arXiv subjects

Gioele Janett

Publications and source records attributed to Gioele Janett.

16 recordsLinked to original sources

arXiv2026

Validity of the CRD limit for modeling scattering polarization in the photospheric Sr I 4607 {\AA} line

Context. Scattering polarization in the Sr I 4607 {\AA} line is a key diagnostic for small-scale, unresolved magnetic fields in the quiet solar photosphere, inaccessible to Zeeman-based techniques. The complete frequency redistribution (CRD) limit is commonly used to model this line, but its validity and impact on magnetic sensitivity have not been systematically investigated. This is timely given new facilities observing this line with unprecedented accuracy, and future synoptic programs targeting long-term quiet-Sun magnetism. Aims. We assess the CRD limit against the general partial frequency redistribution (PRD) description of scattering for the Sr I 4607 {\AA} polarization, focusing on its magnetic sensitivity via the Hanle effect. Methods. We solved the non-LTE radiative transfer problem for polarized radiation in a semi-empirical 1D plane-parallel static atmosphere, with CRD and PRD scattering, across magnetic field configurations relevant for Hanle diagnostics. Results. For small-scale unresolved fields, where the field acts only via Hanle depolarization of Q/I, CRD and PRD emergent profiles and Hanle sensitivity are essentially identical. For deterministic fields, CRD remains accurate when polarization signals exceed about 0.3%; for weaker signals, PRD effects can appreciably affect the emergent profiles. Conclusions. CRD is adequate for modeling Sr I 4607 {\AA} scattering polarization in the vast majority of observationally relevant cases; PRD effects matter only for weak polarization signals.

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arXiv2026

ZIMPOL detects scattering polarization in He I D$_3$ during a solar flare

Spectropolarimetric observations of solar flares in the He I D$_3$ line at 5876 Å are extremely rare, and their diagnostic potential remains largely unexplored. We report the first unambiguous detection of linear polarization in He I D$_3$ during a solar flare. Using the high-precision ZIMPOL polarimeter at the IRSOL observatory in Locarno (Switzerland), we tracked the temporal evolution of the He I D$_3$ Stokes profiles throughout the M7 GOES-class flare that occurred on 3 May 2023 at 10:45 UT. We analyzed the time evolution of the maximum in linear polarization and the absorption depth of the intensity profile. Both the fractional linear polarization, which peaks at $6\times10^{-4}$, and the absorption depth increase rapidly before gradually decaying, with their maxima occurring approximately 5 minutes after the peaks in GOES X-ray flux and SDO/AIA 304 Å emission. From the evolving He I D$_3$ core position, we also derived the temporal evolution of the plasma bulk velocities. The intensity profiles exhibiting strong absorption seems to originate from the flare ribbons. The time evolution of all Stokes parameters in the 3 May 2023 event was driven by changes in ortho-helium density prompted by the different phases of the flare. Our analysis suggests that the observed He I D$_3$ linear polarization is likely not dominated by the theorized impact polarization, as it exhibits neither spatial correspondence with electron precipitation sites nor temporal synchronization with the impulsive phase. Instead, the signals are consistent with scattering polarization produced by anisotropic radiation pumping. We conclude that scattering polarization signal on the order of $0.01\%$ can be produced in the He I D$_3$ line during solar flares. This can provide constraints for flare models.

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arXiv2026

3D radiative transfer modeling of scattering polarization with partial frequency redistribution I. Verification and disk-center results for the solar Ca I 4227 Å line

Several strong solar resonance lines show observable linear scattering polarization signals, holding a great potential for investigating the magnetism of the outer solar atmosphere. Accurately modeling these signals requires solving the radiative transfer (RT) problem for polarized radiation in comprehensive 3D models of the solar atmosphere, in non-local thermodynamic equilibrium, accounting for partial frequency redistribution (PRD) effects. This problem has so far been computationally inaccessible. We present the first scientific application of TRIP, a novel software for the massively parallel solution of the 3D non-LTE RT problem for polarized radiation, including scattering polarization and PRD. We aim to verify the code and explore the combined action of PRD and the 3D structure of the solar atmosphere on scattering polarization. We run TRIP to synthesize the Stokes profiles of the Ca I line at 4227 Å in a 3D model of the solar atmosphere extracted from a radiation magneto-hydrodynamic simulation. We efficiently solve the resulting large-scale problem, with up to $4 \times 10^{10}$ degrees of freedom, with a state-of-the-art preconditioned Krylov method, using up to 20 thousand parallel CPUs. After including verification tests, we find that the joint impact of PRD effects and the detailed 3D structure of the atmospheric model produce disk-center scattering polarization signals in the line wings. These signals are sensitive to the magnetic field, via magneto-optical effects, and to bulk velocity gradients. We also show that the CRD approximation underestimates the amplitude of disk-center line-core signals. This achievement represents a crucial step forward for diagnosing the magnetism of the solar chromosphere and transition region through the quantitative comparisons of synthetic and observational data.

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arXiv2025

A numerical approach for modelling the polarisation signals of strong resonance lines with partial frequency redistribution. Numerical applications to two-term atoms and plane-parallel atmospheres

Aims. The main goal of this paper is to present an accurate and efficient numerical strategy for solving the radiative transfer problem for polarised radiation in strong resonance lines forming out of local thermodynamic equilibrium, taking angle-dependent (AD) partial frequency redistribution (PRD) effects and J-state interference into account. We consider the polarisation produced both by the Zeeman effect and by the scattering of anisotropic radiation, along with its sensitivity to the Hanle and magneto-optical effects. Methods. We introduce a formalism that allows treating both a two-level and a two-term atom in the presence of arbitrary magnetic and bulk velocity fields. The problem is formulated by treating the population of the lower level/term as a fixed input parameter. This approach makes the problem linear with respect to the radiation field, enabling the application of efficient matrix-free preconditioned iterative methods for its solution. Additionally, the computation of the scattering emissivity in the comoving frame, together with a careful choice of the angular and spectral quadrature nodes, allow us to speed up the calculations by reducing the number of evaluations of the redistribution functions. Results. The proposed solution strategy is applied to synthesise the Stokes profiles of the Mg ii h&k doublet and the H i Ly-α line in 1D semi-empirical models. The results demonstrate that the method is both fast and accurate. A comparison with calculations from HanleRT-TIC displays an overall good agreement, thereby validating our solution strategy. Moreover, for the wavelength-integrated polarisation profiles of the H i Ly-α line, we find an excellent agreement between the results obtained including PRD effects in their general AD description and those obtained considering the angle-averaged simplifying approximation.

astro-ph.SR↗

arXiv2024

Accurate PRD modeling of the forward-scattering Hanle effect in the chromospheric CaI 4227 Å line

Measurable linear scattering polarization signals have been predicted and detected at the solar disk center in the core of chromospheric lines. These forward-scattering polarization signals, which are of high interest for magnetic field diagnostics, have always been modeled either under the assumption of complete frequency redistribution (CRD), or taking partial frequency redistribution (PRD) effects into account under the angle-averaged (AA) approximation. This work aims at assessing the suitability of the CRD and PRD-AA approximations for modeling the forward-scattering polarization signals produced by the presence of an inclined magnetic field, the so-called forward-scattering Hanle effect, in the chromospheric CaI 4227 A line. Radiative transfer calculations are performed in semi-empirical 1D solar atmospheres, out of local thermodynamic equilibrium (LTE). A two-step solution strategy is applied: the non-LTE RT problem is first solved considering a multilevel atom and neglecting polarization phenomena. The same problem is then solved including polarization, considering a two-level atom and keeping fixed the lower-level population calculated at the previous step. The emergent linear polarization signals calculated under the CRD and PRD-AA approximations are analyzed and compared to those obtained by modeling PRD effects in their general angle-dependent (AD) formulation. With respect to the PRD-AD case, the CRD and PRD-AA calculations significantly underestimate the amplitude of the line-center polarization signals produced by the forward-scattering Hanle effect. The results of this work suggest that a PRD-AD modeling is required in order to develop reliable diagnostic techniques exploiting the forward-scattering polarization signals observed in the CaI 4227 A line. These results need to be confirmed by full 3D calculations including non-magnetic symmetry-breaking effects.

astro-ph.SR↗

arXiv2023

Assessment of the CRD approximation for the observer's frame RIII redistribution matrix

Approximated forms of the RII and RIII redistribution matrices are frequently applied to simplify the numerical solution of the radiative transfer problem for polarized radiation, taking partial frequency redistribution (PRD) effects into account. A widely used approximation for RIII is to consider its expression under the assumption of complete frequency redistribution (CRD) in the observer frame (RIII CRD). The adequacy of this approximation for modeling the intensity profiles has been firmly established. By contrast, its suitability for modeling scattering polarization signals has only been analyzed in a few studies, considering simplified settings. In this work, we aim at quantitatively assessing the impact and the range of validity of the RIII CRD approximation in the modeling of scattering polarization. Methods. We first present an analytic comparison between RIII and RIII CRD. We then compare the results of radiative transfer calculations, out of local thermodynamic equilibrium, performed with RIII and RIII CRD in realistic 1D atmospheric models. We focus on the chromospheric Ca i line at 4227 A and on the photospheric Sr i line at 4607 A.

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arXiv2023

The impact of angle-dependent partial frequency redistribution on the scattering polarization of the solar Na i D lines

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, both in the absence and presence of magnetic fields. We solved the radiative transfer problem for polarized radiation in a one-dimensional semi-empirical atmospheric model with microturbulent and isotropic magnetic fields, accounting for PRD effects, comparing PRD-AA and PRD-AD modelings. The D1 and D2 lines are modeled separately as 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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arXiv2021

A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer

Context. Several numerical problems require the interpolation of discrete data that present various types of discontinuities. The radiative transfer is a typical example of such a problem. This calls for high-order well-behaved techniques to interpolate both smooth and discontinuous data. Aims. The final aim is to propose new techniques suitable for applications in the context of numerical radiative transfer. Methods. We have proposed and tested two different techniques. Essentially non-oscillatory (ENO) techniques generate several candidate interpolations based on different substencils. The smoothest candidate interpolation is determined from a measure for the local smoothness, thereby enabling the essential non-oscillatory property. Weighted ENO (WENO) techniques use a convex combination of all candidate substencils to obtain high-order accuracy in smooth regions while keeping the essentially non-oscillatory property. In particular, we have outlined and tested a novel well-performing fourth-order WENO interpolation technique for both uniform and nonuniform grids. Results. Numerical tests prove that the fourth-order WENO interpolation guarantees fourth-order accuracy in smooth regions of the interpolated functions. In the presence of discontinuities, the fourth-order WENO interpolation enables the non-oscillatory property, avoiding oscillations. Unlike Bézier and monotonic high-order Hermite interpolations, it does not degenerate to a linear interpolation near smooth extrema of the interpolated function. Conclusions. The novel fourth-order WENO interpolation guarantees high accuracy in smooth regions, while effectively handling discontinuities. This interpolation technique might be particularly suitable for several problems, including a number of radiative transfer applications such as multidimensional problems, multigrid methods, and formal solutions.

math.NA↗

arXiv2021

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

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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arXiv2021

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

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. 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, or (S)SOR. Results. Krylov methods accelerate the convergence, reduce the run time, and improve the robustness 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.

math.NA↗

arXiv2021

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

Context. The correct modeling of the scattering polarization signals observed in several strong resonance lines requires taking partial frequency redistribution (PRD) phenomena into account. Aims. This work aims at assessing the impact and the range of validity of the angle-averaged 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 focus on the solar Ca i 4227 Å line. Methods. Spectral line polarization is 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 is solved through a two-step approach. In step 1, the problem is solved for intensity only, considering a multi-level atom. In step 2, the problem is 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 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.

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arXiv2019

Discontinuities in numerical radiative transfer

Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of the stationary radiative transfer equation is particularly challenging in such situations, because standard numerical methods may perform very inefficiently in the absence of local smoothness. However, a rigorous investigation of the numerical treatment of the radiative transfer equation in discontinuous media is still lacking. The aim of this work is to expose the limitations of standard convergence analyses for this problem and to identify the relevant issues. Moreover, specific numerical tests are performed. These show that discontinuities in the atmospheric physical parameters effectively induce first-order discontinuities in the radiative transfer equation, reducing the accuracy of the solution and thwarting high-order convergence. In addition, a survey of the existing numerical schemes for discontinuous ordinary differential systems and interpolation techniques for discontinuous discrete data is given, evaluating their applicability to the radiative transfer problem.

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arXiv2018

Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems

The numerical computation of reliable and accurate Stokes profiles is of great relevance in solar physics. In the synthesis process, many actors play a relevant role: among them the formal solver, the discrete atmospheric model, and the spectral line. This paper tests the performances of different numerical schemes in the synthesis of polarized spectra for different spectral lines and atmospheric models. The hierarchy between formal solvers is enforced, stressing the peculiarities of high-order and low-order formal solvers. The density of grid points necessary for reaching a given accuracy requirement is quantitatively described for specific situations.

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arXiv2018

Formal solutions for polarized radiative transfer. III. Stiffness and instability

Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-sizes are often necessary to retrieve physical solutions. This work presents stability analyses of formal solvers for the radiative transfer equation of polarized light, identifies instability issues, and suggests practical remedies. In particular, the assumptions and the limitations of the stability analysis of Runge-Kutta methods play a crucial role. On this basis, a suitable and pragmatic formal solver is outlined and tested. An insightful comparison to the scalar radiative transfer equation is also presented.

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arXiv2017

Formal Solutions for Polarized Radiative Transfer. I. The DELO Family

The discussion regarding the numerical integration of the polarized radiative transfer equation is still open and the comparison between the different numerical schemes proposed by different authors in the past is not fully clear. Aiming at facilitating the comprehension of the advantages and drawbacks of the different formal solvers, this work presents a reference paradigm for their characterization based on the concepts of order of accuracy, stability, and computational cost. Special attention is paid to understand the numerical methods belonging to the Diagonal Element Lambda Operator family, in an attempt to highlight their specificities.

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arXiv2017

Formal Solutions for Polarized Radiative Transfer. II. High-order Methods

When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial grids. Aiming to provide a clear comparison between formal solvers, this work presents different high-order numerical schemes and applies the systematic analysis proposed by Janett et al. (2017), emphasizing their advantages and drawbacks in terms of order of accuracy, stability, and computational cost.

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