4.3 Formation of a penumbra

The formation of a penumbra is an integral part of the flux emergence process. To date most numerical models do not show clear evidence for penumbra formation, in part since the grid resolution in most flux emergence simulations is insufficient, the total emerging flux falls short of that of solar active regions, and as described below boundary conditions matter. The recent experiment by Stein et al. (2011bJump To The Next Citation Point) shows some evidence of penumbra formation, although here the magnetic field strength was scaled up artificially during the simulation to reach flux concentrations of sufficient size.

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 8Watch/download Movie). Rempel et al. (2009aJump To The Next Citation Point) 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 15View Image 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,bJump To The Next Citation Point).

View Image

Figure 15: Snapshots in the G band of a spot on July 4, 2009, as it develops a penumbra. The spot is located at 𝜃 = 28° and was observed from 08:32 UT until 13:03 UT at the German VTT in Tenerife (Schlichenmaier et al., 2010b). Flux emergence takes place in the lower right corner of the images. Flux patches of the spot polarity are observed to migrate towards and merge with the spot. As the area and the magnetic flux of the spot increases the penumbra forms on the side opposite to the flux emergence.

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