X-ray Comptonization in an Accreting Kerr Black Hole System with a Tilted Disc and Thermal Corona: A General-Relativistic Monte Carlo Simulation. II. Polarization Signatures

Relativistic precession of the inner accretion flow is widely invoked to explain low-frequency QPOs, and the Relativistic Precession Model (RPM) predicts phase-dependent X-ray polarization. However, IXPE observations challenge simple precession and Comptonization models; for example: SwiftJ1727.8-1613 shows weak or undetected QPO-phase polarization modulation, while IGRJ17091-3624 shows a hard-state polarization degree (DOP) of 9%, versus 4% in other hard-state black hole binaries. In Paper I, we presented a general-relativistic Monte Carlo (GRMC) model of X-ray reprocessing in a misaligned, warped two-zone disc around a Kerr black hole with a hot, optically thin corona. We computed energy spectra, photon path-length and arrival-time distributions, and X-ray lags. Here, we extend the model to track photon polarization using Walker-Penrose parallel transport and polarized Compton and disc scattering. We calculate the energy-resolved degree and angle of polarization and their precession-phase modulation versus coronal optical depth, outer-disc albedo, photon-injection radius, and observer inclination. We find that gravitational light bending raises the mean DOP and enhances modulation, whereas coronal scattering and reflection from the misaligned outer disc lower the DOP and suppress modulation. The steady outer-disc polarization further dilutes the inner-flow signal. Their competition can produce weak, nearly unmodulated polarization or a high, strongly modulated signal. Strong scattering and reflection can explain SwiftJ1727.8-1613's weak modulation, while strong light bending and weak secondary scattering can explain IGRJ17091-3624's high DOP. Our results provide a framework for interpreting unusual X-ray polarization and testable predictions for constraining black hole parameters, coronal properties, and disc-warp geometry with IXPE, XPoSat, and eXTP.