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 post-scattering 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 \sim 0.1 – 0.2 \micron ( x = 2 \pi a / \lambda \sim 1.0 – 2.0 for \lambda = 7000 Å ) .
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 \sim 0.3 % in our simulations ) than circumbinary envelopes ( usually \lesssim 0.1 % ) .
Other geometries ( circumbinary flared disks or prolate envelopes , and non-coplanar 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 inclinations is i _ { true } \gtrsim 45 \arcdeg .
For eccentric orbits , the first-order coefficients of the Fourier fit , instead of second-order ones , can be used to find almost all inclinations .