7.3 Magnetic flux emergence

Magnetic flux emergence through the solar surface is driven by two processes: buoyancy and advection. Magnetic concentrations with strong fields rise toward the surface first, because they are buoyant (to maintain approximate pressure equilibrium with their surroundings the density inside the concentration must be smaller than in its surroundings), and second, because they are advected by convective upflows. As it rises, a magnetic concentration will encounter convective downflows piercing the upflows on smaller and smaller scales, with downflow speeds significantly larger than the upflow speeds. The portions of the magnetic concentration in the downflows will be dragged down or at least have their upward motion slowed, while the portions still in the upflows continue to ascend rapidly. This leads to the formation of Ω-loops of successively smaller dimensions as the surface is approached. In general, the asymmetry of upflow and downflows (amplitudes and topology) leads to a tendency for downward transport of magnetic flux; a process known as “magnetic flux pumping” (Petrovay and Szakaly, 1993Tobias et al., 1998Dorch and Nordlund, 20002001Tobias et al., 2001). This process is likely to be of central importance for the overall flux balance of the solar convection zone, and allows storage of considerable magnetic flux inside the convection zone proper.

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 55View Image).

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 56View Image. 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.

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Figure 56: Horizontal slices of magnetic field strength. Rows are time (in seconds) increasing downward. Columns are height (in km) above the mean visible surface decreasing toward the right. Red and yellow have opposite polarity to blue and black. Gray is weak field. At the right of each image is an emerging bipole whose legs separated with decreasing height and increasing time. At the left is a submerging bipole whose legs approach with increasing time and which disappears at higher elevations at later times.

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 57View Image 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. (2005Jump To The Next Citation Point) and Schaffenberger et al. (2005Jump To The Next Citation Point).

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Figure 57: Magnetic field lines in a simulation snapshot viewed from an angle. 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 with its field lines connecting chaotically to the outside below the surface.

Occasionally, in magneto-convection simulations micropores form in the vertices of where several intergranular lanes meet (Bercik, 2002Jump To The Next Citation PointBercik et al., 2003Jump To The Next Citation PointVögler et al., 2005Cameron 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 58View Image). On the order of a granular timescale the magnetic field is dispersed and the micropore disappears.

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Figure 58: Micropore formation sequence. Left panel is images of the magnetic field strength, center panel is emergent intensity, and right panel is mask showing low intensity, strong field locations (Bercik, 2002Jump To The Next Citation PointBercik et al., 2003Jump To The Next Citation Point).

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 59View Image). 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 60View Image).

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Figure 59: Magnetic field (filled contours at 250 G intervals from 0 G to 3500 G) and temperature (1000 K intervals from 4000 K to 16,000 K). The τ = 1 depth is shown as the thick line around z = 0 Mm. The flux concentrations are significantly cooler than their surroundings (Bercik, 2002Jump To The Next Citation PointBercik et al., 2003Jump To The Next Citation Point).
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Figure 60: Magnetic field (filled contours at 250 G intervals) and ln density (in 0.5 intervals from –2 to 4). The τ = 1 depth is shown as the thick line around z = 0 Mm. The established, strong “flux tube” in the center has been evacuated and is in equilibrium. The smaller flux concentrations on either side are in the process of being evacuated, starting above the surface and piling up plasma below the surface (Bercik, 2002Jump To The Next Citation PointBercik et al., 2003).

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 61View Image). Micropores, like other flux concentrations, are cooled by vertical radiation and heated by radiation from their hotter sidewalls (Figure 62View Image).

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).

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Figure 61: Image of vertical velocity (red and yellow down, blue and green up in  km s–1) with magnetic field contours at 0.5 kG intervals at the surface (left) and 1.5 Mm below the surface (Bercik, 2002Jump To The Next Citation Point).
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Figure 62: Radiative heating and cooling of flux concentrations. The second from top panel shows temperature contours at 1000 K intervals. The third from top panel shows magnetic field contours at 250 G intervals. Units are 1010 erg g–1 s–1. The top three panels show the net radiative heating/cooling and its relation to the temperature and magnetic fields. The bottom three panels show the contribution of vertical, inclined, and nearly horizontal rays (Bercik, 2002).

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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