Convective flows produce a hierarchy of loop structures in rising magnetic flux (Figure 10). Magnetic flux rises through the convection zone because it is advected by broad upflows and because it is buoyant. Along the way, it encounters 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 or that have large density deficits and so large buoyancy continue to ascend rapidly (Figures 10, 11). The different scales of motions produce a hierarchy of magnetic - and -loops with small loops riding piggy-back on larger loops in a serpentine structure (Cheung et al., 2007, 2008; Kitiashvili et al., 2010; Stein et al., 2010b) (Figure 12). As a result, emergence of large, undulated -loops occurs as a collection of small-scale, mixed polarity, emergence events. 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 “turbulent pumping” (Drobyshevskii et al., 1980; Nordlund et al., 1992; Petrovay and Szakály, 1993; Tobias et al., 1998; Dorch and Nordlund, 2000, 2001; Tobias et al., 2001) (Figure 10).
As the magnetic flux rises it expands (Figure 13). For horizontal flux tubes, the horizontal expansion is much larger than the vertical expansion. Consider a purely horizontal field in the x-direction. Suppose the rates of expansion in the horizontal and vertical directions are and , respectively. The rate of change of the magnetic field following the fluid motion is given by the Lagrangian derivativeet al., 2010). For isotropic expansion (), . For vertical expansion small compared to horizontal expansion () .
The fields first appear at the surface in localized regions as small bipoles with a small-scale, mixed pepper and salt polarity. The emergence region spreads in time (Figure 14). As the bipoles begin to emerge, horizontal and vertical fields have similar strengths, but horizontal fields are more common (cover more area) than vertical fields, except for the strongest fields. The mixed polarity fields collect into separated unipolar regions due to the underlying large scale magnetic structures (Figure 14).
Diverging, overturning convective motions quickly sweep magnetic fields (on granular times of minutes) from the granules into the intergranular lanes (Figure 15) (Weiss, 1966; Hurlburt and Toomre, 1988; Tao et al., 1998a; Emonet and Cattaneo, 2001; Weiss et al., 2002; Steiner et al., 1998; Stein and Nordlund, 2004; Vögler et al., 2005; Stein and Nordlund, 2006). In hours (mesogranular times) the field tends to collect on a mesogranule scale. Observations averaged over several hours reveal this magnetic pattern (de Wijn et al., 2005; Ishikawa and Tsuneta, 2010), even though there is no distinct convective meso-granule scale. In days (supergranule times) the slower, large scale supergranule motions sweep the fields to the supergranule boundaries. Eventually a balance is reached where the rate of emergence of new flux balances the rate at which flux is swept to larger horizontal scales. This balance empirically occurs at supergranulation scales and produces the magnetic network at the supergranule boundaries. Here the new flux encounters existing magnetic flux, which it either cancels or augments (Simon et al., 2001; Krijger and Roudier, 2003; Isobe et al., 2008).
The rising magnetic loops are not coherent, but rather have a filamentary structure (Figure 10). Some individual filaments rise more rapidly than others. The small-scale crenulation of the loops produces the “pepper and salt” pattern as the flux emerges through the visible surface. As the bulk of the magnetic loop reaches the surface, the different polarities concentrate in unipolar regions accompanied by flux cancellation where opposite polarities come in contact (Figures 14 and 17). This happens because the mixed polarity emergence is due to the undulating magnetic field lines produced by convective upflows and downdrafts distorting the large loops rising from below. The underlying large-scale magnetic structures organize the mixed polarity fields when they approach the surface. In order for the like polarity branches to collect, the mass trapped in the -loops between the peaks of the small -loops must be removed. This occurs by the -loop getting pinched off and forming plasmoids which may either sink below the surface or get ejected into space (Figure 16) (Lites, 2009; Cheung et al., 2010).
Magnetic flux emergence simulations starting with horizontal, uniform, untwisted field at 20 Mm depth is shown in Figures 10, 11 and 18. Figure 18 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 (Vögler et al., 2005; Schaffenberger et al., 2005). A “flux tube” at the surface forms 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 (Figure 19). 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), Schaffenberger et al. (2005), and Stein and Nordlund (2006).
Magnetic fields alter the granule properties – producing smaller, lower intensity contrast, “abnormal” granules (Bercik et al., 1998; Vögler, 2005). Strong magnetic flux concentrations typically form in convective downflow lanes, especially at the vertices of several such lanes, due to the sweeping of flux by the diverging convective upflows (Vögler et al., 2005; Stein and Nordlund, 2006). They are surrounded by downflows which sometimes become supersonic. The normal convective downflows are enhanced surrounding the flux concentrations by baroclinic driving due to the influx of radiation into the concentration (Deinzer et al., 1984; Knölker et al., 1991; Bercik, 2002; Vögler et al., 2005).
Granules become larger and darker as the field first emerges (due to the suppression of vertical motions by the horizontal section of the bipoles and adiabatic cooling due to their expansion) and elongate in the direction of the horizontal component of the field (Figure 20).
The main differences between these two approaches are that a coherent initial flux tube leads to a more coherent symmetrical structure when it emerges through the surface and field line connections below the surface are more localized. In the minimally structured approach organized magnetic field concentrations develop spontaneously when sufficient flux is present, instead of being imposed as initial and boundary conditions, so the emergent structures are less coherent.
Living Rev. Solar Phys. 9, (2012), 4
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