Magnetic flux concentrations from turbulent stratified convection

(abridged) Context: The mechanisms that cause the formation of sunspots are still unclear. Aims: We study the self-organisation of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods: We perform simulations of magnetoconvection in Cartesian domains that are $8.5$-$24$ Mm deep and $34$-$96$ Mm wide. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow. Results: We find that super-equipartition magnetic flux concentrations are formed near the surface with domain depths of $12.5$ and $24$ Mm. The size of the concentrations increases as the box size increases and the largest structures ($20$ Mm horizontally) are obtained in the 24 Mm deep models. The field strength in the concentrations is in the range of $3$-$5$ kG. The concentrations grow approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in the majority of the domain, which is unfavourable for the negative effective magnetic pressure instability (NEMPI). Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions: The linear growth of large-scale flux concentrations implies that their dominant formation process is tangling of the large-scale field rather than an instability. One plausible mechanism explaining both the linear growth and the concentrate on of the flux in the regions of converging flow pattern is flux expulsion. Possible reasons for the absence of NEMPI are that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign and that there may not be sufficient scale separation.