The Cluster Model of Sunspots

Abstract

More than one decade ago, Parker (1979a) began his famous paper on the cluster model of sunspots with the statement: “The sunspot phenomenon, with its reduced temperature and intense magnetic field, is at present without a scientific explanation.” The aim of the present review is to assess whether the cluster model of sunspots (perhaps more popularly known by the less respectable name “spaghetti model”) has been able to contribute something significant to change the situation since that time. The central idea of the cluster model is that a sunspot is not a single monolithic flux tube as in Figure la, but a collection of many smaller flux tubes herded together as in Figure lb. The first question before us is whether the cluster model is in some sense a “correct” description of a sunspot. If it is so, then the second question is at what depth the individual flux tubes start separating. A third question is how the flux tubes making up a sunspot connect to the global solar magnetic field deep down. Hale’s polarity law clearly tells us that sunspots are just outward manifestations of the global magnetic fields. When the cluster model was first proposed, perhaps the time was still not ripe to raise this third question. Now we may start preliminary enquiries on this vital and difficult question. Apart from these three morphological questions, there remains the challenging dynamical question why a cluster of flux tubes come together to form a sunspot. This set of basic questions is taken to define the scope of this review. In other words, we are going to look at the efforts by both theorists and observers to come up with answers to these four (three morphological and one dynamical) questions.