Equilibrium of a magnetic flux tube in a compressible flow

Three-dimensional cellular convection concentrates magnetic field into thin ropes and sheets when the magnetic Reynolds number is large. We examine the equilibrium structure of an axisymmetric flux rope sustained by turbulent, cellular convection of a compressible, electrically conducting gas. The back-reaction of the magnetic field on the turbulent flow is modeled in both the momentum and energy equations. Using boundary-layer techniques, we show that compressibility of the fluid is responsible for a non-Boussinesq boundary-layer effect which we term "cooling runaway." This is a thermal breakdown which realizes in this model the convective collapse associated with superadiabatic effects. Cooling runaway may limit the flux carried by basic magnetic structures which are formed in the upper layer of the solar convection zone.