X-ray quasi-periodic oscillations in Lense-Thirring precession model -- II. variability of relativistic iron K$\alpha$ line

TL;DR

This paper models how Lense-Thirring precession of the X-ray source in black hole binaries causes periodic variations in the reflection spectrum, especially the iron K$ extalpha$ line, revealing geometric effects on observed QPOs.

Contribution

It introduces a Monte-Carlo simulation of relativistic reflection that links precession phase to spectral and line profile variability in black hole X-ray binaries.

Findings

Reflection fraction varies with precession phase and depends on truncation radius and inclination.

Fe K$ extalpha$ line profile and luminosity change periodically with precession.

Continuum flux may lag line luminosity due to Doppler effects at small truncation radii.

Abstract

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.