The strongest magnetic fields near the solar surface are in approximate pressure balance with their surroundings. That is, the magnetic plus gas pressure inside the magnetic concentration is nearly equal to the gas pressure in its neighborhood. This means that the magnetic energy density can be much larger than the kinetic energy of convective motions. However, as one descends into the convection zone the ratio of gas to magnetic pressure quickly becomes very large and the magnetic fields in the quiet Sun get moved around by the convective flows. Diverging upflows sweep magnetic flux to intergranular downflow lanes (Figure 44) (Tao et al., 1998; Thelen and Cattaneo, 2000; Emonet and Cattaneo, 2001; Weiss et al., 2002; Vögler et al., 2005; Stein and Nordlund, 2006). Larger scale, slower flows – mesogranulation and supergranulation – sweep the flux along the intergranular lanes on longer time scales to the boundaries of increasingly larger scale horizontal patterns, while new flux, with mixed polarity, continually emerges throughout the quiet Sun. 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, where it encounters existing magnetic flux with which it either cancels or augments (Simon et al., 2001; Krijger and Roudier, 2003; Isobe et al., 2008). This balance empirically occurs at supergranulation scales and produces the magnetic network (Schrijver et al., 1997b, point out that ephemeral active regions are actually a more important source of flux for the quiet-Sun network.). In general, the size and shape of a pattern produced by launching finite life time “corks” in the solar multi-scale velocity field depends both on the amplitude spectrum of the velocities, the morphology of the flows, and on the distribution of life times of the corks.
Note that the transportation and concentration of magnetic flux in the solar photosphere – and more generally at a free surface – is a different process than the “flux expulsion” mechanism (Weiss, 1966; Maheswaran, 1969; Peckover and Weiss, 1978; Galloway and Weiss, 1981). Convective motions inside a box with closed boundaries tends to – over a period of time and in the presence of magnetic diffusion – expel magnetic fields from the interior of convection cells. Magnetic field lines penetrating a free surface boundary are efficiently concentrated by purely advective transport, and can subsequently be further concentrated due the suppression of convection associated with a strong magnetic field (Spruit, 1976, 1977a, 1979; Spruit and Zweibel, 1979; Bushby et al., 2008).
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