Theory and observations of the magnetic field in the solar corona

Abstract

Although the solar corona is one of the most studied areas in solar physics, its activity, such as flares, prominence eruptions and CMEs, is far from understood. Since the solar corona is a low-ß plasma, its structure and dynamics are driven by the magnetic field. The aim of this PhD thesis to study the magnetic field in the solar corona. Unfortunately, high quality direct measurements of the coronal magnetic field are not available and theoretical extrapolation using the observed photospheric magnetic field is required. The thesis is mainly divided in two parts. The first part deals with the comparison between theoretical models of magnetic fields and observed structures in the corona. For any theoretical model, a quantitative method to fit magnetic field lines to observed coronal loops is introduced. This method provides a quantity C that measures how closely a theoretical model can reproduce the observed coronal structures. Using linear force-free field extrapolation, the above field line fitting method is used to study the evolution of an active region. The method is also illustrated when the theoretical magnetic field depends on more than one parameter. The second part of the thesis focuses on the linear force-free field assumption using two different geometric configurations. Firstly a vertical rigid magnetic flux tube is considered. The analytical expression of the magnetic field is obtained as an expansion in terms of Bessel functions. The main properties of this system are discussed and compared with two cylindrically symmetric twist profiles. For the second system, the photosphere is assumed to be an infinite plane. Using translational geometry, the analytical expression of the linear force-free magnetic field that matches a prescribed line of sight magnetic field component is obtained. This solution is compared with the non-linear solution obtained by Roumeliotis (1993).