The Origin of Parity Violation in Polarized Dust Emission and Implications for Cosmic Birefringence

Recent measurements of Galactic polarized dust emission have found a nonzero $TB$ signal, a correlation between the total intensity and the $B$-mode polarization component. We present evidence that this parity-odd signal is driven by the relative geometry of the magnetic field and the filamentary interstellar medium in projection. Using neutral hydrogen morphology and Planck polarization data, we find that the angle between intensity structures and the plane-of-sky magnetic field orientation is predictive of the signs of Galactic $TB$ and $EB$. Our results suggest that magnetically misaligned filamentary dust structures introduce nonzero $TB$ and $EB$ correlations in the dust polarization, and that the intrinsic dust $EB$ can be predicted from measurements of dust $TB$ and $TE$ over the same sky mask. We predict correlations between $TE$, $TB$, $EB$, and $EE/BB$, and confirm our predictions using synthetic dust polarization maps from magnetohydrodynamic simulations. We introduce and measure a scale-dependent effective magnetic misalignment angle, $\psi_\ell^{dust} \sim 5^\circ$ for $100 \lesssim \ell \lesssim 500$, and predict a positive intrinsic dust $EB$ with amplitude $\left<D_\ell^{EB}\right> \lesssim 2.5~\mu\mathrm{K^2_{CMB}}$ for the same multipole range at 353 GHz over our sky mask. Both the sign and amplitude of the Galactic $EB$ signal can change with the sky area considered. Our results imply that searches for parity violation in the cosmic microwave background must account for the nonzero Galactic $EB$ and $TB$ signals, necessitating revision of existing analyses of the evidence for cosmic birefringence.