The Effect of Multiple Scattering on the Polarization from Axisymmetric Circumstellar Envelopes. I. Pure Thomson Scattering Envelopes

Abstract

We investigate, via a Monte Carlo computer code, the effect of multipleThomson scattering on the continuum polarization arising fromaxisymmetric circumstellar envelopes such as equatorial disks,ellipsoidal envelopes, and polar jets or plumes. Previoussingle-scattering models that incorporate attenuation by electronscattering find that the polarization is reduced below thesingle-scattering without attenuation results. Furthermore, it is oftenassumed that multiple scattering will only further reduce thepolarization. However, we find instead that multiple scattering in theenvelope increases the polarization above this ''single-scattering plusattenuation'' approximation. This increase in the polarization occursbecause multiple scattering arises predominantly within the opticallythick disk or plume. Thus, the orientation of the scattering planes forthese multiply scattered photons is biased toward a common direction(e.g., the plane of the disk). For equatorial disk geometries, multiplescatterings reduce the component of the electric vector parallel to thisplane, leaving a net increased polarization that is perpendicular to thedisk. In the case of polar jets, multiple scattering occurspreferentially along the optically thick jet axis, leaving the photonsunpolarized until they scatter out of the jet. Those that are scatteredinto the observer's direction all possess similar polarization positionangles, so there is little polarimetric cancellation, yielding anincrease in the polarization.In the absence of any absorptive opacity, which would reduce the numberof multiple scatterings, we find that multiple scattering produces highlevels of polarization (of order 3%-4% or more) in circumstellar disks.This result is in contrast to previous investigations that used thesingle-scattering plus attenuation approximation, which predictedmaximum polarization levels of about 2% for circumstellar diskgeometries.We have also investigated the polarization when the central star iseither 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 andcorrects the point-source approximation. This depolarization factorresults in a reduced single-scattering polarization level for the finitesource compared to the point source. However, when multiple scatteringis included we find that, for large circumstellar optical depths, afinite source yields larger levels of polarization than a point source.This higher polarization occurs because more photons enter the disk froma finite star than from the more highly attenuated point source. Theseadditional photons are multiply scattered, raising the polarization fora finite star above that for a point-source star.