The structure of small-scale magnetic flux tubes

Abstract

Three main mechanisms have been described to determine the maximum field strength and structure of a solar or stellar magnetic flux tube. This paper attempts to relate them to one another through a series of magnetoconvective calculations. The first process is the balancing of the Lorentz force by radial gradients in the buoyancy force. It was first found in the Boussinesq regime, where it was studied in the late 1970s by Galloway, Proctor & Weiss. A similar balance can occur in the fully compressible case, where we refer to it as quasi-Boussinesq (QB). The second process involves a balance between an outward-directed radial pressure gradient and radial gradients in the buoyancy force outside the tube. This is the mechanism proposed in the early 1990s by Kerswell & Childress (the KC mechanism). The third mechanism, convective collapse (CC), is a process whereby a flux tube can evolve to a high field strength because of an instability due to the superadiabaticity of the material within the tube. Until now, it has been studied using the so-called ‘thin flux tube’ approximation in which convective motions are ignored even though there is a background superadiabatic density stratification. Here we place these three mechanisms in a unified framework and explore the transitions between the solutions as various parameters are varied. In particular, we show that the QB solutions are preferred for a wide range of parameters, whereas CC solutions occur only in very specific circumstances. In particular, on the Sun, the latter are probably limited to flux tubes with radii less than approximately 10 km, the turbulent magnetic diffusivity length-scale.