Effects of Synchrotron Self-Absorption on Polarization Diagnostics of MHD Turbulence

Synchrotron polarization is a powerful tool for diagnosing magnetohydrodynamic (MHD) turbulence, yet prior analyses are confined to the optically thin regime, neglecting the effects of synchrotron self-absorption (SSA). Here, we incorporate SSA into the radiative transfer of polarized synchrotron emission and employ 3D MHD turbulence simulations to investigate its impacts on polarization statistics. We show that SSA strongly modulates polarized intensity by suppressing its emission amplitude, steepening its low-frequency power-law slopes, and reducing scale-dependent anisotropy. Notably, SSA does not impede the recovery of the scaling slope of the magnetic turbulence. Our results extend the applicability of synchrotron polarization diagnostics to optically thick astrophysical environments, providing a theoretical foundation for interpreting multi-frequency radio polarization observations. This confirms that polarization statistical techniques remain effective for diagnosing MHD turbulence properties in astrophysical environments where SSA is present.