Effects of Complexity on the Flux-Tube Tectonics Model

The quiet-Sun magnetic field emerges through the solar photosphere in a multitude of mixed-polarity magnetic concentrations and is subsequently tangled up into intricate regions of interconnecting flux. Moreover, since these discrete concentrations are likely to be extremely small in size, with fluxes of around only 1017 Mx, the number of such flux sources in, say, a supergranule, will be extremely large. The flux-tube tectonics model of Priest, Heyvaerts, and Title (2002) demonstrated how the formation and dissipation of current sheets along the separatrices that separate the regions of different connectivity are likely to make an important contribution to coronal heating. Since the full complexity of the magnetic field is below present observable scales, this study examines the effect of having the magnetic flux emerge through configurations structured on smaller and smaller scales. It is found that, by fixing the amount of flux emerging into a given 2D region, the main factors influencing the current build-up along the separatrices are the number of sources through which the flux emerges and the spatial distribution of the sources on the photosphere. The free energy (i.e., that above potential) is stored lower and lower in the atmosphere as the complexity of the system increases. A simple comparison is then made between coronal heating by separator currents and by separatrix currents. It is found that both result in comparable amounts of energy release, with separatrix heating being the more dominant.