Modeling the Optical to Ultraviolet Polarimetric Variability from Thomson Scattering in Colliding Wind Binaries

Massive star binaries are critical laboratories for measuring masses and stellar wind mass-loss rates. A major challenge is inferring viewing inclination and extracting information about the colliding wind interaction (CWI) region. Polarimetric variability from electron scattering in the highly ionized winds provides important diagnostic information about system geometry. We combine for the first time the well-known generalized treatment of \citet{brown_polarisation_1978} for variable polarization from binaries with the semi-analytic solution for the geometry and surface density CWI shock interface between the winds based on Canto et al 1996. Our calculations include some simplifications in the form of inverse square-law wind densities and the assumption of axisymmetry, but in so doing arrive at several robust conclusions. One is that when the winds are nearly equal (e.g., O\,+\,O binaries), the polarization has a relatively mild decline with binary separation. Another is that despite Thomson scattering being a gray opacity, the continuum polarization can show chromatic effects at ultraviolet wavelengths but will be mostly constant at longer wavelengths. Finally, when one wind dominates the other, as for example in WR+OB binaries, the polarization is expected to be larger at wavelengths where the OB component is more luminous, and generally smaller at wavelengths where the WR component is more luminous. This behavior arises because from the perspective of the WR star, the distortion of the scattering envelope from spherical is a minor perturbation situated far from the WR star. By contrast, the polarization contribution from the OB star is dominated by the geometry of the CWI shock.