CMB $B$-mode polarization from Thomson scattering in the local universe

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 $\sim (1–2)\times {10}^{-4}\mu \mathrm{K}$ per logarithmic interval in multipole $\ell$ for $\ell <30$. 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.

Figure 1

The contributions to the $B$-mode polarization power spectrum. The white-noise ($C_{\ell }\propto {\ell }^2$) lines are the lensing signal before cleaning (top line) and after cleaning assuming iterative lensing reconstruction with $0.25\mu \mathrm{K}$ arcmin noise and 2 arcmin beam (bottom line). The dashed line shows the tensor $B$-mode spectrum for $T/S={10}^{-5}$. The Galactic Thomson scattering contribution is shown by the solid line with points; note that due to the approximate parity symmetry of the Galactic electron distribution, the odd $\ell$ modes have much more power than even $\ell$.

Figure 2

The $B$-mode power spectrum on a cut sky (with $|b|<10$ degrees removed) from Thomson scattering in the Galactic disk, computed with Eq. (11). The dotted line is the cleaned-lensing signal assuming iterative lensing reconstruction with $0.25\mu \mathrm{K}$ arcmin noise and 2 arcmin beam, and the dashed line is the tensor contribution for $T/S={10}^{-5}$. The points show the polarization band powers from Thomson scattering (the open squares represent negative band powers). Some power may be missing at $\ell \ge 10$ due to the sparse sampling of the pulsars used to construct the electron density model.

Figure 3

The $B$-mode power spectrum on a cut sky (with $|b|<10$ degrees removed) from Thomson scattering, in (a) the K (23 GHz) band and (b) the W (94 GHz) band. This figure is the same as Fig. 2 except that we have replaced the cosmic quadrupole with the raw K and W band quadrupoles observed by WMAP (no frequency cleaning). Some power may be missing at $\ell \ge 10$ due to the sparse sampling of the pulsars used to construct the electron density model.

Figure 4

The contribution from nearby extragalactic structures to the $B$-modes. Panel (a) shows the power spectrum for the constrained realization method of Sec. 5a (points), the power spectrum method of Sec. 5b (thick line), and the power spectrum method with the integration cut off at $r_{\max }=80h^{-1}\mathrm{Mpc}$ (thin line). Panel (b) shows the total B-mode from local scattering (points), constructed by taking the optical depth map from the Galaxy and nearby structures, computing the resulting $C_{\ell }^{BB}$ using the quadratic estimator, and then adding the estimated power from $r>80h^{-1}\mathrm{Mpc}$. For reference, the cleaned-lensing and tensor curves from Fig. 2 are shown.