Elementary theory of a twisted flux tube. II. Stability

Using models for magnetic flux tubes developed in Paper I, we calculate the total potential energy of a tube embedded in an isothermal horizontally stratified compressible atmosphere. By comparing this with the total energy of a system of n flux tubes having the same total flux as the original tube a necessary condition is obtained that the system is consistent with the adiabatic subdivision of a single untwisted flux tube.It is shown that under nonadiabatic conditions such as exist in the solar photosphere, the subdivision process must be endothermic (i.e., external energy is required) if the temperature within the original tube is significantly less than its surroundings but exothermic if the temperatures are comparable. Thus it is conjectured that magnetic structures are less susceptible to subdivision if they are significantly cooler than their surroundings.While a twisted flux tube cannot subdivide simply like an untwisted tube, it may fray into several spiral filaments; and it is shown that the cooling required to prevent this is actually greater than for an equivalent untwisted tube.It is shown that several features of the growth and decay of sunspots may be explained in terms of this conjecture