A Classical Theory of Coronal Emission Line Polarization

Abstract

We present a classical theory of formation for polarized, magnetic dipole emission lines in the magnetized solar corona. Because of the small Einstein A-coefficients of forbidden lines and the expected magnetic field strengths in the corona, coherences between different magnetic substates can be neglected, so the observed Stokes vector for these lines is the result of the incoherent superposition of the Stokes vectors emitted in the de-excitation of the individual magnetic substates of the transition's upper level. Using classical electrodynamics and a weak-field expansion formalism, we could derive the main polarization properties of the transition J = 1 to J = 0, in the collisionless regime. In particular, we derived the correct amount of atomic alignment in the upper level, induced by the anisotropic, unpolarized illumination from the photosphere, and the dependence of Stokes Q and U linear polarization on the magnetic field direction in the plane of the sky. The influence of atomic alignment on the V profile is also correctly reproduced. This work provides a classical interpretation of the physical process that generates atomic alignment in the radiating ion and how the associated Van Vleck effect in resonance-scattering linear polarization and the alignment contribution to Zeeman effect circular polarization come about.