Turbulent Erosion of Magnetic Flux Tubes

Results from a numerical and analytical investigation of the solution of a nonlinear axisymmetric diffusion equation for the magnetic field are presented for the case when the nonlinear dependence of the diffusivity ν(B) on the magnetic field satisfies basic physical requirements. We find that for sufficiently strong nonlinearity (i.e., for sufficiently strong reduction of ν inside the tube) a current sheet is spontaneously formed around the tube within one diffusion timescale. This sheet propagates inward with a velocity inversely proportional to the ratio of the field strength just inside the current sheet to the equipartition field strength B0/Be, so the lifetime of a tube with constant internal flux density is increased approximately by a factor not exceeding B0/Be, even for infinitely effective inhibition of turbulence inside the tube. Among the applications of these results, we point out that toroidal flux tubes in the solar convective zone are subject to significant flux loss owing to turbulent erosion on a timescale of ~1 month and that turbulent erosion may be responsible for the formation of a current sheet around a sunspot. It is further proposed that, despite the simplifying assumptions involved, our solutions correctly reflect the essential features of the sunspot decay process.