The negative effective magnetic pressure in stratified forced turbulence

To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to be converged for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough.Comment: 15 pages, 18 figures, 2 tables, ApJ, accepte

Active region formation through the negative effective magnetic pressure instability

The negative effective magnetic pressure instability operates on scales encompassing many turbulent eddies and is here discussed in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details in that their onset occurs at the same depth. This depth increases with increasing field strength, such that the maximum growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.Comment: 19 pages, 10 figures, submitted to Solar Physic

From mean-field hydromagnetics to solar magnetic flux concentrations

The main idea behind the work presented in this thesis is to investigate if it is possible to find a mechanism that leads to surface magnetic field concentrations and could operate under solar conditions without postulating the presence of magnetic flux tubes rising from the bottom of the convection zone, a commonly used yet physically problematic approach. In this context we study the ‘negative effective magnetic pressure effect’: it was pointed out in earlier work (Kleeorin et al., 1989) that the presence of a weak magnetic field can lead to a reduction of the mean turbulent pressure on large length scales. This reduction is now indeed clearly observed in simulations. As magnetic fluctuations experience an unstable feedback through this effect, it leads, in a stratified medium, to the formation of magnetic structures, first observed numerically in the fifth paper of this thesis. While our setup is relatively simple, one wonders if this instability, as a mechanism able to concentrate magnetic fields in the near surface layers, may play a role in the formation of sunspots, starting from a weak dynamo-generated field throughout the convection zone rather than from strong flux tubes stored at the bottom. A generalization of the studied case is ongoing.At the time of the the doctoral defence the following paper was unpublished and had a status as follows: Paper nr 7: Submitted</p