Elementary heating events – magnetic interactions between two flux sources

III. Energy considerations

¹ Niels Bohr Institute, Julie Maries Vej 30, 2100 Copenhagen Ø, Denmark e-mail: kg@astro.ku.dk
² School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland

Received: 26 January 2005
Accepted: 5 April 2005

Abstract

The magnetic field plays a crucial role in heating the solar corona – this has been known for many years – but the exact energy release mechanism(s) is(are) still unknown. Here, we investigate in detail, using resistive, non-ideal, MHD models, the process of magnetic energy release in a situation where two initially independent flux systems are forced into each other. Work done by the foot point motions goes into building a current sheet in which magnetic reconnection releases some of the free magnetic energy leading to magnetic connectivity changes. The scaling relations of the energy input and output are determined as functions of the driving velocity and the strength of fluxes in the independent flux systems. In particular, it is found that the energy injected into the system is proportional to the distance travelled. Similarly, the rate of Joule dissipation is related to the distance travelled. Hence, rapidly driven foot points lead to bright, intense, but short-lived events, whilst slowly driven foot points produce weaker, but longer-lived brightenings. Integrated over the lifetime of the events both would produce the same heating if all other factors were the same. A strong overlying field has the effect of creating compact flux lobes from the sources. These appear to lead to a more rapid injection of energy, as well as a more rapid release of energy. Thus, the stronger the overlying field the more compact and more intense the heating. This means observers need to know not only the flux of the magnetic fragments involved in an event, but also their rate and direction of movement, as well as the strength and orientation of the surrounding field to be able to predict the energy dissipated. Furthermore, it is found that rough estimates of the available energy can be obtained from simple models, starting from initial potential situations, but that the time scale for the energy release and, therefore its impact on the coronal plasma, can only be determined from more detailed investigations of the non-ideal behaviour of the plasma.