Theory of magnetic connectivity in the solar corona

Although the analysis of observational data indicates that quasi-separatrix layers (QSLs) of magnetic configurations have to play an important role in solar flares, the corresponding theory is only at an initial stage so far. In particular, there is still a need of a proper definition of QSLs based on a comprehensive mathematical description of magnetic connectivity. Such a definition is given here by analyzing the mapping produced by the field lines which connect photospheric areas of positive and negative magnetic polarities. It is shown that magnetic configurations may have regions, where cross sections of magnetic flux tubes are strongly squashed by this mapping. These are the geometrical features that can be identified as the QSLs. The theory is applied to quadrupole configuration to demonstrate that it may contain two QSLs combined in a special structure called hyperbolic flux tube (HFT). Both theoretical and observational arguments indicate that the HFT is a preferred site for magnetic reconnection processes in solar flares.