Context :

Aims : 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 .

Methods : 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 most cases , it is horizontal , but a vertical and an inclined field are also considered .
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 .

Results : 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 fluid 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 .
A small imposed horizontal field component is necessary to generate bipolar structures .
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 .

Conclusions :