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.
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