In magneto-convection simulations with initial vertical fields, micropores form spontaneously in vertices of the intergranular lanes where several lanes meet (Bercik et al., 2003; Stein et al., 2003; Vögler et al., 2005). In the typical formation scenario a small bright granule is surrounded by strong magnetic fields in the intergranular lanes. The upward velocity in the small granule reverses and it disappears with the area it occupied becoming dark. The surrounding strong fields move into the dark micropore area (Figure 28).
As the upflow velocity in a flux concentration slows and reverses, the upward heat flux decreases and the plasma inside the concentration cools by radiation through the surface (Figure 25). As a result, the density scale height decreases and the plasma settles lower. Initially the material piles up below the surface until a new hydrostatic structure is established (Figure 25). The micropores are also heated by radiation from their hotter sidewalls (Figure 21, Spruit, 1976, 1977). On the order of a granular timescale the magnetic field is dispersed and the micropore disappears.
Micropores have an amoeba-like structure with arms extending along the intergranular lanes. Fluid flows are suppressed inside them and they are surrounded by downflowing plasma which is concentrated into a few downdrafts on their periphery (Figure 26).
Pores have developed spontaneously in magneto-convection emerging flux simulations when rising -loops emerge through the surface and the upper boundary, leaving behind vertical magnetic field concentrations (Stein and Nordlund, 2006). The pores grow by accumulating flux from their surroundings. The pore pictured in Figure 27 has reached a flux of 2.4 × 1020 Mx and occupies an area of 6 Mm2. The flux concentration develops first near the surface. It cools and quickly becomes partially evacuated and flux concentration extends downward, reaching all the way to the bottom of the domain (at 20 Mm depth) – Figure 29 and Figure 30, see also Kitiashvili et al. (2010). Most magnetic field lines in the pore connect to the end of a large scale loop rising from the bottom of the domain, although some connect to various other structures. Additional flux is being transported into the pore by horizontal flows along the intergranular lanes. These flows feeding the pore extend to depths of several megameters. The simulated pores have sometimes lasted for a long time – greater than 8 hrs (Kitiashvili et al., 2010) and 12 hrs in our case.
Pores, like micropores, are surrounded by downflows concentrated into a few downdrafts. The ubiquitous occurrence of downflows in the close vicinity but outside magnetic flux concentrations (see, for example, also Steiner et al., 1998) has been explained in terms of baroclinic flows by Deinzer et al. (1984). The effect has been observationally verified by Langangen et al. (2007). Pores are edge brightened (Figure 27). Cameron et al. (2007b) explain this as due to the fact that the surface of unit optical depth occurs at slightly higher temperature at the edges of pores, possibly due to decreased overlying density because of the spreading magnetic field.
No one has yet produced a sunspot ab initio. Several “realistic” magneto-convection simulations of sunspots have been made starting with idealized, imposed initial magnetic field configurations. See review by Rempel and Schlichenmaier (2011). Cheung et al. (2010) has come closest, starting from an emerging, twisted, half torus magnetic “flux tube”. Others have started with monolithic, self-similar magnetic configurations. Schüssler and Vögler (2006) investigated magneto-convection in a uniform, vertical field representing a sunspot umbra. Heinemann et al. (2007), Scharmer et al. (2008), and Rempel et al. (2009b) studied flaring rectangular slab field configurations. Rempel et al. (2009a) and Rempel (2011) started with a pair of axisymmetric, self-similar funnels (Schüssler and Rempel, 2005), with the same flux but slightly different field strengths (Figure 31). All these simulations develop thin upflow plumes with surrounding downflows that are the observed umbral dots. The most challenging property of spots to model has been their penumbra, which are found to depend crucially on the existence of very inclined magnetic fields in the outer parts of the spots.
In the Cheung et al. (2010) simulation, spots form from an emerging -loop (Figure 14). The field first emerges with mixed polarities. The opposite polarities then counterstream to collect into the opposite polarity sunspots. This counterstreaming of opposite polarities is due to the underlying large-scale structure of the coherent subsurface roots of the emerged “flux tube”, which influence the surface dynamics via the Lorentz force, especially magnetic tension (Cheung et al., 2010).
Although the strong magnetic fields in sunspots inhibit convection, they do not shut it down entirely. Umbral convection is observed as umbral dots and has been simulated by Schüssler and Vögler (2006). In such strong fields, convection manifests itself as very narrow upflow plumes of hot plasma with neighboring, narrow cool return downflows. The tendency of the magnetic field to expand as the gas pressure declines toward the surface pinches the rising plumes and accelerates the upward flow. As in normal convection, the upflows are braked rapidly near the surface where the plasma loses buoyancy due to radiative cooling. The plasma piles up, the gas pressure increases and makes the plasma expand latterly, which reduces the magnetic field strength. As a result of the enhanced density, the optical depth increases and photons can only escape from higher, cooler layers producing a dark lane through the bright umbral dot (Figure 32). Above the plume, which has been decelerated, the magnetic field again closes in, arching over the gap in a cusp shape.
Heinemann et al. (2007), Scharmer et al. (2008), and Rempel (2011) have modeled sunspot penumbra (Figures 31, 33, 34). They find that penumbra are produced by overturning convective motions that occur in an inclined magnetic field and that the observed Evershed outflows (Evershed, 1909) are the horizontal flow of overturning convection channeled along the penumbral magnetic field.
However, unlike normal convection, it is the pressure force that that is pushing the upflow as well as the overturning horizontal flow. The downflows are in nearly hydrostatic equilibrium. Near the lower pressure photosphere the nearly vertical field lines of the penumbra spread outward (tending toward a potential field structure) and become more horizontal. The mass loading by the overturning, horizontal convective motions bends the magnetic field lines downward even more, when the initial inclination is more than 45°, which produces the nearly horizontal penumbral field (Figure 33). Cooling near increases the plasma density and field line bending. The Lorentz force turns the flow along the magnetic field to produce the Evershed outflow (Figure 34).
Living Rev. Solar Phys. 9, (2012), 4
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