Shallow sunspot formation, a numerical study using ILES

Abstract

Sunspots are dark patches at the surface of the Sun where the magnetic field is strong. To the date, the mechanism by which sunspots are generated remains unclear. In the current literature two types of explanations can be found. The first one is related to buoyant emergence of toroidal magnetic fields generated at the tachocline. The second one states that active regions are formed, from an initially diffused magnetic flux, by MHD instabilities that develop in the near-surface layers of the Sun. Using the anelastic MHD code EULAG-MHD we address the problem of sunspot formation by performing implicit large-eddy simulations of stratified magneto-convection in a domain that mimics the uppermost layers of the Sun. By applying a homogeneous magnetic field over an initially stationary hydrodynamic convective state, we investigate the formation of self-organized magnetic structures. The strength of the imposed magnetic field is a free parameter of the model and varies in the range, 0.01 < B0/Beq < 0.5 (where Beq is the characteristic equipartition field strength). Specifically we explore the role of the Negative effective magnetic pressure instability NEMPI (Rogachevskii & Kleeorin (2007), Kleeorin et al. (1996), Brandenburg et al. (2010)) in the formation of such magnetic flux concentrations. Although we observe the formation of magnetic structures with length scales of the order of the largest convective motions, the results are inconclusive to determine whether this instability is the responsible for the formation of the observed structures.