Footpoint switching and the evolution of coronal holes

We discuss the role of footpoint exchanges between open and closed magnetic field lines ( also known as interchange reconnection'') in the formation and rotational evolution of coronal holes. Such exchanges cause open flux to jump from one location to another when active regions emerge; they also act to untie the rotation of coronal holes from that of the underlying plasma. We introduce a quantitative measure of the footpoint exchange rate and apply it to a variety of idealized configurations. During the formation of coronal holes, footpoint switching dominates over the creation of new open flux if the background ( or polar) field is strong compared to that of the emerging active region, so the latter acts to change mainly the direction rather than the magnitude of the Sun's dipole vector. The principal role of footpoint exchanges is to counteract the subsequent rotational shearing of the holes; this result is accomplished by means of continual sideways displacements of open and closed field lines along the hole boundaries. Because the timescale for rotational shearing ( similar to 3 months) is less than that for the decay of the Sun's large-scale nonaxisymmetric field ( similar to 1 yr), interchange reconnection is expected on average to dominate over the closing down of flux throughout the solar cycle.