  This work presents an extensive study of the previously discovered formation
of bipolar flux concentrations in a two-layer model. We interpret the formation
process in terms of negative effective magnetic pressure instability (NEMPI),
which is a possible mechanism to explain the origin of sunspots. In our
simulations, we use a Cartesian domain of isothermal stratified gas that is
divided into two layers. In the lower layer, turbulence is forced with
transverse nonhelical random waves, whereas in the upper layer no flow is
induced. A weak uniform magnetic field is imposed in the entire domain at all
times. In this study we vary the stratification by changing the gravitational
acceleration, magnetic Reynolds number, strength of the imposed magnetic field,
and size of the domain to investigate their influence on the formation process.
Bipolar magnetic structure formation takes place over a large range of
parameters. The magnetic structures become more intense for higher
stratification until the density contrast becomes around $100$ across the
turbulent layer. For the Reynolds numbers considered, magnetic flux
concentrations are generated at magnetic Prandtl number between 0.1 and 1. The
magnetic field in bipolar regions increases with higher imposed field strength
until the field becomes comparable to the equipartition field strength of the
turbulence. A larger horizontal extent enables the flux concentrations to
become stronger and more coherent. The size of the bipolar structures turns out
to be independent of the domain size. In the case of bipolar region formation,
we find an exponential growth of the large-scale magnetic field, which is
indicative of a hydromagnetic instability. Additionally, the flux
concentrations are correlated with strong large-scale downward and converging
flows. These findings imply that NEMPI is responsible for magnetic flux
concentrations.
