Statistical Properties of Magnetic Separators in Model Active Regions

Abstract

Previous theoretical work suggests that magnetic reconnection in the solar corona should occur along particular topological boundaries in the coronal magnetic field known as separators. Thus, a field's topological structure predicts the locations of X-ray/EUV loops, assuming enhanced emission is related to reconnection. We use this topological model in a theoretical study of the statistical properties of active-region loops. We model the interaction of a single element of photospheric magnetic flux with a much larger distribution of flux of the opposite polarity. We first model the large-scale distribution of flux in an active region using a mean-field approach and develop a procedure to determine separator lengths. We then perform Monte Carlo simulations to check the accuracy of this approximation. The results of both methods are similar and are well described by simple scaling laws for separator lengths. Separator lengths scale as ~exp(αr)/N1/2, where N parameterizes the flux in the large-scale distribution and r is the distance of the test element from the distribution's center. This scaling law is a theoretical prediction of X-ray loop lengths, which can be compared with observations.