lower errors than previous constant-coefficient models and it is a computationally affordable tool for various applications such as ray tracing, accretion parameter exploration, and spectral modelling.
Comments20 pages, 9 Figures, 8 tables
