Reprocessing of primary X-ray emission in the accretion disk of black hole X-ray binaries (BHXRBs) produces the reflection spectrum, with the characteristic Fe K$\alpha$ fluorescence line. Strong low frequency quasi-periodic oscillations (QPOs) are observed from BHXRBs, and the dependence of QPO properties (e.g., phase-lag) on the inclination angle suggests that the observed QPO may be associated with a geometrical effect, e.g., the precession of the X-ray source due to frame-dragging near the spining black hole. Here, in the scenario of Lense-Thirring precession of the X-ray source, we use a Monte-Carlo simulation of radiative transfer to study the irradiation/reflection and the resultant spectral properties including the Fe K$\alpha$ line, as a function of precession phase (time). We found that the reflection fraction, i.e., the ratio of the incident flux towards the disk and the direct flux towards to the observer at infinity, is modulated with the precession phase, which depends on the truncation radius (i.e., the spectral state in the truncated disk model) and the inclination angle. The Fe K$\alpha$ line profile also changes as the primary X-ray source precesses, with the line luminosity and the flux-weighted centroid energy varying with the precession phase. The periodically modulated 2-10 keV continuum flux could apparently lag the line luminosity in phase, if the truncation radius is small enough for Doppler effects due to disk orbital motion to significantly affect the observed radiation.

中文翻译：

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Lense-Thirring 岁差模型中的 X 射线准周期振荡。二、相对论铁 Kα 线的可变性

对黑洞 X 射线双星 (BHXRB) 吸积盘中的初级 X 射线发射进行再处理产生反射光谱，具有特征性 Fe K$\alpha$ 荧光线。从 BHXRB 观察到强低频准周期振荡 (QPO)，QPO 特性（例如相位滞后）对倾角的依赖性表明观察到的 QPO 可能与几何效应有关，例如进动由于在旋转的黑洞附近的帧拖曳导致的 X 射线源。在这里，在 X 射线源的 Lense-Thirring 进动的情况下，我们使用辐射转移的蒙特卡罗模拟来研究辐射/反射和由此产生的光谱特性，包括 Fe K$\alpha$ 线，作为岁差阶段（时间）的函数。我们发现反射分数，即 朝向圆盘的入射通量与朝向无穷远处观察者的直接通量之比用进动相位调制，进动相位取决于截断半径（即，截断圆盘模型中的光谱状态）和倾角。Fe K$\alpha$ 线轮廓也随着主 X 射线源进动而变化，线光度和通量加权质心能量随进动相位而变化。如果截断半径足够小，由于圆盘轨道运动的多普勒效应会显着影响观察到的辐射，那么周期性调制的 2-10 keV 连续流通量可能明显滞后于线光度。截圆盘模型中的光谱状态）和倾角。Fe K$\alpha$ 线轮廓也随着主 X 射线源进动而变化，线光度和通量加权质心能量随进动相位而变化。如果截断半径足够小，由于圆盘轨道运动的多普勒效应会显着影响观察到的辐射，那么周期性调制的 2-10 keV 连续流通量可能明显滞后于线光度。截圆盘模型中的光谱状态）和倾角。Fe K$\alpha$ 线轮廓也随着主 X 射线源进动而变化，线光度和通量加权质心能量随进动相位而变化。如果截断半径足够小，由于圆盘轨道运动的多普勒效应会显着影响观察到的辐射，那么周期性调制的 2-10 keV 连续流通量可能明显滞后于线光度。