Topological differences and similarities between force-free and potential models of coronal magnetic fields

Potential fields and linear force-free fields are often used as models for the magnetic field of the Sun's corona. They can be written as analytical e xpressions in terms of boundary values at the photosphere. Because of their relative simplicity compared with nonlinear force-free fields, these two m odels are of particular importance in topological analysis of solar phenome na. However, it has been suggested by Hudson and Wheatland (1999) that the topologies of potential and force-free models are in general not even quali tatively equivalent. In this paper, their example is re-examined and it is found that the opposite conclusions hold. In general, potential and force-f ree fields are topologically similar sufficiently close to localized source s. The exception to this are structurally unstable states, such as bifurcat ion states, where a small change of current can produce a significant chang e of topology.