Elementary heating events – magnetic interactions between two flux sources

II. Rates of flux reconnection

¹ School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland e-mail: clare@mcs.st-and.ac.uk
² Niels Bohr Institute for Astronomy, Physics and Geophysics, Julie Maries vej 31, 2300 Copenhagen Ø, Denmark

Received: 18 September 2003
Accepted: 20 August 2004

Abstract

Magnetic fragments in the photosphere are in continuous motion and, due to the complex nature of the magnetic field in the solar atmosphere, these motions are likely to drive a lucrative coronal energy source: the passing of initially-unconnected opposite-polarity fragments that release energy through both closing and then re-opening the same fieldlines. Three-dimensional, time-dependent MHD and potential models are used to investigate the passing of fragments in an overlying field. 
The processes of closing and opening the field generally occur through separator and separatrix reconnection, respectively. The rates of flux reconnection in these processes are determined. They are found to be dependent on the direction of the surrounding magnetic field relative to the motion of the fragments and the velocity of the sources. In particular, separator reconnection rates (closing) and separatrix-surface reconnection rates (opening) are directly related to the rate of flux transport perpendicular to the current sheet (overlying field). The results suggest that both types of reconnection are fast with the peak rates of separator and separatrix reconnection occurring at 58% and 29% of the peak potential reconnection rate, respectively, when the sources are driven at a hundredth of the peak Alfvén velocity in the box. Moreover, the slower the system is driven the closer the flux reconnection rates are to the instantaneous potential rates. Furthermore, there is a maximum reconnection rate for both types of reconnection as the driving speed tends to the Alfvén speed with the separatrix reconnection rate typically half that of separator reconnection. These results suggest that, on the Sun, reconnection driven by the passing of small-scale network and intranetwork fragments is a highly efficient process that is very likely to contribute significantly to the heating of the background solar corona. 
The three-dimensional reconnection processes are efficient because, unlike in two-dimensions, there are many places within the current sheets where reconnection can take place simultaneously giving rise to fine-scale structure along the boundaries between the open, closed and re-opened flux. Furthermore, due to the complexity of the magnetic field above the photosphere the reconnection all takes place low down at less than a quarter of the separation of the initial fragments above the photosphere.