Convective collapse of flux tubes

Abstract

Flux tubes of constant β extending vertically through the solar convection zone are unstable to a convective instability if the surface field strength is less than 1270 G. By downward displacement of matter along the tube an unstable tube can transform into a new equilibrium state with lower energy which has a higher field strength. Numerical calculations of these ‘collapsed’ states are presented. If the collapse starts in a field with a strength corresponding to equipartition with kinetic energy in the convection zone, it yields a surface field strength of about 1650 G. It is proposed that the small scale magnetic field in active regions consists of such tubes. The collapsed state is not in thermal equilibrium. In the deeper layers the heat exchange following the collapse is very slow but the surface layers return rapidly to temperature equilibrium. It is argued that during the gradual thermal evolution of the collapsed state its surface layers may start an overstable oscillation. A brightness-velocity correlation in this oscillation could account for the observed downdraft in the tubes.