arXiv subjects

L. Belluzzi

Publications and source records attributed to L. Belluzzi.

16 recordsLinked to original sources

arXiv2024

Diagnostic potential of wavelength-integrated scattering polarisation signals of the solar He II Ly-alpha line

Aims: Main goal of this work is to study the potential of He II Ly-alpha wavelength-integrated scattering polarisation for probing the magnetism of the solar upper chromosphere. Methods: Radiative transfer calculations are performed in semi-empirical 1D solar atmospheres considering a two-term atomic model and accounting for the Hanle, Zeeman, and magneto-optical effects. The problem is suitably linearised and discretised, and the resulting numerical system is solved with a matrix-free iterative method. The results obtained modelling scattering processes with three different descriptions, namely in the limit of complete frequency redistribution (CRD), and accounting for partial frequency redistribution (PRD) effects under the angle-averaged (AA) approximation and in the general angle-dependent (AD) formulation, are compared. Results: In the line-core, the synthetic Stokes profiles resulting from CRD, PRD-AA, and PRD-AD calculations show a very good agreement. On the other hand, relevant differences are observed in Q/I outside the line-core region. Besides, the precise structure of the atmospheric model does not noticeably affect the line-core profiles, but it strongly impacts the Q/I signals outside the line-core. As most of the He II Ly-alpha photons originate in the core region, it turns out that wavelength-integrated linear polarisation signals are almost insensitive to both the scattering description and the atmospheric model. Appreciable wavelength-integrated U/I signals, showing observable sensitivity to horizontal magnetic fields in the range 0-1000 G, are also found, particularly near the limb. It turns out that, while the integration time required to detect magnetic fields in the quiet chromosphere with this line is too long for sounding rocket missions, magnetic fields corresponding to typical plage areas would produce detectable signals, especially near the limb.

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arXiv2022

Quiet Sun Center to Limb Variation of the Linear Polarization Observed by CLASP2 Across the Mg II h & k Lines

The CLASP2 (Chromospheric LAyer SpectroPolarimeter 2) sounding rocket mission was launched on 2019 April 11. CLASP2 measured the four Stokes parameters of the Mg II h & k spectral region around 2800 Angstroms along a 200 arcsecond slit at three locations on the solar disk, achieving the first spatially and spectrally resolved observations of the solar polarization in this near ultraviolet region. The focus of the work presented here is the center-to-limb variation of the linear polarization across these resonance lines, which is produced by the scattering of anisotropic radiation in the solar atmosphere. The linear polarization signals of the Mg II h & k lines are sensitive to the magnetic field from the low to the upper chromosphere through the Hanle and magneto-optical effects. We compare the observations to theoretical predictions from radiative transfer calculations in unmagnetized semi-empirical models, arguing that magnetic fields and horizontal inhomogeneities are needed to explain the observed polarization signals and spatial variations. This comparison is an important step in both validating and refining our understanding of the physical origin of these polarization signatures, and also in paving the way toward future space telescopes for probing the magnetic fields of the solar upper atmosphere via ultraviolet spectropolarimetry.

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arXiv2021

Magnetic Imaging of the Outer Solar Atmosphere (MImOSA): Unlocking the driver of the dynamics in the upper solar atmosphere

The magnetic activity of the Sun directly impacts the Earth and human life. Likewise, other stars will have an impact on the habitability of planets orbiting these host stars. The lack of information on the magnetic field in the higher atmospheric layers hampers our progress in understanding solar magnetic activity. Overcoming this limitation would allow us to address four paramount long-standing questions: (1) How does the magnetic field couple the different layers of the atmosphere, and how does it transport energy? (2) How does the magnetic field structure, drive and interact with the plasma in the chromosphere and upper atmosphere? (3) How does the magnetic field destabilise the outer solar atmosphere and thus affect the interplanetary environment? (4) How do magnetic processes accelerate particles to high energies? New ground-breaking observations are needed to address these science questions. We suggest a suite of three instruments that far exceed current capabilities in terms of spatial resolution, light-gathering power, and polarimetric performance: (a) A large-aperture UV-to-IR telescope of the 1-3 m class aimed mainly to measure the magnetic field in the chromosphere by combining high spatial resolution and high sensitivity. (b) An extreme-UV-to-IR coronagraph that is designed to measure the large-scale magnetic field in the corona with an aperture of about 40 cm. (c) An extreme-UV imaging polarimeter based on a 30 cm telescope that combines high throughput in the extreme UV with polarimetry to connect the magnetic measurements of the other two instruments. This mission to measure the magnetic field will unlock the driver of the dynamics in the outer solar atmosphere and thereby greatly advance our understanding of the Sun and the heliosphere.

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arXiv2020

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

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. We aim to develop an efficient algorithm to numerically evaluate the angle-averaged redistribution function for polarized radiation. Our proposed approach is based on a low-rank approximation via trivariate polynomials whose univariate components are represented in the Chebyshev basis. The resulting algorithm is significantly faster than standard quadrature-based schemes for any target accuracy in the range between 10^-6 and 10^-2.

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arXiv2020

Observational indications of magneto-optical effects in the scattering polarization wings of the Ca I 4227 \AA\ line

Several strong resonance lines, such as H I Ly-$\alpha$, Mg II k, Ca II K, Ca I 4227 \AA\, which are characterized by deep and broad absorption profiles in the solar intensity spectrum, show conspicuous linear scattering polarization signals when observed in quiet regions close to the solar limb. Such signals show a characteristic triplet-peak structure, with a sharp peak in the line core and extended wing lobes. The line core peak is sensitive to the presence of magnetic fields through the Hanle effect, which however is known not to operate in the line wings. Recent theoretical studies indicate that, contrary to what was previously believed, the wing linear polarization signals are also sensitive to the magnetic field through magneto-optical effects (MO). We search for observational indications of this recently discovered physical mechanism in the scattering polarization wings of the Ca I 4227 \AA\ line. We performed a series of spectropolarimetric observations of this line using the Zurich IMaging POLarimeter (ZIMPOL) camera at the Gregory-Coud\'e telescope of IRSOL (Switzerland) and at the GREGOR telescope in Tenerife (Spain). Spatial variations of the total linear polarization degree and of the linear polarization angle are clearly appreciable in the wings of the observed line. We provide a detailed discussion of our observational results, showing that the detected variations always take place in regions where longitudinal magnetic fields are present, thus supporting the theoretical prediction that they are produced by MO effects.

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arXiv2018

CLASP Constraints on the Magnetization and Geometrical Complexity of the Chromosphere-Corona Transition Region

The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a suborbital rocket experiment that on 3rd September 2015 measured the linear polarization produced by scattering processes in the hydrogen Ly-$\alpha$ line of the solar disk radiation, whose line-center photons stem from the chromosphere-corona transition region (TR). These unprecedented spectropolarimetric observations revealed an interesting surprise, namely that there is practically no center-to-limb variation (CLV) in the $Q/I$ line-center signals. Using an analytical model, we first show that the geometrical complexity of the corrugated surface that delineates the TR has a crucial impact on the CLV of the $Q/I$ and $U/I$ line-center signals. Secondly, we introduce a statistical description of the solar atmosphere based on a three-dimensional (3D) model derived from a state-of-the-art radiation magneto-hydrodynamic simulation. Each realization of the statistical ensemble is a 3D model characterized by a given degree of magnetization and corrugation of the TR, and for each such realization we solve the full 3D radiative transfer problem taking into account the impact of the CLASP instrument degradation on the calculated polarization signals. Finally, we apply the statistical inference method presented in a previous paper to show that the TR of the 3D model that produces the best agreement with the CLASP observations has a relatively weak magnetic field and a relatively high degree of corrugation. We emphasize that a suitable way to validate or refute numerical models of the upper solar chromosphere is by confronting calculations and observations of the scattering polarization in ultraviolet lines sensitive to the Hanle effect.

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arXiv2018

A Statistical Inference Method for Interpreting the CLASP Observations

On 3rd September 2015, the Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) successfully measured the linear polarization produced by scattering processes in the hydrogen Lyman-$\alpha$ line of the solar disk radiation, revealing conspicuous spatial variations in the $Q/I$ and $U/I$ signals. Via the Hanle effect the line-center $Q/I$ and $U/I$ amplitudes encode information on the magnetic field of the chromosphere-corona transition region (TR), but they are also sensitive to the three-dimensional structure of this corrugated interface region. With the help of a simple line formation model, here we propose a statistical inference method for interpreting the Lyman-$\alpha$ line-center polarization observed by CLASP.

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arXiv2018

Spatial variations of the Sr i 4607 {\AA} scattering polarization peak

Context. The scattering polarization signal observed in the photospheric Sr i 4607 {\AA} line is expected to vary at granular spatial scales. This variation can be due to changes in the magnetic field intensity and orientation (Hanle effect), but also 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 scales, but observations are challenging since both high spatial resolution and high spectropolarimetric sensitivity are required. Aims. We aim to provide observational evidence of the polarization peak spatial variations, and to analyze the correlation they might have with granulation. Methods. Observations conjugating high spatial resolution and high spectropolarimetric precision were performed with the Zurich IMaging POLarimeter, ZIMPOL, at the GREGOR solar telescope, taking advantage of the adaptive optics system and the newly installed image derotator. Results. Spatial variations of the scattering polarization in the Sr i 4607 {\AA} line are clearly observed. The spatial scale of these variations is comparable with the granular size. Small correlations between the polarization signal amplitude and the continuum intensity indicate that the polarization is higher at the center of granules than in the intergranular lanes.

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arXiv2017

Magneto-optical effects in the scattering polarization wings of the Ca I resonance line at 4227 angstroms

The linear polarization pattern produced by scattering processes in the Ca I resonance line at 4227 angstroms is a valuable observable for probing the solar atmosphere. Via the Hanle effect, the very significant Q/I and U/I line-center signals are sensitive to the presence of magnetic fields in the lower chromosphere with strengths between 5 and 125 G, approximately. On the other hand, partial frequency redistribution (PRD) produces sizable signals in the wings of the Q/I profile, which have always been thought to be insensitive to the presence of magnetic fields. Interestingly, novel observations of this line revealed a surprising behavior: fully unexpected signals in the wings of the U/I profile and spatial variability in the wings of both Q/I and U/I. Here we show that the magneto-optical (MO) terms of the Stokes-vector transfer equation produce sizable signals in the wings of U/I and a clear sensitivity of the Q/I and U/I wings to the presence of photospheric magnetic fields with strengths similar to those that produce the Hanle effect in the line core. This radiative transfer investigation on the joint action of scattering processes and the Hanle and Zeeman effects should facilitate the development of more reliable techniques for exploring the magnetism of stellar atmospheres. To this end, we can now exploit the circular polarization produced by the Zeeman effect, the magnetic sensitivity caused by the above-mentioned MO effects in the Q/I and U/I wings, and the Hanle effect in the line core.

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arXiv2017

Discovery of Scattering Polarization in the Hydrogen Lyman-$\alpha$ Line of the Solar Disk Radiation

There is a thin transition region (TR) in the solar atmosphere where the temperature rises from 10,000 K in the chromosphere to millions of degrees in the corona. Little is known about the mechanisms that dominate this enigmatic region other than the magnetic field plays a key role. The magnetism of the TR can only be detected by polarimetric measurements of a few ultraviolet (UV) spectral lines, the Lyman-$\alpha$ line of neutral hydrogen at 121.6 nm (the strongest line of the solar UV spectrum) being of particular interest given its sensitivity to the Hanle effect (the magnetic-field-induced modification of the scattering line polarization). We report the discovery of linear polarization produced by scattering processes in the Lyman-$\alpha$ line, obtained with the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) rocket experiment. The Stokes profiles observed by CLASP in quiet regions of the solar disk show that the $Q/I$ and $U/I$ linear polarization signals are of the order of 0.1 % in the line core and up to a few percent in the nearby wings, and that both have conspicuous spatial variations with scales of $\sim 10$ arcsec. These observations help constrain theoretical models of the chromosphere-corona TR and extrapolations of the magnetic field from photospheric magnetograms. In fact, the observed spatial variation from disk to limb of polarization at the line core and wings already challenge the predictions from three-dimensional magnetohydrodynamical models of the upper solar chromosphere.

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arXiv2014

On the inversion of the scattering polarization and the Hanle effect signals in the hydrogen Lyman-$\alpha$ line

Magnetic field measurements in the upper chromosphere and above, where the gas-to-magnetic pressure ratio $\beta$ is lower than unity, are essential for understanding the thermal structure and dynamical activity of the solar atmosphere. Recent developments in the theory and numerical modeling of polarization in spectral lines have suggested that information on the magnetic field of the chromosphere-corona transition region could be obtained by measuring the linear polarization of the solar disk radiation at the core of the hydrogen Lyman-$\alpha$ line at 121.6~nm, which is produced by scattering processes and the Hanle effect. The Chromospheric Lyman-$\alpha$ Spectropolarimeter (CLASP) sounding rocket experiment aims to measure the intensity (Stokes $I$) and the linear polarization profiles ($Q/I$ and $U/I$) of the hydrogen Lyman-$\alpha$ line. In this paper we clarify the information that the Hanle effect can provide by applying a Stokes inversion technique based on a database search. The database contains all theoretical $Q/I$ and $U/I$ profiles calculated in a one-dimensional semi-empirical model of the solar atmosphere for all possible values of the strength, inclination, and azimuth of the magnetic field vector, though this atmospheric region is highly inhomogeneous and dynamic. We focus on understanding the sensitivity of the inversion results to the noise and spectral resolution of the synthetic observations as well as the ambiguities and limitation inherent to the Hanle effect when only the hydrogen Lyman-$\alpha$ is used. We conclude that spectropolarimetric observations with CLASP can indeed be a suitable diagnostic tool for probing the magnetism of the transition region, especially when complemented with information on the magnetic field azimuth that can be obtained from other instruments.

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arXiv2013

Theoretical formulation of Doppler redistribution in scattering polarization within the framework of the velocity-space density matrix formalism

Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications by adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the Non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding statistical equilibrium equations neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as R_I) is derived starting from the statistical equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.

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arXiv2013

Isotropic inelastic and superelastic collisional rates in a multiterm atom

The spectral line polarization of the radiation emerging from a magnetized astrophysical plasma depends on the state of the atoms within the medium, whose determination requires considering the interactions between the atoms and the magnetic field, between the atoms and photons (radiative transitions), and between the atoms and other material particles (collisional transitions). In applications within the framework of the multiterm model atom (which accounts for quantum interference between magnetic sublevels pertaining either to the same J-level or to different J-levels within the same term) collisional processes are generally neglected when solving the master equation for the atomic density matrix. This is partly due to the lack of experimental data and/or of approximate theoretical expressions for calculating the collisional transfer and relaxation rates (in particular the rates for interference between sublevels pertaining to different J-levels, and the depolarizing rates due to elastic collisions). In this paper we formally define and investigate the transfer and relaxation rates due to isotropic inelastic and superelastic collisions that enter the statistical equilibrium equations of a multiterm atom. Under the hypothesis that the atom-collider interaction can be described by a dipolar operator, we provide expressions that relate the collisional rates for interference between different J-levels to the usual collisional rates for J-level populations. Finally, we apply the general equations to the case of a two-term atom with unpolarized lower term, illustrating the impact of inelastic and superelastic collisions on scattering polarization through radiative transfer calculations in a slab of stellar atmospheric plasma anisotropically illuminated by the photospheric radiation field.

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arXiv2012

Anomalous circular polarization profiles in the He I 1083.0 nm multiplet from solar spicules

We report Stokes vector observations of solar spicules and a prominence in the He I 1083 nm multiplet carried out with the Tenerife Infrared Polarimeter. The observations show linear polarization profiles that are produced by scattering processes in the presence of a magnetic field. After a careful data reduction, we demonstrate the existence of extremely asymmetric Stokes V profiles in the spicular material that we are able to model with two magnetic components along the line of sight, and under the presence of atomic orientation in the energy levels that give rise to the multiplet. We discuss some possible scenarios that can generate the atomic orientation in spicules. We stress the importance of spectropolarimetric observations across the limb to distinguish such signals from observational artifacts.

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arXiv2011

Analytical maximum likelihood estimation of stellar magnetic fields

The polarised spectrum of stellar radiation encodes valuable information on the conditions of stellar atmospheres and the magnetic fields that permeate them. In this paper, we give explicit expressions to estimate the magnetic field vector and its associated error from the observed Stokes parameters. We study the solar case where specific intensities are observed and then the stellar case, where we receive the polarised flux. In this second case, we concentrate on the explicit expression for the case of a slow rotator with a dipolar magnetic field geometry. Moreover, we also give explicit formulae to retrieve the magnetic field vector from the LSD profiles without assuming mean values for the LSD artificial spectral line. The formulae have been obtained assuming that the spectral lines can be described in the weak field regime and using a maximum likelihood approach. The errors are recovered by means of the hermitian matrix. The bias of the estimators are analysed in depth.

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arXiv2009

Observations of the Joint Action of the Hanle and Zeeman Effects in the D2 Line of BaII

We show a selection of high-sensitivity spectropolarimetric observations obtained over the last few years in the Ba II D2-line with the Zurich Imaging Polarimeter (ZIMPOL) attached to the Gregory Coude Telescope of IRSOL. The measurements were collected close to the solar limb, in several regions with varying degree of magnetic activity. The Stokes profiles we have observed show clear signatures of the joint action of the Hanle and Zeeman effects, in very good qualitative agreement with the theoretical expectations. Polarimetric measurements of this line show to be very well suited for magnetic field diagnostics of the lower solar chromosphere, from regions with field intensities as low as 1 gauss to strongly magnetized ones having kG field strengths.

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