Abstract
Magnetic flux is continuously being removed and replenished on the solar surface. To understand the removal process we carried out 3D radiative MHD simulations of the evolution of patches of photospheric magnetic field with equal amounts of positive and negative flux. We find that the flux is removed at a rate corresponding to an effective turbulent diffusivity, of 100--340 km^2/s, depending on the boundary conditions. For average unsigned flux densities above about 70 Gauss, the percentage of surface magnetic energy coming from different field strengths is almost invariant. The overall process is then one where magnetic elements are advected by the horizontal granular motions and occasionally come into contact with opposite-polarity elements. These reconnect above the photosphere on a comparatively short time scale after which the U loops produced rapidly escape through the upper surface while the downward retraction of inverse-U loops is significantly slower, because of the higher inertia and lower plasma beta in the deeper layers.
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