Helicity and eruptivity of solar magnetic flux ropes

The aim of this study is to better understand coronal mass ejections from the Sun. In particular, can the helicity of magnetic flux ropes in the low solar corona be used to predict their eruption, and does it correlate with the topologies of the ejected magnetic clouds?

Background: Magnetic flux ropes are twisted bundles of magnetic field lines in the solar atmo- sphere. They may emerge ready-formed from the solar interior, or may form in the atmosphere through a combination of surface flows and magnetic reconnection. They are observed as fila- ment channels on the solar disk, or as coronal cavities above the limb. There is now general agreement that erupting flux ropes are one a major source of coronal mass ejections (CMEs). Throwing vast quantities of magnetised plasma into interplanetary space, CMEs are one of the major drivers of space weather here at Earth. By disturbing our magnetosphere, this can cause major disruption to satellite communications, aircraft, and even power networks on the ground. At present, we are unable to predict CMEs until they leave the Sun. Even then, we are unable to predict their geo-effectiveness until (and if) they pass one of our near-Earth satellites, since this depends on the CME's internal magnetic structure.

Recently, Yeates & Hornig have developed a measure called field-line helicity that describes the local topology of the magnetic field in the solar corona. Lowder & Yeates then carried out a pioneering study showing that this measure can be used to identify magnetic flux ropes in global simulations of the coronal magnetic field. This project will take this as a starting point to probe the physics of flux rope structure and eruptivity, with an eye to predicting the latter.

Proposed methodology:

Year 1. The project will start by developing a 2D numerical code to model the formation and eruption of a single magnetic flux rope, in Cartesian geometry. The purposes are (i) to develop an understanding of the mathematical model, numerical methods, and their implementation in a simplified setting, and (ii) to carry out a parameter study to determine whether twist or flux is the best predictor of eruptivity in such a flux rope, as well as the role of the overlying magnetic field. In other words, what are the "warning signs" of an impending eruption?
Years 2-3. The project will move on to consider 3D simulations in spherical geometry, modelling the full solar corona. This stage will use an existing parallel magneto-frictional code developed by Yeates, that can follow the formation of flux ropes in the global context, as well as modelling their loss of equilibrium. It is envisaged to extend the work of in two directions. Firstly, to test whether the results of the Year 1 study hold in fully 3D geometry with realistic flux ropes of varying shapes. The ultimate goal here is to be able to look at a flux rope in the simulation and predict ahead of time whether or not it will erupt (at least, with some attached probability). Even in numerical simulations, this has not previously been achieved. Secondly, to determine how much of the pre-eruption field-line helicity of erupting flux rope is ejected through the outer model boundary, and how much is simply lost through reconfiguration of the surrounding coronal magnetic field during the eruption. Determining the structure that is actually ejected is highly relevant for space weather prediction, and can be newly studied with recent tools.