Exploration of the second solar spectrum through polarimetric studies

Abstract

The discovery of Zeeman effect opened a new window to observe the Sun. It enabled to understand the magnetic field which is one of the basic features that govern different physical processes on the Sun. These magnetic fields leave their signatures in the splitting and polarization of spectral lines which can be extracted using spectro-polarimetry. With the advent of increasingly powerful telescopes, like with the SOT/SP instrument on-board the Japanese HINODE satellite, which achieved a spatial resolution of 0.3 arcsec (or 200 km on the Sun), the small-scale structure of solar magnetic fields have been explored via the Zeeman effect. It is however now understood that the fundamental building blocks of solar magnetism are present on scales much smaller than those resolved by HINODE. The polarization of line radiation which is caused by resonance scattering on bound atomic levels acts as a tool to measure these small scale magnetic fields. A modification of this process by external magnetic fields is called the Hanle effect. Comparison between the available constraints from the Hanle effect with the magnetic fluxes resolved by the HINODE spacecraft reveals that about two thirds of the total magnetic flux remains invisible at the HINODE 200 km resolution, since this flux is tangled on very small scales, possibly 10-100 m, which is nearly 4 orders of magnitude smaller than the HINODE resolution limit. While Hanle effect constraints on the properties of this “hidden” magnetic flux exist, very little is known about its depth dependence. One of the main objectives of the thesis is to explore the center-to-limb variation (CLV) of the Stokes profiles which is in turn governed by the height variation of the temperature-density structure in the solar atmosphere. Apart from this we study one of the primary physical quantity needed to carry out the analysis of the scattering process i.e., the redistribution matrix. These studies are motivated by the existence of many unexplained signatures in the Second Solar Spectrum (SSS), which is the linearly polarized spectrum of the Sun caused by coherent scattering process. The thesis is divided into three parts. The first part is dedicated to the observations and modeling of the CLV of the well known Ca I 4227 Å line. Not much progress is done in the literature in the area of modeling the CLV of different lines in the SSS because of the complexity of the problem. The main challenge is to obtain a single model atmosphere which can provide a simultaneous fit to the CLV of the (I,Q=I) spectra. From the theoretical perspective, the line radiative transfer modeling of the observed data in the magnetically quiet regions using the scattering theory is essential. To this end, we have to solve the polarized line transfer equation that governs the absorption, emission and scattering of radiation in the stellar atmosphere. We use the one-dimensional (1D) modeling approach to study the CLV of the Ca I 4227 Å line, which exhibits largest scattering polarization of all the lines in the visible spectrum of the Sun. For the purpose of our studies we have observed the Ca I 4227 Å line at 14 positions from the center-to-limb on the Sun using Zurich Imaging Polarimeter-3 at Istituto Ricerche Solari Locarno in Switzerland. We have modeled the CLV of this line using different realistic solar atmospheres (Chapter 2). From the studies in Chapter 2 we concluded that no single 1D model attempted by us helps us in providing a simultaneous fit to the CLV of the Stokes profile. The solar atmosphere is too complex to be represented by a 1D model atmosphere. We have to go beyond 1D modeling like multi-dimensional modeling to represent the actual solar atmosphere. However this does not represent an impediment to the use of the Ca I 4227 A line for solar magnetic field diagnostics. To demonstrate this we have carried out a model independent analysis to determine the turbulent weak magnetic fields in the solar atmosphere. The second and third part of the thesis is dedicated to the theoretical studies of the fundamental physical quantity called the redistribution matrix which is required to study the physics of scattering processes. The redistribution matrix contains all the information of the scattering process, and hence is an important parameter to be studied in detail. In this regard, there are certain approximations made in different theoretical approaches developed in the literature to enable reduce the complexity of the problem. However, such approximations point towards the existence of spectral features in the SSS which cannot be explained using the available standard theories. Our efforts in the second and third part of the thesis is to relax some of the approximations and study its effects on the emergent Stokes profiles by considering different examples. In second part of the thesis we study a series of problems concerning the polarized line formation with the angle-dependent partial frequency redistribution (PRD). The liner polarization of the strong resonance lines are sensitive to the type of frequency redistribution used. The PRD matrix is dependent on the incoming and outgoing frequencies and angles. In order to reduce the computational efforts angleaveraged PRD functions are used in most of the studies in the literature. In Chapters 3, 4 and 5 we consider different problems and relax this approximation and study the effects of using angle-dependent PRD on emergent Stokes profiles. In Chapter 3 we study the effect of electron scattering redistribution on atomic line polarization in non-magnetic regime. We use angle-dependent electron scattering and atomic redistribution functions and present efficient numerical technique to solve this problem. In Chapter 4 we study the combined effects of angle-dependent PRD and quantum interference phenomena arising between the fine structure (J) states of a two-term atom or between the hyperfine structure (F) states of a two-level atom by restricting our attention to the case of non-magnetic and collisionless line scattering on atoms. From the studies in Chapters 3 and 4 in the non-magnetic regime we conclude that the effect of angle-dependent PRD are sensitive to the optical thickness of the slab used for the radiative transfer studies. In Chapter 5 we study the effect of using angle-dependent PRD in the presence of weak magnetic field, i.e. the Hanle effect. We present efficient decomposition techniques to solve the problem at hand. We point towards the necessity to use angle-dependent PRD to solve the Hanle transfer problem accurately, especially for the Stokes U parameter by taking the example of vertical magnetic fields and turbulent magnetic fields. In the third part we have attempted to relax another common assumption made in our previous calculations, i.e. assuming the polarization of the lower-level of the atom involved in the scattering process is zero. In Chapter 6 we formulate a general theory for magnetized media to handle the problem of radiative transfer including the effects of PRD and polarization of the lower-level of the atom involved in the transition, starting from Kramers-Heisenberg scattering formulation. We then obtain the radiative transfer equation starting from the well established quantumfield theory approach for the problem at hand. Further we apply this theory to two case studies in the non-magnetic regime which leads us to the conclusion that the effects of lower level polarization are significant only in the line core. Based on our conclusion we also propose a simplified numerical approach to solve the problem of polarized radiative transfer with PRD and lower-level polarization.