# The transfer of resonance line polarization with partial frequency redistribution in the presence of arbitrary magnetic fields

- Ernest Alsina Ballester

- Javier Trujillo Bueno Director
- Luca Belluzzi Director

Defence university: Universidad de La Laguna

Year of defence: 2018

- Artemio Herrero Davó Chair
- Andrés Asensio Ramos Secretary
- Marianne Faurobert Committee member

Type: Thesis

## Abstract

The intensity and polarization of spectral lines encode a wealth of information on the thermodynamic, magnetic, and dynamic properties of the solar atmosphere. In this thesis we have considered the complex radiative transfer problem of modeling, in conditions far from local thermodynamic equilibrium (non-LTE), the Stokes profiles of strong resonance lines for which partial frequency redistribution (PRD) phenomena are important, placing particular focus on the role played by magnetic fields of arbitrary strength, both deterministic and micro-structured. There are several physical mechanisms that can generate or modify the polarization of spectral lines. The scattering of anisotropic radiation by an atomic system is one such mechanism, which most notably causes the scattered radiation to be linearly polarized. Such scattering polarization can be further modified by magnetic fields through the joint action of the Hanle and Zeeman effects, both of which are shown to be relevant for the weak fields typical of quiet solar regions. Moreover, PRD effects, which are well known to appreciably impact the Stokes profiles of strong resonance lines outside the Doppler core, also feature prominently in this investigation. We have considered a two-level model atom with an unpolarized and infinitely sharp lower level, which is suitable for modeling several resonance lines (e.g., the Sr I line at 4607 angstroms, the Ca I line at 4227 angstroms, the line core region of the Mg ii k line, etc.). Given the complexity of the problem of the generation and transfer of resonance line polarization taking into account PRD phenomena and the joint action of the Hanle and Zeeman effects, the investigation in this thesis has been restricted to one-dimensional atmospheric models. We have formulated the radiative transfer problem applying a rigorous quantum theory for the generation and transfer of polarized radiation. In particular, we have considered a theory which allows for the inclusion of all the aforementioned physical mechanisms, using the redistribution matrix formalism (see Bommier 1997b). A radiative transfer code has been developed to efficiently solve such problems, which iteratively solves the Stokes-vector transfer equation, taking into account that the emission coefficients depend on the intensity and polarization of the incident radiation field. To this end, we have developed a suitable iterative scheme based on the work of Trujillo Bueno & Manso Sainz (1999) and Belluzzi & Trujillo Bueno (2014). Such iterative method greatly improves the convergence rate with respect to Lambda iteration, for field strengths such that the Zeeman splitting is much smaller than the line’s Doppler width. We have also developed a modified iterative method, which requires more time per iteration, but for which the convergence rate is not as sensitive to the magnetic field strength. The aforementioned radiative transfer code has first been applied to the unmagnetized case, in order to investigate the dependence of the intensity and polarization of the Sr I line at 4607 angstroms and the Sr II line at 4078 angstroms on the atmospheric model. Another point of interest has been to investigate the impact of elastic collisions on different spectral lines, focusing both on their frequency redistribution effect and their depolarizing effect. We have considered the impact of such collisions both for spectral lines originating in the photosphere (for which PRD effects have a neglible impact), and for lines originating in the chromosphere (for which PRD effects are especially apparent in the wings). The rest of the research problems considered, which represent the bulk of the work of this thesis, focus on the influence of the magnetic field on the polarization of resonance lines. An important conclusion is that, for strong spectral lines in which PRD effects produce broad linear polarization profiles that extend into the line wings, it is crucial to take into account the joint action of scattering polarization and the Hanle and Zeeman effects in order to correctly model their Stokes profiles. In particular, we have shown that for such lines an artificial magnetic sensitivity is found in the wings of the Q/I and U/I profiles when the Zeeman effect is neglected, even when the magnetic field is so weak that the Zeeman splitting is much smaller than the Doppler width. Aside from studying the impact of deterministic magnetic fields on spectral lines, we have also considered micro-structured fields, that is, fields whose orientation changes over scales smaller than the mean free path of the line photons. For micro-structured fields with an isotropic distribution of its orientations, the impact of neglecting the Zeeman effect and PRD effects on the line core polarization, in photospheric lines such as the Sr I line at 4607 angstroms, has been investigated. This was motivated by the fact that such effects had been neglected in previous investigations, in which observations of the linear polarization produced by scattering processes in such lines were modeled in order to infer the strength of unresolved magnetic fields in the quiet solar photosphere. We have also studied the impact of strong isotropic magnetic fields on the line scattering polarization, placing particular attention on the case in which elastic collisions are efficient enough to completely destroy the upper level’s atomic polarization. Perhaps, the main contribution of this work is the theoretical discovery that the magneto-optical effects, i.e., the magnetically-induced couplings between different polarization states of the radiation propagating through the medium, produce an observable magnetic sensitivity in the wings of the linear polarization profiles of strong resonance lines, where large Q/I amplitudes are produced by PRD effects. We have performed a detailed investigation on the impact of the magneto-optical effects for different geometries and strengths of the magnetic field, also providing theoretical arguments for the fact that they operate mainly in the line wings, and for field strengths that are typical of the quiet Sun. We have pointed out that the magneto-optical effects enhance the diagnostic capabilities of lines forming in the outer layers of the solar atmosphere since, through them, the polarization signals in the wings encode information on the magnetic activity in deeper atmospheric regions. We have emphasized that this novel magnetic sensitivity further motivates the development of instruments capable of making high-precision spectropolarimetric observations of strong resonance lines of the chromosphere and transition region, such as those of the CLASP sounding rocket experiments (Lyman alpha and Mg II h & k). We have also proposed that the surprising U/I wing signals and the spatial variation found in the wings of the Q/I and U/I profiles of the chromospheric Ca I line at 4227 angstroms can be explained by such effects. Finally, we have also investigated the physical situations in which the magneto-optical effects can produce a net decrease in the polarization fraction of spectral line radiation. The results of this thesis strongly motivate further developments in this line of research. A step of interest is to develop a radiative transfer code that, taking into account the same physical mechanisms investigated in this work, is capable of performing inversions of Stokes-vector observations in chromospheric lines. Additional key developments will be to include more complex atomic models, and to solve the problem of three-dimensional (3D) radiative transfer taking into account all the physical mechanisms studied in this thesis. All of these breakthroughs will lead to a deeper understanding of solar magnetism through the modeling of spectropolarimetric observations.