On the distribution of magnetic null points above the solar photosphere

Many theories predict magnetic energy dissipation at locations, called null points, where the magnetic field vanishes. In several astrophysical contexts, most notably the solar corona, energy is released within a low-beta magnetic field anchored to a lower boundary, the photosphere. A general expression is derived for the distribution of magnetic null points in potential magnetic fields anchored to a random, homogeneous distribution of field on the lower boundary. For all such fields the null point density decreases with height and scales with the inverse cube of the field's characteristic length. For photospheric fields which appear unipolar at the largest scales the nulls are confined to a narrow layer. The results are applied to models of the quiet Sun whose photospheric field consists of discrete sources of mixed polarity. The number of coronal nulls depends on the degree of imbalance between positive and negative sources. Numerical experiments reveal that the greatest column density of null points occurs when similar to20% of the sources are of the minority sign. Were the coronal energy dissipation to occur at magnetic null points this result predicts an observable relationship between flux imbalance and the amplitude and distribution of dissipation. (C) 2003 American Institute of Physics.