A Wideband Polarization Survey of the Extragalactic Sky at 2-4 GHz: A Science White Paper for the VLA Sky Survey

A VLA Sky Survey of the extragalactic sky at S band (2-4 GHz) with polarization information can uniquely probe the magneto-ionic medium in a wide range of astrophysical environments over cosmic time. For a shallow all-sky survey, we expect to detect over 4 million sources in total intensity $>$ 0.45 mJy beam$^{-1}$ and over 2.2$\times$10$^5$ sources in polarized intensity. With these new observations, we expect to discover new classes of polarized radio sources in very turbulent astrophysical environments and those with extreme values of Faraday depth. Moreover, by determining reliable Faraday depths and by modeling depolarization effects, we can derive properties of the magneto-ionic medium associated with AGNs, absorption line systems and galaxies, addressing the following unresolved questions: (1) What is the covering fraction, the degree of turbulence and the origin of absorption line systems? (2) What is the thermal content in AGNs and radio galaxies? (3) How do AGNs and galaxies evolve over cosmic time? (4) What causes the increase in percentage polarization with decreasing flux densities at the low flux density end of the polarized source count? (5) What is the growth rate of large-scale magnetic fields in galaxies?