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We have previously suggested that the appearance of magnetic active regions on the surface of the sun arises from a percolation of flux out of the dynamo layer (1992, Wentzel and Seiden, ApJ 390, 280). We found an exponential distribution of cluster sizes similar to that found by Tang, et al. (1984, Solar Phys. 91, 75). Recently Harvey (1993, Thesis, Univ. Utrecht) and Harvey and Zwaan (1993, Solar Phys. 148, 85) have shown that for very small regions the distribution is a power law in cluster size with an exponent of about -2. This type of distribution, power law at small sizes and exponential for large sizes is, just what is expected for a percolation problem. We have extended our model to take into account the bipolar nature of the flux and to allow for the buildup and diffusion of flux on the surface. The model yields results in good accord with the observations. It has a power law for small clusters with the same exponent as the observations and becomes more nearly exponential like at large sizes. As the size gets larger the exponential scale length increases, in accord with observations selected according to various longevity criteria. The original motivation for percolation, i.e., new active regions arise disproportionately in existing active regions, is confirmed by the present model. However, the physics of percolation, i.e., the dual nature of the size distribution, is demonstrated best upon ignoring internal regions.
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