Polarization simulations of stellar wind bow shock nebulae. I. The case
  of electron scattering
  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.
