Global scale magnetic field extrapolation in the solar corona using a Yin Yang grid
by Argyrios Koumtzis
Date of Examination:2023-07-17
Date of issue:2024-05-06
Advisor:Prof. Dr. Hardi Peter
Referee:Prof. Dr. Hardi Peter
Referee:Prof. Dr. Stefan Dreizler
Persistent Address:
http://dx.doi.org/10.53846/goediss-10299
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Abstract
English
The solar magnetic field significantly influences and structures the solar coronal plasma as magnetic forces are the dominant forces within the solar corona. Therefore, an in-depth understanding of the phenomena that occur there requires the best possible description of the coronal magnetic field. Prominent instances of such phenomena include solar flares, which are abrupt discharges of electromagnetic energy observed through the whole electromagnetic spectrum. Solar flares can unleash as much energy as a billion atomic bombs in just a matter of minutes. Other crucial phenomena are coronal mass ejections (CMEs), colossal solar storms that explosively move vast clouds of hot, magnetized plasma-comprising electrons, protons, and atomic nuclei into interplanetary space at speeds that can exceed several million miles per hour. Lastly, there's the solar wind, a continuous outflow of charged particles, primarily electrons and protons. These particles, streaming along the Sun's highly dynamic magnetic field, permeate the solar system at speeds ranging from 250 to 750 kilometers per second. These phenomena serve as the primary engines behind space weather. They lead to beautiful displays such as the auroras we observe on Earth caused by solar particles colliding with Earth's atmospheric gases. However, these solar events can also provoke catastrophic consequences. These include disruptions to telecommunications and satellite operations, and profound effects on critical infrastructure such as power grids. When severe, these disruptions can lead to extensive power outages and satellite failures, underscoring the importance of monitoring and understanding these dynamic solar processes. Although direct, regular measurements of the coronal magnetic field aren't accessible yet, we can study its structure and dynamics by extrapolating the photospheric vector-field measurements into the corona. This thesis particularly discusses global coronal structures, typically modeled using spherical grids because of the spherical geometry present on the Sun and synoptic vector magnetograms as the boundary conditions. We have developed a new numerical code that facilitates nonlinear force-free magnetic-field extrapolations in spherical geometry. This code is based on a well-tested optimization principle that has been successfully applied to a Cartesian grid and a single spherical finite-difference grid. This is the first instance where the algorithm can reconstruct the magnetic field across the entire corona, encompassing the polar regions. The previous versions of this spherical code experienced numerical inefficiencies due to the convergence of these grids at the solar polar regions. The new code has incorporated the so-called Yin-Yang overhead grid, which effectively tackles this issue. As a result, both the speed and accuracy of the optimization algorithm have been enhanced relative to the earlier versions. We validate our new code using a widely recognized semi-analytical model, the Low and Lou solution, which is often used as a standard to test nonlinear force-free extrapolation codes. We then use vector synoptic magnetograms provided by the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) as a boundary condition for our model and reconstruct the global coronal magnetic field. We chose to study the performance of our model during two periods of significantly different solar activity: one during solar maximum activity and one during solar minimum activity. We compare the resulting field lines with relevant observations to further investigate the quality of our solutions. We then discuss the possible applications of our code and what research questions we could address with this newly developed tool.
Keywords: Solar Corona; Magnetic Fields; Yin yang grid
