Hanle-Zeeman Scattering Matrix for Magnetic Dipole Transitions

Abstract

The polarization of the light that is scattered by the coronal ions is influenced by the anisotropic illumination from the photosphere and the magnetic field structuring in the solar corona. The properties of the coronal magnetic fields can be well studied by understanding the polarization properties of coronal forbidden emission lines that arise from magnetic dipole (M1) transitions in the highly ionized atoms that are present in the corona. We present the classical scattering theory of the forbidden lines for a more general case of arbitrary-strength magnetic fields. We derive the scattering matrix for M1 transitions using the classical magnetic dipole model of Casini & Lin and applying the scattering matrix approach of Stenflo. We consider a two-level atom model and neglect collisional effects. The scattering matrix so derived is used to study the Stokes profiles formed in coronal conditions in those regions where the radiative excitations dominate collisional excitations. To this end, we take into account the integration over a cone of an unpolarized radiation from the solar disk incident on the scattering atoms. Furthermore, we also integrate along the line of sight to calculate the emerging polarized line profiles. We consider radial and dipole magnetic field configurations and spherically symmetric density distributions. For our studies we adopt the atomic parameters corresponding to the [Fe xiii] 10747 Å coronal forbidden line. We also discuss the nature of the scattering matrix for M1 transitions and compare it with that for the electric dipole (E1) transitions.