The Impact of Angle-dependent Partial Frequency Redistribution on the Scattering Polarization of the Solar Na i D Lines

Abstract

The long-standing paradox of the linear polarization signal of the Na i D1 line was recently resolved by accounting for the atom’s hyperfine structure and the detailed spectral structure of the incident radiation field. That modeling relied on the simplifying angle-averaged (AA) approximation for partial frequency redistribution (PRD) in scattering, which potentially neglects important angle–frequency couplings. This work aims at evaluating the suitability of a PRD-AA modeling for the D1 and D2 lines through comparisons with general angle-dependent (AD) PRD calculations in both the absence and presence of magnetic fields. We solved the radiative transfer problem for polarized radiation in a 1D semiempirical atmospheric model with microturbulent and isotropic magnetic fields, accounting for PRD effects and comparing PRD-AA and PRD-AD modelings. The D1 and D2 lines are modeled separately as a two-level atomic system with hyperfine structure. The numerical results confirm that a spectrally structured radiation field induces linear polarization in the D1 line. However, the PRD-AA approximation greatly impacts the Q/I shape, producing an antisymmetric pattern instead of the more symmetric PRD-AD one while presenting a similar sensitivity to magnetic fields between 10 and 200 G. Under the PRD-AA approximation, the Q/I profile of the D2 line presents an artificial dip in its core, which is not found for the PRD-AD case. We conclude that accounting for PRD-AD effects is essential to suitably model the scattering polarization of the Na i D lines. These results bring us closer to exploiting the full diagnostic potential of these lines for the elusive chromospheric magnetic fields.

The Polarization of the Solar Ba ii D1 Line with Partial Frequency Redistribution and Its Magnetic Sensitivity

“…We find a good agreement between the two calculations, which highlights the suitability of the AA approximation for modeling the linear polarization pattern of the Ba II D 1 line, at least in the absence of magnetic fields. This contrasts with the results of the analogous investigation for the Na I D 1 line reported in Janett et al (2023), in which that approximation was found to have a clear impact on the shape of the Q/I profile. Although it is not shown here, we were able to reproduce such findings in the nonmagnetic case using HanleRT.…”

“…This approach is otherwise correct in the absence of magnetic fields. However, in the presence of magnetic fields, the same substitution leads to an incorrect expression of the magnetic Hamiltonian (e.g., Janett et al 2023). Thus, the calculations with HanleRT presented in this work are restricted to the nonmagnetic case.…”