Self-assembly of Shallow Magnetic Spots through Strongly Stratified Turbulence

In developed turbulence, the effective magnetic pressure of a large-scale field (non-turbulent plus turbulent contributions) can become negative. This is known to lead to a large-scale instability in strongly stratified turbulence that produces spontaneous magnetic flux concentrations. Previous studies using a horizontal magnetic field resulted in elongated field concentrations with a strength of a few per cent of the equipartition value. Here we show that a uniform vertical magnetic field leads to circular magnetic spots with a strength at and above the equipartition value. This could represent a minimalistic model of sunspot formation and highlights the importance of two critical ingredients: turbulence and strong stratification. Radiation, ionization, and supergranulation may be important for realistic simulations, but are not critical at the level of a minimalistic model of magnetic spot formation. Subject headings: magnetohydrodynamics (MHD) – stars: starspots – Sun: sunspots – turbulence