Based on more idealized models it has been suggested by Weiss et al. (2004) and Brummell et al. (2008) that turbulent pumping near the outer edge of a penumbra plays a key role in maintaining the overall field geometry required for the existence of a penumbra. While such processes are certainly present in most radiative MHD simulations of sunspots, their overall role has not been quantified. Most recent MHD models point to a strong role of magnetoconvection within the penumbra (not just near the edge) in maintaining the finestructure of sunspots locally. In addition, in most MHD models the extent of penumbrae is subject to boundary conditions (see, e.g., Figure 8). Rempel et al. (2009a) found extended penumbrae only inbetween (relatively close) opposite polarity spots, similarly the setup of Stein et al. (2011b) also involves opposite polarity flux in close proximity. Rempel (2011b) artificially increased the field inclination near the top boundary to obtain an extended penumbra for an individual sunspot in a periodic domain. The difficulty of obtaining penumbrae with realistic extent is most likely an artifact of the use of periodic boundary conditions in horizontal directions that put strong constraints on the allowed global field structure. A more realistic setup including parts of the corona and relaxing horizontal periodicity might be required to address this aspect self-consistently.
On the observational side high resolution observations of flux emergence including the transition from a proto-spot into a penumbra confirm the picture that emerging bi-poles separate, and that the flux patches of the proper polarity merge. Figure 15 displays snapshots that trace the growth of a sunspot as it develops a penumbra. Towards the lower right, elongated granules mark emerging bi-poles. As they separate, the flux patches with the spot polarity migrate toward the spot. As the spot increases in size it forms a penumbra (see Schlichenmaier et al., 2010a,b).
Living Rev. Solar Phys. 8, (2011), 3
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