CORONAL CURRENT-SHEET FORMATION - THE EFFECT OF ASYMMETRIC AND SYMMETRICAL SHEARS

A major issue in coronal-heating research is whether or not current sheets can occur without a null point being present in the initial potential magnetic field. Several analytic studies contend that current sheets form along separatrices between magnetic flux systems whenever the footpoints of the configuration are moved continuously. Both symmetric and asymmetric systems have been investigated, all with the assumption that the magnetic field is line tied at the discontinuous photospheric boundary. On the Sun, however, the interface between the photosphere and chromosphere has finite width, and hence line tying might not be appropriate there. The present work extends our earlier theoretical and numerical studies of the antisymmetric case to systems with asymmetric and symmetric shears. Using a 2.5 dimensional numerical code, we have investigated the results of an asymmetric shear imposed on a potential, quadrupolar magnetic field under two sets of atmospheric and boundary conditions: (1) a low-beta plasma with line tying at the base, similar to the line-tied analytic model; and (2) a hydrostatic-equilibrium atmosphere with solar gravity, typical of the observed photosphere-chromosphere interface. The low-beta simulation confirms the crucial role of the line-tying assumption in producing current sheets. We also examine the effects of a symmetric shear on the same hydrostatic-equilibrium atmosphere, using more grid points to improve the resolution of the current structures which form along the flux surfaces. Again we find that true current sheets do not form in the corona when a more realistic atmospheric model is considered. The amount of Ohmic dissipation in the thick currents is estimated to be two to four orders of magnitude below that required to heat the corona. We conclude, therefore, that magnetic topologies of the type examined here do not contribute significantly to coronal heating.