Search

The nature of dark matter in the Universe is still an open question in astrophysics and cosmology. Axions and axion-like particles (ALPs) offer a compelling solution, and traditionally ground-based experiments have eagerly, but to date unsuccessfully, searched for these hypothetical low-mass particles that are expected to be produced in large quantities in the strong electromagnetic fields in the interior of stars. This work offers a fresh look at axions and ALPs by leveraging their conversion into X-rays in the magnetic field of the Sun's atmosphere rather than a laboratory magnetic field. Unique data acquired with the Nuclear Spectroscopic Telescope Array (NuSTAR) during the solar minimum in 2020 allows us to set stringent limits on the coupling of axions to photons using state-of-the-art magnetic field models of the solar atmosphere. We report pioneering limits on the axion-photon coupling strength of $6.9\times 10^{-12}$ GeV$^{-1}$ at 95\% confidence level for axion masses $m_a \lesssim 2\times 10^{-7}$ eV, surpassing current ground-based searches and further probing unexplored regions of the axion-photon coupling parameter space up to axion masses of $m_a \lesssim 5\times 10^{-4}$ eV., Comment: 23 pages, 12 figures

We investigate the main physical mechanisms that shape the intensity and polarization of the Ba II D1 line at 4934 angstroms via radiative transfer numerical experiments. We focus especially on the scattering linear polarization arising from the spectral structure of the anisotropic radiation in the wavelength interval spanned by the line's hyperfine structure (HFS) components in the odd isotopes of barium. After verifying that the presence of the low-energy metastable levels only impacts the amplitude, but not the shape, of the D1 linear polarization, we relied on a two-term atomic model that neglects such metastable levels but includes HFS. The D1 fractional linear polarization shows a very small variation with the choice of atmospheric model, enhancing its suitability for solar magnetic field diagnostics. Tangled magnetic fields with strengths of tens of gauss reduce the linear polarization and saturation is reached at roughly 300 G. Deterministic inclined magnetic fields produce a U/I profile and, if they have a significant longitudinal component, a V/I profile, whose modeling requires accounting for HFS and the Paschen-Back effect. Because of the overlap between HFS components, the magnetograph formula cannot be applied to infer the longitudinal magnetic field. Accurately modeling the D1 intensity and polarization requires an atomic system that includes the metastable levels and the HFS, the detailed spectral structure of the radiation field, the incomplete Paschen-Back regime for magnetic fields, and an accurate treatment of collisions., Comment: Accepted for publication in the Astrophysical Journal

Details of the magnetic field in the quiet Sun chromosphere are key to our understanding of essential aspects of the solar atmosphere. We aim to determine the longitudinal magnetic field component (B_lon) of quiet Sun regions depending on their size. We estimated B_lon by applying the weak-field approximation (WFA) to high-spatial-resolution Ca II 854.2 nm data taken with the Swedish 1m Solar Telescope. Specifically, we analyzed the estimates inferred for different spectral ranges using the data at the original cadence and temporally integrated signals. The longitudinal magnetic field in each considered plasma structure correlates with its size. Using a spectral range restricted to the line core leads to chromospheric longitudinal fields varying from 50 G at the edges to 150-500 G at the center of the structure. These values increase as the spectral range widens due to the photospheric contribution. However, the difference between this contribution and the chromospheric one is not uniform for all structures. Small and medium-sized concentrations show a steeper height gradient in B_lon compared to their chromospheric values, so estimates for wider ranges are less trustworthy. Signal addition does not alleviate this situation as the height gradients in B_lon are consistent with time. Finally, despite the amplified noise levels that deconvolving processes may cause, data restored with the destretching technique show similar results, though are affected by smearing. We obtained B_lon estimates similar to those previously found, except for large concentrations and wide spectral ranges. In addition, we report a correlation between the height variation of B_lon compared to the chromospheric estimates and the concentration size. This correlation affects the difference between the photospheric and chromospheric magnetic flux values and the reliability of the estimates for wider spectral ranges., Comment: 14 pages, 14 figures. Accepted for publication in Astronomy & Astrophysics; abstract has been abridged

We apply the Tenerife Inversion Code (TIC) to the plage spectropolarimetric observations obtained by the Chromospheric LAyer SpectroPolarimeter (CLASP2). These unprecedented data consist of full Stokes profiles in the spectral region around the Mg II h and k lines for a single slit position, with around two thirds of the 200 arcsec slit crossing a plage region and the rest crossing an enhanced network. A former analysis of these data had allowed us to infer the longitudinal component of the magnetic field by applying the weak field approximation (WFA) to the circular polarization profiles, and to assign the inferred magnetic fields to different layers of the solar atmosphere based on the results of previous theoretical radiative transfer investigations. In this work, we apply the recently developed TIC to the same data. We obtain the stratified model atmosphere that fits the intensity and circular polarization profiles at each position along the spectrograph slit and we compare our results for the longitudinal component of the magnetic field with the previously obtained WFA results, highlighting the generally good agreement in spite of the fact that the WFA is known to produce an underestimation when applied to the outer lobes of the Mg II h and k circular polarization profiles. Finally, we use the inverted model atmospheres to give a rough estimation of the energy that could be carried by Alfv\`en waves propagating along the chromosphere in the plage and network regions, showing that it is sufficient to compensate the estimated energy losses in the chromosphere of solar active regions., Comment: Accepted for publication in The Astrophysical Journal

The CLASP2 (Chromospheric LAyer SpectroPolarimeter 2) sounding rocket mission was launched on 2019 April 11. CLASP2 measured the four Stokes parameters of the Mg II h & k spectral region around 2800 Angstroms along a 200 arcsecond slit at three locations on the solar disk, achieving the first spatially and spectrally resolved observations of the solar polarization in this near ultraviolet region. The focus of the work presented here is the center-to-limb variation of the linear polarization across these resonance lines, which is produced by the scattering of anisotropic radiation in the solar atmosphere. The linear polarization signals of the Mg II h & k lines are sensitive to the magnetic field from the low to the upper chromosphere through the Hanle and magneto-optical effects. We compare the observations to theoretical predictions from radiative transfer calculations in unmagnetized semi-empirical models, arguing that magnetic fields and horizontal inhomogeneities are needed to explain the observed polarization signals and spatial variations. This comparison is an important step in both validating and refining our understanding of the physical origin of these polarization signatures, and also in paving the way toward future space telescopes for probing the magnetic fields of the solar upper atmosphere via ultraviolet spectropolarimetry., Comment: 14 pages, 5 figures, to be published in the Astrophysical Journal (ApJ), initially submitted May 2022, revised submission July 2022

We present the Tenerife Inversion Code (TIC), which has been developed to infer the magnetic and plasma properties of the solar chromosphere and transition region via full-Stokes inversion of polarized spectral lines. The code is based on the HanleRT forward engine, which takes into account many of the physical mechanisms that are critical for a proper modeling of the Stokes profiles of spectral lines originating in the tenuous and highly dynamic plasmas of the chromosphere and transition region: quantum level population imbalance and interference (atomic polarization), frequency coherence effects in polarized resonance scattering (partial frequency redistribution), and the impact of arbitrary magnetic fields on the atomic polarization and the radiation field. We present first results of atmospheric and magnetic inversions, and discuss future developments for the project., Comment: 17pages, 7 figures. Accepted for publication in The Astrophysical Journal

We present novel spectropolarimetric observations of the hydrogen H$\alpha$ line taken with the Z\"urich Imaging Polarimeter (ZIMPOL) at the Gregory Coud\'e Telescope of the Istituto Ricerche Solari Locarno (IRSOL). The linear polarization is clearly dominated by the scattering of anisotropic radiation and the Hanle effect, while the circular polarization by the Zeeman effect. The observed linear polarization signals show a rich spatial variability, the interpretation of which would open a new window for probing the solar chromosphere. We study their spatial variation within coronal holes, finding a different behaviour for the $U/I$ signals near the North and South solar poles. We identify some spatial patterns, which may facilitate the interpretation of the observations. In close-to-the-limb regions with sizable circular polarization signals we find similar asymmetric $Q/I$ profiles. We also show examples of net circular polarization profiles (NCP), along with the corresponding linear polarization signals. The application of the weak field approximation to the observed circular polarization signals gives $10\,$G ($40-60\,$G) in close to the limb quiet (plage) regions for the average longitudinal field strength over the spatio-temporal resolution element., Comment: Accepted in A&A (16/12/2021)

Empirical relations between major UV and extreme UV spectral lines are one of the inputs for models of chromospheric and coronal spectral radiances and irradiances. They are also needed for the interpretation of some of the observations of the Solar Orbiter mission. We aim to determine an empirical relation between the intensities of the HI 121.6 nm and HeII 30.4 nm Lyman $\alpha$ lines. Images at 121.6 nm from the Chromospheric Lyman Alpha Spectro Polarimeter (CLASP) and Multiple XUV Imager (MXUVI) sounding rockets were co-registered with simultaneous images at 30.4 nm from the EIT and AIA orbital telescopes in order to derive a spatially resolved relationship between the intensities. We have obtained a relationship between the HI 121.6 nm and HeII 30.4 nm intensities that is valid for a wide range of solar features, intensities, and activity levels. Additional SUMER data have allowed the derivation of another relation between the HI 102.5 nm (Ly$\beta$) and HeII 30.4 nm lines for quiet-Sun regions. We combined these two relationships to obtain a Ly$\alpha$/Ly$\beta$ intensity ratio that is comparable to the few previously published results. The relationship between the HI 121.6~nm and HeII 30.4 nm lines is consistent with the one previously obtained using irradiance data. We have also observed that this relation is stable in time but that its accuracy depends on the spatial resolution of the observations. The derived Ly$\alpha$/Ly$\beta$ intensity ratio is also compatible with previous results.

We compare maps of scattering polarization signals obtained from three-dimensional (3D) radiation transfer calculations in a magneto-convection model of the solar atmosphere using formal solvers based on the "short characteristics" (SC) and the "long characteristics" (LC) methods. The SC method requires less computational work, but it is known to introduce spatial blurring in the emergent radiation for inclined lines of sight. For polarized radiation this effect is generally more severe due to it being a signed quantity and to the sensitivity of the scattering polarization to the model's inhomogeneities. We study the differences in the polarization signals of the emergent spectral line radiation calculated with such formal solvers. We take as a case study already published results of the scattering polarization in the Sr I $4607~\unicode{xC5}$ line obtained with the SC method, demonstrating that in high-resolution grids it is accurate enough for that type of study. In general, the LC method is the preferred one for accurate calculations of the emergent radiation, reason why it is now one of the options in the public version of the 3D radiative transfer code PORTA., Comment: 16 pages, 12 figures; accepted for publication in The Astrophysical Journal

Theoretical investigations predicted that high spatio-temporal resolution observations in the Sr I 4607 A line must show a conspicuous scattering polarization pattern at the solar disk-center, which encodes information on the unresolved magnetism of the inter-granular photospheric plasma. Here we present a study of the impact of limited time resolution on the observability of such forward scattering (disk-center) polarization signals. Our investigation is based on three-dimensional radiative transfer calculations in a time-dependent magneto-convection model of the quiet solar photosphere, taking into account anisotropic radiation pumping and the Hanle effect. This type of radiative transfer simulation is computationally costly, reason why the time variation had not been investigated before for this spectral line. We compare our theoretical results with recent disk-center filter polarimetric observations in the Sr I 4607 A line, showing that there is good agreement in the polarization patterns. We also show what we can expect to observe with the Visible Spectro-Polarimeter at the upcoming Daniel K. Inouye Solar Telescope., Comment: 11 pages, 10 figures, accepted for publication in the Astrophysical Journal

The sizable linear polarization signals produced by the scattering of anisotropic radiation in the core of the Ca I 4227 $\mathrm{\r{A}}$ line constitute an important observable for probing the inhomogeneous and dynamic plasma of the lower solar chromosphere. Here we show the results of a three-dimensional (3D) radiative transfer complete frequency redistribution (CRD) investigation of the line's scattering polarization in a magneto-hydrodynamical 3D model of the solar atmosphere. We take into account not only the Hanle effect produced by the model's magnetic field, but also the symmetry breaking caused by the horizontal inhomogeneities and macroscopic velocity gradients. The spatial gradients of the horizontal components of the macroscopic velocities produce very significant forward scattering polarization signals without the need of magnetic fields, while the Hanle effect tends to depolarize them at the locations where the model's magnetic field is stronger than about 5 G. The standard 1.5D approximation is found to be unsuitable for understanding the line's scattering polarization, but we introduce a novel improvement to this approximation that produces results in qualitative agreement with the full 3D results. The instrumental degradation of the calculated polarization signals is also investigated, showing what can we expect to observe with the Visible Spectro-Polarimeter at the upcoming Daniel K. Inouye Solar Telescope., Comment: 18 pages, 12 figures; accepted in ApJ

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., Comment: Submitted to Experimental Astronomy (on 28. Jul. 2020). Based on a proposal submitted in response to a call for white papers in the Voyage 2050 long-term plan in the ESA science programme. 36 pages, 10 figures

We carry out a theoretical study of the polarization of the solar Mg II h-k doublet (including its extended wings) and the subordinate UV triplet around 280 nm. These lines are of great diagnostic interest, as they encode information on the physical properties of the solar atmosphere from the upper photosphere to the chromosphere-corona transition region. We base our study on radiative transfer calculations of spectral line polarization in one-dimensional models of quiet and plage regions of the solar atmosphere. Our calculations take into account the combined action of atomic polarization, quantum level interference, frequency redistribution, and magnetic fields of arbitrary strength. In particular, we study the sensitivity of the emergent Stokes profiles to changes in the magnetic field through the Zeeman and Hanle effects. We also study the impact of the chromospheric plasma dynamics on the emergent Stokes profiles, taking into account the angle-dependent frequency redistribution in the h-k resonance transitions. The results presented here are of interest for the interpretation of spectropolarimetric observations in this important region of the solar ultraviolet spectrum.

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., Comment: 2nd edition, December 2019, 138 pages

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

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

One of the key research problems in stellar physics is to decipher the small-scale magnetic activity of the quiet solar atmosphere. Recent magneto-convection simulations that account for small-scale dynamo action have provided three-dimensional (3D) models of the solar photosphere characterized by a high degree of small-scale magnetic activity, similar to that found through theoretical interpretation of the scattering polarization observed in the Sr I 4607 \AA\ line. Here we present the results of a novel investigation of the Hanle effect in this resonance line, based on 3D radiative transfer calculations in a high-resolution magneto-convection model having most of the convection zone magnetized close to the equipartition and a surface mean field strength ${\langle B \rangle}{\approx}170$ G. The Hanle effect produced by the model's magnetic field depolarizes the zero-field scattering polarization signals significantly, to the extent that the center-to-limb variation of the calculated spatially-averaged polarization amplitudes is compatible with the observations. The standard deviation of the horizontal fluctuations of the calculated scattering polarization signals is very sensitive to the model's magnetic field and we find that the predicted spatial variations are sufficiently sizable so as to be able to detect them, especially with the next generation of solar telescopes. We find that at all on-disk positions the theoretical scattering polarization signals are anti-correlated with the continuum intensity. To facilitate reaching new observational breakthroughs, we show how the theoretically predicted polarization signals and spatial variations are modified when deteriorating the signal-to-noise ratio and the spectral and spatial resolutions of the simulated observations., Comment: Submitted to ApJ on May 7

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

The Chromospheric Lyman Alpha Spectropolarimeter (CLASP) observed the Sun in H I Lyman-{\alpha} during a suborbital rocket flight on September 3, 2015. The Interface Region Imaging Telescope (IRIS) coordinated with the CLASP observations and recorded nearly simultaneous and co-spatial observations in the Mg II h&k lines. The Mg II h and Ly-{\alpha} lines are important transitions, energetically and diagnostically, in the chromosphere. The canonical solar atmosphere model predicts that these lines form in close proximity to each other and so we expect that the line profiles will exhibit similar variability. In this analysis, we present these coordinated observations and discuss how the two profiles compare over a region of quiet sun at viewing angles that approach the limb. In addition to the observations, we synthesize both line profiles using a 3D radiation-MHD simulation. In the observations, we find that the peak width and the peak intensities are well correlated between the lines. For the simulation, we do not find the same relationship. We have attempted to mitigate the instrumental differences between IRIS and CLASP and to reproduce the instrumental factors in the synthetic profiles. The model indicates that formation heights of the lines differ in a somewhat regular fashion related to magnetic geometry. This variation explains to some degree the lack of correlation, observed and synthesized, between Mg II and Ly-{\alpha}. Our analysis will aid in the definition of future observatories that aim to link dynamics in the chromosphere and transition region., Comment: Accepted by ApJ

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

We present multilevel radiative transfer modeling of the scattering polarization observed in the solar O I infrared triplet around 777 nm. We demonstrate that the scattering polarization pattern observed on the solar disk forms in the chromosphere, far above the photospheric region where the bulk of the emergent intensity profiles originates. We study the sensitivity of the polarization pattern to the thermal structure of the solar atmosphere and to the presence of weak magnetic fields (0.01 - 100 G) through the Hanle effect, showing that the scattering polarization signals of the oxygen infrared triplet encode information on the magnetism of the solar chromosphere., Comment: To be published in ApJ Letters

Proving the magnetic configuration of solar spicules has hitherto been difficult due to the lack of spatial resolution and image stability during off-limb ground-based observations. We report spectropolarimetric observations of spicules taken in the He I 1083 nm spectral region with the Tenerife Infrared Polarimeter II at the German Vacuum Tower Telescope of the Observatorio del Teide (Tenerife; Canary Islands; Spain). The data provide the variation with geometrical height of the Stokes I, Q, U, and V profiles whose encoded information allows the determination of the magnetic field vector by means of the HAZEL inversion code. The inferred results show that the average magnetic field strength at the base of solar spicules is about 80 gauss and then it decreases rapidly with height to about 30 gauss at a height of 3000 km above the visible solar surface. Moreover, the magnetic field vector is close to vertical at the base of the chromosphere and has mid inclinations (about 50 degree) above 2 Mm height., Comment: Published in ApJ Letters

With the advent of a new generation of solar telescopes and instrumentation, the interpretation of chromospheric observations (in particular, spectro-polarimetry) requires new, suitable diagnostic tools. This paper describes a new code, NICOLE, that has been designed for Stokes non-LTE radiative transfer, both for synthesis and inversion of spectral lines and Zeeman-induced polarization profiles, spanning a wide range of atmospheric heights, from the photosphere to the chromosphere. The code fosters a number of unique features and capabilities and has been built from scratch with a powerful parallelization scheme that makes it suitable for application on massive datasets using large supercomputers. The source code is being publicly released, with the idea of facilitating future branching by other groups to augment its capabilities., Comment: Submitted to A&A. Note: replaced with new version because references were missing in the original submission

Magnetic field measurements in the upper chromosphere and above, where the gas-to-magnetic pressure ratio $\beta$ is lower than unity, are essential for understanding the thermal structure and dynamical activity of the solar atmosphere. Recent developments in the theory and numerical modeling of polarization in spectral lines have suggested that information on the magnetic field of the chromosphere-corona transition region could be obtained by measuring the linear polarization of the solar disk radiation at the core of the hydrogen Lyman-$\alpha$ line at 121.6~nm, which is produced by scattering processes and the Hanle effect. The Chromospheric Lyman-$\alpha$ Spectropolarimeter (CLASP) sounding rocket experiment aims to measure the intensity (Stokes $I$) and the linear polarization profiles ($Q/I$ and $U/I$) of the hydrogen Lyman-$\alpha$ line. In this paper we clarify the information that the Hanle effect can provide by applying a Stokes inversion technique based on a database search. The database contains all theoretical $Q/I$ and $U/I$ profiles calculated in a one-dimensional semi-empirical model of the solar atmosphere for all possible values of the strength, inclination, and azimuth of the magnetic field vector, though this atmospheric region is highly inhomogeneous and dynamic. We focus on understanding the sensitivity of the inversion results to the noise and spectral resolution of the synthetic observations as well as the ambiguities and limitation inherent to the Hanle effect when only the hydrogen Lyman-$\alpha$ is used. We conclude that spectropolarimetric observations with CLASP can indeed be a suitable diagnostic tool for probing the magnetism of the transition region, especially when complemented with information on the magnetic field azimuth that can be obtained from other instruments., Comment: 34 pages, 10 figures, accepted for publication in ApJ

We present high spatial resolution spectropolarimetric observations of a quiescent hedgerow prominence taken in the He I 1083.0 nm triplet. The observation consisted of a time series in sit-and-stare mode of 36 minutes of duration. The spectrograph's slit crossed the prominence body and we recorded the time evolution of individual vertical threads. Eventually, we observed the development of a dark Rayleigh-Taylor plume that propagated upward with a velocity, projected onto the plane of the sky, of 17 km/s. Interestingly, the plume apex collided with the prominence threads pushing them aside. We inferred Doppler shifts, Doppler widths, and magnetic field strength variations by interpreting the He I Stokes profiles with the HAZEL code. The Doppler shifts show that clusters of threads move coherently while individual threads have oscillatory patterns. Regarding the plume we found strong redshifts (9-12 km/s) and large Doppler widths (10 km/s) at the plume apex when it passed through the prominence body and before it disintegrated. We associate the redshifts with perspective effects while the Doppler widths are more likely due to an increase in the local temperature. No local variations of the magnetic field strength associated with the passage of the plume were found; this leads us to conclude that the plumes are no more magnetized than the surroundings. Finally, we found that some of the threads oscillations are locally damped, what allowed us to apply prominence seismology techniques to infer additional prominence physical parameters., Comment: Accepted in ApJ letters

Line scattering polarization can be strongly affected by Rayleigh scattering by neutral hydrogen and Thompson scattering by free electrons. Often a continuum depolarization results, but the Doppler redistribution produced by the continuum scatterers, which are light (hence, fast), induces more complex interactions between the polarization in spectral lines and in the continuum. Here we formulate and solve the radiative transfer problem of scattering line polarization with non coherent continumm scattering consistently. The problem is formulated within the spherical tensor representation of atomic and light polarization. The numerical method of solution is a generalization of the Accelerated Lambda Iteration that is applied to both, the atomic system and the radiation field. We show that the redistribution of the spectral line radiation due to the non coherence of the continuum scattering may modify significantly the shape of the emergent fractional linear polarization patterns, even yielding polarization signals above the continuum level in intrinsically unpolarizable lines., Comment: Accepted for publication in The Astrophysical Journal

We show preliminary results of an ongoing investigation aimed at determining the configuration of the magnetic field vector in the threads of a quiescent hedgerow solar prominence using high-spatial resolution spectropolarimetric observations taken in the He I 1083.0 nm multiplet. The data consist of a two-dimensional map of a quiescent hedgerow prominence showing vertical threads. The observations were obtained with the Tenerife Infrared Polarimeter attached to the German Vacuum Tower Telescope at the Observatorio del Teide (Spain). The He I 1083.0 nm Stokes signals are interpreted with an inversion code, which takes into account the key physical processes that generate and/or modify circular and linear polarization signals in the He I 1083.0 nm triplet: the Zeeman effect, anisotropic radiation pumping, and the Hanle effect. We present initial results of the inversions, i.e, the strength and orientation of the magnetic field vector along the prominence and in prominence threads., Comment: To appear in "Proceedings IAU Symposium No. 300, 2013: Nature of Prominences and their Role in Space Weather"

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

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

We present observational evidence of apparent plasma rotational motions in the feet of a solar prominence. Our study is based on spectroscopic observations taken in the He I 1083.0 nm multiplet with the Tenerife Infrared Polarimeter attached to the German Vacuum Tower Telescope. We recorded a time sequence of spectra with 34 s cadence placing the slit of the spectrograph almost parallel to the solar limb and crossing two feet of an intermediate size, quiescent hedgerow prominence. The data show opposite Doppler shifts, +/- 6 km/s, at the edges of the prominence feet. We argue that these shifts may be interpreted as prominence plasma rotating counterclockwise around the vertical axis to the solar surface as viewed from above. The evolution of the prominence seen in EUV images taken with the Solar Dynamic Observatory provided us clues to interpret the results as swirling motions. Moreover, time-distance images taken far from the central wavelength show plasma structures moving parallel to the solar limb with velocities of about 10-15 km/s. Finally, the shapes of the observed intensity profiles suggest the presence of, at least, two components at some locations at the edges of the prominence feet. One of them is typically Doppler shifted (up to 20 km/s) with respect to the other, thus suggesting the existence of supersonic counter-streaming flows along the line-of-sight., Comment: Accepted in ApJ Letters

We present spectropolarimetric observations in the He I 1083.0 nm multiplet of a quiescent, hedgerow solar prominence. The data were taken with the Tenerife Infrared Polarimeter attached to the German Vacuum Tower Telescope at the Observatorio del Teide (Tenerife; Canary Islands; Spain). The observed He I circular and linear polarization signals are dominated by the Zeeman effect and by atomic level polarization and the Hanle effect, respectively. These observables are sensitive to the strength and orientation of the magnetic field vector at each spatial point of the field of view. We determine the magnetic field vector of the prominence by applying the HAZEL inversion code to the observed Stokes profiles. We briefly discuss the retrieved magnetic field vector configuration., Comment: To appear in Highlights of Spanish Astrophysics VII, Proceedings of the X Scientific Meeting of the Spanish Astronomical Society

Velocity gradients in a stellar atmospheric plasma have an impact on the anisotropy of the radiation field that illuminates each point within the medium, and this may in principle influence the scattering line polarization that results from the induced atomic level polarization. Here we analyze the emergent linear polarization profiles of the Ca II infrared triplet after solving the radiative transfer problem of scattering polarization in time-dependent hydrodynamical models of the solar chromosphere, taking into account the impact of the plasma macroscopic velocity on the atomic level polarization. We discuss the influence that the velocity and temperature shocks in the considered chromospheric models have on the temporal evolution of the scattering polarization signals of the Ca II infrared lines, as well as on the temporally averaged profiles. Our results indicate that the increase of the linear polarization amplitudes caused by macroscopic velocity gradients may be significant in realistic situations. We also study the effect of the integration time, the microturbulent velocity and the photospheric dynamical conditions, and discuss the feasibility of observing with large-aperture telescopes the temporal variation of the scattering polarization profiles. Finally, we explore the possibility of using the differential Hanle effect in the IR triplet of Ca II with the intention of avoiding the characterization of the zero-field polarization to infer magnetic fields in dynamic situations., Comment: 12 pages, 9 figures. Accepted for publication in ApJ. New figure added, typos corrected

Magnetic field topology, thermal structure and plasma motions are the three main factors affecting the polarization signals used to understand our star. In this theoretical investigation, we focus on the effect that gradients in the macroscopic vertical velocity field have on the non-magnetic scattering polarization signals, establishing the basis for general cases. We demonstrate that the solar plasma velocity gradients have a significant effect on the linear polarization produced by scattering in chromospheric spectral lines. In particular, we show the impact of velocity gradients on the anisotropy of the radiation field and on the ensuing fractional alignment of the CaII levels, and how they can lead to an enhancement of the zero-field linear polarization signals. This investigation remarks the importance of knowing the dynamical state of the solar atmosphere in order to correctly interpret spectropolarimetric measurements, which is important, among other things, for establishing a suitable zero field reference case to infer magnetic fields via the Hanle effect., Comment: 14 pages, 10 figures, 3 appendixes, accepted for publication in ApJ

The magnetic field plays a pivotal role in many fields of Astrophysics. This is especially true for the physics of the solar atmosphere. Measuring the magnetic field in the upper solar atmosphere is crucial to understand the nature of the underlying physical processes that drive the violent dynamics of the solar corona -- that can also affect life on Earth. SolmeX, a fully equipped solar space observatory for remote-sensing observations, will provide the first comprehensive measurements of the strength and direction of the magnetic field in the upper solar atmosphere. The mission consists of two spacecraft, one carrying the instruments, and another one in formation flight at a distance of about 200m carrying the occulter to provide an artificial total solar eclipse. This will ensure high-quality coronagraphic observations above the solar limb. Solmex integrates two spectro-polarimetric coronagraphs for off-limb observations, one in the EUV and one in the IR, and three instruments for observations on the disk. The latter comprises one imaging polarimeter in the EUV for coronal studies, a spectro-polarimeter in the EUV to investigate the low corona, and an imaging spectro-polarimeter in the UV for chromospheric studies. SOHO and other existing missions have investigated the emission of the upper atmosphere in detail (not considering polarization), and as this will be the case also for missions planned for the near future. Therefore it is timely that SolmeX provides the final piece of the observational quest by measuring the magnetic field in the upper atmosphere through polarimetric observations., Comment: Submitted to Experimental Astronomy. 30 pages, 19 figures

This paper presents a detailed study of the scattering polarization profiles formed under partial frequency redistribution (PRD) in two thermal models of the solar atmosphere. Particular attention is given to understanding the influence of several atmospheric parameters on the emergent fractional linear polarization profiles. The shapes of these $Q/I$ profiles are interpreted in terms of the anisotropy of the radiation field, which in turn depends on the source function gradient that sets the angular variation of the specific intensity. We define a suitable frequency integrated anisotropy factor for PRD that can be directly related to the emergent linear polarization. We show that complete frequency redistribution is a good approximation to model weak resonance lines. We also show that the emergent linear polarization profiles can be very sensitive to the thermal structure of the solar atmosphere and, in particular, to spatial variations of the damping parameter., Comment: 45 pages, 16 figures, accepted for publication in the Astrophysical Journal (2010)

The chromosphere of the quiet Sun is an important stellar atmospheric region whose thermal and magnetic structure we need to decipher for unlocking new discoveries in solar and stellar physics. To this end, we must identify and exploit observables sensitive to weak magnetic fields (B<100 G) and to the presence of cool and hot gas in the bulk of the solar chromosphere. Here we report on an investigation of the Hanle effect in two semi-empirical models of the quiet solar atmosphere with different chromospheric thermal structures. Our study reveals that scattering polarization in the Ca II IR triplet has thermal and magnetic sensitivities potentially of great diagnostic value. The linear polarization in the 8498 A line shows a strong sensitivity to inclined magnetic fields with strengths between 0.001 and 10 G, while the emergent linear polarization in the 8542 A and 8662 A lines is mainly sensitive to magnetic fields with strengths between 0.001 and 0.1 G. The reason for this is that the scattering polarization of the 8542 A and 8662 A lines, unlike the 8498 A line, is controlled mainly by the Hanle effect in their (metastable) lower levels. Therefore, in regions with magnetic strengths sensibly larger than 1 G, their Stokes Q and U profiles are sensitive only to the orientation of the magnetic field vector. We also find that for given magnetic field configurations the sign of the Q/I and U/I profiles of the 8542 A and 8662 A lines is the same in both atmospheric models, while the sign of the linear polarization profile of the 8498 A line turns out to be very sensitive to the thermal structure of the lower chromosphere. We suggest that spectropolarimetric observations providing information on the relative scattering polarization amplitudes of the Ca II IR triplet will be very useful to improve our empirical understanding of the thermal and magnetic structure of the quiet chromosphere., Comment: 27 pages, 16 figures, to appear in ApJ

The linearly-polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest spectral lines requires solving an involved non-LTE radiative transfer problem accounting for partial redistribution (PRD) effects. Fast radiative transfer methods for the numerical solution of PRD problems are also needed for a proper treatment of hydrogen lines when aiming at realistic time-dependent magnetohydrodynamic simulations of the solar chromosphere. Here we show how the two-level atom PRD problem with and without polarization can be solved accurately and efficiently via the application of highly convergent iterative schemes based on the Gauss-Seidel (GS) and Successive Overrelaxation (SOR) radiative transfer methods that had been previously developed for the complete redistribution (CRD) case. Of particular interest is the Symmetric SOR method, which allows us to reach the fully converged solution with an order of magnitude of improvement in the total computational time with respect to the Jacobi-based local ALI (Accelerated Lambda Iteration) method., Comment: 39 pages, 9 figures, accepted for publication in the Astrophysical Journal (2010), added labels to all the figures to make them more informative for the reader

This paper reviews some recent advances in the development and application of polarized radiation diagnostics to infer the mean magnetization of the quiet solar atmosphere, from the near equilibrium photosphere to the highly non-equilibrium upper chromosphere. In particular, I show that interpretations of the scattering polarization observed in some spectral lines suggest that while the magnetization of the photosphere and upper chromosphere is very significant, the lower chromosphere seems to be weakly magnetized., Comment: To appear in Proceedings 25th NSO Workshop on Chromospheric Structure and Dynamics; editors A. Tritschler, K. Reardon, H. Uitenbroek, Mem. Soc. Astr. Ital

We explore the photospheric and chromospheric magnetic field in an emerging flux region. An image of the equivalent width of the He I 10830 A red blended component shows the presence of filamentary structures that might be interpreted as magnetic loops. We point out that the magnetic field strength in the chromosphere resembles a smoothed version of that found in the photosphere and that it is not correlated at all with the above-mentioned equivalent width map. Lacking other diagnostics, this suggests that one cannot discard the possibility that the chromospheric field we infer from the observations is tracing the lower chromosphere of the active region instead of tracing the magnetic field along loops. If the He I line is formed within magnetic loops, we point out a potential problem that appears when interpreting observations using only one component along the line-of-sight., Comment: 6 pages, to appear in the proceedings of the 25th NSO Workshop "Chromospheric Structure and Dynamics. From Old Wisdom to New Insights"

This paper presents an overview of the radiative transfer problem of calculating the spectral line intensity and polarization that emerges from a (generally magnetized) astrophysical plasma composed of atoms and molecules whose excitation state is significantly influenced by radiative transitions produced by an anisotropic radiation field. The numerical solution of this non-LTE problem of the 2nd kind is facilitating the physical understanding of the second solar spectrum and the exploration of the complex magnetism of the extended solar atmosphere, but much more could be learned if high-sensitivity polarimeters were developed also for the present generation of night-time telescopes. Interestingly, I find that the population ratio between the levels of some resonance line transitions can be efficiently modulated by the inclination of a weak magnetic field when the anisotropy of the incident radiation is significant, something that could provide a new diagnostic tool in astrophysics., Comment: 17 pages, 6 figures, invited review paper

Determining the magnetic field related to solar spicules is vital for developing adequate models of these plasma jets, which are thought to play a key role in the thermal, dynamic and magnetic structure of the Chromosphere. Here we report on the magnetic properties of off-limb spicules in a very quiet region of the solar atmosphere, as inferred from new spectropolarimetric observations in the He I 10830 A triplet obtained with the Tenerife Infrared Polarimeter. We have used a novel inversion code for Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects (HAZEL) to interpret the observations. Magnetic fields as strong as ~40G were detected in a very localized area of the slit, which could represent a possible lower value of the field strength of organized network spicules., Comment: Accepted for publication in ApJ, 24 pages, 5 Figures

Solar magnetic fields leave their fingerprints in the polarization signatures of the emergent spectral line radiation. This occurs through a variety of rather unfamiliar physical mechanisms, not only via the Zeeman effect. In particular, magnetic fields modify the atomic level polarization (population imbalances and quantum coherences) that anisotropic radiative pumping processes induce in the atoms and molecules of the solar atmosphere. Interestingly, this so-called Hanle effect allows us to "see" magnetic fields to which the Zeeman effect is blind within the limitations of the available instrumentation. Here I argue that the IR triplet of Ca II and the He I 10830 \AA multiplet would be very suitable choices for investigating the magnetism of the solar chromosphere via spectropolarimetric observations from a future space telescope, such as JAXA's SOLAR-C mission., Comment: To appear in Second Hinode Meeting: Beyond Discovery -- Toward Understanding; ASP Conf. Series, Vol. in press (2009)

A large set of high precision full-Stokes spectropolarimetric observations of prominences in He-D3, Halpha and Hbeta lines has been recorded with the ZIMPOL polarimeter at the Gregory-Coude Telescope in Locarno. The observational technique allows us to obtain measurements free from seeing induced spurious effects. The instrumental polarization is well under control and taken into account in the data analysis. We present our observational results for each of the above-mentioned lines. Of particular interest is that most of our Halpha measurements show anti-symmetric V profiles that are a characteristic signature of the Zeeman effect in the prominence plasma. A Stokes inversion technique based on the quantum theory of the Hanle and Zeeman effects is being applied on observed Stokes profiles in the He-D3 line in order to obtain information on the magnetic field vector that confines the prominence plasma., Comment: 4 pages, Presented at Solar Polarization Workshop 4, Boulder

A large set of high precision full-Stokes spectropolarimetric observations of the He-D3 line in spicules has been recorded with the ZIMPOL polarimeter at the Gregory-Coude Telescope in Locarno. The observational technique allow us to obtain measurements free from seeing induced spurious effects. The instrumental polarization is well under control and taken into account in the data analysis. The observed Stokes profiles are interpreted according to the quantum theory of the Hanle and Zeeman effects with the aim of obtaining information on the magnetic field vector. To this end, we make use of a suitable Stokes inversion technique. The results are presented giving emphasis on a few particularly interesting measurements which show clearly the operation of the Hanle and Zeeman effects in solar chromospheric spicules., Comment: 6 pages, presented at Solar Polarization Workshop 4 in Boulder

We show a selection of high-sensitivity spectropolarimetric observations obtained over the last few years in the Ba II D2-line with the Zurich Imaging Polarimeter (ZIMPOL) attached to the Gregory Coude Telescope of IRSOL. The measurements were collected close to the solar limb, in several regions with varying degree of magnetic activity. The Stokes profiles we have observed show clear signatures of the joint action of the Hanle and Zeeman effects, in very good qualitative agreement with the theoretical expectations. Polarimetric measurements of this line show to be very well suited for magnetic field diagnostics of the lower solar chromosphere, from regions with field intensities as low as 1 gauss to strongly magnetized ones having kG field strengths., Comment: 6 pages, 6 figures, presented at Solar Polarization Workshop 5, held in Ascona, Switzerland, 17-21 September 2007

I review some recent advances in methods to diagnose polarized radiation with which we may hope to explore the magnetism of the solar chromosphere and corona. These methods are based on the remarkable signatures that the radiatively induced quantum coherences produce in the emergent spectral line polarization and on the joint action of the Hanle and Zeeman effects. Some applications to spicules, prominences, active region filaments, emerging flux regions and the quiet chromosphere are discussed., Comment: Review paper to appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S. S. Hasan and R. J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, 2009

Determining the magnetic field of solar spicules is vital for developing adequate models of these plasma jets, which are thought to play a key role in the thermal, dynamic, and magnetic structure of the chromosphere. Here we report on magnetic spicule properties in a very quiet region of the off-limb solar atmosphere, as inferred from new spectropolarimetric observations in the HeI 10830 A triplet. We have used a novel inversion code for Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects (HAZEL) to interpret the observations. Magnetic fields as strong as 40G were unambiguously detected in a very localized area of the slit, which may represent a possible lower value of the field strength of organized network spicules., Comment: 6 pages, 2 figures. Proceedings of the meeting "Magnetic Coupling between the Interior and the Atmosphere of the Sun: Centenary Commemoration of the Discovery of the Evershed Effect" held in Bangalore (India), 2-5 Dec. 2008

This paper reviews some of the developments that over the last 10 years have allowed us to go from deciphering the physical origin of several of the enigmatic features of the second solar spectrum to discovering unknown aspects of the Sun's hidden magnetism via sophisticated radiative transfer modeling. The second solar spectrum is the observational signature of radiatively induced quantum coherences in the atoms and molecules of the solar atmosphere. Magnetic fields produce partial decoherence via the Hanle effect, giving rise to fascinating observable effects in the emergent spectral line polarization. Interestingly, these effects allow us to "see" magnetic fields to which the Zeeman effect is blind within the limitations of the available instrumentation. In the coming years, the physical interpretation of observations of the spectral line polarization resulting from the joint action of the Hanle and Zeeman effects might lead to a new revolution in our empirical understanding of solar magnetic fields., Comment: Invited review paper accepted for publication in the Proceedings of the Solar Polarization Workshop 5

Here we formulate and solve the 3D radiative transfer problem of the polarization of the solar continuous radiation. Our approach takes into account not only the anisotropy of the continuum radiation, but also the symmetry-breaking effects caused by the horizontal atmospheric inhomogeneities produced by the solar surface convection. Interestingly, our radiative transfer modeling in a well-known 3D hydrodynamical model of the solar photosphere shows remarkable agreement with the empirical data, significantly better than that obtained via the use of 1D atmospheric models. Although this result confirms that the above-mentioned 3D model was indeed a suitable choice for our Hanle-effect estimation of the substantial amount of "hidden" magnetic energy that is stored in the quiet solar photosphere, we have found however some small discrepancies whose origin may be due to uncertainties in the empirical data and/or in the thermal and density structure of the 3D model. For this reason, we have paid some attention also to other (more familiar) observables, like the center-limb variation of the continuum intensity, which we have calculated taking into account the scattering contribution to the continuum source function. The overall agreement with the observed center-limb variation turns out to be impressive, but we find a hint that the model's temperature gradients in the continuum forming layers could be slightly too steep, perhaps because all current simulations of solar surface convection and magnetoconvection compute the radiative flux divergence ignoring the fact that the effective polarizability is not completely negligible, especially in the downward-moving intergranular lane plasma., Comment: Accepted for publication in The Astrophysical Journal