The scattering polarization of the Ly-alpha lines of H I and He II taking into account PRD and J-state interference effects

Recent theoretical investigations have pointed out that the cores of the Ly-alpha 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.Comment: Accepted for publication in The Astrophysical Journal Letter

Scattering Polarization of Hydrogen Lines in Weakly Magnetized Stellar Atmospheres I. Formulation and Application to Isothermal Models

Although the spectral lines of hydrogen contain valuable information on the physical properties of a variety of astrophysical plasmas, including the upper solar chromosphere, relatively little is known about their scattering polarization signals whose modification via the Hanle effect may be exploited for magnetic field diagnostics. Here we report on a basic theoretical investigation of the linear polarization produced by scattering processes and the Hanle effect in Ly-a, Ly-b and H-a taking into account multilevel radiative transfer effects in an isothermal stellar atmosphere model, the fine-structure of the hydrogen levels, as well as the impact of collisions with electrons and protons. The main aim of this first paper is to elucidate the physical mechanisms that control the linear polarization in the three lines, as well as its sensitivity to the perturbers density and to the strength and structure of micro-structured and deterministic magnetic fields. To this end, we apply an efficient radiative transfer code we have developed for performing numerical simulations of the Hanle effect in multilevel systems with overlapping line transitions. For low density plasmas such as that of the upper solar chromosphere collisional depolarization is caused mainly by collisional transitions between the fine-structure levels of n=3, so that it is virtually insignificant for Ly-a but important for Ly-b and H-a. We show the impact of the Hanle effect on the three lines taking into account the radiative transfer coupling between the different hydrogen line transitions. For example, we demonstrate that the linear polarization profile of the H-a line is sensitive to the presence of magnetic field gradients in the line core formation region and that in solar-like chromospheres selective absorption of polarization components does not play any significant role on the emergent scattering polarization.Comment: 24 pages, 16 figures, 2 tables, accepted for publication in Ap

On the magnetic field of off-limb spicules

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 Figure

Scattering Polarization and Hanle Effect in Stellar Atmospheres with Horizontal Inhomogeneities

Scattering of light from an anisotropic source produces linear polarization in spectral lines and the continuum. In the outer layers of a stellar atmosphere the anisotropy of the radiation field is typically dominated by the radiation escaping away, but local horizontal fluctuations of the physical conditions may also contribute, distorting the illumination and hence, the polarization pattern. Additionally, a magnetic field may perturb and modify the line scattering polarization signals through the Hanle effect. Here, we study such symmetry-breaking effects. We develop a method to solve the transfer of polarized radiation in a scattering atmosphere with weak horizontal fluctuations of the opacity and source functions. It comprises linearization (small opacity fluctuations are assumed), reduction to a quasi-planeparallel problem through harmonic analysis, and numerical solution by generalized standard techniques. We apply this method to study scattering polarization in atmospheres with horizontal fluctuations in the Planck function and opacity. We derive several very general results and constraints from considerations on the symmetries and dimensionality of the problem, and we give explicit solutions of a few illustrative problems of especial interest. For example, we show (a) how the amplitudes of the fractional linear polarization signals change when considering increasingly smaller horizontal atmospheric inhomogeneities, (b) that in the presence of such inhomogeneities even a vertical magnetic field may modify the scattering line polarization, and (c) that forward scattering polarization may be produced without the need of an inclined magnetic field. These results are important to understand the physics of the problem and as benchmarks for multidimensional radiative transfer codes.Comment: 27 pages, 13 figures, to appear in Ap

Are collisions with neutral hydrogen important for modelling the Second Solar Spectrum of Ti I and Ca II ?

The physical interpretation of scattering line polarization offers a novel diagnostic window for exploring the thermal and magnetic structure of the quiet regions of the solar atmosphere. Here we evaluate the impact of isotropic collisions with neutral hydrogen atoms on the scattering polarization signals of the 13 lines of multiplet 42 of Ti I and on those of the K line and of the IR triplet of Ca II, with emphasis on the collisional transfer rates between nearby J-levels. To this end, we calculate the linear polarization produced by scattering processes considering realistic multilevel models and solving the statistical equilibrium equations for the multipolar components of the atomic density matrix. We confirm that the lower levels of the 13 lines of multiplet 42 of Ti I are completely depolarized by elastic collisions. We find that upper-level collisional depolarization turns out to have an unnoticeable impact on the emergent linear polarization amplitudes, except for the {\lambda 4536 line for which it is possible to notice a rather small depolarization caused by the collisional transfer rates. Concerning the Ca II lines, we show that the collisional rates play no role on the polarization of the upper level of the K line, while they have a rather small depolarizing effect on the atomic polarization of the metastable lower levels of the Ca II IR triplet.Comment: Accepted for publication in Astronomy and Astrophysic

Determining the Magnetization of the Quiet Sun Photosphere from the Hanle Effect and Surface Dynamo Simulations

The bulk of the quiet solar photosphere is thought to be significantly magnetized, due to the ubiquitous presence of a tangled magnetic field at subresolution scales with an average strength ~ 100 G. This conclusion was reached through detailed three-dimensional (3D) radiative transfer modeling of the Hanle effect in the Sr I 4607 line, using the microturbulent field approximation and assuming that the shape of the probability density function of the magnetic field strength is exponential. Here we relax both approximations by modeling the observed scattering polarization in terms of the Hanle effect produced by the magnetic field of a 3D photospheric model resulting from a (state-of-the-art) magneto-convection simulation with surface dynamo action. We show that the scattering polarization amplitudes observed in the Sr I 4607 line can be explained only after enhancing the magnetic strength of the photospheric model by a sizable scaling factor, F=10, which implies = 130 G in the upper photosphere. We argue also that in order to explain both the Hanle depolarization of the Sr I 4607 line and the Zeeman signals observed in Fe I lines we need to introduce a height-dependent scaling factor, such that the ensuing = 160 G in the low photosphere and = 130 G in the upper photosphere.Comment: To appear in ApJ Letter

On the physical origin of the second solar spectrum of the Sc II line at 4247 A

The peculiar three-peak structure of the linear polarization profile shown in the second solar spectrum by the Ba II line at 4554 A has been interpreted as the result of the different contributions coming from the barium isotopes with and without hyperfine structure (HFS). In the same spectrum, a triple peak polarization signal is also observed in the Sc II line at 4247 A. Scandium has a single stable isotope (^{45}Sc), which shows HFS due to a nuclear spin I=7/2. We investigate the possibility of interpreting the linear polarization profile shown in the second solar spectrum by this Sc II line in terms of HFS. A two-level model atom with HFS is assumed. Adopting an optically thin slab model, the role of atomic polarization and of HFS is investigated, avoiding the complications caused by radiative transfer effects. The slab is assumed to be illuminated from below by the photospheric continuum, and the polarization of the radiation scattered at 90 degrees is investigated. The three-peak structure of the scattering polarization profile observed in this Sc II line cannot be fully explained in terms of HFS. Given the similarities between the Sc II line at 4247 A and the Ba II line at 4554 A, it is not clear why, within the same modeling assumptions, only the three-peak Q/I profile of the barium line can be fully interpreted in terms of HFS. The failure to interpret this Sc II polarization signal raises important questions, whose resolution might lead to significant improvements in our understanding of the second solar spectrum. In particular, if the three-peak structure of the Sc II signal is actually produced by a physical mechanism neglected within the approach considered here, it will be extremely interesting not only to identify this mechanism, but also to understand why it seems to be less important in the case of the barium line.Comment: 8 pages, 8 figures, and 1 table. Accepted for publication in Astronomy and Astrophysic