Lydon, S. (SciCAM) – Magnetic Buoyancy Instabilities in Deep, Twisted Magnetic Layers

In observing the solar magnetic field, possibly the most prominent features visible on the surface are sunspots, which emerge at different latitudes as the solar cycle progresses. Sunspot pairs are believed to be formed by concentrated bundles of mainly toroidal magnetic field (flux tubes) looping through the surface. These regions exhibit surprisingly ordered patterns of behavior such as the Hale's Polarity Law, Joy’s Law, and the Solar Hemispherical Helicity Rule (SHHR). The latter states that emerging flux in the Northern hemisphere generally has left-handed current helicity, whereas the Southern hemisphere has right handed. While there is magnetic field at all scales on the sun, the origins of these active regions and the connection between large-scale dynamo generated fields and active region scales is a long standing and difficult question. The flux tubes that form sunspots most likely originate from magnetic buoyancy instabilities that occur in the solar tachocline and then subsequently rise through the convective zone. Although there are many theories of the origin of the SHHR, the helicity content in the emerging flux is often claimed to be a direct result of the helicity (or angulation) in the originating dynamo field.\

Magnetic buoyancy instabilities and their non-linear evolution have been studied and simulated by others in 2D and 3D, generally using magnetic slabs that possess infinite gradients at their interfaces, which guarantees that said instability occurs. In this work, we extend these ideas, allowing the initial conditions to have a gently varying interface between magnetic and non-magnetic layers with variable width (while still satisfying criteria to initiate the instability). We look for differences in the evolution of the instabilities in this new scenario. This setup allows us to then add a horizontal poloidal field component to the previous horizontal toroidal component, thereby creating a horizontal field that varies in direction over the depth of the magnetic interface. We study the instabilities of this setup and examine the emerging flux tubes for any resultant helicity in order to explore the relationship between helicity in emerging magnetic structures and that in the originating field.

Overall, we found that when the magnetic interface was wider, the instability proceeded in a distinctly different fashion depending on the particular aspects of the originating layer. In our setup, the fluid generally went unstable lower down in the transition layer and created different geometries of the magnetic structures and secondary instabilities due, at least in part to, the stronger buoyancy forces deeper in the layer and to the necessity of deformation of overlaying field. The instabilities are rapid and mix efficiently, reaching a stable end-state much faster in the deep layer cases than the shallow layer version. \

Furthermore, when adding twist to the originating fields, we found that the resultant helicity in the emerging magnetic structures does indeed depend on the initial profile of the field. In general, a dominant outer helical layer of the flux tube is found, the chirality of which is directly dependent on the angle of poloidal and toroidal field at the point of maximum instability in the layer, even if the structure rose through field of the opposite angulation.

Event Host: Sean Lydon, M.S. Candidate, Scientific Computing & Applied Mathematics

Advisor: Nicholas Brummell