UC Santa Cruz

This doctoral work is motivated by magnetic field transport processes in the deep interior of the Sun and their eventual observational signatures at the solar surface. In particular, we are inspired by a combination of previous computational and observational work. First of all, based on observations at the solar surface of sunspots embedded in active regions, it is widely believed that large-scale, strong magnetic flux emerges from the Sun's deep interior in the form of arched, cylindrical tube-like structures often known simply as "magnetic flux tubes." The buoyant transport of these flux tubes from the solar interior towards the surface plays an essential role in the emergence of active regions, the formation of sunspots, and the overall solar dynamo. A range of two- and three-dimensional computational work in the past has focused on the formation and transport of magnetic flux tubes from the deep solar interior. Many such studies have assumed the existence of such magnetic structures and studied highly simplified models like the buoyant rise of an isolated flux tube in a quiescent, field-free environment. Here, motivated by their formation, (e.g. Cline et al., 2003a, Brummell et al., 2002), we systematically attempt to remove some of these restrictive assumptions and study the rise of a toroidal flux tube embedded in a large-scale poloidal background magnetic field, with and without the presence of turbulent convection.

In this thesis, we have divided our work into two major parts. In the first part, we investigate the rise of a \emph{non-isolated} toroidal flux tube through a volume-filling large-scale magnetic field in a quiescent background state. We find that positive and negative twisted flux tubes show starkly different dynamics. In particular, for a given large-scale magnetic field, flux tubes of one sign of the twist are more likely to rise than the other. We have created a mathematical model based on the forces acting on the flux tube that can explain and even predict the observed asymmetric rise dynamics for a given flux tube twist and background field orientation. This reveals a filtering region in the parameter space that we refer to as Selective Rise Regime (SRR). To better understand the statistical relevance of the SRR, we also carry out Monte Carlo (MC) simulations of multiple flux tubes rising through the background field. This study further shows that the SRR, along with the MC simulations, plausibly explains the broad range of solar helicity observations that are collectively known as the Solar Hemispheric Helicity rules (SHHR). The SHHR declare primarily that there is a preferred helicity of the emerging flux in each hemisphere (negative for Northern; positive for Southern). Our model provides an explanation for this major bias. Furthermore, the SHHR is a weak rule, obeyed only 60-80 % of the time. Our models also provide good physical reasons for statistical violations of the rule, and further makes predictions about the cycle dependence of the rule that could be tested.

In the second part, we examine a more realistic and therefore more complex version of the same thing. Specifically, we consider the buoyant rise of magnetic flux tubes from their formation in a deep radiative zone, through a turbulent overshooting convection zone that self-consistently arranges a volume-filling large-scale background field. Despite the presence of much more complicated dynamics, we still find the same preferential rise of flux tubes of a particular twist, thus establishing the robustness of SRR mechanism. The presence of convection does however add another layer of statistical fluctuations to the observed asymmetry in the flux tube dynamics, which we investigate by Monte Carlo-like suites of simulations to again confront variations in the SHHR.