8.1 Evolution in the top layer of the solar convection zone and the photosphere

UpdateJump To The Next Update Information A complete 3D MHD model of emerging active region flux tubes, extending from the base of the solar convection zone up into the visible solar atmosphere, is not yet possible. Thin flux tube calculations of rising flux tubes in the solar convection zone usually extend from the base of the solar convection zone up to roughly 20 – 30 Mm below the surface, at which depths the validity of the thin flux tube approximation breaks down since the diameter of the flux tube begins to exceed the local pressure scale height (see Section 5.1.5 and Moreno-Insertis, 1992). The domain of fully 3D MHD simulations of rising magnetic flux tubes in a model convection zone typically contains a vertical stratification of up to 3 density scale heights (see Abbett et al., 20002001Fan et al., 2003), which corresponds to the density stratification over the range from the bottom of the solar convection zone to roughly 36 Mm below the photosphere. Recent 3D spherical shell simulations of buoyantly rising flux tubes in the solar convective envelope (Fan, 2008) cover depths from the base of the solar convection zone to about 16 Mm below the surface. Because of the rapid decrease of the various scale heights in the top layer of the solar convection zone which demands increasing numerical resolution, it is not yet feasible to perform 3D MHD simulations that extend from the bottom of the convection zone all the way to the photosphere. Furthermore, there is an increased complexity in the physics of the top layer of the solar convection zone. The thermodynamics of the plasma is complicated by ionization effects and the radiative exchange is expected to play an important role in the heat transport (see review by Nordlund et al., 2009Jump To The Next Citation Point). The anelastic approximation breaks down because the plasma flow speed is no longer slow compared to the sound speed.

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, 2000Jump To The Next Citation PointCheung et al., 2007Jump To The Next Citation Point2008Jump To The Next Citation PointMartínez-Sykora et al., 2008Jump To The Next Citation Point2009Jump To The Next Citation PointRempel et al., 2009Nordlund 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. (2008Jump To The Next Citation Point) 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 35Watch/download Movie and the associated movie).

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Figure 35: mpg-Movie (7921 KB) Continuum intensity images and synthetic magnetograms of the simulated emerging flux region resulting from a simulation of flux emergence from the top layer of the solar convection zone into the solar photosphere. From (Cheung et al., 2008Jump To The Next Citation Point). Figure and movie reproduced with permission of the AAS.

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., 2008Fischer 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, 1978Spruit, 1979Spruit and Zweibel, 1979Jump To The Next Citation Point), 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 Ω-shaped tube intensifies to form sunspots with Kilogauss field strength and β ∼ 1 at the photosphere.

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