arXiv subjects

Luca Belluzzi

Publications and source records attributed to Luca Belluzzi.

At least 37 records · Page 2Linked to original sources

arXiv2021

The polarization angle in the wings of Ca i 4227: A new observable for diagnosing unresolved photospheric magnetic fields

When observed in quiet regions close to the solar limb, many strong resonance lines show conspicuous linear polarization signals, produced by scattering processes, with extended wing lobes. Recent studies indicate that, contrary to what was previously believed, the wing lobes are sensitive to the presence of relatively weak longitudinal magnetic fields through magneto-optical (MO) effects. We theoretically investigate the sensitivity of the scattering polarization wings of the Ca I 4227 Å line to the MO effects, and we explore its diagnostic potential for inferring information on the longitudinal component of the photospheric magnetic field. We calculate the intensity and polarization profiles of the Ca I 4227 Å line by numerically solving the problem of the generation and transfer of polarized radiation under non-local thermodynamic equilibrium conditions in one-dimensional semi-empirical models of the solar atmosphere, taking into account the joint action of the Hanle, Zeeman, and MO effects. We consider volume-filling magnetic fields as well as magnetic fields occupying a fraction of the resolution element. In contrast to the circular polarization signals produced by the Zeeman effect, we find that the linear polarization angle in the scattering polarization wings of Ca I 4227 presents a clear sensitivity, through MO effects, not only to the flux of the photospheric magnetic field, but also to the fraction of the resolution element that the magnetic field occupies. We identify the linear polarization angle in the wings of strong resonance lines as a valuable observable for diagnosing unresolved magnetic fields. Used in combination with observables that encode information on the magnetic flux and other properties of the observed atmospheric region, it can provide constraints on the filling factor of the magnetic field.

astro-ph.SR↗

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.

astro-ph.SR↗

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.

astro-ph.SR↗

arXiv2021

Solving the paradox of the solar sodium D1 line polarization

Twenty-five years ago, enigmatic linear polarization signals were discovered in the core of the sodium D1 line. The only explanation that could be found implied that the solar chromosphere is practically unmagnetized, in contradiction with other evidences. This opened a paradox that has challenged physicists for many years. Here we present its solution, demonstrating that these polarization signals can be properly explained in the presence of magnetic fields in the gauss range. This result opens a novel diagnostic window for exploring the elusive magnetism of the solar chromosphere.

astro-ph.SR↗

arXiv2021

Mapping Solar Magnetic Fields from the Photosphere to the Base of the Corona

Routine ultraviolet imaging of the Sun's upper atmosphere shows the spectacular manifestation of solar activity; yet we remain blind to its main driver, the magnetic field. Here we report unprecedented spectropolarimetric observations of an active region plage and its surrounding enhanced network, showing circular polarization in ultraviolet (Mg II $h$ & $k$ and Mn I) and visible (Fe I) lines. We infer the longitudinal magnetic field from the photosphere to the very upper chromosphere. At the top of the plage chromosphere the field strengths reach more than 300 gauss, strongly correlated with the Mg II $k$ line core intensity and the electron pressure. This unique mapping shows how the magnetic field couples the different atmospheric layers and reveals the magnetic origin of the heating in the plage chromosphere.

astro-ph.SR↗

arXiv2019

Magnetic sensitivity in the wing scattering polarization signals of the hydrogen Lyman-alpha line of the solar disk radiation

The linear polarization produced by scattering processes in the hydrogen Lyman alpha line of the solar disk radiation is a key observable for probing the chromosphere-corona transition region (TR) and the underlying chromospheric plasma. While the line-center signal encodes information on the magnetic field and three-dimensional structure of the TR, the sizable scattering polarization signals that the joint action of partial frequency redistribution (PRD) and J-state interference produce in the Lyman alpha wings have generally been thought to be sensitive only to the thermal structure of the solar atmosphere. Here we show that the wings of the Q/I and U/I scattering polarization profiles of this line are actually sensitive to the presence of chromospheric magnetic fields, with strengths similar to those that produce the Hanle effect in the line core (i.e., between 5 and 100 gauss, approximately). In spite of the fact that the Zeeman splitting induced by such weak fields is very small compared to the total width of the line, the magneto-optical effects that couple the transfer equations for Stokes Q and U are actually able to produce sizable changes in the Q/I and U/I wings. The theoretical results presented here further expand the diagnostic content of the unprecedented spectropolarimetric observations provided by the Chromospheric Lyman-Alpha Spectropolarimeter (CLASP).

astro-ph.SR↗

arXiv2019

Observations on spatial variations of the Sr~{\sc i} 4607~Å~scattering polarization signals at different limb distances with ZIMPOL

The Sr~{\sc i} 4607~Å spectral line shows one of the strongest scattering polarization signals in the visible solar spectrum. The amplitude of this polarization signal is expected to vary at granular spatial scales, due to the combined action of the Hanle effect and the local anisotropy of the radiation field. Observing these variations would be of great interest because it would provide precious information on the small-scale activity of the solar photosphere. At present, few detections of such spatial variations have been reported. This is due to the difficulty of these measurements, which require combining high spatial ($\sim$ 0.1"), spectral ($\leq$ 20 mÅ), and temporal resolution (< 1 min) with increased polarimetric sensitivity ($\sim$ 10$^-$$^4$). Aims. We aim to detect spatial variations at granular scales of the scattering polarization peak of the Sr~{\sc i} 4607~Å line at different limb distances, and to study the correlation with the continuum intensity. Methods.Using the Zurich IMaging POLarimeter (ZIMPOL) system mounted at the GREGOR telescope and spectrograph in Tenerife, Spain, we carried out spectro-polarimetric measurements to obtain the four Stokes parameters in the Sr~{\sc i} line at different limb distances, from $μ=0.2$ to $μ=0.8$, on the solar disk. Results.Spatial variations of the scattering polarization signal in the Sr~{\sc i} 4607~Å line, with a spatial resolution of about 0.66", are clearly observed at every $μ$. The spatial scale of these variations is comparable to the granular size. A statistical analysis reveals that the linear scattering polarization amplitude in this Sr~{\sc i} spectral line is positively correlated with the intensity in the continuum, corresponding to the granules, at every $μ$.

astro-ph.SR↗

arXiv2019

Spatial variations of the SrI 4607Åscattering polarization signals at subgranular scale observed with ZIMPOL at GREGOR telescope

Sr I 4607Åspectral line shows one of the strongest scattering polarization signals in the visible solar spectrum. The amplitudes of these signals are expected to vary at granular spatial scales. This variation can be due to changes in the magnetic field intensity and orientation (Hanle effect) as well as due to spatial and temporal variations in the plasma properties. Measuring the spatial variation of such polarization signal would allow us to study the properties of the magnetic fields at subgranular region. But, the observations are challenging since both high spatial resolution and high spectropolarimetric sensitivity are required at the same time. To the aim of measuring these spatial variations at granular scale, we carried out a spectro-polarimetric measurement with the Zurich IMaging POLarimeter (ZIMPOL), at the GREGOR solar telescope at different limb distances on solar disk. Our results show a spatial variation of scattering linear polarization signals in Sr I 4607Åline at the granular scale at every $μ$, starting from 0.2 to 0.8. The correlation between the polarization signal amplitude and the continuum intensity imply statistically that the scattering polarization is higher at the granular regions than in the intergranular lanes.

astro-ph.SR↗

arXiv2019

Structure of the Balmer jump. The isolated hydrogen atom

Context. The spectrum of the hydrogen atom was explained by Bohr more than one century ago. We revisit here some of the aspects of the underlying quantum structure, with a modern formalism, focusing on the limit of the Balmer series. Aims. We investigate the behaviour of the absorption coefficient of the isolated hydrogen atom in the neighbourhood of the Balmer limit. Methods. We analytically computed the total cross-section arising from bound-bound and bound-free transitions in the isolated hydrogen atom at the Balmer limit, and established a simplified semi-analytical model for the surroundings of that limit. We worked within the framework of the formalism of Landi Degl'Innocenti & Landolfi (2004, Astrophys. Space Sci. Lib., 307), which permits an almost straight-forward generalization of our results to other atoms and molecules, and which is perfectly suitable for including polarization phenomena in the problem. Results. We analytically show that there is no discontinuity at the Balmer limit, even though the concept of a "Balmer jump" is still meaningful. Furthermore, we give a possible definition of the location of the Balmer jump, and we check that this location is dependent on the broadening mechanisms. At the Balmer limit, we compute the cross-section in a fully analytical way. Conclusions. The Balmer jump is produced by a rapid drop of the total Balmer cross-section, yet this variation is smooth and continuous when both bound-bound and bound-free processes are taken into account, and its shape and location is dependent on the broadening mechanisms.

physics.atom-ph↗

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.

astro-ph.SR↗

arXiv2017

Measurement of the evolution of the magnetic field of the quiet photosphere during a solar cycle

The solar photosphere is filled by a magnetic field which is tangled on scales much smaller than the resolution capability of solar telescopes. This hidden magnetic field can be investigated via the Hanle effect. In 2007 we started a synoptic program to explore if the magnetic flux of the quiet photosphere varies with the solar cycle. For this purpose we applied a differential Hanle effect technique based on observations of scattering polarization in C$_2$ molecular lines around 514.0 nm, taken generally every month. Our results now span almost one complete solar cycle.

astro-ph.SR↗

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.

astro-ph.SR↗

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.

astro-ph.SR↗

arXiv2016

The magnetic sensitivity of the Mg ii k line to the joint action of Hanle, Zeeman and magneto-optical effects

We highlight the main results of a radiative transfer investigation on the magnetic sensitivity of the solar Mg ii k resonance line at 2795.5 angstrom, accounting for the joint action of the Hanle and Zeeman effects as well as partial frequency redistribution (PRD) phenomena. We confirm that at the line center, the linear polarization signals produced by scattering processes are measurable, and that they are sensitive, via the Hanle effect, to magnetic fields with strengths between 5 and 50 G, approximately. We also show that the Zeeman effect produces conspicuous circular polarization signals, especially for longitudinal fields stronger than 50 G, which can be used to estimate the magnetization of the solar chromosphere via the familiar magnetograph formula. The most novel result is that magneto-optical effects produce, in the wings of the line, a decrease of the Q/I scattering polarization pattern and the appearance of U/I signals (i.e., a rotation of the plane of linear polarization). This sensitivity of the Q/I and U/I wing signals to both weak (around 5 G) and stronger magnetic fields expands the scientific interest of the Mg ii k line for probing the chromosphere in quiet and active regions of the Sun

astro-ph.SR↗

arXiv2016

The transfer of resonance line polarization with partial frequency redistribution in the general Hanle-Zeeman regime

The spectral line polarization encodes a wealth of information about the thermal and magnetic properties of the solar atmosphere. Modeling the Stokes profiles of strong resonance lines is, however, a complex problem both from the theoretical and computational point of view, especially when partial frequency redistribution (PRD) effects need to be taken into account. In this work, we consider a two-level atom in the presence of magnetic fields of arbitrary intensity (Hanle-Zeeman regime) and orientation, both deterministic and micro-structured. Working within the framework of a rigorous PRD theoretical approach, we have developed a numerical code which solves the full non-LTE radiative transfer problem for polarized radiation, in one-dimensional models of the solar atmosphere, accounting for the combined action of the Hanle and Zeeman effects, as well as for PRD phenomena. After briefly discussing the relevant equations, we describe the iterative method of solution of the problem and the numerical tools that we have developed and implemented. We finally present some illustrative applications to two resonance lines that form at different heights in the solar atmosphere, and provide a detailed physical interpretation of the calculated Stokes profiles. We find that in strong resonance lines sensitive to PRD effects the magneto-optical terms of the Stokes-vector transfer equation produce conspicuous U/I wing signals along with a very interesting magnetic sensitivity in the wings of the linear polarization profiles. We also show that the weak-field approximation has to be used with caution when PRD effects are considered.

astro-ph.SR↗

arXiv2015

Radiative transfer modeling of the enigmatic scattering polarization in the solar NaI D1 line

The modeling of the peculiar scattering polarization signals observed in some diagnostically important solar resonance lines requires the consideration of the detailed spectral structure of the incident radiation field as well as the possibility of ground level polarization, along with the atom's hyperfine structure and quantum interference between hyperfine F-levels pertaining either to the same fine structure J-level, or to different J-levels of the same term. Here we present a theoretical and numerical approach suitable for solving this complex non-LTE radiative transfer problem. This approach is based on the density-matrix metalevel theory (where each level is viewed as a continuous distribution of sublevels) and on accurate formal solvers of the transfer equations and efficient iterative methods. We show an application to the D-lines of NaI, with emphasis on the enigmatic D1 line, pointing out the observable signatures of the various physical mechanisms considered. We demonstrate that the linear polarization observed in the core of the D1 line may be explained by the effect that one gets when the detailed spectral structure of the anisotropic radiation responsible for the optical pumping is taken into account. This physical ingredient is capable of introducing significant scattering polarization in the core of the NaI D1 line without the need for ground-level polarization.

astro-ph.SR↗