Statistical Properties of Magnetic Separators in Model Active Regions

Previous theoretical work suggests that magnetic reconnection in the solar corona should occur along particular topological boundaries in the coronal magnetic Ðeld known as separators. Thus, a ÐeldÏs 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 activeregion loops. We model the interaction of a single ““ test ÏÏ element of photospheric magnetic Ñux with a much larger distribution of Ñux of the opposite polarity. We Ðrst model the large-scale distribution of Ñux in an active region using a mean-Ðeld 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 Dexp (ar)/N1@2, where N parameterizes the Ñux in the large-scale distribution and r is the distance of the test element from the distributionÏs center. This scaling law is a theoretical prediction of X-ray loop lengths, which can be compared with observations. Subject headings : plasmas È Sun: corona È Sun: Ñares È Sun: magnetic Ðelds