Author name code: belluzzi ADS astronomy entries on 2022-09-14 author:"Belluzzi, Luca" ------------------------------------------------------------------------ Title: Quiet Sun Center to Limb Variation of the Linear Polarization Observed by CLASP2 Across the Mg II h and k Lines Authors: Rachmeler, L. A.; Bueno, J. Trujillo; McKenzie, D. E.; Ishikawa, R.; Auchère, F.; Kobayashi, K.; Kano, R.; Okamoto, T. J.; Bethge, C. W.; Song, D.; Ballester, E. Alsina; Belluzzi, L.; Pino Alemán, T. del; Ramos, A. Asensio; Yoshida, M.; Shimizu, T.; Winebarger, A.; Kobelski, A. R.; Vigil, G. D.; Pontieu, B. De; Narukage, N.; Kubo, M.; Sakao, T.; Hara, H.; Suematsu, Y.; Štěpán, J.; Carlsson, M.; Leenaarts, J. Bibcode: 2022ApJ...936...67R Altcode: 2022arXiv220701788R The CLASP2 (Chromospheric LAyer Spectro-Polarimeter 2) sounding rocket mission was launched on 2019 April 11. CLASP2 measured the four Stokes parameters of the Mg II h and k spectral region around 2800 Å along a 200″ 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 and 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 semiempirical 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. Title: Numerical solutions to linear transfer problems of polarized radiation. III. Parallel preconditioned Krylov solver tailored for modeling PRD effects Authors: Benedusi, Pietro; Janett, Gioele; Riva, Simone; Krause, Rolf; Belluzzi, Luca Bibcode: 2022A&A...664A.197B Altcode: Context. The polarization signals produced by the scattering of anistropic radiation in strong resonance lines encode important information about the elusive magnetic fields in the outer layers of the solar atmosphere. An accurate modeling of these signals is a very challenging problem from the computational point of view, in particular when partial frequency redistribution (PRD) effects in scattering processes are accounted for with a general angle-dependent treatment.
Aims: We aim at solving the radiative transfer problem for polarized radiation in nonlocal thermodynamic equilibrium conditions, taking angle-dependent PRD effects into account. The problem is formulated for a two-level atomic model in the presence of arbitrary magnetic and bulk velocity fields. The polarization produced by scattering processes and the Zeeman effect is considered.
Methods: The proposed solution strategy is based on an algebraic formulation of the problem and relies on a convenient physical assumption, which allows its linearization. We applied a nested matrix-free GMRES iterative method. Effective preconditioning is obtained in a multifidelity framework by considering the light-weight description of scattering processes in the limit of complete frequency redistribution (CRD).
Results: Numerical experiments for a one-dimensional (1D) atmospheric model show near optimal strong and weak scaling of the proposed CRD-preconditioned GMRES method, which converges in few iterations, independently of the discretization parameters. A suitable parallelization strategy and high-performance computing tools lead to competitive run times, providing accurate solutions in a few minutes.
Conclusions: The proposed solution strategy allows the fast systematic modeling of the scattering polarization signals of strong resonance lines, taking angle-dependent PRD effects into account together with the impact of arbitrary magnetic and bulk velocity fields. Almost optimal strong and weak scaling results suggest that this strategy is applicable to realistic 3D models. Moreover, the proposed strategy is general, and applications to more complex atomic models are possible. Title: The transfer of polarized radiation in resonance lines with partial frequency redistribution, J-state interference, and arbitrary magnetic fields. A radiative transfer code and useful approximations Authors: Alsina Ballester, E.; Belluzzi, L.; Trujillo Bueno, J. Bibcode: 2022A&A...664A..76A Altcode: 2022arXiv220412523A
Aims: We present the theoretical framework and numerical methods we have implemented to solve the problem of the generation and transfer of polarized radiation in spectral lines without assuming local thermodynamical equilibrium, while accounting for scattering polarization, partial frequency redistribution (due to both the Doppler effect and elastic collisions), J-state interference, and hyperfine structure. The resulting radiative transfer code allows one to model the impact of magnetic fields of an arbitrary strength and orientation through the Hanle, incomplete Paschen-Back, and magneto-optical effects. We also evaluate the suitability of a series of approximations for modeling the scattering polarization in the wings of strong resonance lines at a much lower computational cost, which is particularly valuable for the numerically intensive case of three-dimensional radiative transfer.
Methods: We examine the suitability of the considered approximations by using our radiative transfer code to model the Stokes profiles of the Mg II h & k lines and of the H I Lyman-α line in magnetized one-dimensional models of the solar atmosphere.
Results: Neglecting Doppler redistribution in the scattering processes that are unperturbed by elastic collisions (i.e., treating them as coherent in the observer's frame) produces a negligible error in the scattering polarization wings of the Mg II resonance lines and a minor one in the Lyman-α wings, although it is unsuitable to model the cores of these lines. For both lines, the scattering processes that are perturbed by elastic collisions only give a significant contribution to the intensity component of the emissivity. Neglecting collisional as well as Doppler redistribution (so that all scattering processes are coherent) represents a rough but suitable approximation for the wings of the Mg II resonance lines, but a very poor one for the Lyman-α wings. The magnetic sensitivity in the scattering polarization wings of the considered lines can be modeled by accounting for the magnetic field in only the ηI and ρV coefficients of the Stokes-vector transfer equation (i.e., using the zero-field expression for the emissivity). Title: Hanle rotation signatures in Sr I 4607 Å Authors: Zeuner, F.; Belluzzi, L.; Guerreiro, N.; Ramelli, R.; Bianda, M. Bibcode: 2022A&A...662A..46Z Altcode: 2022arXiv220208659Z Context. Measuring small-scale magnetic fields and constraining their role in energy transport and dynamics in the solar atmosphere are crucial, albeit challenging, tasks in solar physics. To this aim, observations of scattering polarization and the Hanle effect in various spectral lines are increasingly used to complement traditional magnetic field determination techniques.
Aims: One of the strongest scattering polarization signals in the photosphere is measured in the Sr I line at 4607.3 Å when observed close to the solar limb. Here, we present the first observational evidence of Hanle rotation in the linearly polarized spectrum of this line at several limb distances.
Methods: We used the Zurich IMaging POLarimeter, ZIMPOL at the IRSOL observatory, with exceptionally good seeing conditions and long integration times. We combined the fast-modulating polarimeter with a slow modulator installed in front of the telescope. This combination allows for a high level of precision and unprecedented accuracy in the measurement of spectropolarimetric data.
Results: Fixing the reference direction for positive Stokes Q parallel to the limb, we detected singly peaked U/I signals well above the noise level. We can exclude any instrumental origins for such U/I signals. These signatures are exclusively found in the Sr I line, but not in the adjoining Fe I line, therefore eliminating the Zeeman effect as the mechanism responsible for their appearance. However, we find a clear spatial correlation between the circular polarization produced by the Zeeman effect and the U/I amplitudes. This suggests that the detected U/I signals are the signatures of Hanle rotation caused by a spatially resolved magnetic field.
Conclusions: A novel measurement technique allows for determining the absolute level of polarization with unprecedented precision. Using this technique, high-precision spectropolarimetric observations reveal, for the first time, unambiguous U/I signals attributed to Hanle rotation in the Sr I line. Title: The polarization angle in the wings of Ca I 4227: A new observable for diagnosing unresolved photospheric magnetic fields Authors: Capozzi, Emilia; Alsina Ballester, Ernest; Belluzzi, Luca; Trujillo Bueno, Javier Bibcode: 2022A&A...657A..44C Altcode: 2021arXiv211108967C Context. When observed in quiet regions close to the solar limb, many strong resonance lines show conspicuous linear polarization signals, produced by scattering processes (i.e., scattering polarization), 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.
Aims: 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.
Methods: 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.
Results: 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.
Conclusions: 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 (e.g., temperature and density), it can provide constraints on the filling factor of the magnetic field. Title: Demonstration of Chromospheric Magnetic Mapping with CLASP2.1 Authors: McKenzie, David; Ishikawa, Ryohko; Trujillo Bueno, Javier; Auchere, F.; Kobayashi, Ken; Winebarger, Amy; Kano, Ryouhei; Song, Donguk; Okamoto, Joten; Rachmeler, Laurel; De Pontieu, Bart; Vigil, Genevieve; Belluzzi, Luca; Alsina Ballester, Ernest; del Pino Aleman, Tanausu; Bethge, Christian; Sakao, Taro; Stepan, Jiri Bibcode: 2021AGUFMSH52A..06M Altcode: Probing the magnetic nature of the Suns atmosphere requires measurement of the Stokes I, Q, U and V profiles of relevant spectral lines (of which Q, U and V encode the magnetic field information). Many of the magnetically sensitive lines formed in the chromosphere and transition region are in the ultraviolet spectrum, necessitating observations above the absorbing terrestrial atmosphere. The Chromospheric Layer Spectro-Polarimeter (CLASP2) sounding rocket was flown successfully in April 2019, as a follow-on to the successful flight in September 2015 of the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP). Both projects were funded by NASAs Heliophysics Technology and Instrument Development for Science (H-TIDeS) program to develop and test a technique for observing the Sun in ultraviolet light, and for quantifying the polarization of that light. By demonstrating successful measurement and interpretation of the polarization in hydrogen Lyman-alpha and the Mg II h and k spectral lines, the CLASP and CLASP2 missions are vital first steps towards routine quantitative characterization of the local thermal and magnetic conditions in the solar chromosphere. In October of 2021, we re-flew the CLASP2 payload with a modified observing program to further demonstrate the maturity of the UV spectropolarimetry techniques, and readiness for development into a satellite observatory. During the reflight, called CLASP2.1, the spectrograph slit was scanned across an active region plage to acquire a two-dimensional map of Stokes V/I, to demonstrate the ability of UV spectropolarimetry to yield chromospheric magnetic fields over a large area. This presentation will display preliminary results from the flight of CLASP2.1. Title: Numerical solutions to linear transfer problems of polarized radiation. I. Algebraic formulation and stationary iterative methods Authors: Janett, Gioele; Benedusi, Pietro; Belluzzi, Luca; Krause, Rolf Bibcode: 2021A&A...655A..87J Altcode: 2021arXiv211011861J 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.
Results: Numerical analysis shows that the choice of the formal solver significantly affects, and can even prevent, the convergence of an iterative method. Moreover, the use of a suitable damping factor can both enforce stability and increase the convergence rate.
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. Title: Modeling the scattering polarization of the solar Ca I 4227 Å line with angle-dependent partial frequency redistribution Authors: Janett, Gioele; Ballester, Ernest Alsina; Guerreiro, Nuno; Riva, Simone; Belluzzi, Luca; del Pino Alemán, Tanausú; Bueno, Javier Trujillo Bibcode: 2021A&A...655A..13J Altcode: 2021arXiv211011990J Context. The correct modeling of the scattering polarization signals observed in several strong resonance lines requires taking partial frequency redistribution (PRD) phenomena into account. Modeling scattering polarization with PRD effects is very computationally demanding and the simplifying angle-averaged (AA) approximation is therefore commonly applied.
Aims: This work aims to assess the impact and the range of validity of the 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 a focus on the solar Ca I 4227 Å line.
Methods: Spectral line polarization was 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 was solved through a two-step approach. In step 1, the problem was solved for the intensity only, considering a multilevel atom. In step 2, the problem was 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 the 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. Title: Numerical solutions to linear transfer problems of polarized radiation. II. Krylov methods and matrix-free implementation Authors: Benedusi, Pietro; Janett, Gioele; Belluzzi, Luca; Krause, Rolf Bibcode: 2021A&A...655A..88B Altcode: 2021arXiv211011873B Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary iterative methods have been replaced by state-of-the-art preconditioned Krylov iterative methods for many applications. However, a general description and a convergence analysis of Krylov methods in the polarized radiative transfer context are still lacking.
Aims: We describe the practical application of preconditioned Krylov methods to linear transfer problems of polarized radiation, possibly in a matrix-free context. The main aim is to clarify the advantages and drawbacks of various Krylov accelerators with respect to stationary iterative methods and direct solution strategies.
Methods: After a brief introduction to the concept of Krylov methods, we report the convergence rate and the run time of various Krylov-accelerated techniques combined with different formal solvers when applied to a 1D benchmark transfer problem of polarized radiation. In particular, we analyze the GMRES, BICGSTAB, and CGS Krylov methods, preconditioned with Jacobi, (S)SOR, or an incomplete LU factorization. Furthermore, specific numerical tests were performed to study the robustness of the various methods as the problem size grew.
Results: Krylov methods accelerate the convergence, reduce the run time, and improve the robustness (with respect to the problem size) of standard stationary iterative methods. Jacobi-preconditioned Krylov methods outperform SOR-preconditioned stationary iterations in all respects. In particular, the Jacobi-GMRES method offers the best overall performance for the problem setting in use.
Conclusions: Krylov methods can be more challenging to implement than stationary iterative methods. However, an algebraic formulation of the radiative transfer problem allows one to apply and study Krylov acceleration strategies with little effort. Furthermore, many available numerical libraries implement matrix-free Krylov routines, enabling an almost effortless transition to Krylov methods. Title: A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer Authors: Janett, Gioele; Steiner, Oskar; Alsina Ballester, Ernest; Belluzzi, Luca; Mishra, Siddhartha Bibcode: 2021arXiv211011885J Altcode: 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. Title: Magnetic imaging of the outer solar atmosphere (MImOSA) Authors: Peter, H.; Ballester, E. Alsina; Andretta, V.; Auchère, F.; Belluzzi, L.; Bemporad, A.; Berghmans, D.; Buchlin, E.; Calcines, A.; Chitta, L. P.; Dalmasse, K.; Alemán, T. del Pino; Feller, A.; Froment, C.; Harrison, R.; Janvier, M.; Matthews, S.; Parenti, S.; Przybylski, D.; Solanki, S. K.; Štěpán, J.; Teriaca, L.; Bueno, J. Trujillo Bibcode: 2021ExA...tmp...95P Altcode: 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. Although the magnetic field at the surface of the Sun is reasonably well characterised by observations, the information on the magnetic field in the higher atmospheric layers is mainly indirect. This lack of information 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. Placed in a near-Earth orbit, the data downlink would be maximised, while a location at L4 or L5 would provide stereoscopic observations of the Sun in combination with Earth-based observatories. This mission to measure the magnetic field will finally unlock the driver of the dynamics in the outer solar atmosphere and thereby will greatly advance our understanding of the Sun and the heliosphere. Title: Solving the Paradox of the Solar Sodium D1 Line Polarization Authors: Alsina Ballester, Ernest; Belluzzi, Luca; Trujillo Bueno, Javier Bibcode: 2021PhRvL.127h1101A Altcode: 2021arXiv210808334A 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. Title: Mapping of Solar Magnetic Fields from the Photosphere to the Top of the Chromosphere with CLASP2 Authors: McKenzie, D.; Ishikawa, R.; Trujillo Bueno, J.; Auchere, F.; del Pino Aleman, T.; Okamoto, T.; Kano, R.; Song, D.; Yoshida, M.; Rachmeler, L.; Kobayashi, K.; Narukage, N.; Kubo, M.; Ishikawa, S.; Hara, H.; Suematsu, Y.; Sakao, T.; Bethge, C.; De Pontieu, B.; Vigil, G.; Winebarger, A.; Alsina Ballester, E.; Belluzzi, L.; Stepan, J.; Asensio Ramos, A.; Carlsson, M.; Leenaarts, J. Bibcode: 2021AAS...23810603M Altcode: Coronal heating, chromospheric heating, and the heating & acceleration of the solar wind, are well-known problems in solar physics. Additionally, knowledge of the magnetic energy that powers solar flares and coronal mass ejections, important drivers of space weather, is handicapped by imperfect determination of the magnetic field in the sun's atmosphere. Extrapolation of photospheric magnetic measurements into the corona is fraught with difficulties and uncertainties, partly due to the vastly different plasma beta between the photosphere and the corona. Better results in understanding the coronal magnetic field should be derived from measurements of the magnetic field in the chromosphere. To that end, we are pursuing quantitative determination of the magnetic field in the chromosphere, where plasma beta transitions from greater than unity to less than unity, via ultraviolet spectropolarimetry. The CLASP2 mission, flown on a sounding rocket in April 2019, succeeded in measuring all four Stokes polarization parameters in UV spectral lines formed by singly ionized Magnesium and neutral Manganese. Because these ions produce spectral lines under different conditions, CLASP2 thus was able to quantify the magnetic field properties at multiple heights in the chromosphere simultaneously, as shown in the recent paper by Ishikawa et al. In this presentation we will report the findings of CLASP2, demonstrating the variation of magnetic fields along a track on the solar surface and as a function of height in the chromosphere; and we will illustrate what is next for the CLASP missions and the demonstration of UV spectropolarimetry in the solar chromosphere. Title: Mapping solar magnetic fields from the photosphere to the base of the corona Authors: Ishikawa, Ryohko; Bueno, Javier Trujillo; del Pino Alemán, Tanausú; Okamoto, Takenori J.; McKenzie, David E.; Auchère, Frédéric; Kano, Ryouhei; Song, Donguk; Yoshida, Masaki; Rachmeler, Laurel A.; Kobayashi, Ken; Hara, Hirohisa; Kubo, Masahito; Narukage, Noriyuki; Sakao, Taro; Shimizu, Toshifumi; Suematsu, Yoshinori; Bethge, Christian; De Pontieu, Bart; Dalda, Alberto Sainz; Vigil, Genevieve D.; Winebarger, Amy; Ballester, Ernest Alsina; Belluzzi, Luca; Štěpán, Jiří; Ramos, Andrés Asensio; Carlsson, Mats; Leenaarts, Jorrit Bibcode: 2021SciA....7.8406I Altcode: 2021arXiv210301583I 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. Title: Magnetic Imaging of the Outer Solar Atmosphere (MImOSA): Unlocking the driver of the dynamics in the upper solar atmosphere Authors: Peter, H.; Alsina Ballester, E.; Andretta, V.; Auchere, F.; Belluzzi, L.; Bemporad, A.; Berghmans, D.; Buchlin, E.; Calcines, A.; Chitta, L. P.; Dalmasse, K.; del Pino Aleman, T.; Feller, A.; Froment, C.; Harrison, R.; Janvier, M.; Matthews, S.; Parenti, S.; Przybylski, D.; Solanki, S. K.; Stepan, J.; Teriaca, L.; Trujillo Bueno, J. Bibcode: 2021arXiv210101566P Altcode: 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. Title: Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation Authors: Paganini, A.; Hashemi, B.; Alsina Ballester, E.; Belluzzi, L. Bibcode: 2021A&A...645A...4P Altcode: 2020arXiv201003508P Context. Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized radiation) are taken into account. Frequency redistribution effects are conveniently described through the redistribution function formalism, and the angle-averaged approximation is often introduced to simplify the problem. Even in this case, the evaluation of the emission coefficient for polarized radiation remains computationally costly, especially when magnetic fields are present or complex atomic models are considered.
Aims: We aim to develop an efficient algorithm to numerically evaluate the angle-averaged redistribution function for polarized radiation.
Methods: The proposed approach is based on a low-rank approximation via trivariate polynomials whose univariate components are represented in the Chebyshev basis.
Results: The resulting algorithm is significantly faster than standard quadrature-based schemes for any target accuracy in the range [10-6, 10-2]. Title: Imaging spectropolarimetry for magnetic field diagnostics in solar prominences Authors: Di Campli, R.; Ramelli, R.; Bianda, M.; Furno, I.; Kumar Dhara, S.; Belluzzi, L. Bibcode: 2020A&A...644A..89D Altcode: Context. Narrowband imaging spectropolarimetry is one of the most powerful tools available to infer information about the intensity and topology of the magnetic fields present in extended plasma structures in the solar atmosphere.
Aims: We describe the instrumental set-up and the observing procedure that we have developed and optimized at the Istituto Ricerche Solari Locarno in order to perform imaging spectropolarimetry. A measurement that highlights the potential of the ensuing observations for magnetic field diagnostics in solar prominences is presented.
Methods: Monochromatic images of solar prominences were obtained by combining a tunable narrowband filter, based on two Fabry-Perot etalons, with a Czerny-Turner spectrograph. Linear and circular polarization were measured at every pixel of the monochromatic image with the Zurich Imaging Polarimeter, ZIMPOL. A wavelength scan was performed across the profile of the considered spectral line. The HAZEL inversion code was applied to the observed Stokes profiles to infer a series of physical properties of the observed structure.
Results: We carried out a spectropolarimetric observation of a prominence, consisting of a set of quasi-monochromatic images across the He I D3 line at 5876 Å in the four Stokes parameters. The map of observed Stokes profiles was inverted with HAZEL, finding magnetic fields with intensities between 15 and 30 G and directed along the spine of the prominence, which is in agreement with the results of previous works. Title: Observational indications of magneto-optical effects in the scattering polarization wings of the Ca I 4227 Å line Authors: Capozzi, Emilia; Ballester, Ernest Alsina; Belluzzi, Luca; Bianda, Michele; Dhara, Sajal Kumar; Ramelli, Renzo Bibcode: 2020A&A...641A..63C Altcode: 2020arXiv200613653C Context. Several strong resonance lines, such as H I Ly-α, Mg II k, Ca II K, and Ca I 4227 Å, are characterized by deep and broad absorption profiles in the solar intensity spectrum. These resonance lines 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 (MO) effects.
Aims: We search for observational indications of this recently discovered physical mechanism in the scattering polarization wings of the Ca I 4227 Å line.
Methods: We performed a series of spectropolarimetric observations of this line using the Zurich IMaging POLarimeter camera at the Gregory-Coudé telescope at Istituto Ricerche Solari Locarno in Switzerland and at the GREGOR telescope in Tenerife (Spain).
Results: Spatial variations of the total linear polarization degree and 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 in which longitudinal magnetic fields are present, thus supporting the theoretical prediction that they are produced by MO effects. Title: Science Requirement Document (SRD) for the European Solar Telescope (EST) (2nd edition, December 2019) Authors: Schlichenmaier, R.; Bellot Rubio, L. R.; Collados, M.; Erdelyi, R.; Feller, A.; Fletcher, L.; Jurcak, J.; Khomenko, E.; Leenaarts, J.; Matthews, S.; Belluzzi, L.; Carlsson, M.; Dalmasse, K.; Danilovic, S.; Gömöry, P.; Kuckein, C.; Manso Sainz, R.; Martinez Gonzalez, M.; Mathioudakis, M.; Ortiz, A.; Riethmüller, T. L.; Rouppe van der Voort, L.; Simoes, P. J. A.; Trujillo Bueno, J.; Utz, D.; Zuccarello, F. Bibcode: 2019arXiv191208650S Altcode: The European Solar Telescope (EST) is a research infrastructure for solar physics. It is planned to be an on-axis solar telescope with an aperture of 4 m and equipped with an innovative suite of spectro-polarimetric and imaging post-focus instrumentation. The EST project was initiated and is driven by EAST, the European Association for Solar Telescopes. EAST was founded in 2006 as an association of 14 European countries. Today, as of December 2019, EAST consists of 26 European research institutes from 18 European countries. The Preliminary Design Phase of EST was accomplished between 2008 and 2011. During this phase, in 2010, the first version of the EST Science Requirement Document (SRD) was published. After EST became a project on the ESFRI roadmap 2016, the preparatory phase started. The goal of the preparatory phase is to accomplish a final design for the telescope and the legal governance structure of EST. A major milestone on this path is to revisit and update the Science Requirement Document (SRD). The EST Science Advisory Group (SAG) has been constituted by EAST and the Board of the PRE-EST EU project in November 2017 and has been charged with the task of providing with a final statement on the science requirements for EST. Based on the conceptual design, the SRD update takes into account recent technical and scientific developments, to ensure that EST provides significant advancement beyond the current state-of-the-art. The present update of the EST SRD has been developed and discussed during a series of EST SAG meetings. The SRD develops the top-level science objectives of EST into individual science cases. Identifying critical science requirements is one of its main goals. Those requirements will define the capabilities of EST and the post-focus instrument suite. The technical requirements for the final design of EST will be derived from the SRD. Title: Observations on spatial variations of the Sr I 4607 Å scattering polarization signals at different limb distances with ZIMPOL Authors: Dhara, Sajal Kumar; Capozzi, Emilia; Gisler, Daniel; Bianda, Michele; Ramelli, Renzo; Berdyugina, Svetlana; Alsina, Ernest; Belluzzi, Luca Bibcode: 2019A&A...630A..67D Altcode: 2019arXiv190803366D Context. The Sr 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 (∼0.1″), spectral (≤20 mÅ), and temporal resolution (< 1 min) with increased polarimetric sensitivity (∼10-4).
Aims: We aim to detect spatial variations at granular scales of the scattering polarization peak of the Sr 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 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 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 I spectral line is positively correlated with the intensity in the continuum, corresponding to the granules, at every μ. Title: Magnetic Sensitivity in the Wings of the Linear Polarization Profiles of the Hydrogen Lyman-α Line Authors: Ballester, E. A.; Belluzzi, L.; Bueno, J. T. Bibcode: 2019spw..confE..11B Altcode: No abstract at ADS Title: Magnetic Sensitivity in the Wing Scattering Polarization Signals of the Hydrogen Lyman-α Line of the Solar Disk Radiation Authors: Alsina Ballester, E.; Belluzzi, L.; Trujillo Bueno, J. Bibcode: 2019ApJ...880...85A Altcode: 2019arXiv190110994A The linear polarization produced by scattering processes in the hydrogen Lyα 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 the three-dimensional structure of the TR, the sizable scattering polarization signals that the joint action of partial frequency redistribution and J-state interference produce in the Lyα 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 G, 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. We find that magnetic fields with longitudinal components larger than 100 G produce an almost complete depolarization of the wings of the Lyα Q/I profiles within a ±5 Å spectral range around the line center, while stronger fields are required for the U/I wing signals to be depolarized to a similar extent. The theoretical results presented here further expand the diagnostic content of the unprecedented spectropolarimetric observations provided by the Chromospheric Lyman-Alpha Spectro-Polarimeter. Title: Measurement of the Evolution of the Magnetic Field of the Quiet Photosphere over a Solar Cycle Authors: Ramelli, R.; Bianda, M.; Berdyugina, S.; Belluzzi, L.; Kleint, L. Bibcode: 2019ASPC..526..283R Altcode: The solar photosphere is filled by magnetic fields tangled at scales much smaller than the resolution capability of solar telescopes. These hidden magnetic fields can be investigated via the Hanle effect. In 2007, we started a synoptic program to explore whether 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 C2 molecular lines around 514.0 nm, taken with a cadence of approximately one month. Our results now span almost one complete solar cycle. Title: Numerical Methods for the Radiative Transfer Equation of Polarized Light Authors: Janett, G.; Steiner, O.; Belluzzi, L. Bibcode: 2019ASPC..526..133J Altcode: The quest of the "best formal solver" available is still open and the lack of a clear comparison between the different numerical methods proposed by the community does not facilitate a conclusion. This work presents a reference paradigm for the characterization of formal solvers, based on the concepts of order of accuracy, stability and computational cost. This overview aims to facilitate the comprehension of the advantages and weaknesses of the already existing formal solvers and of those yet to come. Title: CLASP2: The Chromospheric LAyer Spectro-Polarimeter Authors: McKenzie, D. E.; Ishikawa, R.; Trujillo Bueno, J.; Auchére, F.; Rachmeler, L. A.; Kubo, M.; Kobayashi, K.; Winebarger, A. R.; Bethge, C. W.; Narukage, N.; Kano, R.; Ishikawa, S.; de Pontieu, B.; Carlsson, M.; Yoshida, M.; Belluzzi, L.; Štěpán, J.; del Pino Alemán, T.; Alsina Ballester, E.; Asensio Ramos, A. Bibcode: 2019ASPC..526..361M Altcode: The hydrogen Lyman-α line at 121.6 nm and the Mg k line at 279.5 nm are especially relevant for deciphering the magnetic structure of the chromosphere since their line-center signals are formed in the chromosphere and transition region, with unique sensitivities to magnetic fields. We propose the Chromospheric LAyer Spectro-Polarimeter (CLASP2), to build upon the success of the first CLASP flight, which measured the linear polarization in H I Lyman-α. The existing CLASP instrument will be refitted to measure all four Stokes parameters in the 280 nm range, including variations due to the anisotropic radiation pumping, the Hanle effect, and the Zeeman effect. Title: Relaxation Phenomena Due to Collisions with Neutral Perturbers in Hyperfine Structure Multiplets Authors: Landi Degl'Innocenti, E.; Belluzzi, L. Bibcode: 2019ASPC..526...29L Altcode: A connection is established between the depolarizing rates, due to collisions with neutral perturbers, of the statistical tensors of a hyperfine structure multiplet and those of the statistical tensors of the parent fine structure level. This connection is described by a simple equation involving a 12-j symbol of the second kind. An application is performed to derive an analytical expression for the scattering matrix of a hyperfine structured two-level atom in the presence of collisions and a magnetic field. Numerical results are presented. Title: The Transfer of Resonance Line Polarization with PRD in the General Hanle-Zeeman Regime Authors: Alsina Ballester, E.; Belluzzi, L.; Trujillo Bueno, J. Bibcode: 2019ASPC..526..119A Altcode: We present numerical radiative transfer calculations of the four Stokes parameters of the radiation emerging from one-dimensional model atmospheres. In this investigation we account for the impact of partial frequency redistribution (PRD) in scattering and the joint action of the Hanle and Zeeman effects. Strong resonance lines of interest for chromospheric magnetic field diagnostics have been considered, namely the Ca I line at 4227 Å and the Mg II k line at 2795 Å. The Stokes profiles of these lines have been obtained by considering two-level atomic models, both in the absence and in the presence of magnetic fields. We draw attention to the fact that the magneto-optical terms of the transfer equations for Stokes Q and U are responsible for an interesting and previously unnoticed magnetic sensitivity of their scattering polarization profiles beyond the Doppler core. This important discovery contributes to paint a more detailed picture of the influence of relatively weak magnetic fields on the observable linear polarization signals of strong chromospheric lines, highlighting the importance of a PRD treatment for such lines. Title: Solar Polarization Workshop 8 Authors: Belluzzi, L.; Casini, R.; Romoli, M.; Trujillo Bueno, J. Bibcode: 2019ASPC..526.....B Altcode: No abstract at ADS Title: Comparison of Scattering Polarization Signals Observed by CLASP: Possible Indication of the Hanle Effect Authors: Ishikawa, R.; Trujillo Bueno, J.; Uitenbroek, H.; Kubo, M.; Tsuneta, S.; Goto, M.; Kano, R.; Narukage, N.; Bando, T.; Katsukawa, Y.; Ishikawa, S.; Giono, G.; Suematsu, Y.; Hara, H.; Shimizu, T.; Sakao, T.; Winebarger, A.; Kobayashi, K.; Cirtain, J.; Champey, P.; Auchère, F.; Štěpán, J.; Belluzzi, L.; Asensio Ramos, A.; Manso Sainz, R.; De Pomtieu, B.; Ichimoto, K.; Carlsson, M.; Casini, R. Bibcode: 2019ASPC..526..305I Altcode: The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP; Kano et al. 2012; Kobayashi et al. 2012; Kubo et al. 2014) observed, for the first time, the linear polarization produced by scattering processes in the hydrogen Lyman-α (121.57 nm) and Si III (120.56 nm) lines of the solar disk radiation. The complexity of the observed scattering polarization (i.e., conspicuous spatial variations in Q/I and U/I at spatial scales of 10″-20″ and the absence of center-to- limb variation at the Lyman-α center; see Kano et al. 2017) motivated us to search for possible hints of the operation of the Hanle effect by comparing: (a) the Lyman-α line center signal, for which the critical field strength (BH) for the onset of the Hanle effect is 53 G, (b) the Lyman-α wing, which is insensitive to the Hanle effect, and (c) the Si III line, whose BH = 290 G. We focus on four regions with different total unsigned photospheric magnetic fluxes (estimated from SDO/HMI observations), and compare the corresponding U/I spatial variations in the Lyman-α wing, Lyman-α center, and Si III line. The U/I signal in the Lyman-α wing shows an antisymmetric spatial distribution, which is caused by the presence of a bright structure in all the selected regions, regardless of the total unsigned photospheric magnetic flux. In an internetwork region, the Lyman-α center shows an antisymmetric spatial variation across the selected bright structure, but it does not show it in other more magnetized regions. In the Si III line, the spatial variation of U/I deviates from the above-mentioned antisymmetric shape as the total unsigned photospheric magnetic flux increases. We argue that a plausible explanation of this differential behavior is the operation of the Hanle effect.

This work, presented in an oral contribution at this Workshop, has been published on The Astrophysical Journal (Ishikawa et al. 2017). Title: Second Solar Spectrum Observations with ZIMPOL Authors: Bianda, M.; Ramelli, R.; Gisler, D.; Belluzzi, L.; Carlin, E. S. Bibcode: 2019ASPC..526..223B Altcode: The observational activity of IRSOL takes advantage of the high-precision instrumentation available, and of the possibility to carry out programs requiring observing time spread over weeks or months. Particular attention is paid to scattering polarization signals modified by the Hanle effect in spectral lines. Several programs at IRSOL are also aimed at getting the technical know-how necessary to exploit the potentialities of the new generation of large-aperture solar telescopes, which will provide observations with unprecedented spatial and temporal resolution without sacrificing spectropolarimetric sensitivity. In this contribution, we provide a brief description of some projects that are presently carried out at IRSOL. Title: Spatial variations of the SrI 4607Åscattering polarization signals at subgranular scale observed with ZIMPOL at GREGOR telescope Authors: Dhara, Sajal Kumar; Capozzi, Emilia; Gisler, Daniel; Bianda, Michele; Ramelli, Renzo; Berdyugina, Svetlana; Alsina, Ernest; Belluzzi, Luca Bibcode: 2019arXiv190403986D Altcode: 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 $\mu$, 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. Title: A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer Authors: Janett, Gioele; Steiner, Oskar; Alsina Ballester, Ernest; Belluzzi, Luca; Mishra, Siddhartha Bibcode: 2019A&A...624A.104J Altcode: Context. Several numerical problems require the interpolation of discrete data that present at the same time (i) complex smooth structures and (ii) various types of discontinuities. The radiative transfer in solar and stellar atmospheres is a typical example of such a problem. This calls for high-order well-behaved techniques that are able to interpolate both smooth and discontinuous data.
Aims: This article expands on different nonlinear interpolation techniques capable of guaranteeing high-order accuracy and handling discontinuities in an accurate and non-oscillatory fashion. The final aim is to propose new techniques which could be 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 essentially 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. Conclusion. 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. Title: Spatial variations of the Sr I 4607 Åscattering polarization signals at subgranular scale observed with ZIMPOL at the GREGOR telescope Authors: Kumar Dhara, Sajal; Capozzi, Emilia; Gisler, Daniel; Bianda, Michele; Ramelli, Renzo; Berdyugina, Svetlana; Alsina, Ernest; Belluzzi, Luca Bibcode: 2019NCimC..42....6K Altcode: Sr I 4607 Åspectral 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 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 4607 Åline at the granular scale at every μ, starting from 0.2 to 0.8. The correlation between the scattering linear polarization signal amplitude and the continuum intensity imply statistically that the scattering polarization is higher at the granular regions than in the intergranular lanes. Title: CLASP Constraints on the Magnetization and Geometrical Complexity of the Chromosphere-Corona Transition Region Authors: Trujillo Bueno, J.; Štěpán, J.; Belluzzi, L.; Asensio Ramos, A.; Manso Sainz, R.; del Pino Alemán, T.; Casini, R.; Ishikawa, R.; Kano, R.; Winebarger, A.; Auchère, F.; Narukage, N.; Kobayashi, K.; Bando, T.; Katsukawa, Y.; Kubo, M.; Ishikawa, S.; Giono, G.; Hara, H.; Suematsu, Y.; Shimizu, T.; Sakao, T.; Tsuneta, S.; Ichimoto, K.; Cirtain, J.; Champey, P.; De Pontieu, B.; Carlsson, M. Bibcode: 2018ApJ...866L..15T Altcode: 2018arXiv180908865T The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a suborbital rocket experiment that on 2015 September 3 measured the linear polarization produced by scattering processes in the hydrogen Lyα line of the solar disk radiation. The line-center photons of this spectral line radiation mostly 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 geometric 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. Second, we introduce a statistical description of the solar atmosphere based on a 3D model derived from a state-of-the-art radiation magnetohydrodynamic 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. Title: A Statistical Inference Method for Interpreting the CLASP Observations Authors: Štěpán, J.; Trujillo Bueno, J.; Belluzzi, L.; Asensio Ramos, A.; Manso Sainz, R.; del Pino Alemán, T.; Casini, R.; Kano, R.; Winebarger, A.; Auchère, F.; Ishikawa, R.; Narukage, N.; Kobayashi, K.; Bando, T.; Katsukawa, Y.; Kubo, M.; Ishikawa, S.; Giono, G.; Hara, H.; Suematsu, Y.; Shimizu, T.; Sakao, T.; Tsuneta, S.; Ichimoto, K.; Cirtain, J.; Champey, P.; De Pontieu, B.; Carlsson, M. Bibcode: 2018ApJ...865...48S Altcode: 2018arXiv180802725S On 2015 September 3, the Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) successfully measured the linear polarization produced by scattering processes in the hydrogen Lyα 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, 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 Lyα line-center polarization observed by CLASP. Title: Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems Authors: Janett, Gioele; Steiner, Oskar; Belluzzi, Luca Bibcode: 2018ApJ...865...16J Altcode: 2018arXiv180906604J 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. Title: Current State of UV Spectro-Polarimetry and its Future Direction Authors: Ishikawa, Ryohko; Sakao, Taro; Katsukawa, Yukio; Hara, Hirohisa; Ichimoto, Kiyoshi; Shimizu, Toshifumi; Kubo, Masahito; Auchere, Frederic; De Pontieu, Bart; Winebarger, Amy; Kobayashi, . Ken; Kano, Ryouhei; Narukage, Noriyuki; Trujillo Bueno, Javier; Song, Dong-uk; Manso Sainz, Rafael; Asensio Ramos, Andres; Leenaarts, Jorritt; Carlsson, Mats; Bando, Takamasa; Ishikawa, Shin-nosuke; Tsuneta, Saku; Belluzzi, Luca; Suematsu, Yoshinori; Giono, Gabriel; Yoshida, Masaki; Goto, Motoshi; Del Pino Aleman, Tanausu; Stepan, Jiri; Okamoto, Joten; Tsuzuki, Toshihiro; Uraguchi, Fumihiro; Champey, Patrick; Alsina Ballester, Ernest; Casini, Roberto; McKenzie, David; Rachmeler, Laurel; Bethge, Christian Bibcode: 2018cosp...42E1564I Altcode: To obtain quantitative information on the magnetic field in low beta regions (i.e., upper chromosphere and above) has been increasingly important to understand the energetic phenomena of the outer solar atmosphere such as flare, coronal heating, and the solar wind acceleration. In the UV range, there are abundant spectral lines that originate in the upper chromosphere and transition region. However, the Zeeman effect in these spectral lines does not give rise to easily measurable polarization signals because of the weak magnetic field strength and the larger Doppler broadening compared with the Zeeman effect. Instead, the Hanle effect in UV lines is expected to be a suitable diagnostic tool of the magnetic field in the upper atmospheric layers. To investigate the validity of UV spectro-polarimetry and the Hanle effect, the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP), which is a NASA sounding- rocket experiment, was launched at White Sands in US on September 3, 2015. During its 5 minutes ballistic flight, it successfully performed spectro-polarimetric observations of the hydrogen Lyman-alpha line (121.57 nm) with an unprecedentedly high polarization sensitivity of 0.1% in this wavelength range. CLASP observed the linear polarization produced by scattering process in VUV lines for the first time and detected the polarization signals which indicate the operation of the Hanle effect. Following the success of CLASP, we are confident that UV spectro-polarimetry is the way to proceed, and we are planning the second flight of CLASP (CLASP2: Chromospheric LAyer SpectroPolarimeter 2). For this second flight we will carry out spectro-polarimetry in the Mg II h and k lines around 280 nm, with minimum modifications of the CLASP1 instrument. The linear polarization in the Mg II k line is induced by scattering processes and the Hanle effect, being sensitive to magnetic field strengths of 5 to 50 G. In addition, the circular polarizations in the Mg II h and k lines induced by the Zeeman effect can be measurable in at least plage and active regions. The combination of the Hanle and Zeeman effects could help us to more reliably infer the magnetic fields of the upper solar chromosphere. CLASP2 was selected for flight and is being developed for launch in the spring of 2019.Based on these sounding rocket experiments (CLASP1 and 2), we aim at establishing the strategy and refining the instrument concept for future space missions to explore the enigmatic atmospheric layers via UV spectro-polarimetry. Title: Structure of the Balmer jump. The isolated hydrogen atom Authors: Calvo, F.; Belluzzi, L.; Steiner, O. Bibcode: 2018A&A...613A..55C Altcode: 2019arXiv190110241C 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. Title: Spatial variations of the Sr I 4607 Å scattering polarization peak Authors: Bianda, M.; Berdyugina, S.; Gisler, D.; Ramelli, R.; Belluzzi, L.; Carlin, E. S.; Stenflo, J. O.; Berkefeld, T. Bibcode: 2018A&A...614A..89B Altcode: 2018arXiv180303531B Context. The scattering polarization signal observed in the photospheric Sr I 4607 Å 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 Å 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. Title: Magneto-optical Effects in the Scattering Polarization Wings of the Ca I 4227 Å Resonance Line Authors: Alsina Ballester, E.; Belluzzi, L.; Trujillo Bueno, J. Bibcode: 2018ApJ...854..150A Altcode: 2017arXiv171100372A; 2017arXiv171100372B The linear polarization pattern produced by scattering processes in the Ca I 4227 Å resonance line 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. 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 in the Ca I 4227 Å line 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. Title: The Physics and Diagnostic Potential of Ultraviolet Spectropolarimetry Authors: Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio; Belluzzi, Luca Bibcode: 2018smf..book..183T Altcode: No abstract at ADS Title: The Physics and Diagnostic Potential of Ultraviolet Spectropolarimetry Authors: Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio; Belluzzi, Luca Bibcode: 2017SSRv..210..183T Altcode: 2017SSRv..tmp...15T The empirical investigation of the magnetic field in the outer solar atmosphere is a very important challenge in astrophysics. To this end, we need to identify, measure and interpret observable quantities sensitive to the magnetism of the upper chromosphere, transition region and corona. This paper provides an overview of the physics and diagnostic potential of spectropolarimetry in permitted spectral lines of the ultraviolet solar spectrum, such as the Mg ii h and k lines around 2800 Å, the hydrogen Lyman-α line at 1216 Å, and the Lyman-α line of He ii at 304 Å. The outer solar atmosphere is an optically pumped vapor and the linear polarization of such spectral lines is dominated by the atomic level polarization produced by the absorption and scattering of anisotropic radiation. Its modification by the action of the Hanle and Zeeman effects in the inhomogeneous and dynamic solar atmosphere needs to be carefully understood because it encodes the magnetic field information. The circular polarization induced by the Zeeman effect in some ultraviolet lines (e.g., Mg ii h & k) is also of diagnostic interest, especially for probing the outer solar atmosphere in plages and more active regions. The few (pioneering) observational attempts carried out so far to measure the ultraviolet spectral line polarization produced by optically pumped atoms in the upper chromosphere, transition region and corona are also discussed. We emphasize that ultraviolet spectropolarimetry is a key gateway to the outer atmosphere of the Sun and of other stars. Title: Measurement of the evolution of the magnetic field of the quiet photosphere during a solar cycle Authors: Ramelli, Renzo; Bianda, Michele; Berdyugina, Svetlana; Belluzzi, Luca; Kleint, Lucia Bibcode: 2017arXiv170803287R Altcode: 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. Title: CLASP2: The Chromospheric LAyer Spectro-Polarimeter Authors: Rachmeler, Laurel; E McKenzie, David; Ishikawa, Ryohko; Trujillo Bueno, Javier; Auchère, Frédéric; Kobayashi, Ken; Winebarger, Amy; Bethge, Christian; Kano, Ryouhei; Kubo, Masahito; Song, Donguk; Narukage, Noriyuki; Ishikawa, Shin-nosuke; De Pontieu, Bart; Carlsson, Mats; Yoshida, Masaki; Belluzzi, Luca; Stepan, Jiri; del Pino Alemná, Tanausú; Ballester, Ernest Alsina; Asensio Ramos, Andres Bibcode: 2017SPD....4811010R Altcode: We present the instrument, science case, and timeline of the CLASP2 sounding rocket mission. The successful CLASP (Chromospheric Lyman-Alpha Spectro-Polarimeter) sounding rocket flight in 2015 resulted in the first-ever linear polarization measurements of solar hydrogen Lyman-alpha line, which is sensitive to the Hanle effect and can be used to constrain the magnetic field and geometric complexity of the upper chromosphere. Ly-alpha is one of several upper chromospheric lines that contain magnetic information. In the spring of 2019, we will re-fly the modified CLASP telescope to measure the full Stokes profile of Mg II h & k near 280 nm. This set of lines is sensitive to the upper chromospheric magnetic field via both the Hanle and the Zeeman effects. Title: Formal Solutions for Polarized Radiative Transfer. II. High-order Methods Authors: Janett, Gioele; Steiner, Oskar; Belluzzi, Luca Bibcode: 2017ApJ...845..104J Altcode: 2017arXiv170901280J 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., emphasizing their advantages and drawbacks in terms of order of accuracy, stability, and computational cost. Title: CLASP2: The Chromospheric LAyer Spectro-Polarimeter Authors: Rachmeler, Laurel A.; McKenzie, D. E.; Ishikawa, R.; Trujillo-Bueno, J.; Auchere, F.; Kobayashi, K.; Winebarger, A.; Bethge, C.; Kano, R.; Kubo, M.; Song, D.; Narukage, N.; Ishikawa, S.; De Pontieu, B.; Carlsson, M.; Yoshida, M.; Belluzzi, L.; Stepan, J.; del Pino Alemán, T.; Alsina Ballester, E.; Asensio Ramos, A. Bibcode: 2017shin.confE..79R Altcode: We present the instrument, science case, and timeline of the CLASP2 sounding rocket mission. The successful CLASP (Chromospheric Lyman-Alpha Spectro-Polarimeter) sounding rocket flight in 2015 resulted in the first-ever linear polarization measurements of solar hydrogen Lyman-alpha line, which is sensitive to the Hanle effect and can be used to constrain the magnetic field and geometric complexity of the upper chromosphere. Ly-alpha is one of several upper chromospheric lines that contain magnetic information. In the spring of 2019, we will re-fly the modified CLASP telescope to measure the full Stokes profile of Mg II h & k near 280 nm. This set of lines is sensitive to the upper chromospheric magnetic field via both the Hanle and the Zeeman effects. Title: Indication of the Hanle Effect by Comparing the Scattering Polarization Observed by CLASP in the Lyα and Si III 120.65 nm Lines Authors: Ishikawa, R.; Trujillo Bueno, J.; Uitenbroek, H.; Kubo, M.; Tsuneta, S.; Goto, M.; Kano, R.; Narukage, N.; Bando, T.; Katsukawa, Y.; Ishikawa, S.; Giono, G.; Suematsu, Y.; Hara, H.; Shimizu, T.; Sakao, T.; Winebarger, A.; Kobayashi, K.; Cirtain, J.; Champey, P.; Auchère, F.; Štěpán, J.; Belluzzi, L.; Asensio Ramos, A.; Manso Sainz, R.; De Pontieu, B.; Ichimoto, K.; Carlsson, M.; Casini, R. Bibcode: 2017ApJ...841...31I Altcode: The Chromospheric Lyman-Alpha Spectro-Polarimeter is a sounding rocket experiment that has provided the first successful measurement of the linear polarization produced by scattering processes in the hydrogen Lyα line (121.57 nm) radiation of the solar disk. In this paper, we report that the Si III line at 120.65 nm also shows scattering polarization and we compare the scattering polarization signals observed in the Lyα and Si III lines in order to search for observational signatures of the Hanle effect. We focus on four selected bright structures and investigate how the U/I spatial variations vary between the Lyα wing, the Lyα core, and the Si III line as a function of the total unsigned photospheric magnetic flux estimated from Solar Dynamics Observatory/Helioseismic and Magnetic Imager observations. In an internetwork region, the Lyα core shows an antisymmetric spatial variation across the selected bright structure, but it does not show it in other more magnetized regions. In the Si III line, the spatial variation of U/I deviates from the above-mentioned antisymmetric shape as the total unsigned photospheric magnetic flux increases. A plausible explanation of this difference is the operation of the Hanle effect. We argue that diagnostic techniques based on the scattering polarization observed simultaneously in two spectral lines with very different sensitivities to the Hanle effect, like Lyα and Si III, are of great potential interest for exploring the magnetism of the upper solar chromosphere and transition region. Title: Formal Solutions for Polarized Radiative Transfer. I. The DELO Family Authors: Janett, Gioele; Carlin, Edgar S.; Steiner, Oskar; Belluzzi, Luca Bibcode: 2017ApJ...840..107J Altcode: 2017arXiv170901274J 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. Title: Polarization Calibration of the Chromospheric Lyman-Alpha SpectroPolarimeter for a 0.1% Polarization Sensitivity in the VUV Range. Part II: In-Flight Calibration Authors: Giono, G.; Ishikawa, R.; Narukage, N.; Kano, R.; Katsukawa, Y.; Kubo, M.; Ishikawa, S.; Bando, T.; Hara, H.; Suematsu, Y.; Winebarger, A.; Kobayashi, K.; Auchère, F.; Trujillo Bueno, J.; Tsuneta, S.; Shimizu, T.; Sakao, T.; Cirtain, J.; Champey, P.; Asensio Ramos, A.; Štěpán, J.; Belluzzi, L.; Manso Sainz, R.; De Pontieu, B.; Ichimoto, K.; Carlsson, M.; Casini, R.; Goto, M. Bibcode: 2017SoPh..292...57G Altcode: The Chromospheric Lyman-Alpha SpectroPolarimeter is a sounding rocket instrument designed to measure for the first time the linear polarization of the hydrogen Lyman-α line (121.6 nm). The instrument was successfully launched on 3 September 2015 and observations were conducted at the solar disc center and close to the limb during the five-minutes flight. In this article, the disc center observations are used to provide an in-flight calibration of the instrument spurious polarization. The derived in-flight spurious polarization is consistent with the spurious polarization levels determined during the pre-flight calibration and a statistical analysis of the polarization fluctuations from solar origin is conducted to ensure a 0.014% precision on the spurious polarization. The combination of the pre-flight and the in-flight polarization calibrations provides a complete picture of the instrument response matrix, and a proper error transfer method is used to confirm the achieved polarization accuracy. As a result, the unprecedented 0.1% polarization accuracy of the instrument in the vacuum ultraviolet is ensured by the polarization calibration. Title: Discovery of Scattering Polarization in the Hydrogen Lyα Line of the Solar Disk Radiation Authors: Kano, R.; Trujillo Bueno, J.; Winebarger, A.; Auchère, F.; Narukage, N.; Ishikawa, R.; Kobayashi, K.; Bando, T.; Katsukawa, Y.; Kubo, M.; Ishikawa, S.; Giono, G.; Hara, H.; Suematsu, Y.; Shimizu, T.; Sakao, T.; Tsuneta, S.; Ichimoto, K.; Goto, M.; Belluzzi, L.; Štěpán, J.; Asensio Ramos, A.; Manso Sainz, R.; Champey, P.; Cirtain, J.; De Pontieu, B.; Casini, R.; Carlsson, M. Bibcode: 2017ApJ...839L..10K Altcode: 2017arXiv170403228K 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 Lyα 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 Lyα 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 ∼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. Title: The Transfer of Resonance Line Polarization with Partial Frequency Redistribution in the General Hanle-Zeeman Regime Authors: Alsina Ballester, E.; Belluzzi, L.; Trujillo Bueno, J. Bibcode: 2017ApJ...836....6A Altcode: 2016arXiv160905723B; 2016arXiv160905723A; 2017ApJ...836....6B 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 a 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 that 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 magneto-optical effects have a strong impact on the linear polarization signals that PRD effects produce in the wings of strong resonance lines. We also show that the weak-field approximation has to be used with caution when PRD effects are considered. Title: Discovery of Ubiquitous Fast-Propagating Intensity Disturbances by the Chromospheric Lyman Alpha Spectropolarimeter (CLASP) Authors: Kubo, M.; Katsukawa, Y.; Suematsu, Y.; Kano, R.; Bando, T.; Narukage, N.; Ishikawa, R.; Hara, H.; Giono, G.; Tsuneta, S.; Ishikawa, S.; Shimizu, T.; Sakao, T.; Winebarger, A.; Kobayashi, K.; Cirtain, J.; Champey, P.; Auchère, F.; Trujillo Bueno, J.; Asensio Ramos, A.; Štěpán, J.; Belluzzi, L.; Manso Sainz, R.; De Pontieu, B.; Ichimoto, K.; Carlsson, M.; Casini, R.; Goto, M. Bibcode: 2016ApJ...832..141K Altcode: High-cadence observations by the slit-jaw (SJ) optics system of the sounding rocket experiment known as the Chromospheric Lyman Alpha Spectropolarimeter (CLASP) reveal ubiquitous intensity disturbances that recurrently propagate in either the chromosphere or the transition region or both at a speed much higher than the speed of sound. The CLASP/SJ instrument provides a time series of two-dimensional images taken with broadband filters centered on the Lyα line at a 0.6 s cadence. The multiple fast-propagating intensity disturbances appear in the quiet Sun and in an active region, and they are clearly detected in at least 20 areas in a field of view of 527″ × 527″ during the 5 minute observing time. The apparent speeds of the intensity disturbances range from 150 to 350 km s-1, and they are comparable to the local Alfvén speed in the transition region. The intensity disturbances tend to propagate along bright elongated structures away from areas with strong photospheric magnetic fields. This suggests that the observed fast-propagating intensity disturbances are related to the magnetic canopy structures. The maximum distance traveled by the intensity disturbances is about 10″, and the widths are a few arcseconds, which are almost determined by a pixel size of 1.″03. The timescale of each intensity pulse is shorter than 30 s. One possible explanation for the fast-propagating intensity disturbances observed by CLASP is magnetohydrodynamic fast-mode waves. Title: The Magnetic Sensitivity of the Mg II k Line to the Joint Action of Hanle, Zeeman, and Magneto-optical Effects Authors: Alsina Ballester, E.; Belluzzi, L.; Trujillo Bueno, J. Bibcode: 2016ApJ...831L..15A Altcode: 2016arXiv161000649A 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 Å, accounting for the joint action of the Hanle and Zeeman effects as well as partial frequency redistribution 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 (∼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. Title: Chromospheric LAyer SpectroPolarimeter (CLASP2) Authors: Narukage, Noriyuki; McKenzie, David E.; Ishikawa, Ryoko; Trujillo-Bueno, Javier; De Pontieu, Bart; Kubo, Masahito; Ishikawa, Shin-nosuke; Kano, Ryouhei; Suematsu, Yoshinori; Yoshida, Masaki; Rachmeler, Laurel A.; Kobayashi, Ken; Cirtain, Jonathan W.; Winebarger, Amy R.; Asensio Ramos, Andres; del Pino Aleman, Tanausu; Štępán, Jiri; Belluzzi, Luca; Larruquert, Juan Ignacio; Auchère, Frédéric; Leenaarts, Jorrit; Carlsson, Mattias J. L. Bibcode: 2016SPIE.9905E..08N Altcode: The sounding rocket Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) was launched on September 3rd, 2015, and successfully detected (with a polarization accuracy of 0.1 %) the linear polarization signals (Stokes Q and U) that scattering processes were predicted to produce in the hydrogen Lyman-alpha line (Lyα 121.567 nm). Via the Hanle effect, this unique data set may provide novel information about the magnetic structure and energetics in the upper solar chromosphere. The CLASP instrument was safely recovered without any damage and we have recently proposed to dedicate its second flight to observe the four Stokes profiles in the spectral region of the Mg II h and k lines around 280 nm; in these lines the polarization signals result from scattering processes and the Hanle and Zeeman effects. Here we describe the modifications needed to develop this new instrument called the "Chromospheric LAyer SpectroPolarimeter" (CLASP2). Title: Spectro-polarimetric observation in UV with CLASP to probe the chromosphere and transition region Authors: Kano, Ryouhei; Ishikawa, Ryohko; Winebarger, Amy R.; Auchère, Frédéric; Trujillo Bueno, Javier; Narukage, Noriyuki; Kobayashi, Ken; Bando, Takamasa; Katsukawa, Yukio; Kubo, Masahito; Ishikawa, Shin-Nosuke; Giono, Gabriel; Hara, Hirohisa; Suematsu, Yoshinori; Shimizu, Toshifumi; Sakao, Taro; Tsuneta, Saku; Ichimoto, Kiyoshi; Goto, Motoshi; Cirtain, Jonathan W.; De Pontieu, Bart; Casini, Roberto; Manso Sainz, Rafael; Asensio Ramos, Andres; Stepan, Jiri; Belluzzi, Luca; Carlsson, Mats Bibcode: 2016SPD....4710107K Altcode: The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a NASA sounding-rocket experiment that was performed in White Sands in the US on September 3, 2015. During its 5-minute ballistic flight, CLASP successfully made the first spectro-polarimetric observation in the Lyman-alpha line (121.57 nm) originating in the chromosphere and transition region. Since the Lyman-alpha polarization is sensitive to magnetic field of 10-100 G by the Hanle effect, we aim to infer the magnetic field information in such upper solar atmosphere with this experiment.The obtained CLASP data showed that the Lyman-alpha scattering polarization is about a few percent in the wings and the order of 0.1% in the core near the solar limb, as it had been theoretically predicted, and that both polarization signals have a conspicuous spatio-temporal variability. CLASP also observed another upper-chromospheric line, Si III (120.65 nm), whose critical field strength for the Hanle effect is 290 G, and showed a measurable scattering polarization of a few % in this line. The polarization properties of the Si III line could facilitate the interpretation of the scattering polarization observed in the Lyman-alpha line.In this presentation, we would like to show how the upper chromosphere and transition region are seen in the polarization of these UV lines and discuss the possible source of these complicated polarization signals. Title: Polarized radiative transfer in discontinuous media Authors: Steiner, O.; Züger, F.; Belluzzi, L. Bibcode: 2016A&A...586A..42S Altcode: Context. Observations of the solar atmosphere of ever increasing spatial resolution reveal steep gradients in the magnetic field and in thermal states. Likewise, numerical simulations of the solar atmosphere show contact discontinuities and shock fronts. This asks for the development of robust methods for computing the radiative transfer of polarized light in discontinuous media.
Aims: Here, we propose a new concept for dealing with discontinuities in the radiative transfer of polarized light and carry out a few basic test calculations. While in the past, the focus was on interpolating the source function with ever-increasing accuracy and smoothness, we propose to take the opposite approach by reconstructing it with piecewise continuous functions, taking discontinuities on purpose into account. This concept is known from computational fluid dynamics.
Methods: Test calculations were carried out for (I) a Milne-Eddington atmosphere; (II) an atmosphere featuring a single discontinuity that is shifted across one grid cell; and (III) a two-layered atmosphere with discontinuities in the source function, the velocity, and the magnetic field.
Results: It is shown that the method of piecewise continuous reconstruction is a viable approach to solving the radiative transfer equation for polarized light. In the special case where a discontinuity coincides with a computational cell interface, the method is capable of producing the exact solution. Overall, the assessment of the piecewise continuous reconstruction method turns out to be cautiously positive, but it does not lead to an order-of-magnitude improvement in accuracy over conventional methods for the examples considered here. More realistic model atmospheres need to be considered for judging practical applicability. Title: Radiative Transfer Modeling of the Enigmatic Scattering Polarization in the Solar Na I D1 Line Authors: Belluzzi, Luca; Trujillo Bueno, Javier; Landi Degl'Innocenti, Egidio Bibcode: 2015ApJ...814..116B Altcode: 2015arXiv151105801B 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 Na i, 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 Na i D1 line without the need for ground-level polarization. Title: Atomic Scattering Polarization. Observations, Modeling, Predictions Authors: Trujillo Bueno, J.; Del Pino Alemán, T.; Belluzzi, L. Bibcode: 2015IAUS..305..127T Altcode: 2015IAUS..305..127B This paper highlights very recent advances concerning the identification of new mechanisms that introduce polarization in spectral lines, which turn out to be key for understanding some of the most enigmatic scattering polarization signals of the solar visible spectrum. We also show a radiative transfer prediction on the scattering polarization pattern across the Mg ii h & k lines, whose radiation can only be observed from space. Title: Isotropic Inelastic Collisions in a Multiterm Atom with Hyperfine Structure Authors: Belluzzi, Luca; Landi Degl'Innocenti, Egidio; Trujillo Bueno, Javier Bibcode: 2015ApJ...812...73B Altcode: A correct modeling of the scattering polarization profiles observed in some spectral lines of diagnostic interest, the sodium doublet being one of the most important examples, requires taking hyperfine structure (HFS) and quantum interference between different J-levels into account. An atomic model suitable for taking these physical ingredients into account is the so-called multiterm atom with HFS. In this work, we introduce and study the transfer and relaxation rates due to isotropic inelastic collisions with electrons, which enter the statistical equilibrium equations (SEE) for the atomic density matrix of this atomic model. Under the hypothesis that the electron-atom interaction is described by a dipolar operator, we provide useful relations between the rates describing the transfer and relaxation of quantum interference between different levels (whose numerical values are in most cases unknown) and the usual rates for the atomic level populations, for which experimental data and/or approximate theoretical expressions are generally available. For the particular case of a two-term atom with HFS, we present an analytical solution of the SEE for the spherical statistical tensors of the upper term, including both radiative and collisional processes, and we derive the expression of the emission coefficient in the four Stokes parameters. Finally, an illustrative application to the Na i D1 and D2 lines is presented. Title: Synoptic program to measure the evolution of the photospheric magnetic field during a solar cycle Authors: Ramelli, Renzo; Bianda, Michele; Berdyugina, Svetlana; Stenflo, Jan Olof; Belluzzi, Luca Bibcode: 2015IAUGA..2257074R Altcode: The solar photosphere is seething with a vast amount of magnetic flux tangled on scales much smaller than the resolution scale of solar telescopes that can be investigated by considering the Hanle effect. In 2007, near a minimum of the solar cycle, we started a synoptic program to explore possible variations of such hidden magnetic flux with the solar cycle, through the application of a differential Hanle effect technique on observations of scattering polarization in C2 molecular lines in the region around 514.0 nm. The observing program is still ongoing generally with the cadence of about one month. The observations obtained up to now, which include the recent maximum of the solar activity, don't show large variations of the turbulent unresolved magnetic field. If the apparent constancy is confirmed through the current cycle, than it will have important implications, since it provides hints on the existence of a local dynamo effect at granular and sub-granular scale, uncorrelated with the global magnetic field varying with the solar cycle. Title: CLASP: A UV Spectropolarimeter on a Sounding Rocket for Probing theChromosphere-Corona Transition Regio Authors: Ishikawa, Ryohko; Kano, Ryouhei; Winebarger, Amy; Auchere, Frederic; Trujillo Bueno, Javier; Bando, Takamasa; Narukage, Noriyuki; Kobayashi, Ken; Katsukawa, Yukio; Kubo, Masahito; Ishikawa, Shin-nosuke; Giono, Gabriel; Tsuneta, Saku; Hara, Hirohisa; Suematsu, Yoshinori; Shimizu, Toshifumi; Sakao, Taro; Ichimoto, Kiyoshi; Cirtain, Jonathan; De Pontieu, Bart; Casini, Roberto; Manso Sainz, Rafael; Asensio Ramos, Andres; Stepan, Jiri; Belluzzi, Luca Bibcode: 2015IAUGA..2254536I Altcode: The wish to understand the energetic phenomena of the outer solar atmosphere makes it increasingly important to achieve quantitative information on the magnetic field in the chromosphere-corona transition region. To this end, we need to measure and model the linear polarization produced by scattering processes and the Hanle effect in strong UV resonance lines, such as the hydrogen Lyman-alpha line. A team consisting of Japan, USA, Spain, France, and Norway has been developing a sounding rocket experiment called the Chromospheric Lyman-alpha Spectro-Polarimeter (CLASP). The aim is to detect the scattering polarization produced by anisotropic radiation pumping in the hydrogen Lyman-alpha line (121.6 nm), and via the Hanle effect to try to constrain the magnetic field vector in the upper chromosphere and transition region. In this talk, we will present an overview of our CLASP mission, its scientific objectives, ground tests made, and the latest information on the launch planned for the Summer of 2015. Title: A Sounding Rocket Experiment for the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) Authors: Kubo, M.; Kano, R.; Kobayashi, K.; Bando, T.; Narukage, N.; Ishikawa, R.; Tsuneta, S.; Katsukawa, Y.; Ishikawa, S.; Suematsu, Y.; Hara, H.; Shimizu, T.; Sakao, T.; Ichimoto, K.; Goto, M.; Holloway, T.; Winebarger, A.; Cirtain, J.; De Pontieu, B.; Casini, R.; Auchère, F.; Trujillo Bueno, J.; Manso Sainz, R.; Belluzzi, L.; Asensio Ramos, A.; Štěpán, J.; Carlsson, M. Bibcode: 2014ASPC..489..307K Altcode: A sounding-rocket experiment called the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is presently under development to measure the linear polarization profiles in the hydrogen Lyman-alpha (Lyα) line at 121.567 nm. CLASP is a vacuum-UV (VUV) spectropolarimeter to aim for first detection of the linear polarizations caused by scattering processes and the Hanle effect in the Lyα line with high accuracy (0.1%). This is a fist step for exploration of magnetic fields in the upper chromosphere and transition region of the Sun. Accurate measurements of the linear polarization signals caused by scattering processes and the Hanle effect in strong UV lines like Lyα are essential to explore with future solar telescopes the strength and structures of the magnetic field in the upper chromosphere and transition region of the Sun. The CLASP proposal has been accepted by NASA in 2012, and the flight is planned in 2015. Title: Theoretical Schemes for the Interpretation of Solar Polarimetric Observations: An Overview and Some New Ideas Authors: Landi Degl'Innocenti, E.; Belluzzi, L. Bibcode: 2014ASPC..489...99L Altcode: The theoretical scheme based on the density matrix formalism, and self-consistently derived from the principles of Quantum Electrodynamics, is presently one of the most solid frameworks for the interpretation of solar polarimetric observations. This scheme has been highly successful, mainly for the interpretation of polarimetric signals that can be described in the so-called limit of complete frequency redistribution (CRD). However, it suffers from the severe limitation that partial frequency redistribution (PRD) effects cannot be accounted for. The metalevel theory can handle PRD effects, but all the attempts for its generalization to account consistently for collisions and lower-level coherences have failed. The redistribution matrix approach is very suitable for taking PRD effects into account. However, it can consistently describe only two-level atoms with unpolarized lower level. New heuristic approaches have been proposed for treating two-term atoms, but they are based on rather crude approximations and their validity and physical consistency are far from being firmly established. Some few reflections that may lead to the establishment of a self-consistent set of equations, fully derived from first principles, are put forward. These reflections are based on the introduction of the Fourier transform of the density matrix. Title: On the Inversion of the Scattering Polarization and the Hanle Effect Signals in the Hydrogen Lyα Line Authors: Ishikawa, R.; Asensio Ramos, A.; Belluzzi, L.; Manso Sainz, R.; Štěpán, J.; Trujillo Bueno, J.; Goto, M.; Tsuneta, S. Bibcode: 2014ApJ...787..159I Altcode: 2014arXiv1404.0786I Magnetic field measurements in the upper chromosphere and above, where the gas-to-magnetic pressure ratio β 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 Lyα 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 Lyα 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 Lyα 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. Title: The transfer of resonance line polarization with partial frequency redistribution and J-state interference. Theoretical approach and numerical methods Authors: Belluzzi, L.; Trujillo Bueno, J. Bibcode: 2014A&A...564A..16B Altcode: 2014arXiv1403.1701B The linear polarization signals produced by scattering processes in strong resonance lines are rich in information on the magnetic and thermal structure of the chromosphere and transition region of the Sun and of other stars. A correct modeling of these signals requires accounting for partial frequency redistribution effects, as well as for the impact of quantum interference between different fine structure levels (J-state interference). In this paper, we present a theoretical approach suitable for modeling the transfer of resonance line polarization when taking these effects into account, along with an accurate numerical method of solution of the problem's equations. We consider a two-term atom with unpolarized lower term and infinitely sharp lower levels, in the absence of magnetic fields. We show that by making simple formal substitutions on the quantum numbers, the theoretical approach derived here for a two-term atom can also be applied to describe a two-level atom with hyperfine structure. An illustrative application to the Mg ii doublet around 2800 Å is presented. Title: A Key Physical Mechanism for Understanding the Enigmatic Linear Polarization of the Solar Ba II and Na I D1 Lines Authors: Belluzzi, Luca; Trujillo Bueno, Javier Bibcode: 2013ApJ...774L..28B Altcode: 2013arXiv1308.5422B The linearly polarized spectrum of the solar limb radiation produced by scattering processes is of great diagnostic potential for exploring the magnetism of the solar atmosphere. This spectrum shows an impressive richness of spectral details and enigmatic Q/I signals, whose physical origin must be clearly understood before they can be exploited for diagnostic purposes. The most enduring enigma is represented by the polarization signals observed in the D1 resonance lines of Na I (5896 Å) and Ba II (4934 Å), which were expected to be intrinsically unpolarizable. The totality of sodium and 18% of barium have hyperfine structure (HFS), and it has been argued that the only way to produce a scattering polarization signal in such lines is through the presence of a substantial amount of atomic polarization in their lower HFS levels. The strong sensitivity of these long-lived levels to depolarizing mechanisms led to the paradoxical conclusion that the observed D1-line polarization is incompatible with the presence in the lower solar chromosphere of inclined magnetic fields sensibly stronger than 0.01 G. Here we show that by properly taking into account the fact that the solar D1-line radiation has a non-negligible spectral structure over the short frequency interval spanned by the HFS transitions, it is possible to produce scattering polarization signals in the D1 lines of Na I and Ba II without the need of ground-level polarization. The resulting linear polarization is not so easily destroyed by elastic collisions and/or magnetic fields. Title: Chromospheric Lyman Alpha SpectroPolarimeter: CLASP Authors: Kobayashi, Ken; Kano, R.; Trujillo Bueno, J.; Winebarger, A. R.; Cirtain, J. W.; Bando, T.; De Pontieu, B.; Ishikawa, R.; Katsukawa, Y.; Kubo, M.; Narukage, N.; Sakao, T.; Tsuneta, S.; Auchère, F.; Asensio Ramos, A.; Belluzzi, L.; Carlsson, M.; Casini, R.; Hara, H.; Ichimoto, K.; Manso Sainz, R.; Shimizu, T.; Stepan, J.; Suematsu, Y.; Holloway, T. Bibcode: 2013SPD....44..142K Altcode: The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a VUV spectropolarimeter optimized for measuring the linear polarization of the Lyman-alpha line (121.6 nm). The Lyman-alpha line is predicted to show linear polarization caused by atomic scattering in the chromosphere and modified by the magnetic field through the Hanle effect. The Hanle effect is sensitive to weaker magnetic fields than Zeeman effect, and is not canceled by opposing fields, making it sensitive to tangled or unresolved magnetic field structures. These factors make the Hanle effect a valuable tool for probing the magnetic field in the chromosphere above the quiet sun. To meet this goal, CLASP is designed to measure linear polarization with 0.1% polarization sensitivity at 0.01 nm spectral resolution and 10" spatial resolution. CLASP is scheduled to be launched in 2015. Title: Theoretical formulation of Doppler redistribution in scattering polarization within the framework of the velocity-space density matrix formalism Authors: Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2013A&A...552A..72B Altcode: 2013arXiv1302.2887B 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 when 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 RI) 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. Title: Isotropic inelastic and superelastic collisional rates in a multiterm atom Authors: Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2013A&A...551A..84B Altcode: 2013arXiv1302.0990B 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 for the atomic density matrix of a multiterm atom. Under the hypothesis that the interaction between the collider and the atom 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, for which experimental data or approximate theoretical expressions are generally available. We show that the rates for populations and interference within the same J-level reduce to those previously obtained for the multilevel model atom (where quantum interference is assumed to be present only between magnetic sublevels pertaining to any given J-level). 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 the scattering line polarization through radiative transfer calculations in a slab of stellar atmospheric plasma anisotropically illuminated by the photospheric radiation field. Title: Anomalous Circular Polarization Profiles in the He I 1083.0 nm Multiplet from Solar Spicules Authors: Martínez González, M. J.; Asensio Ramos, A.; Manso Sainz, R.; Beck, C.; Belluzzi, L. Bibcode: 2012ApJ...759...16M Altcode: 2012arXiv1209.2589M 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. Title: Chromospheric Lyman-alpha spectro-polarimeter (CLASP) Authors: Kano, Ryouhei; Bando, Takamasa; Narukage, Noriyuki; Ishikawa, Ryoko; Tsuneta, Saku; Katsukawa, Yukio; Kubo, Masahito; Ishikawa, Shin-nosuke; Hara, Hirohisa; Shimizu, Toshifumi; Suematsu, Yoshinori; Ichimoto, Kiyoshi; Sakao, Taro; Goto, Motoshi; Kato, Yoshiaki; Imada, Shinsuke; Kobayashi, Ken; Holloway, Todd; Winebarger, Amy; Cirtain, Jonathan; De Pontieu, Bart; Casini, Roberto; Trujillo Bueno, Javier; Štepán, Jiří; Manso Sainz, Rafael; Belluzzi, Luca; Asensio Ramos, Andres; Auchère, Frédéric; Carlsson, Mats Bibcode: 2012SPIE.8443E..4FK Altcode: One of the biggest challenges in heliophysics is to decipher the magnetic structure of the solar chromosphere. The importance of measuring the chromospheric magnetic field is due to both the key role the chromosphere plays in energizing and structuring the outer solar atmosphere and the inability of extrapolation of photospheric fields to adequately describe this key boundary region. Over the last few years, significant progress has been made in the spectral line formation of UV lines as well as the MHD modeling of the solar atmosphere. It is found that the Hanle effect in the Lyman-alpha line (121.567 nm) is a most promising diagnostic tool for weaker magnetic fields in the chromosphere and transition region. Based on this groundbreaking research, we propose the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) to NASA as a sounding rocket experiment, for making the first measurement of the linear polarization produced by scattering processes and the Hanle effect in the Lyman-alpha line (121.567 nm), and making the first exploration of the magnetic field in the upper chromosphere and transition region of the Sun. The CLASP instrument consists of a Cassegrain telescope, a rotating 1/2-wave plate, a dual-beam spectrograph assembly with a grating working as a beam splitter, and an identical pair of reflective polarization analyzers each equipped with a CCD camera. We propose to launch CLASP in December 2014. Title: The Scattering Polarization of the Lyα Lines of H I and He II Taking into Account Partial Frequency Redistribution and J-state Interference Effects Authors: Belluzzi, Luca; Trujillo Bueno, Javier; Štěpán, Jiří Bibcode: 2012ApJ...755L...2B Altcode: 2012arXiv1207.0415B Recent theoretical investigations have pointed out that the cores of the Lyα lines of H I and He II should show measurable scattering polarization signals when observing the solar disk, and that the magnetic sensitivity, through the Hanle effect, of such linear polarization signals is suitable for exploring the magnetism of the solar transition region. Such investigations were carried out in the limit of complete frequency redistribution (CRD) and neglecting quantum interference between the two upper J-levels of each line. Here we relax both approximations and show that the joint action of partial frequency redistribution and J-state interference produces much more complex fractional linear polarization (Q/I) profiles, with large amplitudes in their wings. Such wing polarization signals turn out to be very sensitive to the temperature structure of the atmospheric model, so that they can be exploited for constraining the thermal properties of the solar chromosphere. Finally, we show that the approximation of CRD without J-state interference is however suitable for estimating the amplitude of the linear polarization signals in the core of the lines, where the Hanle effect operates. Title: The Chromospheric Lyman-Alpha SpectroPolarimeter: CLASP Authors: Kobayashi, K.; Kano, R.; Trujillo-Bueno, J.; Asensio Ramos, A.; Bando, T.; Belluzzi, L.; Carlsson, M.; De Pontieu, R. C. B.; Hara, H.; Ichimoto, K.; Ishikawa, R.; Katsukawa, Y.; Kubo, M.; Manso Sainz, R.; Narukage, N.; Sakao, T.; Stepan, J.; Suematsu, Y.; Tsuneta, S.; Watanabe, H.; Winebarger, A. Bibcode: 2012ASPC..456..233K Altcode: The magnetic field plays a crucial role in the chromosphere and the transition region, and our poor empirical knowledge of the magnetic field in the upper chromosphere and transition region is a major impediment to advancing the understanding of the solar atmosphere. The Hanle effect promises to be a valuable alternative to Zeeman effect as a method of measuring the magnetic field in the chromosphere and transition region; it is sensitive to weaker magnetic fields, and also sensitive to tangled, unresolved field structures.

CLASP is a sounding rocket experiment that aims to observe the Hanle effect polarization of the Lyman α (1215.67Å) line in the solar chromosphere and transition region, and prove the usefulness of this technique in placing constraints on the magnetic field strength and orientation in the low plasma-β region of the solar atmosphere. The Ly-α line has been chosen because it is a chromospheric/transition-region line, and because the Hanle effect polarization of this line is predicted to be sensitive to 10-250 Gauss, encompassing the range of interest. The CLASP instrument is designed to measure linear polarization in the Ly-α line with a polarization sensitivity of 0.1%. The instrument is currently funded for development. The optical design of the instrument has been finalized, and an extensive series of component-level tests are underway to validate the design. Title: The Polarization of the Solar Mg II h and k Lines Authors: Belluzzi, Luca; Trujillo Bueno, Javier Bibcode: 2012ApJ...750L..11B Altcode: 2012arXiv1203.4351B Although the h and k lines of Mg II are expected to be of great interest for probing the upper solar chromosphere, relatively little is known about their polarization properties which encode the information on the magnetic field. Here we report the first results of an investigation whose main goal is to understand the physical mechanisms that control the scattering polarization across these resonance lines and to achieve a realistic radiative transfer modeling in the presence of arbitrary magnetic fields. We show that the joint action of partial frequency redistribution (PRD) and quantum interference between the upper J-levels of the two lines produces a complex fractional linear polarization (Q/I) pattern with large polarization amplitudes in the blue and red wings, and a negative feature in the spectral region between the two lines. Another remarkable peculiarity of the Q/I profile is a conspicuous antisymmetric signal around the center of the h line, which cannot be obtained unless both PRD and J-state interference effects are taken into account. In the core of the k line, PRD effects alone produce a triplet peak structure in the Q/I profile, the modeling of which can also be achieved via the two-level atom approximation. In addition to the Hanle effect in the core of the k line, we also emphasize the diagnostic potential of the circular polarization produced by the Zeeman effect in the h and k lines, as well as in other Mg II lines located in their wings. Title: The Hanle Effect in the Lyα Lines of H I and He II for Measuring the Magnetic Fields of the Solar Transition Region Authors: Trujillo Bueno, J.; Štepán, J.; Belluzzi, L. Bibcode: 2012ASPC..456..225T Altcode: 2012ASPC..456..225B The Ly α lines of H I and He II are two of the spectral lines of choice for FUV and EUV channels of narrowband imagers on board sounding rockets and space telescopes, which provide spectacular intensity images of the outer solar atmosphere. Since the magnetic field information is encoded in the polarization of the spectral line radiation, it is important to investigate whether the ensuing Ly α radiation from the solar disk can be polarized, along with its magnetic sensitivity. Here we present some theoretical predictions concerning the amplitudes and magnetic sensitivities of the linear polarization signals produced by scattering processes in these strong emission lines of the solar transition region, taking into account radiative transfer and the Hanle effect caused by the presence of organized and random magnetic fields. We find that the line-center amplitudes of the fractional polarization signals vary typically between a fraction of a percent and ∼1%, depending on the Ly α line under consideration, the scattering geometry and the strength and orientation of the magnetic field. Interestingly, while the Ly α line of He II starts to be sensitive to the Hanle effect for magnetic strengths B>̰100 G the hydrogen Lyα line is mainly sensitive to magnetic strengths between 10 and 100 G. These results encourage the development of FUV and EUV polarimeters for sounding rockets and space telescopes with the aim of opening up a diagnostic window for magnetic field measurements in the upper chromosphere and transition region of the Sun. Title: The Lyα Lines of H I and He II: A Differential Hanle Effect for Exploring the Magnetism of the Solar Transition Region Authors: Trujillo Bueno, Javier; Štěpán, Jiří; Belluzzi, Luca Bibcode: 2012ApJ...746L...9T Altcode: 2011arXiv1112.4746T The Lyα line of He II at 304 Å is one of the spectral lines of choice for EUV channels of narrowband imagers on board space telescopes, which provide spectacular intensity images of the outer solar atmosphere. Since the magnetic field information is encoded in the polarization of the spectral line radiation, it is important to investigate whether the He II line radiation from the solar disk can be polarized, along with its magnetic sensitivity. Here we report some theoretical predictions concerning the linear polarization signals produced by scattering processes in this strong emission line of the solar transition region, taking into account radiative transfer and the Hanle effect caused by the presence of organized and random magnetic fields. We find that the fractional polarization amplitudes are significant (~1%), even when considering the wavelength-integrated signals. Interestingly, the scattering polarization of the Lyα line of He II starts to be sensitive to the Hanle effect for magnetic strengths B >~ 100 G (i.e., for magnetic strengths of the order of and larger than the Hanle saturation field of the hydrogen Lyα line at 1216 Å). We therefore propose simultaneous observations of the scattering polarization in both Lyα lines to facilitate magnetic field measurements in the upper solar chromosphere. Even the development of a narrowband imaging polarimeter for the He II 304 Å line alone would be already of great diagnostic value for probing the solar transition region. Title: Analytical maximum likelihood estimation of stellar magnetic fields Authors: Martínez González, M. J.; Manso Sainz, R.; Asensio Ramos, A.; Belluzzi, L. Bibcode: 2012MNRAS.419..153M Altcode: 2011MNRAS.tmp.1583M; 2011arXiv1108.4366M The polarized 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 polarized flux. In the 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 least-squares deconvolution (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 is analysed in depth. Title: The Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP)j Authors: Kobayashi, K.; Tsuneta, S.; Trujillo Bueno, J.; Bando, T.; Belluzzi, L.; Casini, R.; Carlsson, M.; Cirtain, J. W.; De Pontieu, B.; Hara, H.; Ichimoto, K.; Ishikawa, R.; Kano, R.; Katsukawa, Y.; Kim, T.; Kubo, M.; Manso Sainz, R.; Narukage, N.; Asensio Ramos, A.; Robinson, B.; Sakao, T.; Shimizu, T.; Stepan, J.; Suematsu, Y.; Watanabe, H.; West, E.; Winebarger, A. R. Bibcode: 2011AGUFM.P14C..05K Altcode: We present an overview of the Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) program. CLASP is a proposed sounding rocket experiment currently under development as collaboration between Japan, USA and Spain. The aim is to achieve the first measurement of magnetic field in the upper chromosphere and transition region of the Sun through the detection and measurement of Hanle effect polarization of the Lyman alpha line. The Hanle effect (i.e. the magnetic field induced modification of the linear polarization due to scattering processes in spectral lines) is believed to be a powerful tool for measuring the magnetic field in the upper chromosphere, as it is more sensitive to weaker magnetic fields than the Zeeman effect, and also sensitive to magnetic fields tangled at spatial scales too small to be resolved. The Lyman-alpha (121.567 nm) line has been chosen because it is a chromospheric/transition-region line, and because the Hanle effect polarization of the Lyman-alpha line is predicted to be sensitive to 10-250 Gauss, encompassing the range of interest. Hanle effect is predicted to be observable as linear polarization or depolarization, depending on the geometry, with a fractional polarization amplitude varying between 0.1% and 1% depending on the strength and orientation of the magnetic field. This quantification of the chromospheric magnetic field requires a highly sensitive polarization measurement. The CLASP instrument consists of a large aperture (287 mm) Cassegrain telescope mated to a polarizing beamsplitter and a matched pair of grating spectrographs. The polarizing beamsplitter consists of a continuously rotating waveplate and a linear beamsplitter, allowing simultaneous measurement of orthogonal polarizations and in-flight self-calibration. Development of the instrument is underway, and prototypes of all optical components have been tested using a synchrotron beamline. The experiment is proposed for flight in 2014. Title: The Impact of Quantum Interference between Different J-levels on Scattering Polarization in Spectral Lines Authors: Belluzzi, Luca; Trujillo Bueno, Javier Bibcode: 2011ApJ...743....3B Altcode: 2011arXiv1109.0424B The spectral line polarization produced by optically pumped atoms contains a wealth of information on the thermal and magnetic structure of a variety of astrophysical plasmas, including that of the solar atmosphere. A correct decoding of such information from the observed Stokes profiles requires a clear understanding of the effects that radiatively induced quantum interference (or coherence) between pairs of magnetic sublevels produces on these observables, in the absence of and in the presence of magnetic fields of arbitrary strength. Here we present a detailed theoretical investigation of the role of coherence between pairs of sublevels pertaining to different fine-structure J-levels, clarifying when it can be neglected for facilitating the modeling of the linear polarization produced by scattering processes in spectral lines. To this end, we apply the quantum theory of spectral line polarization and calculate the linear polarization patterns of the radiation scattered at 90° by a slab of stellar atmospheric plasma, both taking into account and neglecting the above-mentioned quantum interference. Particular attention is given to the 2 S - 2 P, 5 S - 5 P, and 3 P - 3 S multiplets. We point out the observational signatures of this kind of interference and analyze its sensitivity to the energy separation between the interfering levels, to the amount of emissivity in the background continuum radiation, to lower-level polarization, and to the presence of a magnetic field. Some interesting applications to the following spectral lines are also presented: Ca II H and K, Mg II h and k, Na I D1 and D2, the Ba II 4554 Å and 4934 Å resonance lines, the Cr I triplet at 5207 Å, the O I triplet at 7773 Å, the Mg I b-lines, and the Hα and Lyα lines of H I. Title: The Hanle Effect from Space for Measuring the Magnetic Fields of the Upper Solar Chromosphere Authors: Trujillo Bueno, J.; Stepan, J.; Belluzzi, L.; Manso Sainz, R. Bibcode: 2011AGUFM.P11F1626T Altcode: We present some theoretical predictions concerning the amplitudes and magnetic sensitivities of the linear polarization signals produced by scattering processes in some UV and FUV spectral lines of the upper chromosphere and transition region, such as Ly-alpha and Mg II k. To this end, we have calculated the atomic level polarization (population imbalances and quantum coherences) induced by anisotropic radiation pumping in semi-empirical and hydrodynamical models of the solar atmosphere, taking into account radiative transfer and the Hanle effect caused by the presence of organized and random magnetic fields. The amplitudes of the emergent linear polarization signals are found to vary typically between a fraction of a percent and a few percent, depending on the scattering geometry and the strength and orientation of the magnetic field. The results shown here encourage the development of UV polarimeters for sounding rockets and space telescopes with the aim of opening up a true diagnostic window for magnetic field measurements in the upper chromosphere and transition region of the Sun. Title: Overview of Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) Authors: Narukage, Noriyuki; Tsuneta, Saku; Bando, Takamasa; Kano, Ryouhei; Kubo, Masahito; Ishikawa, Ryoko; Hara, Hirohisa; Suematsu, Yoshinori; Katsukawa, Yukio; Watanabe, Hiroko; Ichimoto, Kiyoshi; Sakao, Taro; Shimizu, Toshifumi; Kobayashi, Ken; Robinson, Brian; Kim, Tony; Winebarger, Amy; West, Edward; Cirtain, Jonathan; De Pontieu, Bart; Casini, Roberto; Trujillo Bueno, Javier; Stepan, Jiri; Manso Sainz, Rafael; Belluzzi, Luca; Asensio Ramos, Andres; Carlsson, Mats Bibcode: 2011SPIE.8148E..0HN Altcode: 2011SPIE.8148E..16N The solar chromosphere is an important boundary, through which all of the plasma, magnetic fields and energy in the corona and solar wind are supplied. Since the Zeeman splitting is typically smaller than the Doppler line broadening in the chromosphere and transition region, it is not effective to explore weak magnetic fields. However, this is not the case for the Hanle effect, when we have an instrument with high polarization sensitivity (~ 0.1%). "Chromospheric Lyman- Alpha SpectroPolarimeter (CLASP)" is the sounding rocket experiment to detect linear polarization produced by the Hanle effect in Lyman-alpha line (121.567 nm) and to make the first direct measurement of magnetic fields in the upper chromosphere and lower transition region. To achieve the high sensitivity of ~ 0.1% within a rocket flight (5 minutes) in Lyman-alpha line, which is easily absorbed by materials, we design the optical system mainly with reflections. The CLASP consists of a classical Cassegrain telescope, a polarimeter and a spectrometer. The polarimeter consists of a rotating 1/2-wave plate and two reflecting polarization analyzers. One of the analyzer also works as a polarization beam splitter to give us two orthogonal linear polarizations simultaneously. The CLASP is planned to be launched in 2014 summer. Title: Spectropolarimetric forward modelling of the lines of the Lyman-series using a self-consistent, global, solar coronal model Authors: Khan, A.; Belluzzi, L.; Landi Degl'Innocenti, E.; Fineschi, S.; Romoli, M. Bibcode: 2011A&A...529A..12K Altcode: Context. The presence and importance of the coronal magnetic field is illustrated by a wide range of phenomena, such as the abnormally high temperatures of the coronal plasma, the existence of a slow and fast solar wind, the triggering of explosive events such as flares and CMEs.
Aims: We investigate the possibility of using the Hanle effect to diagnose the coronal magnetic field by analysing its influence on the linear polarisation, i.e. the rotation of the plane of polarisation and depolarisation.
Methods: We analyse the polarisation characteristics of the first three lines of the hydrogen Lyman-series using an axisymmetric, self-consistent, minimum-corona MHD model with relatively low values of the magnetic field (a few Gauss).
Results: We find that the Hanle effect in the above-mentioned lines indeed seems to be a valuable tool for analysing the coronal magnetic field. However, great care must be taken when analysing the spectropolarimetry of the Lα line, given that a non-radial solar wind and active regions on the solar disk can mimic the effects of the magnetic field, and, in some cases, even mask them. Similar drawbacks are not found for the Lβ and Lγ lines because they are more sensitive to the magnetic field. We also briefly consider the instrumental requirements needed to perform polarimetric observations for diagnosing the coronal magnetic fields.
Conclusions: The combined analysis of the three aforementioned lines could provide an important step towards better constrainting the value of solar coronal magnetic fields. Title: Polarized Radiative Transfer: from Solar Applications to Laboratory Experiments Authors: Landi Degl'Innocenti, E.; Belluzzi, L.; Bommier, V. Bibcode: 2011ASPC..437...45L Altcode: The theory of radiative transfer for polarized radiation, developed from Quantum Electrodynamics for the interpretation of solar observations, predicts the existence of a variety of physical phenomena that, in many cases, would deserve being directly tested through laboratory experiments, also in view of possible practical applications. In this report we will focus on the description of some of these atomic-physics phenomena that have been disregarded, or overlooked, in terrestrial laboratories. Title: Theoretical Approaches to the Physics of Spectral Line Polarization Authors: Belluzzi, L. Bibcode: 2011ASPC..437...29B Altcode: 2011arXiv1103.5394B Due to the continuous developments in polarimetric instrumentation, which will become even more dramatic in the near future with the availability of new generation solar telescopes, we are now severely confronted with a variety of new detailed observations of high diagnostic potential, whose interpretation requires a firmly established theoretical framework. In this contribution, I review the fundamental physical processes that underlie the generation and transfer of polarized radiation in stellar atmospheres, and I discuss the present status of the theoretical schemes now available, pointing out their main successes and limitations. I also present some ideas about the theoretical improvements that I consider necessary to achieve a correct interpretation of the complex phenomenology shown by polarimetric observations, focusing particularly on the second solar spectrum, which can be considered as one of the most important test benches of the theory. Title: Magnetic field diagnostics through the second solar spectrum: a spectroscopic analysis of the most polarizing atomic lines Authors: Belluzzi, L.; Landi Degl'Innocenti, E. Bibcode: 2010MmSAI..81..710B Altcode: Detailed observations of the second solar spectrum have shown a complex phenomenology whose detailed interpretation is still in a preliminary phase. The only certain thing is that the observed polarization is due to the phenomenon of resonance scattering. It is well known that such polarization can be strongly modified by the presence of a magnetic field through the so-called Hanle effect. It then follows that the second solar spectrum is, at least potentially, a fundamental instrument for diagnosing the intensity and topology of the weak magnetic fields lying in the higher layers of the solar atmosphere. Obviously, to fully exploit such potential, it is absolutely necessary to arrive at the correct theoretical interpretation, a task that has been revealed to involve many difficulties. We present an analysis of the second solar spectrum, carried out with the aim of investigating its general properties. The most interesting results concern an empirical classification of the wide variety of polarization signals that are observed, and the formulation of three empirical laws describing a series of properties common to the strongest signals. Title: On the physical origin of the second solar spectrum of the Sc II line at 4247 Å Authors: Belluzzi, L. Bibcode: 2009A&A...508..933B Altcode: 2009arXiv0909.5552B Context: The peculiar three-peak structure of the linear polarization profile shown in the second solar spectrum by the Ba ii line at 4554 Å has been interpreted as the result of the different contributions coming from the barium isotopes with and without hyperfine structure. In the same spectrum, a triple peak polarization signal is also observed in the Sc ii line at 4247 Å. Scandium has a single stable isotope (45Sc), which shows hyperfine structure due to a nuclear spin I = 7/2.
Aims: We investigate the possibility of interpreting the linear polarization profile shown in the second solar spectrum by this Sc ii line in terms of hyperfine structure.
Methods: A two-level model atom with hyperfine structure is assumed. Adopting an optically thin slab model, the role of atomic polarization and of hyperfine structure is investigated, avoiding the complications caused by radiative transfer effects. The slab is assumed to be illuminated from below by the photospheric continuum, and the polarization of the radiation scattered at 90° is investigated.
Results: The three-peak structure of the scattering polarization profile observed in this Sc ii line cannot be fully explained in terms of hyperfine structure.
Conclusions: Given the similarities between the Sc ii line at 4247 Å and the Ba ii line at 4554 Å, it is not clear why, within the same modeling assumptions, only the three-peak Q/I profile of the barium line can be fully interpreted in terms of hyperfine structure. The failure to interpret this Sc ii polarization signal raises important questions, whose resolution might lead to significant improvements in our understanding of the second solar spectrum. In particular, if the three-peak structure of the Sc ii signal is actually produced by a physical mechanism neglected within the approach considered here, it will be extremely interesting not only to identify this mechanism, but also to understand why it seems to be less important in the case of the barium line. Title: The Physical Origin and the Diagnostic Potential of the Scattering Polarization in the Li I Resonance Doublet at 6708 Å Authors: Belluzzi, Luca; Landi Degl'Innocenti, Egidio; Trujillo Bueno, Javier Bibcode: 2009ApJ...705..218B Altcode: 2009arXiv0909.3748B High-sensitivity measurements of the linearly polarized solar limb spectrum produced by scattering processes in quiet regions of the solar atmosphere showed that the Q/I profile of the lithium doublet at 6708 Å has an amplitude ~10-4 and a curious three-peak structure, qualitatively similar to that found and confirmed by many observers in the Na I D2 line. Given that a precise measurement of the scattering polarization profile of the lithium doublet lies at the limit of the present observational possibilities, it is worthwhile to clarify the physical origin of the observed polarization, its diagnostic potential, and what kind of Q/I shapes can be expected from theory. To this end, we have applied the quantum theory of atomic level polarization taking into account the hyperfine structure of the two stable isotopes of lithium, as well as the Hanle effect of a microturbulent magnetic field of arbitrary strength. We find that quantum interferences between the sublevels pertaining to the upper levels of the D2 and D1 line transitions of lithium do not cause any observable effect on the emergent Q/I profile. Our theoretical calculations show that only two Q/I peaks can be expected, with the strongest one caused by the D2 line of 7Li I and the weakest one due to the D2 line of 6Li I. Interestingly, we find that these two peaks in the theoretical Q/I profile stand out clearly only when the kinetic temperature of the thin atmospheric region that produces the emergent spectral line radiation is lower than 4000 K. The fact that such a thin atmospheric region is located around a height of 200 km in standard semi-empirical models, where the kinetic temperature is about 5000 K, leads us to suggest that the most likely Q/I profile produced by the Sun in the lithium doublet should be slightly asymmetric and dominated by the 7Li I peak. Title: The Sensitivity of the Second Solar Spectrum of the Li I 6708 Å Doublet to the Lithium Isotopic Abundance and to a Microturbulent Magnetic Field Authors: Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J. Bibcode: 2009ASPC..405..107B Altcode: The second solar spectrum offers a novel diagnostic window not only to explore the magnetic field of our nearest star, but also to determine the atomic and isotopic abundances in the solar atmosphere. A very interesting example, concerning this second aspect, is the Li I resonance doublet at 6708~Å. Here we present a detailed theoretical investigation, carried out within the framework of the density matrix formalism, on the atomic physics that is involved in the generation of the observed Q/I profile, which is the result of a complex blend of the D_1 and D_2 lines of the two stable isotopes of lithium (^6Li and ^7Li), both showing hyperfine structure. We discuss the diagnostic potential of this linear polarization profile for the determination of the lithium isotopic abundance in the quiet Sun, and we investigate the magnetic sensitivity of this profile to a microturbulent magnetic field. Title: Observations of the Joint Action of the Hanle and Zeeman Effects in the D_2 Line of Ba II Authors: Ramelli, R.; Bianda, M.; Trujillo Bueno, J.; Belluzzi, L.; Landi Degl'Innocenti, E. Bibcode: 2009ASPC..405...41R Altcode: 2009arXiv0906.2320R We show a selection of high-sensitivity spectropolarimetric observations obtained over the last few years in the Ba II D_2-line with the Zürich Imaging Polarimeter (ZIMPOL) attached to the Gregory Coudé 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. Title: A spectroscopic analysis of the most polarizing atomic lines of the second solar spectrum Authors: Belluzzi, L.; Landi Degl'Innocenti, E. Bibcode: 2009A&A...495..577B Altcode: We present an analysis of the second solar spectrum, as plotted in graphical form in the three volumes of the atlas “The Second Solar Spectrum”, in the wavelength range between 3160 Å and 6995 Å. All the strongest positive linear polarization signals produced by atomic spectral lines are identified, and their amplitudes are listed, along with the most relevant spectroscopic properties of the lines. The various signals are divided into five classes according to the shape of their Q/I profiles. Three empirical rules are formulated from the analysis of the amplitude and shape of the various signals, and of the spectroscopic properties of the spectral lines.

Tables 1 and 2 are only available in electronic form at http://www.aanda.org