Fabio Riva

Context. 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 consideration of the detailed 3D structure of the solar atmosphere and accounting for partial frequency redistribution (PRD) effects in scattering processes. This setting has so far been computationally inaccessible. Aims. We aim to present the first scientific application of the TRIP code, which is a novel software for modeling the polarization of strong resonance lines in comprehensive 3D models of the solar atmosphere, accounting for PRD effects. We aim to verify the code and explore the combined action of magnetic fields, plasma bulk velocities, PRD effects, and the 3D structure of the solar atmosphere on scattering polarization. Methods. We ran TRIP to synthesize the Stokes profiles of the Ca I line at 4227 Å, accounting for angle-dependent PRD effects, in a 3D atmospheric model extracted from a radiation-magneto-hydrodynamic simulation. We effectively solved the resulting large-scale radiative transfer problem iteratively and in parallel using the flexible Generalized Minimal Residual (FGMRES) method with a physics-based preconditioner. Results. We successfully cross-checked TRIP with the established PORTA code, modeling scattering processes in the limit of complete frequency redistribution (CRD). We analyzed the relative impact of PRD effects, horizontal atmospheric inhomogeneities, magnetic fields, and bulk velocities on the polarization of the radiation emergent at the disk center, finding that bulk velocities are a dominant factor, while magnetic fields play a comparatively minor role. Conclusions. TRIP has been successfully tested and is ready for large-scale applications in state-of-the-art, 3D atmospheric models, allowing quantitative comparisons between synthetic and observational spectropolarimetric data of strong resonance lines.

Context. Scattering polarization in the Sr I 4607 Å line has become a key diagnostic tool for the small-scale unresolved magnetic fields in the quiet solar photosphere, which are inaccessible to Zeeman-based techniques. The limit of complete frequency redistribution (CRD) is commonly used to model the Sr I 4607 Å line signals, but its validity and impact on the magnetic sensitivity of this line have not yet been systematically investigated. The proposed study is timely, given the advent of new facilities capable of observing this line with unprecedented accuracy, and of future synoptic programs targeting long-term variations in the quiet-Sun magnetism. Aims. We aim to systematically assess the CRD limit against the general partial frequency redistribution (PRD) description of scattering processes for modeling the Sr I 4607 Å scattering polarization, focusing on its magnetic sensitivity through the Hanle effect. Methods. We solved the radiative transfer (RT) problem for polarized radiation out of local thermodynamic equilibrium (non-LTE) in a semi-empirical 1D plane-parallel static atmosphere, considering both the CRD and PRD scattering descriptions, across a range of magnetic field configurations relevant for Hanle diagnostics. Results. In the presence of small-scale unresolved magnetic fields, where the magnetic field manifests only through Hanle depolarization of the Q/I signal, we found no significant differences between the CRD and PRD emergent profiles, which also exhibit essentially identical Hanle magnetic sensitivity. In the presence of deterministic magnetic fields, the CRD approximation remains accurate when the scattering polarization signals are sufficiently strong (typically greater than 0.3%). For weaker signals, PRD effects may have an appreciable impact on the emergent polarization profiles. Conclusions. We support the use of the CRD description for modeling Sr I 4607 Å scattering polarization in the vast majority of observationally relevant cases, with PRD effects becoming important only for weak polarization signals.

Context. Granular collapse is a ubiquitous process of granular evolution on the solar surface, but it is hard to analyze in sufficient spatial, temporal, and spectral detail. Aims. We analyzed the change in physical conditions in the photosphere during a specific granular collapse event and the subsequent atmospheric response. Methods. We contrasted a high-resolution radiative magnetohydrodynamic simulation of a granular collapse performed using the CO5BOLD code with the recent integral field unit observations carried out using the MiHI instrument at the Swedish 1-m Solar Telescope. Results. The observed and simulated granular collapses are remarkably similar. Specifically, they both exhibit the signature of a wave pulse excited in the deep photosphere that is visible up to the temperature minimum. This wave is detectable through a blue-wing emission in the observed and synthetic Na I D1 line. We also estimated the acoustic energy flux carried by the wave and analyzed its initiation. Conclusions. Combining high-resolution integral field unit spectropolarimetry and state-of-the-art simulations of the solar lower atmosphere, this study showcases our current capabilities in identifying specific physical processes taking place during granular collapse and their impact on the atmosphere above.

About 20% of white dwarfs are observed to host large-scale magnetic fields, but the origin of white-dwarf magnetism remains uncertain. Small-scale turbulent dynamos (SSDs), which efficiently generate magnetic fields in solar- and stellar-convection simulations, have only been studied in white dwarfs through equipartition arguments in one-dimensional models so far. We therefore investigated whether turbulent convection in white-dwarf surface layers can sustain SSD action through local, three-dimensional, radiation–magnetohydrodynamics simulations of a white dwarf with a convective pure-hydrogen (DA) atmosphere, including the full convection zone together with the underlying overshoot and stably stratified layers. Starting from a weak seed field of 1 mG, the magnetic energy undergoes exponential amplification before saturating at a magnetic-to-kinetic energy-density ratio of about 5.5% at the visible surface, demonstrating that SSD action naturally generates kilogauss-strength magnetic fields in convective white-dwarf atmospheres. The resulting magnetic field is characterised by a mixed-polarity small-scale structure, with kilogauss field concentrations contributing about 14% of the total unsigned magnetic flux at the visible surface. Despite a rate of magnetic-energy generation amounting to roughly one-seventh of the bolometric flux, no significant modification of the mean stratification is found. Although these fields remain spatially unresolved for observations, they may contribute to spectral line broadening, suggesting that small-scale magnetism in white dwarfs could be more widespread than currently inferred from observations.

Context. 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. Aims. 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. Methods. 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 × 10 ⁻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. Results. 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. Conclusions. 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.

Inferring the weak magnetic field present in the outer layers of the solar atmosphere is a long-standing challenge in modern solar physics. Spectropolarimetric diagnostic techniques based on the Zeeman effect are ineffective in this context, highlighting the need for alternative approaches. Our goal is to develop a novel inference method that fits a depth-dependent vector magnetic field in a solar model atmosphere to observations of Hanle and Zeeman signals from strong resonance lines, including partial frequency redistribution (PRD) effects. We assumed that the thermal stratification of the atmosphere is given, and we used an efficient radiative transfer forward engine tailored to strong resonance lines, while accounting for PRD, scattering polarization, and the Hanle and Zeeman effects. By formulating the inverse problem as a nonlinear least-squares problem, we applied an efficient iterative optimization algorithm that enables an efficient retrieval of the searched magnetic field vector through fast computation of the Jacobian. We tested this inversion approach by inverting synthetic Stokes profiles of the Ca i line at 4227,Å. We successfully retrieved the original height-dependent vector magnetic and bulk velocity fields in different 1D plane-parallel models. We considered both semi-empirical models and models extracted from a snapshot of a 3D MHD simulation of the solar atmosphere. Our proposed inversion tool has demonstrated its reliability and promise for inverting vector magnetic fields in strong solar resonance lines that exhibit scattering polarization. Future plans include testing the approach in more complex scenarios, featuring intricate magnetic field structures. This assessment paves the way for applying our inversion tool to new spectropolarimetric observations.

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 while taking angle-dependent partial frequency redistribution (PRD) effects and J-state interference into account. We considered 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 for 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 or 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 co-moving frame, together with a careful choice of the angular and spectral quadrature nodes, allowed us to speed up the calculations by reducing the number of evaluations of the redistribution functions. Results. We applied the proposed solution strategy in order 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 displayed an overall good agreement, thereby validating our solution strategy. Moreover, for the wavelength-integrated polarisation profiles of the H I Ly-α line, we found an excellent agreement between the results obtained including PRD effects in their general angle-dependent description and those obtained considering the angle-averaged simplifying approximation.

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.

In recent years, the Mg ii h and k lines have become increasingly important for the diagnostics of magnetic fields in the solar chromosphere, motivated both by the advances in the modeling capabilities of their polarization and by the unprecedented spectropolarimetric observations provided by the CLASP missions. In this paper, we investigate the impact of the angular and frequency coupling in coherent scattering processes in the radiative transfer modeling of the Mg ii doublet polarization profiles. In particular, we aim to assess how the widely used angle-average approximation affects the predicted polarization. By solving the radiative transfer problem in 1D semiempirical atmospheric models, we find that this approximation is suitable in the absence of magnetic fields, but there can be measurable differences in magnetized models, mainly in the linear polarization profiles close to the core of the Mg ii k line. We then test the suitability of the approximation in more realistic scenarios, solving the radiative transfer problem pixel-by-pixel in a 3D atmospheric model resulting from a magnetohydrodynamic simulation and mimicking the degradation of the CLASP2 instrument, as well as in several 1D atmospheric models resulting from the Stokes inversion of the CLASP2 data. We find that the impact of the angle-average approximation is greatly diminished at the resolution of the CLASP2 observations. We also find that to suitably include angle-dependent effects in 1D radiative transfer modeling, it is sufficient to initialize the problem with the angle-average solution and then perform a few (angle-dependent) iterations, dramatically reducing the computational cost.

Context. Measurable linear scattering polarization signals have been predicted and detected at the solar disk center in the cores 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. Aims. The aim of this work is to assess 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 Ca I 4227 Å line. Methods. We performed radiative transfer calculations for polarized radiation in semi-empirical 1D solar atmospheres out of local thermodynamic equilibrium. We applied a two-step solution strategy. We first solved the problem considering a multilevel atom and neglecting polarization phenomena. Subsequently, we solved the same problem, this time considering a two-level atom and including polarization and magnetic fields. By keeping the population of the lower level calculated in the previous step fixed, the problem of step two is linear and is solved with a preconditioned FGMRES iterative method. We analyzed the emergent fractional linear polarization signals calculated under the CRD and PRD–AA approximations and compared them to those obtained by modeling PRD effects in their general angle-dependent (AD) formulation. Result. 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. Conclusions. 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 Ca I 4227 Å line. These results need to be confirmed by full 3D calculations including non-magnetic symmetry-breaking effects.