Modeling the scattering polarization of the solar Ca I 4227 Å line with angle-dependent partial frequency redistribution

Abstract

Context. The correct modeling of the scattering polarization signals observed in several strong resonance lines requires taking partial frequency redistribution (PRD) phenomena into account. Modeling scattering polarization with PRD effects is very computationally demanding and the simplifying angle-averaged (AA) approximation is therefore commonly applied. Aims. This work aims to assess the impact and the range of validity of the AA approximation with respect to the general angle-dependent (AD) treatment of PRD effects in the modeling of scattering polarization in strong resonance lines, with a focus on the solar Ca I 4227 Å line. Methods. Spectral line polarization was modeled by solving the radiative transfer problem for polarized radiation, under nonlocal thermodynamic equilibrium conditions, taking PRD effects into account in static one-dimensional semi-empirical atmospheric models presenting arbitrary magnetic fields. The problem was solved through a two-step approach. In step 1, the problem was solved for the intensity only, considering a multilevel atom. In step 2, the problem was solved including polarization, considering a two-level atom with an unpolarized and infinitely sharp lower level, and fixing the lower level population calculated at step 1. Results. The results for the Ca I 4227 Å line show a good agreement between the AA and AD calculations for the Q/I and U/I wings’ signals. However, AA calculations reveal an artificial trough in the line-core peak of the linear polarization profiles, whereas AD calculations show a sharper peak in agreement with the observations. Conclusions. An AD treatment of PRD effects is essential to correctly model the line-core peak of the scattering polarization signal of the Ca I 4227 Å line. By contrast, in the considered static case, the AA approximation seems to be suitable to model the wing scattering polarization lobes and their magnetic sensitivity through magneto-optical effects.

The Potential of the Wavelength-integrated Scattering Polarization of the Hydrogen Lyα Line for Probing the Solar Chromosphere

“…The redistribution matrix is given by the sum of two terms, which characterize scattering processes that are coherent (R ii ) and completely incoherent (R iii ) in the atomic rest frame. In the observer's frame, we consider for computational simplicity the so-called angle-averaged approximation for R ii (Rees & Saliba 1982), which we expect to be suitable for modeling the wings of resonance lines (see Janett et al 2021). We also make the assumption that scattering is completely incoherent in the observer's frame for R iii .…”

Numerical solutions to linear transfer problems of polarized radiation

“…This quantity is proportional to the population of the lower level, which in turn depends on I in a nonlinear way through the statistical equilibrium equations. The redistribution matrix R only depends on local atmospheric quantites, therefore a suitable assumption to retrieve linearity with respect to I is to fix the coefficient k L a priori (see Belluzzi & Trujillo Bueno 2014;Alsina Ballester et al 2017;Janett et al 2021a). In this way, K is independent of I and ε linearly depends on it.…”

“…We considered the Ca I line at 4227 Å, which is an ideal benchmark for new approaches to the modeling of scattering polarization including PRD effects and can be suitably modeled by considering a simple two-level atom (e.g., Faurobert-Scholl 1992;Sampoorna et al 2009;Supriya et al 2014;Alsina Ballester et al 2018;Janett et al 2021a). We considered the wavelength interval [λ min , λ max ] = [4220, 4234] Å, discretized with N ν = 99 nodes.…”

“…We A&A 664, A197 (2022) recall that scattering polarization is intimately related to the geometrical properties (i.e., the anisotropy) of the radiation field that pumps the atoms. It therefore becomes apparent that a general angle-dependent treatment of PRD effects, without introducing simplifying assumptions, such as the angle-averaged one (e.g., Rees & Saliba 1982;Leenaarts et al 2012;Alsina Ballester et al 2017), can be essential for an accurate modeling (Janett et al 2021a). When angle-dependent PRD effects are accounted for, the numerical modeling of scattering polarization signals results in an extremely challenging computational problem with significant memory requirements.…”

The polarization signals of the solar K I D lines and their magnetic sensitivity

“…Appreciable errors in numerical calculations due to the angle-averaged approximation in R ii were reported in the past, both when considering semi-infinite and isothermal atmospheric models (Faurobert 1988;Sampoorna et al 2017) and when synthesizing strong resonance lines in semi-empirical atmospheric models (e.g., Janett et al 2021). The suitability of assuming CRD in the observer's reference frame for R iii in the polarized case was called into question by Bommier (1997), but more recent RT investigations by Sampoorna et al (2017) suggest that that the incurred error is minor when considering atmospheres with a large optical depth relative to the considered line.…”