Magnetic Helicity Modeling in Solar Flares

The understanding of the variations in the conditions of the near-Earth environment, our space weather, is becoming increasingly important, given the growing reliance of human society on space-based technology. Solar storms, such as flares and coronal mass ejections, may severely impact our space weather. Flares and coronal mass ejections are the most energetic events in our solar system, yet is the physics behind these events still not well understood. Related research still seeks answers to the question: When will a flare happen and will it evolve into a coronal mass ejection? Solar storms are caused by the interaction of magnetic field in coronal loops that are rooted in active regions. One of the key challenges in solar physics today is to understand the physics of the magnetic field connecting the photosphere to the corona in active regions. Direct measurements of the photospheric vector magnetic field are well-established and routinely performed. It is still challenging, however, to measure the coronal magnetic field on a routine basis, where we currently rely on sophisticated three-dimensional modeling techniques. The proposed innovative research focuses on the systematic assessment of the complexity of the coronal magnetic field in active regions, based on numerical models, in the context of the upcoming flare activity. In particular, the magnetic helicity, a quantity which is uniquely tied to the complexity of the coronal magnetic field, will be studied systematically. We aim to answer the following scientific questions, for better understanding the physics behind solar flares and to improve our abilities in space weather forecasts: (1) Which degree of coronal magnetic field complexity inevitably leads to a flare? (2) Which time scales are important for the replenishment of magnetic helicity? (3) How is magnetic helicity related to the flare type (eruptive vs. confined), in context with the structural properties of the coronal magnetic field surrounding the flare site?

The main aim of this project was to investigate the link between solar eruptions and the magnetic complexity of the underlying magnetic field. We aimed to study magnetic helicity, a quantity which is uniquely tied to the complexity of the underlying coronal magnetic field, systematically for a large number of solar eruptions. Solar eruptions are caused by the interaction of magnetic fields in coronal loops that are rooted in regions of strong magnetic field on the solar surface (the photosphere), so-called active regions (ARs). Direct measurements of the photospheric vector magnetic field are well-established and routinely performed, where the unprecedented full-disk high-resolution and high-cadence observations of the Sun's surface magnetic field by NASA's Solar Dynamics Observatory represent a unique data source. To measure the coronal magnetic field on a routine basis we rely on sophisticated three-dimensional modeling techniques, using the surface magnetic field as an input. Based on the modeling, we aimed to clarify whether the characteristics of the time evolution of magnetic helicity hints at upcoming flare activity (Aim 1), how helicity is related to the type of upcoming flaring (confined or eruptive; Aim 2) and other structural properties of the host AR, and which time scales are relevant regarding the replenishment of the helicity budget. We summarize our main findings in respect of the research aims above in the following. (1) We find that neither the overall preflare level (magnitude) of the coronal preflare helicity and energy budget, nor their change rate (time derivative) are strong indicators for upcoming flare activity or the type of flaring. Instead, relative measures, such as the free energy ratio and the helicity ratio appear much more indicative and more clearly relate to the flare type. (2) We provide refined suggestions for "critical values" that indicate upcoming CME-associated flaring and to predict the type of major flaring (GOES class M5 or larger) correctly in about 70% of the events. Noteworthy, when involving an additional measure of stability (the critical height for torus instability) the success rate of flare type prediction is raised to over 90%. (3) The time needed for replenishment of the coronal budgets distinctly relates to the flare size. In smaller eruptive flares (GOES classes M1 to M4) the budgets of the total energy and helicity are reduced only minimally (by a few percent) and replenished essentially instantly. In contrast, after eruptive X-class flares, the budgets of free energy and current-carrying helicity remain diminished for at least 12 hours. Together with the flare-related reductions of ~20% and ~30%, respectively, this represents a strong conditioning to the flare ability of the corona.