Abstract.We have developed a 3D magnetohydrodynamics simulation code for applications in the solar convection zone and photosphere. The code includes a non-local and non-grey radiative transfer module and takes into account the effects of partial ionization. Its parallel design is based on domain decomposition, which makes it suited for use on parallel computers with distributed memory architecture. We give a description of the equations and numerical methods and present the results of the simulation of a solar plage region. Starting with a uniform vertical field of 200 G, the processes of flux expulsion and convective field amplification lead to a dichotomy of strong, mainly vertical fields embedded in the granular downflow network and weak, randomly oriented fields filling the hot granular upflows. The strong fields form a magnetic network with thin, sheetlike structures extending along downflow lanes and micropores with diameters of up to 1000 km which form occasionally at vertices where several downflow lanes merge. At the visible surface around optical depth unity, the strong field concentrations are in pressure balance with their weakly magnetized surroundings and reach field strengths of up to 2 kG, strongly exceeding the values corresponding to equipartition with the kinetic energy density of the convective motions. As a result of the channelling of radiation, small flux concentrations stand out as bright features, while the larger micropores appear dark in brightness maps owing to the suppression of the convective energy transport. The overall shape of the magnetic network changes slowly on a timescale much larger than the convective turnover time, while the magnetic flux is constantly redistributed within the network leading to continuous formation and dissolution of flux concentrations.

Results from a realistic simulation of three-dimensional radiative magnetoconvection in a strong background magnetic field corresponding to the conditions in sunspot umbrae are shown. The convective energy transport is dominated by narrow upflow plumes with adjacent downflows, which become almost field-free near the surface layers. The strong external magnetic field forces the plumes to assume a cusplike shape in their top parts, where the upflowing plasma loses its buoyancy. The resulting bright features in intensity images correspond well (in terms of brightness, size, and lifetime) to the observed umbral dots in the central parts of sunspot umbrae. Most of the simulated umbral dots have a horizontally elongated form with a central dark lane. Above the cusp, most plumes show narrow upflow jets, which are driven by the pressure of the piled-up plasma below. The large velocities and low field strengths in the plumes are effectively screened from spectroscopic observation because the surfaces of equal optical depth are locally elevated, so that spectral lines are largely formed above the cusp. Our simulations demonstrate that nearly fieldfree upflow plumes and umbral dots are a natural result of convection in a strong, initially monolithic magnetic field.

Context. Observations indicate that the "quiet" solar photosphere outside active regions contains considerable amounts of magnetic energy and magnetic flux, with mixed polarity on small scales. The origin of this flux is unclear. Aims. We test whether local dynamo action of the near-surface convection (granulation) can generate a significant contribution to the observed magnetic flux. Methods. We have carried out MHD simulations of solar surface convection, including the effects of strong stratification, compressibility, partial ionization, radiative transfer, as well as an open lower boundary. Results. Exponential growth of a weak magnetic seed field (with vanishing net flux through the computational box) is found in a simulation run with a magnetic Reynolds number of about 2600. The magnetic energy approaches saturation at a level of a few percent of the total kinetic energy of the convective motions. Near the visible solar surface, the (unsigned) magnetic flux density reaches at least a value of about 25 G. Conclusions. A realistic flow topology of stratified, compressible, non-helical surface convection without enforced recirculation is capable of turbulent local dynamo action near the solar surface.