Measuring the Free Energy and Helicity Leading to Solar Eruptive Events
Abstract
The essential ingredients determining solar coronal activity are believed to be the availability of magnetic free energy and the constraint of magnetic helicity conservation. Direct measurements of the helicity and magnetic free energy in the corona are difficult, but it should be possible to infer them from measurements of the helicity and free energy transport through the photosphere. We examine the rate of change of helicity and free energy for a topological open system such as the corona in which the magnetic fields have a non-zero normal component at the boundaries and derive a new formula for the helicity transport rate through the boundaries. A key feature of this formula is that it is manifestly gauge invariant. The result is somewhat counter-intuitive in that only the irrotational electric field transports helicity across boundaries and the inductive electric field does not contribute. We discuss the physical interpretation of our result and demonstrate its application with instructive examples. Furthermore, we derive an expression for the free energy flux, and show that a necessary condition for free energy transport across a boundary is the presence of normal electric currents at the boundary. We discuss the implications of our results for using photospheric vector magnetic and velocity field measurements to derive the solar coronal helicity and magnetic free energy, which can then be used to constrain and drive space weather models for coronal activity.
- Publication:
-
Solar Heliospheric and INterplanetary Environment (SHINE 2018)
- Pub Date:
- July 2018
- Bibcode:
- 2018shin.confE.151A