Scattering polarization with Paschen-Back effect as a tool to diagnose the magnetic structuring of the solar atmosphere

Abstract

The Sun is a unique physical laboratory in which the various domains of physics inaccessible to laboratories on earth can be studied in great detail. Its proximity allows us to understand it in great depths. George Ellery Hale, in 1908, discovered the magnetic fields in sunspots through his observations of the Zeeman effect (splitting of atomic lines in the presence of a magnetic field). Advancements in observational techniques, and instrumentation since then enabled us to see the Sun with a high resolution. This revealed that the magnetic fields are present everywhere on the Sun and they govern its structure and dynamics. The terrestrial environment is now known to be influenced by the solar magnetic fields. This is one of the reasons why their study is of great importance. One of the methods to study and measure these magnetic fields is to analyze the polarization of the light emitted by the Sun. The traditionally observed intensity spectrum of the Sun called the first solar spectrum gives substantial information about the structure and composition of the solar surface layers (photosphere, chromosphere, transition region, and corona). However, more detailed information like the strength and spatial distribution of the solar magnetic fields can be obtained from the polarized light emitted by the Sun. The line polarization arises due to the magnetic fields and the coherent scattering processes taking place due to anisotropic illumination of the radiating atoms by the limb darkened radiation. The linearly polarized solar spectrum produced by coherent scattering mechanisms is called the ‘second solar spectrum’. Magnetic fields generate polarization via Zeeman effect and also modify the scattering polarization (via the Hanle effect). The fingerprints of the magnetic fields are encoded in the polarization signals. The analysis of these fingerprints is of high scientific interest, since they can be suitably exploited to investigate the magnetic fields present in the solar atmosphere. The most commonly used technique for the magnetic field diagnostics is the Zeeman effect in which case the spectral lines are split by the external magnetic field. However, if the magnetic field is very weak then Zeeman effect cannot be used for diagnosing the field because it is practically difficult to measure extremely small splitting by instruments with finite spectral resolution. Also, the Zeeman effect is blind to mixed polarity fields within the resolution element of the telescope. These drawbacks can be overcome by the Hanle effect which refers to the modification of the non-magnetic scattering polarization by the magnetic fields. The Hanle effect can help to detect the fields that are either weak or turbulent. Thus, it acts as a complementary diagnostic tool to the Zeeman effect. In some situations, the magnetic field is so strong that it produces a splitting whose pattern is very different from that expected for the Zeeman effect. Apart from completely splitting the atomic lines, it also causes the magnetic substates of different atomic states belonging to a given term to interfere. Such an effect of the magnetic field is called Paschen–Back effect. It acts in those domains of field strength that are not accessible through the standard techniques based on the Zeeman effect. Due to the different magnetic field strength regimes in which they operate, the Hanle, Zeeman, and Paschen–Back effects complement one another. The role played by the Paschen–Back effect in shaping the polarization profiles of the spectral lines needs to be understood in order to explore the possibility of using the Paschen–Back effect as a diagnostic tool for magnetic fields. To this end, in this thesis, we develop the scattering theory of Paschen–Back effect in atomic states by accounting for the redistribution in the frequencies of the photons due to Doppler shift and apply it to analyze the polarization profiles of diagnostically important solar spectral lines. This study is an important step forward in understanding the effects of strong magnetic fields and their manifestation in the polarized line radiation emerging from the solar (or stellar) atmosphere. We have divided the thesis into two parts. The first part (Chapters 2 and 3) concerns the problem of line radiative transfer in the presence of polarized blend lines and a polarized continuum. Polarizing blend lines are known to influence the polarization of the spectral lines as well as the polarized background continuum. The theoretical modeling of any spectral line in the second solar spectrum requires a proper treatment of these blend lines. With this motivation, in Chapter 2, we develop a formalism to include a blend line resulting from transition in a two-level atom, having a non-zero intrinsic polarization, formed under nonlocal thermodynamic equilibrium conditions, in the polarized radiative transfer equation in the presence of a weak magnetic field (the Hanle effect). Considering one-dimensional isothermal atmosphere, we study in detail its influence on the main spectral line of interest, also resulting from the transition in a two-level atom. In Chapter 3, we extend the formalism developed in Chapter 2 to incorporate multiple blend lines in the polarized transfer equation. This is important because generally more than one blend line will be present in the wings of the main spectral line. Our formalism can treat any number of blend lines, however, for the sake of simplicity, we present the results of our study involving only two polarized blend lines. In this case we find that the blend line effects are important and needs to be considered when it is lying very close to the main line and is relatively strong. As mentioned earlier, this study becomes important while modeling the spectral lines in the second solar spectrum in order to extract the physical quantities related to the magnetic field and the solar atmosphere. In the second part of the thesis (Chapters 4, 5, 6, and 7), we develop the scattering theory of Paschen–Back effect using the Kramers–Heisenberg scattering matrix approach. We study the problem of quantum interfere (interference between the scattering amplitudes of transitions) in the presence of a magnetic field of arbitrary strength with a particular interest in the Paschen–Back effect regime. The second solar spectrum hosts many spectral lines which are governed by the quantum interference effects. The polarization features of such lines can be explained only when interference effects are consistently accounted for. The quantum interference occurring between the atomic states gets modified in the presence of a magnetic field. We identify and study the signatures imprinted in the polarization profiles by the quantum interference taking place in the presence of a magnetic field. In Chapter 4, we develop the scattering theory of Paschen–Back effect in hyperfine structure states by considering a two-level atom which undergoes hyperfine structure splitting because of the interaction between the total angular momentum of the electron and the nuclear spin. We consider frequency coherent scattering of the photons in the atom’s rest frame and account for the partial frequency redistribution effects in the laboratory frame that arise due to Doppler motions of the atoms. We test this theory by taking example of the Na I D2 line for which observable effects from the Paschen–Back regime are expected for the magnetic fields present on the Sun. Since our aim is to identify and study the fingerprints of Paschen–Back effect on polarization, we consider only a single scattering of the incident unpolarized radiation by the Na atom, avoiding the complications due to radiative transfer. We then formulate the theory of quantum interference between the fine structure states in a two-term atom in the presence of arbitrarily strong magnetic fields (including the Paschen–Back regime) by accounting for the effects due to partial frequency redistribution. We present the theoretical formulation as well as the results of the tests performed in a single scattering on the Li I D1 & D2 lines in Chapter 5. This is the only line system which is sensitive to Paschen–Back effect for the field strengths that are seen in the Sun (the magnetic field strength required to see Paschen–Back effect in fine structure states for other lines is much higher than those present in the Sun). For this line system, the effects from the Paschen–Back regime are seen for field strengths typically present in sunspots. We identify the various signatures of the level-crossings and avoided-crossings that take place in the Paschen–Back regime.We also develop a more general scattering theory in Chapter 6 which accounts for fine and hyperfine structure interference simultaneously in the presence of arbitrary strength magnetic fields, for a two-term atom with hyperfine structure. We account for the effects due to partial frequency redistribution. Due to the relevance to solar applications, we again consider the Li I D1 & D2 lines to test this theory in a single scattering of the unpolarized incident radiation. We find that Paschen–Back effect results in net circular polarization value (which is not seen in the case of Zeeman effect) and that this value has a particular pattern of variation with an increase in the magnetic field strength. This net circular polarization could serve as a diagnostic tool for solar magnetic fields.