Origin of solar surface activity and sunspots
Abstract: In the last few years, there has been significant progress in the development of a new model for explaining magnetic flux concentrations, by invoking the negative effective magnetic pressure instability (NEMPI) in a highly stratified turbulent plasma. According to this model, the suppression of the turbulent pressure by a large-scale magnetic field leads to a negative contribution of turbulence to the effective magnetic pressure (the sum of non-turbulent and turbulent contributions). For large magnetic Reynolds numbers the negative turbulence contribution is large enough, so that the effective magnetic pressure is negative, which causes a large-scale instability (NEMPI). One of the potential applications of NEMPI is to explain the formation of active regions on the solar surface. On the other hand, the solar dynamo is known to be responsible for generating large-scale magnetic field in the Sun. Therefore, one step toward developing a more realistic model is to study a system where NEMPI is excited from a dynamo-generated magnetic field. In this context, the excitation of NEMPI in spherical geometry was studied here from a mean- field dynamo that generates the background magnetic field. Previous studies have shown that for NEMPI to work, the background field can neither be too weak nor too strong. To satisfy this condition for the dynamo-generated magnetic field, we adopt an “alpha squared dynamo” with an ? effect proportional to the cosine of latitude and taking into account alpha quenching. We performed these mean-field simulations (MFS) using the Pencil Code. The results show that dynamo and NEMPI can work at the same time such that they become a coupled system. This coupled system has then been studied separately in more detail in plane geometry where we used both mean-field simulations and direct numerical simulations (DNS).Losada et al. (2013) showed that rotation suppresses NEMPI. However, we now find that for higher Coriolis numbers, the growth rate increase again. This implies that there is another source that provides the excitation of an instability. This mechanism acts at the same time as NEMPI or even after NEMPI was suppressed. One possibility is that for higher Coriolis numbers, an ?2 dynamo is activated and causes the observed growth rate. In other words, for large values of the Coriolis numbers we again deal with the coupled system of NEMPI and mean-field dynamo. Both, MFS and DNS confirm this assumption. Using the test-field method, we also calculated the dynamo coefficients for such a system which again gave results consistent with previous studies. There was a small difference though, which is interpreted as being due to the larger scale separation that we have used in our simulations.Another important finding related to NEMPI was the result of Brandenburg et al. (2013), that in the presence of a vertical magnetic field NEMPI results in magnetic flux concentrations of equipartition field strength. This leads to the formation of a magnetic spot. This finding stimulated us to investigate properties of NEMPI for imposed vertical fields in more detail. We used MFS and DNS together with implicit large eddy simulations (ILES) to confirm that an initially uniform weak vertical magnetic field will lead to a circular magnetic spot of equipartition field strength if the plasma is highly stratified and scale separation is large enough. We determined the parameter ranges for NEMPI for a vertical imposed field. Our results show that, as we change the magnitude of the vertical imposed field, the growth rate and geometry of the flux concentrations is unchanged, but their position changes. In particular, by increasing the imposed field strength, the magnetic concentration forms deeper down in the domain.
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