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 timescale increases over that in a straight field by a factor of between 2 and 5, with a scaling determined by the ratio of the {\it{average}} and base areas of a flux element. There is {\it{no explicit dependence}} on the very large areas that can arise near the null.