Abstract
According to recent data analyses, the relationship between the coronal energy flux density and the photospheric magnetic flux density is approximately power law; estimates of the exponent tend to be noninteger and fall in the range 1-2. The index is closer to 2 for quiet regions and closer to 1 for active regions. We here examine this relationship on the basis of a recent model of coronal heating. We assume that the coronal energy flux is derived from reconnection of neighboring flux tubes at the level of the chromosphere, and we examine the rate at which such reconnection would occur in terms of a simple kinetic-theory model. In this model, flux elements appear randomly within supergranulation cells, are carried into the network according to a prescribed velocity field, and cancel in the network due to "collisions" between elements of opposite polarity. For any limited range of magnetic flux density, the relationship is approximately power law. We find that the power-law index is in the range 1-2: for weak fields it is close to 2, and for strong fields it is close to 1, in agreement with available evidence.
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