CMBB-mode polarization from Thomson scattering in the local universe

Abstract

The polarization of the cosmic microwave background (CMB) is widely recognized as a potential source of information about primordial gravitational waves. The gravitational wave contribution can be separated from the dominant CMB polarization created by density perturbations at the times of recombination and reionization because it generates both $E$ and $B$ polarization modes, whereas the density perturbations create only $E$ polarization. The limits of our ability to measure gravitational waves are thus determined by statistical and systematic errors from CMB experiments, foregrounds, and nonlinear evolution effects such as gravitational lensing of the CMB. Usually it is assumed that most foregrounds can be removed because of their frequency dependence, however Thomson scattering of the CMB quadrupole by electrons in the Galaxy or nearby structures shares the blackbody frequency dependence of the CMB. If the optical depth from these nearby electrons is anisotropic, the polarization generated can include $B$ modes even if no tensor perturbations are present. We estimate this effect for the Galactic disk and nearby extragalactic structures, and find that it contributes to the $B$ polarization at the level of $\ensuremath{\sim}(1--2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }\ensuremath{\mu}\mathrm{K}$ per logarithmic interval in multipole $\ensuremath{\ell}$ for $\ensuremath{\ell}<30$. This is well below the detectability level even for a future CMB polarization satellite and hence is negligible. Depending on its structure and extent, the Galactic corona may be a source of $B$-modes comparable to the residual large-scale lensing $B$-mode after the latter has been cleaned using lensing reconstruction techniques. For an extremely ambitious post-Planck CMB experiment, Thomson scattering in the Galactic corona is thus a potential contaminant of the gravitational wave signal; conversely, if the other foregrounds can be cleaned out, such an experiment might be able to constrain models of the corona.