Polarimetric Variations of Binary Stars. I. Numerical Simulations for Circular and Eccentric Binaries in Thomson Scattering Envelopes

We present numerical simulations of the polarimetric variations produced by a binary star placed at the center of an empty spherical cavity inside a circumbinary ellipsoidal and optically thin envelope. Thomson single-scattering is considered along with pre- and postscattering extinction factors which produce a time-varying optical depth. The orbits are circular or eccentric. The mass ratio (and luminosity ratio) is in general equal to 1.0. As a function of the orbital (and envelope) inclination, the polarization follows a sin2(i) law. High polarization levels will result from a high inclination, a high optical depth, a flat envelope, or a big central cavity. Polarimetric variations are more apparent for a low inclination, a high optical depth, a flat envelope, a small cavity, or an orbit that brings the stars close to the inner edge of the cavity. It is then shown that the 1978 BME (Brown, McLean, & Emslie) model can be used to find the orbital inclination if it is >~45°, even though this model does not include variable absorption effects as in our simulations. The geometry (flatness of the envelope, size of the central cavity) and size of the orbit have no significant influence on the inclination found by the BME model. For eccentric orbits, single-periodic variations (variations seen once per orbit) appear for eccentricities as low as 0.10. As the eccentricity increases, these single-periodic variations dominate over the double-periodic (seen twice per orbit) ones. The inclinations found by the BME model with the first-order coefficients are then more reliable than those found with the second-order coefficients, especially for the highest eccentricities. For low eccentricities, e<~0.3, the inclinations can be found with the first or second-order coefficients, if i>20^deg and i>45^deg, respectively. For the high eccentricities, 0.3<e<0.6, only the first-order coefficients should be used, if i>10^deg. Since with polarimetric observations the true inclination is not known a priori, we discuss how to use the BME model in that context.