Predictions for the X-ray polarisation modulation in Cygnus X-1 from reflection off the stellar companion and its wind

Abstract

Context. Cyg X-1 is one of the brightest X-ray binaries and has been observed multiple times with the Imaging X-ray Polarimetry Explorer (IXPE). Recent studies report tentative evidence for a polarisation modulation with the orbital period P, but a half-period (P/2) signal, expected from reflection off the companion star and its stellar wind, has not been reported. Aims. We aim to quantify the reflection-induced variations of the polarisation degree PD and polarisation angle PA in Cyg X-1 as a function of orbital phase and energy, and interpret these in terms of binary geometry and wind structure. Methods. We set up a radiative transfer model combining a general relativistic description of the polarised source emission (kerrC) with a focussed stellar wind model for the binary medium. Using the 3D X-ray radiative transfer code SKIRT, we simulate broadband Stokes I, Q, and U fluxes, surface brightness maps, and linear polarisation maps over one binary orbit. Results. We find a prominent double-peaked (P/2) polarisation modulation, with a peak-to-peak PD amplitude of 0.25, 0.81, and 1.24 percentage points in the 2-4, 4-6, and 6-8 keV bands, respectively, with a strong energy dependence. The PA modulation is more modest, with |ΔPA| < 4.6°. Crucially, X-ray reprocessing reduces the overall PD relative to the source polarisation. Conclusions. The modulation is driven by reflection off the companion star and the focussed wind, which induces a polarisation signal that alternately reinforces and counteracts the source polarisation throughout the orbit. The diffuse scattering halo surrounding the source systematically reduces the PD, an effect that should be accounted for in all wind-fed XRBs. The PD amplitude increases with energy as absorption disproportionately attenuates the distant-reflection signal; as the extinction drops, the reflection signal becomes increasingly important.