The magnetic field is the main driver of the activity in the solar upper atmosphere, but its measurement is notoriously difficult. In order to determine the magnetic field in the chromosphere, transition region, and corona, we need to measure and interpret the polarization signals that the scattering of anisotropic radiation and the Hanle and Zeeman effects introduce in the emitted spectral line radiation. A number of recent advances have activated the development of this research field. ▪ The quantum theory of the generation and transfer of polarized radiation explains allows us to explain the polarization signals observed in chromospheric and coronal lines and to make successful predictions in unexplored spectral regions. ▪ The development of diagnostic techniques for the solar upper atmosphere has served to improve our empirical knowledge of the magnetic field in a variety of plasma structures, as well as to pave the way for their application to the unprecedented data that the new generation of solar telescopes are expected to provide. However, further improvements are required. ▪ The CLASP suborbital experiments have opened a new diagnostic window, namely ultraviolet (UV) spectropolarimetry as a tool for probing the magnetism and geometry of the upper chromosphere and transition region. A space telescope equipped with a UV spectropolarimeter would lead to major advances in our empirical understanding of solar magnetism. Expected final online publication date for the Annual Review of Astronomy and Astrophysics Volume 60 is August 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Magnetic Field Diagnostics in the Solar Upper Atmosphere

Context. The numerical modeling of the generation and transfer of polarized radiation is a key task in solar and stellar physics research and has led to a relevant class of discrete problems that can be reframed as linear systems. In order to solve such problems, it is common to rely on efficient stationary iterative methods. However, the convergence properties of these methods are problem-dependent, and a rigorous investigation of their convergence conditions, when applied to transfer problems of polarized radiation, is still lacking. Aims. After summarizing the most widely employed iterative methods used in the numerical transfer of polarized radiation, this article aims to clarify how the convergence of these methods depends on different design elements, such as the choice of the formal solver, the discretization of the problem, or the use of damping factors. The main goal is to highlight advantages and disadvantages of the different iterative methods in terms of stability and rate of convergence. Methods. We first introduce an algebraic formulation of the radiative transfer problem. This formulation allows us to explicitly assemble the iteration matrices arising from different stationary iterative methods, compute their spectral radii and derive their convergence rates, and test the impact of different discretization settings, problem parameters, and damping factors. Conclusions. The general methodology used in this article, based on a fully algebraic formulation of linear transfer problems of polarized radiation, provides useful estimates of the convergence rates of various iterative schemes. Additionally, it can lead to novel solution approaches as well as analyses for a wider range of settings, including the unpolarized case.

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Numerical solutions to linear transfer problems of polarized radiation I. Algebraic formulation and stationary iterative methods

Aims. This work aims to identify the relevant physical processes in shaping the intensity and polarization patterns of the solar K I D lines through spectral syntheses, placing particular emphasis on the D 2 line. Methods. The theoretical Stokes profiles were obtained by numerically solving the radiative transfer problem for polarized radiation considering one-dimensional semi-empirical models of the solar atmosphere. The calculations account for scattering polarization, partial frequency redistribution (PRD) effects, hyperfine structure (HFS), J - and F -state interference, multiple isotopes, and magnetic fields of arbitrary strength and orientation. Results. The intensity and circular polarization profiles of both D lines can be suitably modeled while neglecting both J -state interference and HFS. The magnetograph formula can be applied to both lines, without including HFS, to estimate weak longitudinal magnetic fields in the lower chromosphere. By contrast, modeling the scattering polarization signal of the D lines requires the inclusion of HFS. The amplitude of the D 2 scattering polarization signal is strongly depolarized by HFS, but it remains measurable. A small yet appreciable error is incurred in the scattering polarization profile if PRD effects are not taken into account. Collisions during scattering processes have a clear depolarizing effect, although a quantitative analysis is left for a forthcoming publication. Finally, the D 2 scattering polarization signal is particularly sensitive to magnetic fields with strengths around 10 G and it strongly depends on their orientation. Despite this, its center-to-limb variation relative to the amplitude at the limb is largely insensitive to the field strength and orientation. Conclusions. These findings highlight the value of the K I D 2 line polarization for diagnostics of the solar magnetism, and show that the linear and circular polarization signals of this line are primarily sensitive to magnetic fields in the lower chromosphere and upper photosphere, respectively. 

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

The intensity and the linear scattering polarization profiles of the hydrogen Lyα line encode valuable information on the thermodynamic and magnetic structure of the upper layers of the solar chromosphere. The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) sounding rocket experiment provided unprecedented spectropolarimetric data of this line, as well as two-dimensional broadband images in intensity and linear polarization. We theoretically investigate the potential of the Lyα broadband polarimetric signals for probing the solar chromosphere and its magnetic fields. We analyze the synthetic Stokes profiles obtained from a series of radiative transfer (RT) calculations out of local thermodynamic equilibrium, considering semi-empirical one-dimensional models of the solar atmosphere. The wavelength-integrated linear polarization signal is found to be dominated by the contribution from the wings when considering a Gaussian weighting function with a FWHM that corresponds to the CLASP slit-jaw broadband filter. These broadband linear polarization signals are strongly sensitive to magnetic fields of strengths on the order of 50 G, via the action of magneto-optical (MO) effects, and are expected to encode information on the middle–upper chromosphere. The two-dimensional broadband intensity and linear polarization images observed by CLASP can be suitably mimicked using synthetic wavelength-integrated signals obtained considering atmospheric models and magnetic fields that are representative of solar regions with different levels of activity, provided that the impact of MO effects is taken into account. Despite the limitations of a one-dimensional RT modeling, this work illustrates the diagnostic potential of filter-polarimetric Lyα signals for probing the solar chromosphere and its magnetism.

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

Scalable matrix-free solver for 3D transfer of polarized radiation in stellar atmospheres

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 A 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 A 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 A 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.

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Nuno Guerreiro

Papers

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