MAGNETOSEISMOLOGY OF THE SUN AND INFERENCES OF SOLAR ROTATION USING NORMAL MODE COUPLING

Abstract

The Sun is our closest star and is composed of self-gravitating ionized gas called plasma. Subject to complicated shearing motion in the solar interior, the plasma generates magnetic fields via inductive effects. The large-scale global magnetic field is responsible for the observed 11-year solar activity cycle. Since solar activity critically impacts the near-Earth space environment and terrestrial life, understanding solar internal dynamics is imperative. This motivates the underlying theme of this dissertation --- using normal-mode helioseismology to image solar internal magnetism and to estimate corrections to differential rotation. As a first step, analytical, closed form expressions of sensitivity kernels for the full second rank Lorentz-stress tensor are proposed. This enables, for the first time, a formal way to infer a general configuration global internal magnetic field. Thereafter, the equivalent Lorentz-stress kernels for probing the subsurface magnetic field underlying localized features on the solar surface are also formulated. Such features of interest may include supergranules and emerging active regions appearing over complicated patches on the photosphere. Further, Slepian basis functions borrowed from terrestrial geophysics are implemented to optimally parameterize the model unknowns in these patches. This renders the inversion significantly better constrained as compared to previously used methods in local normal-mode helioseismology. As a direct application of this Slepian approach, subsurface flow under an average supergranule is inferred. The results are hypothesized to serve as indirect evidence for the entropy rain phenomenon. Using the newly found sensitivity kernels and synthetic yet realistic magnetic fields, forward problems show that helioseismic signatures of magnetism are overshadowed by differential rotation. Therefore, a significant part of this dissertation is dedicated to estimating differential rotation and the associated uncertainty by considering full mode coupling. This marks an advancement over the traditionally adopted approximation where cross-talk between distinct solar modes of oscillation is disregarded. By virtue of the distribution of modes in frequency domain, the full coupling approach was expected to yield near surface corrections over the rotation profile that is inferred when ignoring mode coupling. However, this correction was found to have an upper limit of 0.003 nHz which is negligible for all practical considerations.