Thin flux tube models of emerging flux loops through the solar convective envelope (Section 5.1) have inferred a strong super-equipartition field strength of order 105 G for the toroidal magnetic field at the base of the solar convection zone. Generation of such a strong field is dynamically difficult since the magnetic energy density of a 105 G field is about 10 – 100 times the kinetic energy density of the differential rotation (Parker, 1994; Rempel and Schüssler, 2001). An alternative mechanism for amplifying the toroidal magnetic field has been proposed which converts the potential energy associated with the stratification of the convection zone into magnetic energy. It is shown that upflow of high entropy plasma towards the inflated and “exploding” top of a rising -loop developed from an initial toroidal field of equipartition field strength ( 104 G) can significantly intensify the submerged part of the field by extracting plasma out of it (Parker, 1994; Moreno-Insertis et al., 1995; Rempel and Schüssler, 2001). This process is a barometric effect and is caused by the entropy gradient in the solar convection zone maintained by the energy transport.
In the thin flux tube simulations of rising -loops in the solar convection zone, it is found that flux loops with a low initial field strength of 104 G do not reach the upper half of the solar convection zone before the apexes of the loops loose pressure confinement and effectively “explode” (Moreno-Insertis et al., 1995). This loss of pressure confinement at the top of the emerging loop occurs as plasma inside the tube establishes hydrostatic equilibrium along the tube which happens if the emerging loop rises sufficiently slowly (Moreno-Insertis et al., 1995). The loop rises adiabatically carrying the high entropy plasma from the base of the solar convection zone while the entropy outside the flux tube decreases with height in the superadiabatically stratified convection zone. Hydrostatic equilibrium therefore dictates that the plasma pressure inside the flux tube decreases with height slower than the outside and becomes equal to the external pressure at a certain height where the magnetic field can no longer be confined. This “explosion” height for the emerging loop is found to be a function of the initial tube field strength at the base of the solar convection zone (see Figure 33).
For loops with an initial field strength 104 G, the explosion height is at about the middle of the solar convection zone. When the loop apex approaches the explosion height, it expands drastically and the buoyancy of the high entropy material in the tube is expected to drive an outflow which extracts plasma out of the lower part of the flux tube at the base of the solar convection zone. This process has been demonstrated by Rempel and Schüssler (2001), who performed MHD simulations of exploding magnetic flux sheets in two-dimensional Cartesian geometry.
The simulations of Rempel and Schüssler (2001) start with a magnetic sheet with a higher value of entropy placed at the bottom of an adiabatically stratified layer (constant entropy layer). This setup avoids the complication of involving convective flows in the simulations while keeping the essential effect of the entropy decrease in the solar convection zone by assuming a constant entropy difference between the flux sheet and the isentropic layer. The central portion of the flux sheet is perturbed upward which subsequently forms a rising loop as a result of its magnetic buoyancy (see Figure 34).
The apex of the rising loop explodes into a cloud of weak magnetic field as it crosses the predicted explosion height (middle panel) and high entropy plasma, driven by buoyancy, continues to flow out of the “stumps”, draining mass from the lower horizontal part of the flux sheet (bottom panel). The field strength of the horizontal part of the flux sheet is visibly intensified. It is found that the final field strength the horizontal part of the field can reach is roughly the value for which the explosion height is close to the top of the stratification. For the solar convection zone, this value corresponds to 105 G (see Figure 33). This implies that the large field strength of order 105 G may be achieved by the process of flux “explosion”, which draws energy from the potential energy associated with the stratification of the solar convection zone. A coherent picture maybe as follows. Differential rotation in the tachocline shear layer generates and amplifies the toroidal magnetic field to an equipartition value of about 104 G, at which point magnetic buoyancy becomes important dynamically, and magnetic buoyancy instability, radiative heating or other convective perturbations drive the formation of buoyant flux loops rising into the solar convection zone. These rising loops explode in the middle of the convection zone and fail to rise all the way to the surface. These “failed” eruptions “pump” out the plasma from the toroidal field at the base of the solar convection zone (Parker, 1994) and amplify the toroidal field until it reaches strongly super-equipartition field strength of order 105 G, whose eruptions then lead to the emergence of solar active regions at the surface.
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