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The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the three-dimensional (3D) radiative transfer out of local thermodynamic equilibrium (NLTE), the task becomes extremely computationally expensive. Instead of generalizing 1D methods to 3D, we have developed a new approach to the inverse problem. In our meshfree method, we do not consider the requirement of 3D\,NLTE consistency as an obstacle, but as a natural regularization with respect to the traditional pixel-by-pixel methods. This leads to more robust and less ambiguous solutions. We solve the 3D\,NLTE inverse problem as an unconstrained global minimization problem that avoids repetitive evaluations of the $\Lambda$ operator. Apart from the 3D\,NLTE consistency, the method allows us to easily include additional conditions of physical consistency such as the zero divergence of the magnetic field. Stochastic ingredients make the method less prone to ending up within the local minima of the loss function. Our method is capable of solving the inverse problem faster by several orders of magnitude than by using grid-based methods. The method can provide accurate and physically consistent results if sufficient computing time is available, along with approximate solutions in the case of very complex plasma structures or limited computing time., Comment: 18 pages, 13 figures, accepted for publication in A&A

The Mg II h and k lines are among the strongest in the near-ultraviolet solar spectrum and their line core originates in the upper chromosphere, just below the transition region. Consequently, they have become one of the main targets for investigating the magnetism of the upper solar atmosphere. The recent CLASP2 mission obtained unprecedented spectropolarimetric data of these lines in an active region plage, which have already been used to infer the longitudinal component of the magnetic field by applying the weak field approximation. In this paper, we aim at improving our understanding of the diagnostic capabilities of these lines by studying the emergent Stokes profiles resulting from radiative transfer calculations in a radiative magneto-hydrodynamic (rMHD) time-dependent model representative of a solar plage. To this end, we create a synthetic observation with temporal and spatial resolutions similar to those of CLASP2. We find strong asymmetries in the circular polarization synthetic profiles which considerably complicate the application of the weak field approximation. We demonstrate that the selective application of the weak field approximation to fit different spectral regions in the profile allows to retrieve information about the longitudinal component of the magnetic field at different regions of the model atmosphere, even when the circular polarization profiles are not anti-symmetric and are formed in the presence of strong velocity and magnetic field gradients., Comment: Accepted for publication in ApJ

When observed in quiet regions close to the solar limb, many strong resonance lines show conspicuous linear polarization signals, produced by scattering processes, with extended wing lobes. Recent studies indicate that, contrary to what was previously believed, the wing lobes are sensitive to the presence of relatively weak longitudinal magnetic fields through magneto-optical (MO) effects. We theoretically investigate the sensitivity of the scattering polarization wings of the Ca I 4227 {\AA} line to the MO effects, and we explore its diagnostic potential for inferring information on the longitudinal component of the photospheric magnetic field. We calculate the intensity and polarization profiles of the Ca I 4227 {\AA} line by numerically solving the problem of the generation and transfer of polarized radiation under non-local thermodynamic equilibrium conditions in one-dimensional semi-empirical models of the solar atmosphere, taking into account the joint action of the Hanle, Zeeman, and MO effects. We consider volume-filling magnetic fields as well as magnetic fields occupying a fraction of the resolution element. In contrast to the circular polarization signals produced by the Zeeman effect, we find that the linear polarization angle in the scattering polarization wings of Ca I 4227 presents a clear sensitivity, through MO effects, not only to the flux of the photospheric magnetic field, but also to the fraction of the resolution element that the magnetic field occupies. We identify the linear polarization angle in the wings of strong resonance lines as a valuable observable for diagnosing unresolved magnetic fields. Used in combination with observables that encode information on the magnetic flux and other properties of the observed atmospheric region, it can provide constraints on the filling factor of the magnetic field., Comment: 9 pages, 9 figures

We study the circular polarization of the Mn i resonance lines at 279.56, 279.91, and 280.19 nm (hereafter, UV multiplet) by means of radiative transfer modeling. In 2019, the CLASP2 mission obtained unprecedented spectropolarimetric data in a region of the solar ultraviolet including the Mg ii h and k resonance lines and two lines of a subordinate triplet, as well as two Mn i resonance lines. The first analysis of such data, in particular those corresponding to a plage region, allowed the inference of the longitudinal magnetic field from the photosphere to the upper chromosphere just below the transition region. This was achieved by applying the weak field approximation to the circular polarization profiles of the Mg ii and Mn i lines. While the applicability of this approximation to the Mg ii lines was already demonstrated in previous works, this is not the case for the Mn i UV multiplet. These lines are observed as absorptions between the Mg ii h and k lines, a region whose intensity is shaped by their partial frequency redistribution effects. Moreover, the only Mn i stable isotope has nuclear spin I = 5/2 and thus hyperfine structure must be, a priori, taken into account. Here we study the generation and transfer of the intensity and circular polarization of the Mn i resonance lines accounting for these physical ingredients. We analyze their sensitivity to the magnetic field by means of their response function, and we demonstrate the applicability of the weak field approximation to determine the longitudinal component of the magnetic field.

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., Comment: Main article has a length of 5 pages and contains 2 figures. Supplemental Material has a length of 6 pages and contains 3 figures. Note that the main article and the Supplemental Material have separate reference lists. Article published in open access by Physical Review Letters on 18/08/2021; Link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.081101

The Zeeman effect is of limited utility for probing the magnetism of the quiet solar chromosphere. The Hanle effect in some spectral lines is sensitive to such magnetism, but the interpretation of the scattering polarization signals requires taking into account that the chromospheric plasma is highly inhomogeneous and dynamic (i.e., that the magnetic field is not the only cause of symmetry breaking). Here we investigate the reliability of a well-known formula for mapping the azimuth of chromospheric magnetic fields directly from the scattering polarization observed in the \ion{Ca}{2}~8542~\AA\, line, which is typically in the saturation regime of the Hanle effect. To this end, we use the Stokes profiles of the \ion{Ca}{2}~8542~\AA\, line computed with the PORTA radiative transfer code in a three-dimensional (3D) model of the solar chromosphere, degrading them to mimic spectropolarimetric observations for a range of telescope apertures and noise levels. The simulated observations are used to obtain the magnetic field azimuth at each point of the field of view, which we compare with the actual values within the 3D model. We show that, apart from intrinsic ambiguities, the method provides solid results. Their accuracy depends more on the noise level than on the telescope diameter. Large-aperture solar telescopes, like DKIST and EST, are needed to achieve the required noise-to-signal ratios using reasonable exposure times., Comment: Accepted for publication in ApJ, 8 pages, 4 figures

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., 50 pages, 11 figures, 1 table, published in Science Advances

Chromospheric LAyer Spectro-Polarimeter (CLASP2) was a sounding rocket experiment, which is a follow-up mission to the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP1) in 2015. To measure the magnetic fields in the upper solar atmosphere in a highly quantitative manner, CLASP2 changes the target wavelengths from the hydrogen Ly-α line (121.567 nm) to Mg II lines near 280 nm. We reused the main structure and most of the optical components in the CLASP1 instrument, which reduced the turnaround time and cost. We added a magnifying optical system to maintain the wavelength resolution, even at the longer wavelength of CLASP2. Here, we describe the optical design and performance of the CLASP2 instrument.

Accurate angular quadratures are crucial for the numerical solution of three-dimensional (3D) radiative transfer problems, especially when the spectral line polarisation produced by the scattering of anisotropic radiation is included. There are two requirements for obtaining an optimal quadrature and they are difficult to satisfy simultaneously: high accuracy and short computing time. By imposing certain symmetries, we were recently able to derive a set of near optimal angular quadratures. Here, we extend our previous investigation by considering other symmetries. Moreover, we test the performance of our new quadratures by numerically solving a radiative transfer problem of resonance line polarisation in a 3D model of the solar atmosphere resulting from a magneto-hydrodynamical simulation. The new angular quadratures derived here outperform the previous ones in terms of the number of rays needed to achieve any given accuracy., Comment: 6 pages, 4 figures; published version in A&A

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 A, the hydrogen Lyman- $\alpha$ line at 1216 A, and the Lyman- $\alpha$ line of He ii at 304 A. 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.

第19回宇宙科学シンポジウム (2019年1月9日-10日. 宇宙航空研究開発機構宇宙科学研究所(JAXA)(ISAS)相模原キャンパス), 相模原市, 神奈川県, 19th Space Science Symposium (January 9-10, 2019. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency(JAXA)(ISAS)Sagamihara Campus), Sagamihara, Kanagawa Japan, 著者人数: 18名, 資料番号: SA6000144104, レポート番号: P-069

In three-dimensional (3D) radiative transfer (RT) problems, the tensor product quadratures are generally not optimal in terms of the number of discrete ray directions needed for a given accuracy of the angular integration of the radiation field. In this paper, we derive a new set of angular quadrature rules that are more suitable for solving 3D RT problems with the short- and long-characteristics formal solvers. These quadratures are more suitable than the currently used ones for the numerical calculation of the radiation field tensors that are relevant in the problem of the generation and transfer of polarised radiation without assuming local thermodynamical equilibrium (non-LTE). We show that our new quadratures can save up to about 30\,\% of computing time with respect to the Gaussian-trapezoidal product quadratures with the same accuracy., 7 pages, 3 figures, 2 tables; accepted for publication in A&A

Chromospheric LAyer Spectro-Polarimeter (CLASP2) is our next sounding rocket experiment after the success of Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP1). CLASP2 is scheduled to launch in 2019, and aims to achieve high precision measurements of the linear and circular polarizations in the Mg II h & k lines near the 280 nm, whose line cores originate in the upper solar chromosphere. The CLASP2 spectro-polarimeter follows very successful design concept of the CLASP1 instrument with the minimal modification. A new grating was fabricated with the same radius of curvature as the CLASP1 grating, but with a different ruling density. This allows us to essentially reuse the CLASP1 mechanical structures and layout of the optics. However, because the observing wavelength of CLASP2 is twice longer than that of CLASP1, a magnifier optical system was newly added in front of the cameras to double the focal length of CLASP2 in order to maintain the same wavelength resolution as CLASP1 (0.01 nm). Meanwhile, a careful optical alignment of the specto-polarimeter is required to reach the 0.01 nm wavelength resolution. Therefore, we established an efficient alignment procedure for the CLASP2 spectro-polarimeter based on an experience of CLASP1. Here, we explain in detail the methods for achieving the optical alignment of the CLASP2 spectro-polarimeter and discuss our results by comparing with the performance requirements.

The solar abundances of Fe and of the CNO elements play an important role in addressing a number of important issues such as the formation, structure, and evolution of the Sun and the solar system, the origin of the chemical elements, and the evolution of stars and galaxies. Despite the large number of papers published on this issue, debates about the solar abundances of these elements continue. The aim of the present investigation is to quantify the impact of photospheric magnetic fields on the determination of the solar chemical abundances. To this end, we used two 3D snapshot models of the quiet solar photosphere with a different magnetization taken from recent magneto-convection simulations with small-scale dynamo action. Using such 3D models we have carried out spectral synthesis for a large set of Fei, Ci, Ni, and Oi lines, in order to derive abundance corrections caused by the magnetic, Zeeman broadening of the intensity profiles and the magnetically induced changes of the photospheric temperature structure. We find that if the magnetism of the quiet solar photosphere is mainly produced by a small-scale dynamo, then its impact on the determination of the abundances of iron, carbon, nitrogen and oxygen is negligible.

N. Narukage et al. ; 12 pags., 5 figs., 3 tabs., 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 (Ly¿; 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). © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only., We acknowledge M. Hasumoto and K. Tanaka at the, Institute for Molecular Science S. Kimura at Osaka University, and K. Fukui at Fukui University for their support of our experiment at Ultraviolet Synchrotron Orbital Radiation Facility (UVSOR). Japanese participation for CLASP1 and CLASP2 is funded by the basic research program of ISAS/JAXA, internal research funding of NAOJ, and JSPS KAK- ENHI Grant Numbers 23340052, 24740134, 24340040, 25220703, and 16H03963. US participation for CLASP1 is funded by NASA Low Cost Access to Space (Award Number 12-SHP 12/2-0283). Spanish participation for CLASP1 is funded by the Ministry of Economy and Competitiveness through project AYA2010-18029 (Solar Magnetism and Astrophysical Spectropolarimetry). French hardware participation for CLASP1 was funded by Centre National d'Etudes Spatiales (CNES).

A few years before the Hinode space telescope was launched, an investigation based on the Hanle effect in atomic and molecular lines indicated that the bulk of the quiet solar photosphere is significantly magnetized, due to the ubiquitous presence of an unresolved magnetic field with an average strength = 130 G. It was pointed out also that this "hidden" field must be much stronger in the intergranular regions of solar surface convection than in the granular regions, and it was suggested that this unresolved magnetic field could perhaps provide the clue for understanding how the outer solar atmosphere is energized. In fact, the ensuing magnetic energy density is so significant that the energy flux estimated using the typical value of 1 km/s for the convective velocity (thinking in rising magnetic loops) or the Alfven speed (thinking in Alfven waves generated by magnetic reconnection) turns out to be substantially larger than that required to balance the chromospheric energy losses. Here we present a brief review of the research that led to such conclusions, with emphasis on a new three-dimensional radiative transfer investigation aimed at determining the magnetization of the quiet Sun photosphere from the Hanle effect in the Sr I 460,7 nm line and the Zeeman effect in FeI lines., Invited talk in IAU Symposium 294 on Solar and Astrophysical Dynamos; IAU General Assembly, Beijing 2012

We report on a detailed radiative transfer modeling of the observed scattering polarization in the H-alpha line, which allows us to infer quantitative information on the magnetization of the quiet solar chromosphere. Our analysis suggests the presence of a magnetic complexity zone with a mean field strength > 30 G lying just below the sudden transition region to the coronal temperatures. The chromospheric plasma directly underneath is very weakly magnetized, with ~ 1 G. The possible existence of this abrupt change in the degree of magnetization of the upper chromosphere of the quiet Sun might have large significance for our understanding of chromospheric (and, therefore, coronal) heating., 12 pages, 3 figures, accepted for publication in The Astrophysical Journal Letters (2010)

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 A 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 D_2 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 D_2 and D_1 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 D_2 line of ^7Li I and the weakest one due to the D_2 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 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., Comment: 9 pages, 7 figures, and 2 tables. Accepted for publication in The Astrophysical Journal (ApJ)

Velocity oscillations "measured" simultaneously at the photosphere and the chromosphere -from time series of spectropolarimetric data in the 10830 A region- of different solar magnetic features allow us to study the properties of wave propagation as a function of the magnetic flux of the structure (i.e. two different-sized sunspots, a tiny pore and a facular region). While photospheric oscillations have similar characteristics everywhere, oscillations measured at chromospheric heights show different amplitudes, frequencies and stages of shock development depending on the observed magnetic feature. The analysis of the power and the phase spectra, together with simple theoretical modeling, lead to a series of results concerning wave propagation within the range of heights of this study. We find that, while the atmospheric cut-off frequency and the propagation properties of the different oscillating modes depend on the magnetic feature, in all the cases the power that reaches the high chromosphere above the atmospheric cut-off comes directly from the photosphere by means of linear vertical wave propagation rather than from non-linear interaction of modes., Comment: Accepted for publication in The Astrophysical Journal. 29 pages, 9 figures, 12pt, preprint

Polarized light provides the most reliable source of information at our disposal for diagnosing the physical properties of astrophysical plasmas, including the magnetic fields of the solar atmosphere. The interaction between radiation and hydrogen plus free electrons through Rayleigh and Thomson scattering gives rise to the polarization of the stellar continuous spectrum, which is very sensitive to the medium's thermal and density structure. Anisotropic radiative pumping processes induce population imbalances and quantum coherences among the sublevels of degenerate energy levels (that is, atomic level polarization), which produce polarization in spectral lines without the need of a magnetic field. The Hanle effect caused by the presence of relatively weak magnetic fields modifies the atomic polarization of the upper and lower levels of the spectral lines under consideration, allowing us to detect magnetic fields to which the Zeeman effect is blind. After discussing the physical origin of the polarized radiation in stellar atmospheres, this paper highlights some recent developments in polarized radiation diagnostic methods and a few examples of their application in solar physics.

One of the greatest challenges in solar and stellar physics in coming years will be to observe the Second Solar Spectrum with a spatial resolution significantly better than 1 arcsec. This type of scattering polarization observations would probably allow us to discover hitherto unknown aspects of the Sun's hidden magnetism. Here we report on some theoretical predictions for the photospheric line of Sr I at 4607 \AA, which we have obtained by solving the three-dimensional (3D) radiative transfer problem of scattering line polarization in a realistic hydrodynamical model of the solar photosphere. We have taken into account not only the anisotropy of the radiation field in the 3D medium and the Hanle effect of a tangled magnetic field, but also the symmetry breaking effects caused by the horizontal atmospheric inhomogeneities produced by the solar surface convection. Interestingly, the Q/I and U/I linear polarization signals of the emergent spectral line radiation have sizable values and fluctuations, even at the very center of the solar disk where we meet the forward scattering case. The ensuing small-scale patterns in Q/I and U/I turn out to be sensitive to the assumed magnetic field model, and are of great diagnostic value. We argue that it should be possible to observe them with the help of a 1-m telescope equipped with adaptive optics and a suitable polarimeter., Comment: Accepted for publication in The Astrophysical Journal Letters (12 pages and 2 color figures)

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

This paper summarizes the results of a recent investigation on the Hanle effect in atomic and molecular lines, which indicates that there is a vast amount of “hidden” magnetic energy and (unsigned) magnetic flux in the internetwork regions of the quiet solar photosphere. This hidden magnetic energy, localized in the (intergranular) downflowing plasma of the solar photosphere, is carried mainly by tangled fields at sub-resolution scales with strengths between the equipartition field values and ∼1 kG, and is more than sufficient to compensate the radiative energy losses of the solar outer atmosphere.

19 pags.; 3 figs.; 8 tabs., Depolarizing collisions are elastic or quasielastic collisions that equalize the populations and destroy the coherence between the magnetic sublevels of atomic levels. In astrophysical plasmas, the main depolarizing collider is neutral hydrogen. We consider depolarizing rates on the lowest levels of neutral and singly ionized alkali earths Mg I, Sr I, Ba I, Mg II, Ca II, and Ba II, due to collisions with H°. We compute ab initio potential curves of the atom-H° system and solve the quantum mechanical dynamics. From the scattering amplitudes, we calculate the depolarizing rates for Maxwellian distributions of colliders at temperatures T ≤ 10,000 K. A comparative analysis of our results and previous calculations in the literature is completed. We discuss the effect of these rates on the formation of scattering polarization patterns of resonant lines of alkali earths in the solar atmosphere, and their effect on Hanle effect diagnostics of solar magnetic fields. © 2014. The American Astronomical Society. All rights reserved.., Financial support by the Spanish Ministry of Economy and Competitiveness through projects CONSOLIDER INGENIO CSD2009-00038 (Molecular Astrophysics: The Herschel and Alma Era), FIS2011-29596-C02 and AYA2010–18029 is gratefully acknowledged.

A sounding-rocket program called the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is proposed to be launched in the summer of 2014. CLASP will observe the solar chromosphere in Ly-alpha (121.567 nm), aiming to detect the linear polarization signal produced by scattering processes and the Hanle effect for the first time. The polarimeter of CLASP consists of a rotating half-waveplate, a beam splitter, and a polarization analyzer. Magnesium Fluoride (MgF2) is used for these optical components, because MgF2 exhibits birefringent property and high transparency at ultraviolet wavelength. The development and comprehensive testing program of the optical components of the polarimeter is underway using the synchrotron beamline at the Ultraviolet Synchrotron Orbital Radiation Facility (UVSOR). The first objective is deriving the optical constants of MgF2 by the measurement of the reflectance and transmittance against oblique incident angles for the s-polarized and the p-polarized light. The ordinary refractive index and extinction coefficient along the ordinary and extraordinary axes are derived with a least-square fitting in such a way that the reflectance and transmittance satisfy the Kramers-Kronig relation. The reflection at the Brewster's Angle of MgF2 plate is confirmed to become a good polarization analyzer at Ly-alpha. The second objective is the retardation measurement of a zeroth-order waveplate made of MgF2. The retardation of a waveplate is determined by observing the modulation amplitude that comes out of a waveplate and a polarization analyzer. We tested a waveplate with the thickness difference of 14.57 um. The 14.57 um waveplate worked as a half-waveplate at 121.74 nm. We derived that a waveplate with the thickness difference of 15.71 um will work as a half-waveplate at Ly-alpha wavelength. We developed a prototype of CLASP polarimeter using the MgF2 half-waveplate and polarization analyzers, and succeeded in obtaining the modulation patterns that are consistent with the theoretical prediction. We confirm that the performance of the prototype is optimized for measuring linear polarization signal with the least effect of the crosstalk from the circular polarization.

This paper presents the results of a detailed theoretical investigation of the iron line formation NLTE problem in a three-dimensional model of the solar photosphere, which we have obtained from a very recent radiation hydrodynamics simulation of solar surface convection. In this first paper we have neglected the effects of horizontal radiative transfer on the atomic level populations, but we have considered a realistic atomic model for iron that contains hundreds of radiative transitions from the UV to the IR. The self-consistent solutions of the kinetic and transfer equations have been obtained with a new NLTE code, which is based on very efficient iterative methods. We find that overionization due to the near-UV radiation field does take place but mainly in the granular atmospheric regions. This well-known NLTE mechanism tends to produce underpopulation of all the Fe I levels and a very small overexcitation of the Fe II levels. All over the three-dimensional photospheric model Fe II is the dominant ionization stage. We find significant LTE versus NLTE discrepancies mainly for the low-excitation Fe I lines. This applies to both the vertically emergent profiles from the granular regions and also to the spatially averaged profiles. These discrepancies are due to the line opacity deficits that result from the aforementioned underpopulation of the Fe I levels. The emergent profiles of the low-excitation lines of Fe I are thus weaker in NLTE than in LTE. In particular, the largest errors in the equivalent widths (due to the LTE assumption) are found for the weakest low-excitation lines of Fe I. We also give quantitative estimates of the errors in the temperature structure of semiempirical solar granulation models obtained via the application of LTE inversion techniques to several groups of Fe I lines. For instance, the widely used Fe I 6301 and 6302 A lines tend to lead to an overestimation of about 100-200 K in the granular regions but to a similar underestimation in the intergranular plasma. The present paper considers also the case of the Sun observed with low spatial resolution, with particular emphasis on the long-standing iron abundance problem. We show that it is possible to obtain a very good fit to the observed spectral line shapes by slightly changing the iron abundance (for both the LTE and NLTE cases). In general, the iron abundance we need for reaching the best NLTE fit to observed equivalent widths is 0.074 ± 0.03 dex larger than that needed to obtain the best LTE fit. Our most relevant conclusion with regard to the solar iron abundance issue is the following: if NLTE effects are fully taken into account in the three-dimensional model of the solar photosphere, we obtain the meteoritic iron abundance value (AFe = 7.50). However, if the abundance analysis is done assuming LTE, we find AFe = 7.43, in close agreement with the recent LTE analysis of Asplund and collaborators. Our results do indicate that NLTE effects are significant but not above the 0.1 dex level in the Sun. We consider our NLTE result for the iron abundance as an additional hint of the realism of such three-dimensional hydrodynamic simulations. We conclude that the success of the LTE fitting approach is no proof that NLTE effects are negligible because the existing NLTE effects are compensated for in the LTE analysis by a change in the derived iron abundance. The paper ends emphasizing the great importance of a full three-dimensional NLTE approach in order to be able to lead to new advances in the field of quantitative stellar spectroscopy and, in particular, for a correct derivation of elemental abundance ratios in the atmospheres of metal-poor stars.

This paper shows how to generalize to non-LTE polarization transfer some operator splitting methods that were originally developed for solving unpolarized transfer problems. These are the Jacobi-based accelerated Λ-iteration (ALI) method of Olson, Auer, & Buchler and the iterative schemes based on Gauss-Seidel and successive overrelaxation (SOR) iteration of Trujillo Bueno and Fabiani Bendicho. The theoretical framework chosen for the formulation of polarization transfer problems is the quantum electrodynamics (QED) theory of Landi Degl'Innocenti, which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. This first paper establishes the grounds of our numerical approach to non-LTE polarization transfer by concentrating on the standard case of scattering line polarization in a gas of two-level atoms, including the Hanle effect due to a weak microturbulent and isotropic magnetic field. We begin demonstrating that the well-known Λ-iteration method leads to the self-consistent solution of this type of problem if one initializes using the "exact" solution corresponding to the unpolarized case. We show then how the above-mentioned splitting methods can be easily derived from this simple Λ-iteration scheme. We show that our SOR method is 10 times faster than the Jacobi-based ALI method, while our implementation of the Gauss-Seidel method is 4 times faster. These iterative schemes lead to the self-consistent solution independently of the chosen initialization. The convergence rate of these iterative methods is very high; they do not require either the construction or the inversion of any matrix, and the computing time per iteration is similar to that of the Λ-iteration method.

The possible generation of linear polarization in spectral lines due to depopulation-pumping processes in stellar atmospheres is investigated within the framework of a quantum electrodynamic theory for the transfer of polarized radiation based on the atomic density-matrix formalism. It is shown that the radiation field's anisotropy in solar-like atmospheres induces population imbalances among the lower level sublevels of optical line transitions. The depolarizing rates that are assumed to model some typical spectral lines are not capable of completely destroying such a lower level atomic alignment, and the corresponding linear polarization signals are found to lie above the sensitivity limit of some recently developed spectropolarimeters.

We study in some detail one-dimensional NLTE effects in solar Fei lines. The lines selected are frequently used in solar polarimetry, and also in studies of line asymmetries and for abundance determinations. Our model atom for Fei–Feii–Feiii is realistic: it takes account of multiplet structure and it includes over 200 bound–bound and bound–free transitions in detail. We use very efficient iterative methods for the self-consistent solution of the kinetic and radiative transfer equations (Auer, Fabiani Bendicho, and Trujillo Bueno, 1994). We have applied these fast methods of solution because they are suitable for the investigation of 2D and 3D NLTE transfer effects with multilevel atoms, which constitutes the next step of our ongoing research project on the iron line formation problem.

We present an overview of solar sounding rocket instruments developed jointly by NASA Marshall Space Flight Center and the University of Alabama in Huntsville. The High Resolution Coronal Imager (Hi-C) is an EUV (19.3 nm) imaging telescope which was flown successfully in July 2012. The Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) is a Lyman Alpha (121.6 nm) spectropolarimeter developed jointly with the National Astronomical Observatory of Japan and scheduled for launch in 2015. The Marshall Grazing Incidence X-ray Spectrograph is a soft X-ray (0.5-1.2 keV) stigmatic spectrograph designed to achieve 5 arcsecond spatial resolution along the slit.

The interpretation of the intensity and polarization of the spectral line radiation produced in the atmosphere of the Sun and of other stars requires solving a radiative transfer problem that can be very complex, especially when the main interest lies in modeling the spectral line polarization produced by scattering processes and the Hanle and Zeeman effects. One of the difficulties is that the plasma of a stellar atmosphere can be highly inhomogeneous and dynamic, which implies the need to solve the non-equilibrium problem of the generation and transfer of polarized radiation in realistic three-dimensional (3D) stellar atmospheric models. Here we present PORTA, an efficient multilevel radiative transfer code we have developed for the simulation of the spectral line polarization caused by scattering processes and the Hanle and Zeeman effects in 3D models of stellar atmospheres. The numerical method of solution is based on the non-linear multigrid iterative method and on a novel short-characteristics formal solver of the Stokes-vector transfer equation which uses monotonic B\'ezier interpolation. Therefore, with PORTA the computing time needed to obtain at each spatial grid point the self-consistent values of the atomic density matrix (which quantifies the excitation state of the atomic system) scales linearly with the total number of grid points. Another crucial feature of PORTA is its parallelization strategy, which allows us to speed up the numerical solution of complicated 3D problems by several orders of magnitude with respect to sequential radiative transfer approaches, given its excellent linear scaling with the number of available processors. The PORTA code can also be conveniently applied to solve the simpler 3D radiative transfer problem of unpolarized radiation in multilevel systems., Comment: 15 pages, 15 figures, to appear in Astronomy and Astrophysics

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 A) and Ba II (4934 A), 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., Comment: Accepted for publication in The Astrophysical Journal Letters

We highlight the main results of a three-dimensional (3D) multilevel radiative transfer investigation about the solar disk-center polarization of the Ca {\sc ii} 8542 \AA\ line. First, we investigate the linear polarization due to the atomic level polarization produced by the absorption and scattering of anisotropic radiation in a 3D model of the solar atmosphere, taking into account the symmetry breaking effects caused by its thermal, dynamic and magnetic structure. Second, we study the contribution of the Zeeman effect to the linear and circular polarization. Finally, we show examples of the Stokes profiles produced by the joint action of atomic level polarization and the Hanle and Zeeman effects. We find that the Zeeman effect tends to dominate the linear polarization signals only in the localized patches of opposite magnetic polarity where the magnetic field is relatively strong and slightly inclined, while outside such very localized patches the linear polarization is often dominated by the contribution of atomic level polarization. We demonstrate that a correct modeling of this last contribution requires taking into account the symmetry breaking effects caused by the thermal, dynamic and magnetic structure of the solar atmosphere, and that in the 3D model used the Hanle effect in forward-scattering geometry (disk center observation) mainly reduces the polarization corresponding to the zero-field case. We emphasize that, in general, a reliable modeling of the linear polarization in the Ca {\sc ii} 8542 \AA\ line requires taking into account the joint action of atomic level polarization and the Hanle and Zeeman effects., Comment: 11 pages, 5 figures, accepted for publication in The Astrophysical Journal Letters