Yelles Chaouche et al. (2005), Cheung et al. (2007), and Martínez-Sykora et al. (2008) have simulated the rise of a coherent, twisted (necessary to retain its coherence) flux tube through the solar surface. As the tube rises it widens as it enters lower pressure levels. When it reaches the surface (with a width larger than the size if typical granules) it produces a string of larger than normal granules along its length. As it emerges through the surface the granular flows disperse the magnetic field into the intergranular lanes and the granular pattern returns to normal (Figure 55).
In simulations where a uniform horizontal magnetic field is advected into the computational domain at the bottom by upflows in the interiors of mesogranules, flux emerges through the surface, merges, fragments, cancels, and submerges pulled down by intergranular downflows. An example from the simulation showing both a bipole emerging through the surface and another bipole being pulled back down below the surface is shown in Figure 56. In the emerging bipole, the footpoints spread apart over time and are wider apart at lower elevations. In the submerging bipole, the flux in the upper level weakens over time, while the bipole remains visible at increasingly lower levels as time progresses.
Simulations where uniform horizontal magnetic field is advected in through the bottom of the computational domain can also be used to study “flux tubes”. Figure 57 shows magnetic field lines in the simulation box viewed from the side and slightly above. The red line in the lower left is horizontal field being advected into the domain. In the lower center is a loop like flux concentration rising toward the surface. In the upper right is a vertical flux concentration or “flux tube” through the surface (Stein and Nordlund, 2006). While the field lines form a coherent bundle near the surface, below the surface they become tangled and spread out in many different directions. This “flux tube” and others form by a loop-like flux concentration rising up through the surface and opening up through the upper boundary where the condition is that the field tends toward a potential field. This leaves behind the legs of the loop. Typically one leg is more compact and coherent than the other and persists for a longer time as a coherent entity while the other is quickly dispersed by the convective motions. Cattaneo et al. (2006) have studied the existence of flux tubes using an idealized simulation of a stably stratified atmosphere with shear in both the vertical and one horizontal direction driven by a forcing term in the momentum equation. They find that in the absence of symmetries, even in this laminar flow case, there are no flux surfaces separating the inside of a flux concentration from the outside, so that the magnetic field lines in the concentration connect chaotically to the outside and the “flux tube” is leaky. They conclude that in the highly turbulent solar environment the chance of finding isolated “flux tubes” is slim. Numerical simulations are of course much more magnetically diffusive than the Sun, but here also the field lines in the flux tube connect chaotically to the outside except over a small height range at the surface.
The fact that magnetic fields that are concentrated close to the surface tend to tangle and spread out in many directions below the surface has been demonstrated earlier by Grossmann-Doerth et al. (1998) – see also Vögler et al. (2005) and Schaffenberger et al. (2005).
Occasionally, in magneto-convection simulations micropores form in the vertices of where several intergranular lanes meet (Bercik, 2002; Bercik et al., 2003; Vögler et al., 2005; Cameron et al., 2007b). 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 58). On the order of a granular timescale the magnetic field is dispersed and the micropore disappears.
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 59). 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 60).
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 61). Micropores, like other flux concentrations, are cooled by vertical radiation and heated by radiation from their hotter sidewalls (Figure 62).
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).
Emonet and Cattaneo (2001)have shown that dynamo action will occur in a turbulent medium even in the absence of rotation. This led to the suggestion that in addition to the global solar dynamo there is a local, surface dynamo acting in the Sun, a proposition that has recently been confirmed by Vögler and Schüssler (2007). It must be remembered, however, that even though dynamo action occurs in the surface layers of the Sun, these layers are not isolated from the rest of the convection zone. The plasma and magnetic field are mixed throughout the convection zone.
The nature of the large scale solar dynamo has been reviewed by, among many others, Brandenburg and Dobler (2002), Ossendrijver (2003), and Charbonneau (2005).
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