Topological Quantification of the "Anemone" (Branching) Solar Flares

The so-called "anemone" solar flares are an interesting type of the space plasma phenomena, where multiple null points of the magnetic field are connected with each other and with the magnetic sources by the separators, thereby producing the complex branching configurations. Here, using the methods of dynamical systems and Morse-Smale theory, we derive a few universal topological relations between the numbers of the null points and sources of various kinds with arbitrary arrangement in the above-mentioned structures. Such relations can be a valuable tool both for a quantification of the already-observed anemone flares and for a prediction of the new ones in complex magnetic configurations.Comment: LaTeX2e, elsarticle documentclass, 19 pages, 5 EPS figures; v2: Theorem 3 substantially modified, minor changes in other parts of the text; v3: Ref. 19 replaced, formulation of Theorem 1 extended, minor misprints correcte