Rapid progress has been made in recent years in fully compressible 3D MHD simulations of magneto-convection, emerging magnetic flux, and sunspot structure within the top few Mm layer of the solar convection zone and the overlying photospheric layer, incorporating realistic physics of partial ionization of the dominant constituents and radiative transfer (see e.g. Stein and Nordlund, 2000; Cheung et al., 2007, 2008; Martínez-Sykora et al., 2008, 2009; Rempel et al., 2009; Nordlund et al., 2009). These simulations have produced results that can be directly compared with high resolution photospheric observations of the solar granulations, emerging flux regions, sunspot fine structure and the associated flows. Cheung et al. (2008) carried out 3D radiation MHD simulations of a twisted magnetic flux tube rising through the top layer of the solar convection zone (from a depth of about 5.5 Mm below the photosphere) into the photosphere. It is found that due to the strong stratification of the top layer of the convection zone, the rise of the flux tube is accompanied by a strong lateral expansion. By the time it has reached the photosphere, it appears more like a flux sheet which acts as a reservoir for small-scale flux emergence events at the granulation scale. Detailed comparisons of the simulation results of flux emergence at the photosphere layer and the new observational data from SOT of Hinode provide physical interpretations for many of the observed features in emerging flux regions (EFRs). For example, convective downflows produce serpentine-shaped emerging field lines which result in the observed mixed-polarity pattern in the interior of EFRs, where opposite-polarity flux concentrations appear to counter-stream (see Figure 35 and the associated movie).
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At each of the two opposite edges of the EFR, flux of one sign tends to coalesce. This may eventually lead to the formation of solar pores and sunspots, although the simulations so far have not been able to run long enough to see this actually happening.
Another interesting observed feature reproduced by the simulations is the presence of supersonic downflows at some flux “cancellation” sites. This is revealed by the simulations to correspond to the retraction of inverted U-loops due to the magnetic tension force. Simulations also found examples of surface flux concentrations undergoing convective intensification leading to the formation of Kilogauss fields and associated bright points. Such events have recently been directly observed by the high resolution Solar Optical Telescope (SOT) of the Hinode satellite (e.g. Nagata et al., 2008; Fischer et al., 2009). The intensification process is consistent with the basic theory of “convective collapse”, which results from the convective instability of plasma inside the vertical thin flux tubes in the top few hundred kilometers of the solar convection zone (see Parker, 1978; Spruit, 1979; Spruit and Zweibel, 1979), but is operating under the more realistic conditions with the effect of radiative energy transfer included (e.g. Cheung et al., 2008)
Realistic magneto-convection simulations of the evolution of emerging active region scale flux tubes in the top 20 Mm layer of the solar convection zone are yet to be carried out. It remains an open question how the top of the emerging -shaped tube intensifies to form sunspots with Kilogauss field strength and at the photosphere.
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