Effects of rotation and stratification on magnetic flux concentrations

The formation of magnetic flux concentrations in the Sun is still a matter of debate. One observable manifestations of such concentrations is sunspots. A mechanism able to spontaneously form magnetic flux concentrations in strongly stratified hydromagnetic turbulence and in the presence of a weak magnetic field is the negative effective magnetic pressure instability (NEMPI). This instability is caused by the local suppression of the turbulence by the magnetic field. Due to the complexity of the system, and in order to understand the fundamental physics behind the instability, the study started by considering simplified conditions. In this thesis we aim to move towards the complexity of the Sun. Here we want to know whether the instability can develop under rotation and in the case of a polytropic stratification instead of the simpler isothermal stratification. We perform different kinds of simulations, namely direct numerical simulations (DNS)and mean field simulations (MFS) of strongly stratified turbulence in the presence of weak magnetic fields. We then study separately the effects of rotation and the change in stratification. It is found that slow rotation can suppress the instability. For Coriolis numbers larger than $0.1$ the MFS no longer result in growth, whereas the DNS start first with adecreaseof the growth rate of the instability % with the speed-up of rotation is alleviated and then, for $\Co > 0.06$, an increase owing to the fact that rotation leads to the onset of the dynamo instability, which couples with NEMPI in a combined system. In fact, the suppression implies a constraint on the depth where the instability can operate in the Sun. Since rotation is very weak in the uppermost layers of the Sun, the formation of the flux concentration through this instability might be a shallow phenomenon. The same constraint is found when we study the effects of polytropic stratificationon NEMPI. In this case, the instability also develops, but it is much more concentrated in the upper parts of the ...