Bow shocks and related density enhancements produced by the winds of massive stars moving through the interstellar medium provide important information regarding the motions of the stars, the properties of their stellar winds, and the characteristics of the local medium. Since bow shocks are aspherical structures, light scattering within them produces a net polarization signal even if the region is spatially unresolved. Scattering opacity arising from free electrons and dust leads to a distribution of polarized intensity across the bow shock structure. That polarization encodes information about the shape, composition, opacity, density, and ionisation state of the material within the structure. In this paper we use the Monte Carlo radiative transfer code SLIP to investigate the polarization created when photons scatter in a bow shock-shaped region of enhanced density surrounding a stellar source. We present results assuming electron scattering, and investigate the polarization behaviour as a function of optical depth, temperature, and source of photons for two different cases: pure scattering and scattering with absorption. In both regimes we consider resolved and unresolved cases. We discuss the implication of these results as well as their possible use along with observational data to constrain the properties of observed bow shock systems. In different situations and under certain assumptions, our simulations can constrain viewing angle, optical depth and temperature of the scattering region, and the relative luminosities of the star and shock.
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