The Shocking Origin of the Flat $EE/BB$ Ratio

Polarized emission from dust and synchrotron radiation from the ISM are the dominant foregrounds for CMB polarization and are a major challenge for extracting the primordial signal on large angular scales. A key characteristic of the galactic foreground emission is its $EE/BB$ ratio. We argue that MHD shocks play an important role in setting the observed $EE/BB$ ratio. To support this, we first analyze quasi-linear magnetohydrodynamics (MHD) simulations to obtain an $EE/BB$ ratio that increases as $\sim k^2$, then show that with increasing energy injection rates, the $EE/BB$ ratio flattens to a value $\gtrsim 1$, approaching observational results. Looking at the distribution of the velocity divergence, a tail with power law $-7/2$ develops around the same injection rates where the $EE/BB$ ratio flattens. While the system becomes more isotropic, MHD shocks are intrinsically anisotropic and lead to the $E/B$ power asymmetry. We also observe total pressure balance among all our simulations, indicating slow wave dominance. Therefore, in the regime we consider, it is important to go beyond linear MHD equations to understand the foreground radiation.