Polarized Line Formation in Arbitrary Strength Magnetic Fields: The Case of a Two-level Atom with Hyperfine Structure Splitting

Sampoorna, M.; Nagendra, K. N.; Sowmya, K.; Stenflo, J. O.; Anusha, L. S.

doi:10.3847/1538-4357/ab3805

Cited by 11 publications

(14 citation statements)

References 39 publications

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“…Nonetheless, there is still high interest in modeling scattering polarization under this approximation. The main reason is that the computational cost for carrying out detailed angle-dependent calculations in the presence of polarization phenomena is still prohibitive except when taking the simplest modeling of the solar atmosphere (see Sampoorna et al 2019) or when introducing other simplifying assumptions such as cylindrical symmetry (see del Pino Alemán et al 2020). It is also for this reason that, to date, few quantitative analyses of the impact of the angle-averaged assumption on the modeling of scattering polarization have been carried out.…”

Section: The Angle-averaged Approximationmentioning

confidence: 99%

Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation

Paganini

Hashemi

Ballester

et al. 2020

A&A

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Context. Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized radiation) are taken into account. Frequency redistribution effects are conveniently described through the redistribution function formalism, and the angle-averaged approximation is often introduced to simplify the problem. Even in this case, the evaluation of the emission coefficient for polarized radiation remains computationally costly, especially when magnetic fields are present or complex atomic models are considered. Aims. We aim to develop an efficient algorithm to numerically evaluate the angle-averaged redistribution function for polarized radiation. Methods. The proposed approach is based on a low-rank approximation via trivariate polynomials whose univariate components are represented in the Chebyshev basis. Results. The resulting algorithm is significantly faster than standard quadrature-based schemes for any target accuracy in the range [10 −6 , 10 −2 ].

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Section: The Angle-averaged Approximationmentioning

confidence: 99%

Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation

Paganini

Hashemi

Ballester

et al. 2020

A&A

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“…The basic equations and the numerical method of solution for the problem at hand are presented in detail in Sampoorna et al (2019a). Therefore, we do not repeat them here.…”

Section: The Model Parameterizationmentioning

confidence: 99%

“…For our studies we consider the case of D 2 line of Na i. The atomic parameters corresponding to this line have been taken from Steck (2003) and are detailed in Table 1 of Sampoorna et al (2019a). In the present paper the D 2 line of Na i is modeled using a two-level atom with HFS and neglecting lower level polarization.…”

Section: The Model Parameterizationmentioning

confidence: 99%

“…In a recent paper (Sampoorna et al 2019a, see also Sampoorna et al 2019b), we solved the problem of polarized line formation in arbitrary fields taking into account scattering on a two-level atom with hyperfine structure splitting (HFS) and an unpolarized lower level, incomplete and complete Paschen-Back effect (PBE) regimes, and the angle-averaged partial frequency redistribution (AA-PRD). For this purpose, we generalized the so-called scattering expansion method of Frisch et al (2009) to handle arbitrary fields.…”

Section: Introductionmentioning

confidence: 99%

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Importance of Angle-dependent Partial Frequency Redistribution in Hyperfine Structure Transitions Under Incomplete Paschen-Back Effect Regime

Nagendra,

Sowmya,

Sampoorna

et al. 2020

Preprint

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Angle-frequency coupling in scattering of polarized light on atoms is represented by the angledependent (AD) partial frequency redistribution (PRD) matrices. There are several lines in the linearly polarized solar spectrum, for which PRD combined with quantum interference between hyperfine structure states play a significant role. Here we present the solution of the polarized line transfer equation including the AD-PRD matrix for scattering on a two-level atom with hyperfine structure splitting (HFS) and an unpolarized lower level. We account for the effects of arbitrary magnetic fields (including the incomplete Paschen-Back effect regime) and elastic collisions. For exploratory purposes we consider a self-emitting isothermal planar atmosphere and use atomic parameters that represent an isolated Na i D 2 line. For this case we show that the AD-PRD effects are significant for field strengths below about 30G, but that the computationally much less demanding approximation of angle-averaged (AA) PRD may be used for stronger fields.

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“…For the sake of simplicity, these papers are limited to the study of hypothetical lines in isothermal atmospheric models. Finally, Anusha & Nagendra (2013) used the BICGSTAB method to model the Ca ii K 3993 Å resonance line using an ad-hoc 3D atmospheric model, and Sampoorna et al (2019) applied the GMRES method to model the D 2 lines of Li i and Na i, taking the hyperfine structure of these atoms into account. However, Krylov methods have not been fully exploited in the numerical solution of transfer of polarized radiation.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions to linear transfer problems of polarized radiation II. Krylov methods and matrix-free implementation

Benedusi,

Janett,

Belluzzi

et al. 2021

Preprint

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Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary iterative methods have been replaced by state-of-the-art preconditioned Krylov iterative methods for many applications. However, a general description and a convergence analysis of Krylov methods in the polarized radiative transfer context are still lacking. Aims. We describe the practical application of preconditioned Krylov methods to linear transfer problems of polarized radiation, possibly in a matrix-free context. The main aim is to clarify the advantages and drawbacks of various Krylov accelerators with respect to stationary iterative methods and direct solution strategies. Methods. After a brief introduction to the concept of Krylov methods, we report the convergence rate and the run time of various Krylov-accelerated techniques combined with different formal solvers when applied to a 1D benchmark transfer problem of polarized radiation. In particular, we analyze the GMRES, BICGSTAB, and CGS Krylov methods, preconditioned with Jacobi, (S)SOR, or an incomplete LU factorization. Furthermore, specific numerical tests were performed to study the robustness of the various methods as the problem size grew. Results. Krylov methods accelerate the convergence, reduce the run time, and improve the robustness (with respect to the problem size) of standard stationary iterative methods. Jacobi-preconditioned Krylov methods outperform SOR-preconditioned stationary iterations in all respects. In particular, the Jacobi-GMRES method offers the best overall performance for the problem setting in use. Conclusions. Krylov methods can be more challenging to implement than stationary iterative methods. However, an algebraic formulation of the radiative transfer problem allows one to apply and study Krylov acceleration strategies with little effort. Furthermore, many available numerical libraries implement matrix-free Krylov routines, enabling an almost effortless transition to Krylov methods.

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Polarized Line Formation in Arbitrary Strength Magnetic Fields: The Case of a Two-level Atom with Hyperfine Structure Splitting

Cited by 11 publications

References 39 publications

Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation

Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation

Importance of Angle-dependent Partial Frequency Redistribution in Hyperfine Structure Transitions Under Incomplete Paschen-Back Effect Regime

Numerical solutions to linear transfer problems of polarized radiation II. Krylov methods and matrix-free implementation

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