One possible resolution of the above problem is that some other processes that can form -loops of much shorter length scale compared to the undulatory buoyancy instability (Section 4.1) is responsible for the formation of active region emerging tubes, although it is not immediately clear what these processes might be. Another alternative is that the active region magnetic fields on the photosphere become dynamically disconnected from the interior flux tubes. Fan et al. (1994) speculated on the process of “dynamic disconnection” which has the same physical cause as that of the so called flux tube “explosion” described in Section 7. It can be seen from Figure 23, that even for an emerging flux loop with a field strength at the convection zone base that is as high as , the flux tube is expected to loose pressure confinement and hence “explode” at a height of about below the surface as a result of plasma establishing hydrostatic equilibrium (HE) along the tube. While a flux loop is rising, especially in the top few tens of Mm of the convection zone where the rise speed becomes comparable to the Alfvén speed, the variation with depth of the magnetic field strength can deviate significantly from the conditions of HE. However, after flux emergence at the surface, the plasma inside the submerged flux tube will try to establish HE. Tube plasma near the surface can cool through radiation and probably undergoes “convective collapse”, forming sunspots and pores (see Spruit and Zweibel, 1979; Stein and Nordlund, 2000) at the photosphere. However in deeper depths where plasma evolution is still nearly adiabatic, a catastrophic weakening of the magnetic field or flux tube “explosion” (Section 7) may occur, which is caused by an upflow of high entropy plasma as it tries to establish HE along the tube. This weakening of the field leads to the effective dynamic disconnection of the active region fields on the photosphere from the interior flux tubes. Fan et al. (1994) suggested that “dynamic disconnection” can explain
A first quantitative calculation of the above process of “dynamic disconnection” has been carried out by Schüssler and Rempel (2005), using a 1-D self-similar vertical flux tube model whose top end has reached the photosphere. The model computes the quasi-static evolution of the flux tube under the effects of radiative cooling, convective energy transport, and a pressure buildup by a prescribed inflow at the bottom of the tube due to the high entropy tube plasma flowing upward to establish hydrostatic equilibrium along the field. The calculation shows that after emergence, the radiative losses near the surface drives an inward propagating cooling front accompanied by a downflow, which leads to a decrease of the gas pressure and an intensification of the magnetic field in the surface layers. In the mean time, the convergence of the radiative cooling driven downflow and the buoyancy driven upflow results in an increase of the gas pressure and a weakening of the magnetic field in the tube at a depth of a few Mms. It is found that for a reasonable range of the upflow speed, the magnetic field weakens to fall below the local equipartition value (i.e. dynamic disconnection takes place) at a depth between 2 and 6 Mm, in a time scale of up to 3 days. This is consistent with the time scale over which the evolution of a newly emerging active region changes from an “active phase” of growth with increasing polarity separation to a “passive phase” which can be well represented by transport by near surface flows and supergranular diffusion.
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