Testing new ideas of sunspot formation: the negative effective magnetic pressure instability
The formation of active regions and its most visible outcome-sunspots-are still a matter of research. Magnetic flux tubes theory tends to explain the formation of sunspots, but it still faces some unresolved questions: How are they generated? Why can they survive all along the convective zone? How do they rise? I will review this theory and introduce a new way to understand sunspot formation: the negative effective magnetic pressure instability (NEMPI). NEMPI was predicted long ago (Kleeorin et al., 1989, 1990; Kleeorin \& Rogackevskii, 1994; Kleeorin et al., 1996) but has only been seen recently (Branderburg et. al., 2011). It arised as a effect of strong stratication and the presence of turbulence with a weak mean magnetic field. Under suitable conditions, a large-scale instability resulting in the formation of non-uniform magnetic structures, can be excited over the scale of many turbulent eddies or convection cells. This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions and perhaps sunspots. Now, we want to understand the effects of rotation on this instability in both two and three dimensions. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to be in agreement with those of direct numerical simulations. We find that the instability is suppressed already for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. The prograde rotation of the magnetic pattern near the equator is argued to be a possible explanation for the faster rotation speed of magnetic tracers found on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern.
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