Topology and Current Ribbons: a Model for Current, Reconnection and Aring in a Complex, Evolving Corona

Magnetic eld enters the corona from the interior of the Sun through isolated magnetic features on the solar surface. These features correspond to the tops of submerged magnetic ux tubes, and coronal eld lines often connect one ux tube to another, deening a pattern of inter-linkage. Using a model eld, in which ux tubes are represented as point magnetic charges, it is possible to quantify this inter-linkage. If the coronal eld were current free then motions of the magnetic features would change the inter-linkage through implicit (vacuum) magnetic reconnection. Without reconnection the conductive corona develops currents to avoid changing the ux linkage. This current forms singular layers (ribbons) owing along topologically signiicant eld lines called separators. Current ribbons store magnetic energy as internal stress in the eld; the amount of energy stored is a function of the ux tube displacement. To explore this process we develop a model called the minimum current corona (MCC) which approximates the current arising on a separator in response to displacement of photospheric ux. This permits a model of the quasi-static evolution of the corona above a complex active region. We also introduce aring to rapidly change the ux inter-linkage between magnetic features when the internal stress on a separator becomes too large. This eliminates the separator current and releases the energy stored by it. Implementation of the MCC in two examples reveals repeated aring during the evolution of simple active regions, releasing anywhere from 10 27 {10 29 ergs, at intervals of hours. Combining the energy and frequency gives a general expression for heat deposition due to aring (i.e. reconnection).