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

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

The potential of the wavelength-integrated scattering polarization of the hydrogen Ly-alpha line for probing the solar chromosphere

The intensity and the linear scattering polarization profiles of the hydrogen Ly-alpha line encode valuable information on the thermodynamic and magnetic structure of the upper layers of the solar chromosphere. The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) sounding rocket experiment provided unprecedented spectropolarimetric data of this line, as well as two-dimensional broadband images in intensity and linear polarization. We theoretically investigate the potential of the Ly-alpha broadband polarimetric signals for probing the solar chromosphere and its magnetic fields. We analyze the synthetic Stokes profiles obtained from a series of radiative transfer (RT) calculations out of local thermodynamic equilibrium, considering semi-empirical one-dimensional models of the solar atmosphere. The wavelength-integrated linear polarization signal is found to be dominated by the contribution from the wings when considering a Gaussian weighting function with a FWHM that corresponds to the CLASP slit-jaw broadband filter. These broadband linear polarization signals are strongly sensitive to magnetic fields of strengths on the order of 50 G, via the action of magneto-optical (MO) effects, and are expected to encode information on the middle-upper chromosphere. The two-dimensional broadband intensity and linear polarization images observed by CLASP can be suitably mimicked using synthetic wavelength-integrated signals obtained considering atmospheric models and magnetic fields that are representative of solar regions with different levels of activity, provided that the impact of MO effects is taken into account. Despite the limitations of a one-dimensional RT modeling, this work illustrates the diagnostic potential of filter-polarimetric Ly-alpha signals for probing the solar chromosphere and its magnetism.Comment: 16 pages (12 main text + 4 appendix). 7 figures in the main text (2 panels in Fig.1 , 2 panels in Fig.2, 4 panels in Fig.3, 9 panels in Fig.4, 4 panels in Fig.5, 2 panels in Fig.6, single panel in Fig. 7). 3 figures in appendices (single panel in Fig.8, single panel in Fig.9, 6 panels in Fig.10). Accepted for publication in The Astrophysical Journal on 03/03/202

Spatial variations of the SrI 4607\AA scattering polarization signals at subgranular scale observed with ZIMPOL at GREGOR telescope

Sr I 4607\AA spectral line shows one of the strongest scattering polarization signals in the visible solar spectrum. The amplitudes of these signals are expected to vary at granular spatial scales. This variation can be due to changes in the magnetic field intensity and orientation (Hanle effect) as well as due to spatial and temporal variations in the plasma properties. Measuring the spatial variation of such polarization signal would allow us to study the properties of the magnetic fields at subgranular region. But, the observations are challenging since both high spatial resolution and high spectropolarimetric sensitivity are required at the same time. To the aim of measuring these spatial variations at granular scale, we carried out a spectro-polarimetric measurement with the Zurich IMaging POLarimeter (ZIMPOL), at the GREGOR solar telescope at different limb distances on solar disk. Our results show a spatial variation of scattering linear polarization signals in Sr I 4607\AA line at the granular scale at every $\mu$, starting from 0.2 to 0.8. The correlation between the polarization signal amplitude and the continuum intensity imply statistically that the scattering polarization is higher at the granular regions than in the intergranular lanes.Comment: 4 pages, 3 figures, Proceeding of Third Meeting of the Italian Solar and Heliospheric Community, OCTOBER 28-31, 2018 - TURI

The impact of angle-dependent partial frequency redistribution on the scattering polarization of the solar Na i D lines

The long-standing paradox of the linear polarization signal of the Na i D1 line was recently resolved by accounting for the atom's hyperfine structure and the detailed spectral structure of the incident radiation field. That modeling relied on the simplifying angle-averaged (AA) approximation for partial frequency redistribution (PRD) in scattering, which potentially neglects important angle-frequency couplings. This work aims at evaluating the suitability of a PRD-AA modeling for the D1 and D2 lines through comparisons with general angle-dependent (AD) PRD calculations, both in the absence and presence of magnetic fields. We solved the radiative transfer problem for polarized radiation in a one-dimensional semi-empirical atmospheric model with microturbulent and isotropic magnetic fields, accounting for PRD effects, comparing PRD-AA and PRD-AD modelings. The D1 and D2 lines are modeled separately as two-level atomic system with hyperfine structure. The numerical results confirm that a spectrally structured radiation field induces linear polarization in the D1 line. However, the PRD-AA approximation greatly impacts the Q/I shape, producing an antisymmetric pattern instead of the more symmetric PRD-AD one, while presenting a similar sensitivity to magnetic fields between 10 and 200 G. Under the PRD-AA approximation, the Q/I profile of the D2 line presents an artificial dip in its core, which is not found for the PRD-AD case. We conclude that accounting for PRD-AD effects is essential to suitably model the scattering polarization of the Na i D lines. These results bring us closer to exploiting the full diagnostic potential of these lines for the elusive chromospheric magnetic fields

Observations on spatial variations of the Sr~{\sc i} 4607~\AA~scattering polarization signals at different limb distances with ZIMPOL

The Sr~{\sc i} 4607~\AA\ spectral line shows one of the strongest scattering polarization signals in the visible solar spectrum. The amplitude of this polarization signal is expected to vary at granular spatial scales, due to the combined action of the Hanle effect and the local anisotropy of the radiation field. Observing these variations would be of great interest because it would provide precious information on the small-scale activity of the solar photosphere. At present, few detections of such spatial variations have been reported. This is due to the difficulty of these measurements, which require combining high spatial ($\sim$ 0.1"), spectral ($\leq$ 20 m\AA), and temporal resolution (< 1 min) with increased polarimetric sensitivity ($\sim$ 10$^-$$^4$). Aims. We aim to detect spatial variations at granular scales of the scattering polarization peak of the Sr~{\sc i} 4607~\AA\ line at different limb distances, and to study the correlation with the continuum intensity. Methods.Using the Zurich IMaging POLarimeter (ZIMPOL) system mounted at the GREGOR telescope and spectrograph in Tenerife, Spain, we carried out spectro-polarimetric measurements to obtain the four Stokes parameters in the Sr~{\sc i} line at different limb distances, from $\mu=0.2$ to $\mu=0.8$, on the solar disk. Results.Spatial variations of the scattering polarization signal in the Sr~{\sc i} 4607~\AA\ line, with a spatial resolution of about 0.66", are clearly observed at every $\mu$. The spatial scale of these variations is comparable to the granular size. A statistical analysis reveals that the linear scattering polarization amplitude in this Sr~{\sc i} spectral line is positively correlated with the intensity in the continuum, corresponding to the granules, at every $\mu$.Comment: 8 pages, 6 figures, accepted for publication in A&

Evidence for the Operation of the Hanle and Magneto-Optical Effects in the Scattering Polarization Signals Observed by CLASP2 Across the Mg II h and k Lines

Radiative transfer investigations of the solar Mg II h and k resonance lines around 280~nm showed that, while their circular polarization (Stokes V) signals arise from the Zeeman effect, the linear polarization profiles (Stokes Q and U) are dominated by the scattering of anisotropic radiation and the Hanle and magneto-optical (MO) effects. Using the unprecedented observations of the Mg II and Mn I resonance lines obtained by the Chromospheric LAyer Spectro-Polarimeter (CLASP2), here we investigate how the linear polarization signals at different wavelengths (i.e., at the center, and at the near and far wings of the k line) vary with the longitudinal component of the magnetic field ($B_{L}$) at their approximate height of formation. The $B_{L}$ is estimated from the V signals in the aforementioned spectral lines. Particular attention is given to the following quantities that are expected to be influenced by the presence of magnetic fields through the Hanle and MO effects: the sign of the U signals, the total linear polarization amplitude ($LP$) and its direction ($\chi$) with respect to a reference direction. We find that at the center and near wings of the $k$ line, the behavior of these quantities is significantly different in the observed quiet and plage regions, and that both $LP$ and $\chi$ seem to depend on $B_{L}$. These observational results are indicative of the operation of the Hanle effectComment: 26 pages, 18 figures, accepted for publication in the Astrophysical Journa

Mapping Solar Magnetic Fields from the Photosphere to the Base of the Corona

Routine ultraviolet imaging of the Sun's upper atmosphere shows the spectacular manifestation of solar activity; yet we remain blind to its main driver, the magnetic field. Here we report unprecedented spectropolarimetric observations of an active region plage and its surrounding enhanced network, showing circular polarization in ultraviolet (Mg II $h$ & $k$ and Mn I) and visible (Fe I) lines. We infer the longitudinal magnetic field from the photosphere to the very upper chromosphere. At the top of the plage chromosphere the field strengths reach more than 300 gauss, strongly correlated with the Mg II $k$ line core intensity and the electron pressure. This unique mapping shows how the magnetic field couples the different atmospheric layers and reveals the magnetic origin of the heating in the plage chromosphere.Comment: 50 pages, 11 figures, 1 table, published in Science Advance

The Polarization of the Solar Ba ii D1 Line with Partial Frequency Redistribution and Its Magnetic Sensitivity

We investigate the main physical mechanisms that shape the intensity and polarization of the Ba ii D _1 line at 4934 Å 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 D _1 linear polarization, we relied on a two-term atomic model that neglects such metastable levels but includes HFS. The D _1 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 D _1 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

The polarization angle in the wings of Ca I 4227: A new observable for diagnosing unresolved photospheric magnetic fields

Context. When observed in quiet regions close to the solar limb, many strong resonance lines show conspicuous linear polarization signals, produced by scattering processes (i.e., scattering polarization), with extended wing lobes. Recent studies indicate that, contrary to what was previously believed, the wing lobes are sensitive to the presence of relatively weak longitudinal magnetic fields through magneto-optical (MO) effects. Aims. We theoretically investigate the sensitivity of the scattering polarization wings of the Ca