Heating and cooling at a coronal magnetic null

ABSTRACT Conductive cooling of the solar corona at a magnetic null is examined. An initial equilibrium is set up, balancing thermal conduction and a constant spatially uniform coronal heating. The heating is then turned off and the subsequent conductive cooling calculated. An equation for the cooling is obtained using the method of separation of variables and it is shown that the equations for the equilibrium between conduction and heating, and the time-dependent cooling are mathematically identical with a simple change of variables. Thus, the properties of the cooling phase are automatically determined by the equilibrium state. For a two-dimensional null, the characteristic cooling time-scale increases over that in a straight field by a factor of between 2 and 5, with a scaling determined by the ratio of the average and base areas of a flux element. There is no explicit dependence on the very large areas that can arise near the null.