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 iih & 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 G, strongly correlated with the Mg iik 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.

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 4607Å 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 B ≈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.

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 Bézier 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.

We highlight the main results of a three-dimensional (3D) multilevel radiative transfer investigation about the solar disk-center polarization of the Ca ii 8542 Å line. First, through the use of a 3D model of the solar atmosphere, we investigate the linear polarization that occurs due to the atomic level polarization produced by the absorption and scattering of anisotropic radiation, 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 the 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; 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 ii 8542 Å line requires taking into account the joint action of atomic level polarization and the Hanle and Zeeman effects.

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

Recent theoretical investigations have pointed out that the cores of the Lyα lines of H i and He ii should show measurable scattering polarization signals when observing the solar disk, and that the magnetic sensitivity, through the Hanle effect, of such linear polarization signals is suitable for exploring the magnetism of the solar transition region. Such investigations were carried out in the limit of complete frequency redistribution (CRD) and neglecting quantum interference between the two upper J-levels of each line. Here we relax both approximations and show that the joint action of partial frequency redistribution (PRD) and J-state interference produces much more complex fractional linear polarization (Q/I) profiles, with large amplitudes in their wings. Such wing polarization signals turn out to be very sensitive to the temperature structure of the atmospheric model, so that they can be exploited for constraining the thermal properties of the solar chromosphere. Finally, we show that the approximation of CRD without J-state interference is however suitable for estimating the amplitude of the linear polarization signals in the core of the lines, where the Hanle effect operates.

Probing the magnetism of the upper solar chromosphere requires measuring and modeling the scattering polarization produced by anisotropic radiation pumping in UV spectral lines. Here we apply PORTA (a novel radiative transfer code) to investigate the hydrogen Ly α line in a 3D model of the solar atmosphere resulting from a state of the art MHD simulation. At full spatial resolution the linear polarization signals are very significant all over the solar disk, with a large fraction of the field of view showing line-center amplitudes well above the 1 % level. Via the Hanle effect the line-center polarization signals are sensitive to the magnetic field of the model's transition region, even when its mean field strength is only 15 G. The breaking of the axial symmetry of the radiation field produces significant forward-scattering polarization in Ly α, without the need of an inclined magnetic field. Interestingly, the Hanle effect tends to decrease such forward-scattering polarization signals in most of the points of the field of view. When the spatial resolution is degraded, the line-center polarization of Ly α drops below the 1 % level, reaching values similar to those previously found in 1D semi-empirical models (i.e., up to about 0.5 %). The center to limb variation of the spatially-averaged polarization signals is qualitatively similar to that found in 1D models, with the largest line-center amplitudes at µ = cos θ ≈ 0.4 (θ being the heliocentric angle). These results are important, both for designing the needed space-based instrumentation and for a reliable interpretation of future observations of the Ly α polarization.

A sounding rocket experiment aiming the followings:• highͲprecision (0.1%) measurements of linear polarizations in vacuumͲUV (VUV) lights, • the first measurement of the linear polarization induced by atomic polarization and Hanle effect in the LymanͲalpha line (121.567nm), and • the first exploration of magnetic fields in the upper chromosphere and transition region of the Sun.