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

摘要

Following a previous paper on Thomson scattering, we present numerical simulations of the periodic polarimetric variations produced by a binary star placed at the center of an empty spherical cavity inside a circumbinary ellipsoidal and optically thin envelope made of dust grains. Mie single scattering (on spherical dust grains) is considered, along with pre- and postscattering extinction factors, which produce a time-varying optical depth and affect the morphology of the periodic variations. The orbits are circular or eccentric. The mass ratio (and luminosity ratio) is equal to 1.0. We are interested in the effects that various parameters (grain characteristics, geometry of the envelope, orbital eccentricity, etc.) will have on the average polarization, the amplitude of the polarimetric variations, and the morphology of the variability. We show that the absolute amplitudes of the variations are smaller for Mie scattering than for Thomson scattering, which makes harder the detection of polarimetric variations for binary stars surrounded by dust grains. The average polarization produced depends on the grains' composition and size and on the wavelength of observation. Among the four grain types that we have studied (astronomical silicates, graphite, amorphous carbon, and dirty ice), the highest polarizations are produced by grains with sizes in the range a ~ 0.1–0.2 μm (x = 2πa/λ ~ 1.0–2.0 for λ = 7000 ?). Composition and size also determine if the polarization will be positive or negative. In general, the variations are double periodic (seen twice per orbit). In some cases, because spherical dust grains have an asymmetric scattering function, the polarimetric curves produced show single-periodic variations (seen once per orbit) in addition to the double-periodic ones. A mixture of grains of different sizes does not affect those conclusions. Circumstellar disks produce polarimetric variations of greater amplitude (up to ~0.3% in our simulations) than circumbinary envelopes (usually 0.1%). Other geometries (circumbinary flared disks or prolate envelopes and noncoplanar envelopes) do not present particularly interesting polarimetric characteristics. Another goal of these simulations is to see if the 1978 BME (Brown, McLean, & Emslie) formalism, which uses a Fourier analysis of the polarimetric variations to find the orbital inclination for Thomson-scattering envelopes, can still be used for Mie scattering. We find that this is the case, if the amplitude of the variations is sufficient and the true inclination is itrue 45°. For eccentric orbits, the first-order coefficients of the Fourier fit, instead of second-order ones, can be used to find almost all inclinations.