Tearing mode instability in the atmosphere above a sunspot

We derived the energy balance equation in steady state and made numerical calculations for 37 sets of parameter values for three layers of the atmosphere. The main results are: 1) The energy density released by tearing mode instability rapidly falls with rising temperature. It is much greater in the colmnar pinch than in the thin plate pinch. 2) The critical temperature increases with the intensity of the sheared magnetic field and decreases with its width. It is higher in the columnar pinch, and the rise time is shorter, than in the thin plate pinch. 3) At the surface of the photosphere, the energy released by tearing mode instability raises the local temperature by less than 1 K. 4) When the sheared width of the magnetic field is below a certain threshold, the local temperature is raised sharply to over (+6) K. This threshold is an increasing function of the strength of the sheared field. Our calculated results fit the observations to within one order of magnitude.