The effect of multiple scattering on the polarization from axisymmetric circumstellar envelopes .1. Pure Thomson scattering envelopes

We investigate, via a Monte Carlo computer code, the effect of multiple Thomson scattering on the continuum polarization arising from axisymmetric circumstellar envelopes such as equatorial disks, ellipsoidal envelopes, and polar jets or plumes. Previous single-scattering models that incorporate attenuation by electron scattering find that the polarization is reduced below the single-scattering without attenuation results. Furthermore, it is often assumed that multiple scattering will only further reduce the polarization. However, we find instead that multiple scattering in the envelope increases the polarization above this ''single-scattering plus attenuation'' approximation. This increase in the polarization occurs because multiple scattering arises predominantly within the optically thick disk or plume. Thus, the orientation of the scattering planes for these multiply scattered photons is biased toward a common direction (e.g., the plane of the disk). For equatorial disk geometries, multiple scatterings reduce the component of the electric vector parallel to this plane, leaving a net increased polarization that is perpendicular to the disk. In the case of polar jets, multiple scattering occurs preferentially along the optically thick jet axis, leaving the photons unpolarized until they scatter out of the jet. Those that are scattered into the observer's direction all possess similar polarization position angles, so there is little polarimetric cancellation, yielding an increase in the polarization. In the absence of any absorptive opacity, which would reduce the number of multiple scatterings, we find that multiple scattering produces high levels of polarization (of order 3%-4% or more) in circumstellar disks. This result is in contrast to previous investigations that used the single-scattering plus attenuation approximation, which predicted maximum polarization levels of about 2% for circumstellar disk geometries. We have also investigated the polarization when the central star is either a finite sphere or a point source of radiation. Single-scattering calculations include a geometrical ''depolarization factor'' that accounts for the finite solid angle subtended by the star and corrects the point-source approximation. This depolarization factor results in a reduced single-scattering polarization level for the finite source compared to the point source. However, when multiple scattering is included we find that, for large circumstellar optical depths, a finite source yields larger levels of polarization than a point source. This higher polarization occurs because more photons enter the disk from a finite star than from the more highly attenuated point source. These additional photons are multiply scattered, raising the polarization for a finite star above that for a point-source star.