Polarized Light Scattering With the Paschen-Back Effect, Level-Crossing of Fine Structure States, and Partial Frequency Redistribution

Abstract

The quantum interference between the fine structure states of an atom modifies the shapes of the emergent Stokes profiles in the Second Solar Spectrum. This phenomenon has been studied in great detail both in the presence and absence of magnetic fields. By assuming a flat-spectrum for the incident radiation, the signatures of this effect have been explored for arbitrary field strengths. Even though the theory which takes into account the frequency dependence of the incident radiation is well developed, it is restricted to the regime in which the magnetic splitting is much smaller than the fine structure splitting. In the present paper, we carry out a generalization of our scattering matrix formalism including the effects of partial frequency redistribution (PRD) for arbitrary magnetic fields. We test the formalism using available benchmarks for special cases. In particular we apply it to the Li i 6708Å D 1 and D 2 line system, for which observable effects from the Paschen-Back regime are expected in the Sun's spectrum.

Polarized Scattering of Light for Arbitrary Magnetic Fields With Level-Crossings From the Combination of Hyperfine and Fine Structure Splittings

“…When HFS is included, the HFS magnetic components are distributed around the positions of the FS magnetic components in the absence of HFS. We find that the positions of the HFS magnetic components in Figure 4 correspond well with the wavelength positions of the FS magnetic components in Figure 3 of Sowmya et al (2014a), except for the bunch of magnetic components to the extreme left represented by solid lines. The magnetic field leads to a large blue shift of this bunch, which consists of three σ b (Δμ = μ b − μ a = +1), two π (Δμ = 0) and one σ r (Δμ = −1) components.…”

“…A rapid transformation in the eigenvector basis takes place around the region of avoided crossing. This is described in Bommier (1980) and in LL04 (see also Sowmya et al 2014aSowmya et al , 2014b.…”

“…From Figure 8 it is clear that this difference in the far blue wings is only due to the 7 Li isotope (compare panels (a)-(c)). This can be understood with the help of the line splitting diagrams for level-crossing fields in Figure 4 in comparison with the corresponding diagrams in Figure 3 of Sowmya et al (2014a; a direct comparison of the displacements can be made as the zero points in the two figures are the same). In a two-term atom without HFS, when a magnetic field is applied, the various FS magnetic components are either blue or redshifted from the line center depending on their energies.…”

“…When I s = 0, Equation (12) reduces to the PRD matrix for J state interference alone (see Equation (11) of Sowmya et al 2014a). When FS is neglected, Equation (12) reduces to the expression of RM for pure F state interference (see Equation (16) of Sowmya et al 2014b).…”

“…We refer the reader to Section 4.3 of Sowmya et al (2014a) for details on how we add the continuum contribution and on the parameters used for the continuum. We compare this figure with Figure 4 of Sowmya et al (2014a) and find that the HFS does not cause any change in the intensities. When B = 0 the HFS causes a depolarization in the core of Q/I without affecting the shape of the profile.…”