Stability and equilibrium of emerged magnetic flux

Abstract

We analyse stability and equilibrium of a unipolar large-scale magnetic field pervading a plane horizontal subphotospheric layer with the possible implications for sunspots in mind. Eddy diffusivity is applied to account for the effects of the small-scale convective turbulence. Diffusivity quenching by magnetic field results in a secondary large-scale instability. A linear stability analysis is performed to define the marginal stability boundary in parametric space and the unstable mode structure. The nonlinear dynamics of the unstable modes are followed numerically. The original state of a uniform vertical magnetic field is transformed via the instability into the nonlinear dynamical equilibrium with a highly intermittant distribution of the magnetic field. Magnetic flux is concentrated in a relatively small area surrounded by an almost field-free region. The role of the fluid motion in the hydromagnetic equilibrium is emphasized. Although the relevance of the instability to the process of sunspot formation is rather questionable, the resulting equilibrium structures are similar to mature spots in their thermal and magnetic properties. Also, the simulated flow structure agrees with helioseismic tomography results.