Effect of Stratified Turbulence on Magnetic Flux Concentrations

According to conventional view, sunspots form when coherent magnetic flux tubes intersect the surface. Such tubes would rise from the bottom of the convection zone as a result of an instability. In this study an alternative view is advanced where the field is produced throughout the entire convection zone and sunspots may form from local flux concentrations near the surface. In order to understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer, where a weak uniform horizontal mean magnetic field is applied. In a first setup, the turbulent intensity is nearly constant in height, so the kinetic energy density decreases with height due to the decrease in density, while in a second series of numerical experiments, the turbulent intensity increases with height such that the kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. Corresponding mean-field numerical models are used to assess whether or not a large-scale instability is to be expected. A negative turbulence contribution to the effective mean magnetic pressure is confirmed and found to be in agreement with results of earlier work. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions, but the turbulent pumping velocity is found to be equal to the negative gradient of turbulent magnetic diffusivity without the 1/2 factor expected from the kinematic mean-field theory. Mean-field numerical modelling confirms the excitation of the instability for both setups, although no large-scale instability is found in the direct numerical simulations. Subject headings: MHD – Sun: magnetic fields – sunspots – Turbulence