  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.
