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

Benedusi, Pietro; Riva, Simone; Zulian, Patrick; Štěpán, Jiří; Belluzzi, L.; Krause, Rolf

doi:10.1016/j.jcp.2023.112013

Cited by 9 publications

(6 citation statements)

References 69 publications

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“…The problem is thus characterized by axial symmetry, which allows us to keep computational costs down to a manageable level. It can be expected that the impact of the general AD treatment of PRD effects will be greater when the radiation field scattered by the atom has a more complex angular dependence, as happens when the complex 3D geometrical structure of the solar chromospheric plasma is taken into account (e.g., Anusha 2023; Benedusi et al 2023, and references therein).…”

Section: D Semiempirical Atmospheric Modelmentioning

confidence: 99%

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

Janett,

Alsina Ballester,

Belluzzi

et al. 2023

ApJ

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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.

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Section: D Semiempirical Atmospheric Modelmentioning

confidence: 99%

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

Janett,

Alsina Ballester,

Belluzzi

et al. 2023

ApJ

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“…Finally, this investigation has allowed us to assess the suitability of the solution strategy and implementation for dynamic scenarios. This facilitates the ongoing development of a software framework for solving the non-LTE RT problem for polarized radiation in realistic 3D models of the solar atmosphere, while taking AD PRD effects into account (Benedusi et al 2023).…”

Section: Discussionmentioning

confidence: 99%

“…( 6). More details on the algorithm for calculating the contribution of R II to the emissivity can be found in Benedusi et al (2023). In order to speed up the calculation of the emissivity, the scattering inte-gral is evaluated in the comoving reference frame (i.e.…”

Section: Methodsmentioning

confidence: 99%

Modeling the scattering polarization in the solar Ca I 4227Å line with angle-dependent PRD effects and bulk velocities

Guerreiro,

Janett,

Riva

et al. 2024

A&A

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Modeling the scattering polarization signals of strong chromospheric lines requires solving the radiative transfer (RT) problem for polarized radiation, out of local thermodynamic equilibrium, taking partial frequency redistribution (PRD) effects into account. This problem is extremely challenging from a computational standpoint and, so far, most studies have been carried out by either modeling PRD effects under the angle-average approximation or by considering academic models of the solar atmosphere. Thanks to a new solution strategy, applicable to atomic systems that allow for a linearization of the problem, accurate solutions can now be routinely obtained in realistic 1D models, taking angle-dependent (AD) PRD effects into account. This work is aimed at assessing the suitability and performance of this new approach to handling dynamic scenarios. At the same time, it aims to explore the joint impact of magnetic fields and bulk velocities on the scattering polarization profiles of strong resonance lines, accounting for AD PRD effects and considering more realistic atmospheric models than in previous investigations. By using a two-level atomic model for neutral calcium, we synthesized the intensity and polarization profiles of the Ca i AA line. Our calculations were performed in 1D atmospheric models, both semi-empirical and extracted from 3D MHD simulations, including vertical bulk velocities and magnetic fields of arbitrary strength and orientation, both constant and varying with height. We obtained accurate solutions after only a few iterations across all considered scenarios. Even when formulating the problem in the observer's reference frame, the frequency and angular grids required for accurate results were easily manageable. The calculated profiles showed the expected signatures of bulk velocities: wavelength shifts, enhancement of the line-core polarization amplitude, and prominent asymmetries in the wing signals. The results obtained in atmospheric models with complex thermal, dynamic, and magnetic structures unveiled the broad diversity of features in the emergent radiation that can be expected from realistic scenarios. The presented results assess the suitability of the proposed solution strategy and its parallel implementation, thus supporting its generalization to the 3D case. Our applications in increasingly realistic atmospheric models showed the difficulty related to precisely establishing the individual weight of bulk velocities and magnetic fields in the shape of the emergent profiles. This highlights the need to account for both these physical ingredients to perform reliable inversions of observed scattering polarization profiles.

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“…However, stationary iterative methods have been largely superseded by Krylov subspace methods (e.g., Ipsen & Meyer 1998;Saad 2003;Meurant & Duintjer Tebbens 2020;Pearson & Pestana 2020), which also gained popularity in the radiative transfer context (e.g., Warsa et al 2003;Anusha et al 2009;Ren et al 2019;Badri et al 2018Badri et al , 2019Benedusi et al 2021). Lately, Benedusi et al (2021Benedusi et al ( , 2022Benedusi et al ( , 2023 analyzed the application of Krylov methods to linear radiative transfer problems of polarized radiation, showing that they outperform standard stationary iterative methods in terms of convergence rate, time-to-solution, and are also favorable in terms of robustness with respect to the problem size. Moreover, Krylov methods can be applied in a matrix-free context, making them highly effective solution strategies for large linear systems.…”

Section: Matrix-free Krylov Methodsmentioning

confidence: 99%

“…A correct theoretical interpretation of such signals requires solving the radiative transfer problem for polarized radiation, taking partial frequency redistribution (PRD) effects into account (e.g., Stenflo 1994;Bommier 1997aBommier ,b, 2017Belluzzi & Trujillo Bueno 2014;Casini et al 2014Casini et al , 2017a. Recently, Janett et al (2021a) pointed out that a relevant class of radiative transfer problems involving scattering polarization can be reframed, once discretized, as linear systems through a convenient physical assumption (see also Trujillo Bueno & Manso Sainz 1999;Štěpán 2008;Janett et al 2021b;Benedusi et al 2022Benedusi et al , 2023. Such linear problems can then be solved iteratively by exploiting powerful tools from numerical linear algebra, such as Krylov iterative methods.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions to linear transfer problems of polarized radiation

Janett,

Benedusi,

Riva

2024

A&A

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A relevant class of radiative transfer problems for polarized radiation is linear, or can be linearized, and can thus be reframed as linear systems once discretized. In this context, depending on the considered physical models, there are both highly coupled and computationally expensive problems, for which state-of-the-art iterative methods struggle to converge, and lightweight ones, for which solutions can be obtained efficiently. This work aims to exploit lightweight physical models as preconditioners for iterative solution strategies to obtain accurate and fast solutions for more complex problems. We considered a highly coupled linear transfer problem for polarized radiation, which we solved iteratively using a matrix-free generalized minimal residual (GMRES) method. Different preconditioners and initial guesses, designed in a physics-based framework, are proposed and analyzed. The action of preconditioners was also computed by applying GMRES. The overall approach thus consists of two nested GMRES iterations, one for the original problem and one for its lightweight version. As a benchmark, we considered the modeling of the intensity and polarization of the solar Ca i AA line, the Sr ii AA line, and the Mg ii h k lines in a semi-empirical 1D atmospheric model, accounting for partial frequency redistribution effects in scattering processes and considering a general angle-dependent treatment. Numerical experiments show that using tailored preconditioners based on simplified models of the considered problem has a noticeable impact, reducing the number of iterations to convergence by a factor of 10-20. By designing efficient preconditioners in a physics-based context, it is possible to significantly improve the convergence of iterative processes, obtaining fast and accurate numerical solutions to the considered problems. The presented approach is general, requiring only the selection of an appropriate lightweight model, and can be applied to a larger class of radiative transfer problems in combination with arbitrary iterative procedures.

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

Cited by 9 publications

References 69 publications

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

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

Modeling the scattering polarization in the solar Ca I 4227Å line with angle-dependent PRD effects and bulk velocities

Numerical solutions to linear transfer problems of polarized radiation

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

Cited by 9 publications

References 69 publications

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

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

Modeling the scattering polarization in the solar Ca I 4227Å line with angle-dependent PRD effects and bulk velocities

Numerical solutions to linear transfer problems of polarized radiation

Contact Info

Product

Resources

About

Modeling the scattering polarization in the solar Ca I 4227Å line with angle-dependent PRD effects and bulk velocities